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ERRATA SHE}<~T.

Document 51, a.

TOPOGRAPHY FOR FIELD ARTILLERY.

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Page 7, par. 20, 4th line. Change 13° to read 12".

Page 10, lines 5 and 12. Place bracket about 1/1000 so that 800 will not

Page 53, Fig. 33. Line BC should be the chord of angle, a., and not

appeai' as part of the denominator.

perpendicular to A lJ.

Page 86, line 17. Should read figure 71.

Page 156, line 20. Should read, 50.1-49=1:11It.

Page 165, par. 358, line 8. Change last word from "of" to "or".

Page 201, Fig. 137. Inverted.

Page 207, Fig. 145. Inverted.

Page 255. Second paragraph On.this page should be 573 instead of 773.

Page 255, par. 573. Beginning with the tenth line the balance of the paragraph should read, "G' to G until the sight shank falls in the line of

vision when the alidade is laid on the line pg. This wil~ bring the

plotted positon of the gun, g, in accord with the actual position, and the

direction, Ggp, may then be taken as the true plane of sight ..

'age 255, par. 574, line 7. Insert after the word Assume, the following

II words, "that the orientation is correct and". .

1 :e 257, par 576, line 9. Insert after the words "equal to", the following

words. "6400111, minus".

Page 265, Fig. 194. Prolong the arrow of the angle, M until it intersects

"'-- the line, GC prolonged.

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r"'~OPOGRAPHY

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for. Field Artillery

School of Fire

Document No. 51~

MARCH: 1919

This document replaces

Documents 51,40a, and 37b

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Published

Under the Direction of

THE CHIEF OF FIELD ARTILLERY

SCHOOL of FIRE for FIELD ARTILLERY

FORT SILL, OKLAHOMA
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PREFACE.

This text, which is an outgrowth of the course in Topography and

Orientation at the School of Fire for Field Artillery, has been written at the

instance of Col. W. H. Williams. director of instruction of the School and of

Lt. ~oL Mert Proctor, head of the Department of Reconnaissance, whose'desire it was to do away with the numerous pamphlets and mimeographed

sheets heretofore used in the course, and to place the information on the subject in such form that any artilleryman might use the text for purposes

of Flelfinstruction. .

Since the refinements of topography were largely neglected in the

artillery branch of the service prior to the late war it was natural that the

subject should be treated in a rather sketchy manner during U.e / early

months of the War Course at the School of Fire. .

After the publication of the translation of the Manual for the Artillery

Orientation Officer an attempt was made to use this as a text but it was out

of date in some:>respects, was i'':lund to be incomplete, and also so confusing

to the student officers, that the text was abandoned.

In the early spring of 1918 the arrival of Lt. Jean Viallet and Lt.

George Payen and later of Lt. L. Jaudoin of the French mission proved of

I great benefit in the development of the course in topography under the

) Jirection of Major J. E. Edmonds. Returning officers of the A. E. F. also

I ;ave valuable suggestions.

While there are innumerable works on topograph~r extant. there are

( .none, so far as the author is aware, which will satisfy the needs of the

American field artillery officer. The French have a number of publications

f but none are suitable as instruction texts for American artillery schools .

The same applies to instruction sheets and pamphlets from training centers.

1 and service schools, which, instead of going into the details of topographic

.. steps, characteristically take too much for granted.

In this work'some chapters, to an engineer. will seem unusually brief.

This is because the artillery officer does not need to go to the same detail as

•. the engineer in all of the work. On the other hand there are chapters in

his work in which the subject has been treated at great length. This is

j ~ue, for example, of Chapter II where there is an exhaustive discussion of

j ~le subject of the true mil, the artillery mil, and the tangent, and the relai" :ons between them. It is believed that this has. not been undertaken in

,yother text, yet it .is absolutely ~ecessary that the artillery officer have

thorough understandmg of the subject, and of the limits within which each

lethod may be used.

The same holds true of Chapter XV dealing with dead space. The •

ajority of texts instea~ of going into any explanation of the subject or of

1 discussion and comparIson of methods. dismiss dead space with a few sen-

: tfllCeS, leaving the student mor~ confused that ever. It is true that Chapter

-' .\ Ii contains more matter than IS necessary for purposes of ordinary instrucTopography for Field Artillery

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-ivtion, but it was thought advisable to clear this subject completely while it

was under consideration.

In the preparation of this work cl'edit is due to Majors C. C. Hield,

L. L. Boggs; Captains C. S. Wilson, J. H. Ferris, C. S. Blomshield, L.O.

Shropshire, and J. G. Faes; and to 1st Lt. John Starr Pope, all of the

Topography Section, Department of Reconnaissance to each of whom was

assigned the task of writing certain chapters.

Definitions employed in this text are those authorized by Artillery

Firing, so far as such definitions apply to this subject.

Texts used in the preparation of subject matter and of the cuts required in this work include; Artillery Firing, The Manual for the Artillery

. Orientation Officer, The Engineer Field Manual, other engineer manuals.

Spaulding's Training Manual in Topography, Map Reading and Reconnaissance, and the Lambert Conformal Conic Projection by Dietz. For the most

part, however, as indicated above, the subject matter is representative of the

course as developed at the School of Fire. As such it is believed that thi~

book will be of value to all artillery officers who have to instruct in the

suhject of topography or who may have to preform the topographical operatiU'l'l connected with the occupation of a position.

Fort Sill, Okla., Feb. 1, 1919.

H. C. Jackson,

Major, Field Artillery, U. S. A.

Topography for Field Artillery

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PREFACE.

CHAPTER I.

CHAPTER II.

TABLE OF CONTENTS.

Introduction.

Distance And Direction.

Page iii-h.

Par. 1-5

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Linear measure -.................................... 8-14

A. Metric system .....•....•........ ,...................... 8-9

B. Conversion between English and metric system 10-14

Angular measure............................................. 15-~3

A. Degree system....................................... 18-20

B. Grade system /'21-22

C. ~fil system............................................ 23-29

D. Conversion in angular measure....................... 30-31

E. Expl;ession of angles by tangents ............•....... 32-45

Table~howing accuracy of tangent calculation of angular

values ; . . .. . .. .. . . 42

F. Gradients 46-47

G. Per cent ..•........•.....•......•.••..•..•.......... 48-51

H. Conversions in tangents and angular measure 52-53

Measuring instruments 54-75

A. Scales ...........•..•............................... 54-59

Metric measuring scale 55

Triangular scale .............• :...................... 55

1'apes and chains ......................•.............. 57

/ Testing of edges .................•................... 58

B. r'>rotractors 60-62

C. Emergency devices ; -.. . . 63

D. Methods of construction...................... . . . . . . . . . 64-71

I<j. Right angles 72-75~

CHAPTElt III ~hps And Scales 76-130

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The elements of a map : . . . . . 76-86

A. Definition 76

IJ. Classes of maps -_ ........•.... -.. . . . . . . 77

C. Map making and map reading -.. . . . . . . . . . . . . . . 78-80

1. ~fap making......................................... 79

2. l\lap reading......................................... 80

D. Ground relations ,...................... 81-86

1. Distance ....................•.................. -..... 82

2. Direction .-. . . . . . . . . . . . . . . 83

3. Altitude 84

4. l\fap essentials 86

Topography for Field Artillerv

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-viDistances and scales 87-95

A. Definitions ..•.......................................... 87

B. Scales ".................................... 88-95

1. Representative fraction 89

2. Words and figures 90

3. Graphical scale •.............. . . . . . . . . . . . . . . . . . . . 91-95

Map scale problems ..•..................................... , 96-130

A. Classes of problems ".. . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

B. Simple rules of map scale calculations 97-103

1. ~Iap to ground 97-98

a. By R. F. . .•....•.........•............. :........ 97

b. By words and figures scales 98

2. Ground to map 99-103

a. By R. F. 100

b. By words and figures scales 101-103

C. Scale conversions................................... 104-106

D. Types of graphical scales 107-130

1. Construction of reading scales 108-111

2. \Vorking scales 112-130

a. Stride scales ,............................. 112-117

b. Mounted working scales 118-121

c. Interchange of graphical scales 122

d. Working scale graphs .•..................... 123-130

CHAPTER IV. Elevation And Ground Forms. 131-138

Ho\v shown .................•................................. 131

A. Bench marks, hachures, and contours 132-137

1. Definitions •..... ,.............................. 132-135

a. Bench mark .................•..............•.. 132

b. Hachures ........•..•..•........•.............. 133

c. Contours :. . . . 134

2. Vertical interval ...•............................... 136

3. Critical points :............................... 137

B. Logical contouring .....•.....•.......•...........•..... 138

CHAPTER V Instruments Used In Topographic Operations. 139-170

Description and use :................ 139-170

A. Aiming circles ..................•...................... 139

B. Battery 'commander telescopes •.....•.....•........•.... 140

C. Transit ••••........................................... 141

D. Prismatic compass' .........•....••................. ... 142

E. Peigne' compass 143-147

1. To read bearings .......•.........•.......•........ 144

2. To plot this direction with the compass 145

3. To plot the direction with a protractor 146

4. To measure a slope .......•...•....•.....•.......... 147

F. Plane table •••.•..••........•..•..•. '. . . . . • . . . . . . . . . 148-149

1. To level the plane table .••..•....................... 149

G. Alidades ........•.....•..............•... ;........ 150-158

Topography for Field Artillery

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-vii1. Triangular alidades 150

2. Sighting alidades 151

3. Leveling alidade ......•. :........................... 152

a. To measure a gradient 152

b. Laying off directions 152

4. Telescopic alidade •.......•....•.........•...... 153-158

a. To measure distance with the stadia' . . . . . . . . . . . . . 155

b. Horizontal distance 156-158

fl. 'Abney level ~.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159-160

To use Abney level ...............•............. 160-161

I. 'Gravity clinometer 162

J. Levels ..........•........................•............ 163

K. Slope board ..•..................................... 164-165 I

L. Sito-goniolneter 166-169

1. To measure site and find the minimum range 167-168

a. Site .........•.............•................... 167

b. Minimum range ..•........... .'f................ 168

2. To measure angles and deflections 169

M. Protractors 170

CHAPTER VI. Orientation 171-180

Definitions 171

Methods of orientation...................................... 172-180

A. By a declinated table .•...•......................... 173-174

1. With declinator unattached 173

2. With declinator attached ..............•............. 174

B. By known line ............•.......•....••.......... 175-180

1. When the plane table is on a station over one of the

known points of a given line ..•....••.••.•.•.••...... 175

2. When the plane table is somewhere on. the line joining

two points of known location ....••••... . . . . . • . . . . 176

3. By angle traverse . ........••..•...•.•............ 177

4. When known point on given line cannot be occupied 178-180

5. By resection .................•...•....•..•.•...... 180

CHAPTER VII. Traverses. 181-191-

Definition ; . . . . . . . . . . . . . . . . . 181

A. Kinds of traverse ...........•........•.....•.....•..... 181

B. Instruments used 182

C. Methods of traverse ........•..•.................... 183-185

1. Fore sight-back sight method •........•.•............ 183

2. Needle traverse ...............•..••.•..•........... 184

3. Angle traverse .................•.................. 185

D. ,Measurements .••.................•.....•..•..• ;... 186-189

1. Pacing •••..•.....•............•.•..•.............. 187

2. Chaining or taping ............••..•.•..... ;......... 188

3. Stadia readings •..•............•..•...........•.. '. . 189 .

E. Special case ••••.•..•.....•......•..•.•.•....•......... 190

F. Errors in traversing ...•...............•.••••......•.... 191

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CHAPTER VIII. Intersection

Definition .

A. Purpose •.••.....•...............................•... '.

B. Accuracy ..•..•...•••......................•..........

C. The operation •••..•...........•....•..••..............

To locate a point by intersection .

CHAPTER IX. Resection. 196-214

Definition .......••..•..••...............•.......•............. 196

Conditions which 'must be fulfilled if accurate results are to be

expected ......•..•...................••..•.................... 197

Methods of resection •.•.................................... 198-214

A. Transparent paper methcd 198-200

B. Two point method •••.............................. 201-202

1. Using a known line.......................... . . . .. . . 201

2. Using the declinator ................•............... 202

C. Three point method 203-206

Triangle of error 204-206

1. Operator's position inside triangle 204

2. Operator's station outside triangle 205-206

a. By inverse triangle method :. 205.

b. By arcs of circle8 206

D. Back azimuth method 207

E. Italian resection 208-212

1. The process :....... 209-211

2. The proof ;.. 212

F. British resection :.......... 213

,G. l\leasured angles 214

CHAPTER X. Measurement Of Slopes And Elevations 215-229

Discussion 215-21.6

A. Instruments used •.•••............................. ,.. 216

B. Units in which slopes are expressed 217-223

1. Degrees and minutes .. '.. . . . . . . .. . . . . . . . . . . . . . . . .. . . 218

2. l\fils ..•..••....................................... 219

3. Percentages . . .. . . . . . . . . . . . . . . . . . . 220

4. Gradients 221

5. Tangents'.......................................... 222

Type problem 223

C. Slope scale •....................................... 224-229

1. Construction of slope scale ,225-227

a. For American map 225

b. For metric map 226-227

Degree slope ~cale ;...... 226

l\lil slope scale '. . . . . . . . . . . . . 227

2. Use 'of slope scale 228-229

a. In contouring 228

b. In reading slopeR 229

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CHAPTER XI.

--:ixSketching 230-245

Position and area sketches ......................•..•.••....... 230-245

A. Characteristics ..•.•..•...•••........•.•••...••••••••.• 230

n. Technique .....•.•...•....•...........•.•.......... 231-239

1. Whole. to part method •....•........•.............. 231

2. Determination of critical' points • ~:.. . . . . • . . . . . . . . . . . . 232

3. Information to be included •..••..................... 233.

4. Conventional signs •.•.••.•••.•••......•......•. 234-236

5. Title .••.....•..•...........••.......•............. 237

6. Border . . . . . . . • . . . . . . . . . . 238

7. Lettering :................................... 239

l-~oad sketches •••••..........................••.....•...... 240-245

A. Characteristics '. . .. . .. .•. .•. ..•.... .. . 240-241

n. Technique ••...•.••..••.....•...... :............... 242-245

1. Method of sketching •••••••••.....•............. 242-243

2. Lateral limits to be considered ..... . . . . . . . . . . . • . • 244

3. Information to be included ..• :...................... 245

. Information to be included ....................•..•..........

l\:lethod of procedure ....••..•.....•..........•••..••. : ....

Making a road sketch from a road report and vice versa

CHAPTER XII.

CHAPTER XIII.

Road Rep~rt •

Panoramic Sketches.

246-253

246-249

250-251

252-253

254-308

~haracteristics ....................•........•............... 254-257

rypes of sketches :......................................... 258-260

f~Hsentials .••.....•........••..........•....•.............. 261-282

A. Identification .... _..................................... 262

n. Information ........................•..........•.... 263-264

C. Drawing .••••........................••.....•..... 265-282

1. Perspective ••..••.•...............•.•...•...... 268-271

a. Parallel horizontal lines ..•...•..•...•.•........ 269

b. Parallel vertical lines ••••••..•.....•.........•.. 270

c. Parallel lines not horizontal •....... :............ 271 "-------

2. Consecutive crest lines ..•....................... 272-273

3. Broken. lines .....•.....•........•.................• 274

4. Ground slope and form 275-276

5. Shading ........................•..•........... 277-278

6. Conventional signs 279-282

:\1ethod of procedure .....................•.................. 283-307

A. Equipment .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . • 284.

B. Identification and orientation ......•................ 285-288

C. Analysis of the sector 289

D. Selection of reference point and horizontal control 290-292

~;. Vertical control !.......... . 293-29-1

I". Drawing in framework. A comparison of methods ... 295-298

1. First method ..........•....•.••.••••.•.......•...• . 296

2. Second method ...................•••.•.....•.•• 297-298

Topography for Field Artillery

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G. Filling in ............•....••...... ,." •. """"", 299-300

H. Designation of targets and important points ",.",." 301-305

I. Subsketches , •.•...••. , .. ..•..••.•..... , .. , •... ,. 306-307

l\fap and panoramic sketch .....•...................... , ..•.. ", 308

CHAPTER XIV. Visibility And Defilade. . 309-325

Definitions .",.............. . , :309

Visibility , .. , ',.,... 310-316

A. Similar triangles ;., , , ". 311

B. With elastic band ." , , .. , .. , 312

C. Angle of site •.. : .........••..•....•.....•.••......... , 313

D. Graphic method , ".... 314

E .. Visibility charts ..•......•.......... '. . . • . . . . . . . . . 315-316

Defilade .........•.•.... . ,............ 317-325

. I A. Angle of site .....• . ...•...•.•..•..... , 318-319

1. Measured from enemy O. P. . •. , ..........• .. "., 318

2. Measured from covering crest ,.................. 31t}

B. l>rofiles.. .•.••......•......•..... , , , 320

C. Table of defilade •.....•..•......•....•................ 321

D. Type problems ...............•........•............. 322-325

1. First problem ,.... 323

2. Second problem ............••..........••. '. . . . . . . . . 324

3. Third problem , .•.............. , ..•.... , , 323

CHAPTER XV. Minimum Elevation, Minimum Range And Dead Space

326-389

G~neral .... ,., .................•......... •......... , .•. , • . . 326-328

Determination of minimum elevation and range , ,... 329-344

A. Steps of calculation .•................................ ,. 331

B. Effect of ground forms , 332-336

1. Level terrain ., ..•....•................. , .. , .. , 332-333

2. Irregular terrain ...........•....... ,........... 334-335

3, Effect of slopes ..", , .. ,.,." "."", 336

C. Accuracy .......•••..........•........• ,.......... . 337 -338

D. Type problems ............................•.•..•.. 339-344

Example 1 .....•..•........•.•...............•...... 339

Example 2 ...........••...•...................•....... , 340

Example 3 ••.•..••....•..•..•••••.•••..••..•.•... ,.... 341

Example 4 ••. ...•. ,., ...••••• , .......•........ ,."" 342

Example 5 ...•............•..•..••...........•...... ,. 343

Determination of dead space , .• , , , , .•..... , 345-389

A. Limits of dead space , , .....••..• .....•. . , ...•. , 346

B. Dead space charts •..•••.••.•.•.•..••.• , ..•••...... ,... 347

C. Methods of determination ..••.• , ••. , •.. , ....• , ,. 348

,D. Comparison of angles •.•.....•••... , ...•.• "....... 349-355

1. Tangent slope scal~ .......•...... ,............. 352-353

2. Use of tangent scales •.•..•... , , ".. 354-335

E. Allowable limits ..•.•...•........... """".. 356-3»7

F. Accuracy .•••. , :."." ,'. , , , , , , ., . , , . , , . , . , . . ~r)g

Topography for Field Artillery

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1. Steps to be taken 359

2. Type cases .....•.....•.................•...... 360-374

Case I. Level ground .:........................ 360-~G2

Example 1. Trees on level ground.......... '361.362

Case II. Ground sloping downward ;36;3-.36G

Example 2. Trees on dovmward slope 364-~65

Example 3 Downward slope beyond ridge 366

Case III. Ground sloping upward ••............ 367-370

Example 4. Trees on upward slope 368-36:)

Example 5. Upward slope beyond ridge........ 3'7(1

Case IV. All around method on regular and irregular

ground '........... ............•••............ 371-374

Example 6. Rolling ground beyond ridge ... 372-374

H. Graphical method ...........................•...... 375-382

Method 376-380

Example 1 . . . . . . . . . . a81-~&2

I. Graphical method with slope of fall chart 383-385

Example 2. • ................•..................... ,... 3S4

J. Graphical method with special charts 386-389

1. Description of the graph 3R7

2. Use of graph ....•............................. 383-::189

CHAPTER XVI Map Projections. 390-397

, Definition 390

Kinds of projection 391-397

A. Mercator's projection 391

D. Polyhedral projection 392

C. Conic projection ................•...................... 393

D. Polyconic projection :.............. . , 394

E. Donne projection 395

F. Lambert projection ..................•............. 396-397

CHAPTER XVII l\Iaps. 398-417

Preparation of maps 398-404

A. Triangulation system •.....•..•.......•.........•.. 398-399

B. Range triangulation detachment.. .....••............ 400-401

C. Service of information .............•...••........•.. 402-404

Maps of various countries ...........•.......••.•...••...... 405-417

A. French maps .•...•............•..•.....•••••....•• 405-415

1. History of French maps 405-410

2. Battle maps (Plan Directeur) ......•••........... , 411-415

a. 1/20,000 .•••••.•..•••••.•••.•••••••••••......• 412

b. 1/10,000 •••..••••..•••••••••••••••••.•.....•.. 413

c. 1/5,000 ..•..•...•.•.•..•••••••••••••....•.•.•• 414

, B. Maps of Belgium ...•................... :.............. 416

C. Maps of Germany ..•.............•. ,.................. 417

D. British maps (See Appendix II.) •..........•..•.... 630-635

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Origin ..............•.......................•.......•........ 418

Coordinates . . .. . . . . .• . . .. .. . . 419-426

A. Coordinates of origin ,.............................. 420

B. Complete coordinates .•....•...................... '..... 421

C. Reduced hectometric coordinates .......•............ 422-424

1. Error introduced ...........•..............•..•....• 423

D. Plotting points..................................... 425-426

Convergence of meredians ........•...........•.••..•.•..... 427-429

Y-Azimuth ...........•....••.....•.......•••..•......•.... 430

CHAPTER XVIII.

-xiiThe Lambert Grid. 418-430

CHAPTER XIX. Use Of Grid In Map l~eading And Map Firing. 431-449

Advantages of the grid ...........•......................... 431-449

A. Method of plotting a point 432-433

1. When ruler graduations are longer than the distance

bet\veen grids .....•....•............••............. 432

2. 'Vhen the ruler graduations are too small 433

B. Methcd of reading the coordinates of a point 434-437

,1. When the rule is correctly scaled 434

2. When the scale is too large ...........•............ 435

3. When the scale is too small ..••.•.....•.....•....... 436

4. 'With the right angled rule 437

C. Plotting directions ......•....•..................... 438-444

1. By Y-azimuth . . . . . . . . . . . . . . . . . . . . . . . . . . ,438

2. By coordinates ................•................ 439-444

a. By auxiliary points ..............•............. 441

b. By similar triangles ........•...•............... 442

c. By reduced similar triangles .................•... 443

d. By reversing direction •.••....•••.•.......•.... 444

D. Determination of range and Y-azimuth by coordinates.. 445-447

1. Range by square root 445

2. Direction ...•.......•..........•..••..•••..•... 446-447

E. To locate on the ground a point the coordinates of which

are given 448-449

CHAPTER XX. The Compass. 450-469

General ...................................•..................• 450

North .......................•............•................ 451-454

Azimuth ................................................•. 452

l\Iagnetic bearing .....•.....•.....•.......•........... '. • . • 453

Y-azimuth ................................•..•..•......•.. 454

Declination '. . . . . • . . . . . . . . . . . . . . . • . . . . . . • . . . . . . . 455-466

A. Magnetic declination ..•....... .'...................... 455-459

1. :Magnetic variations ...........•........•..•......•.. 457

2. Use. of isogonic chart 458-459

B. Compass declination ........•...... :................ 460-467

1. Sighting on pole star .........•.•..•••...........••• 461

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483-523

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-xiii2. Usmg sun to establish meridian ..•.................. 462

3. Comparison of azimuths and bearings 463

4. Re2ding bearings of sun or of a star ••••.•.••.... 464-465

5. Declination constant .....•..•..•.....•...•...... 466-467

Y-Declination •.•.•.•.•......•...........•.•....... 467

Use of compass and map ...•.•..•....•..•••..•..••..... .... . 468-469

A. To find magnetic bearing on a map witp. a protractor ..... 468

B. l\iagnetic resection •.•.••.••.....•.. •..•••••••.•.•..•. . . . 469

CHAPTER XXI. Laying Guns 'Vith A Declinated Instrument. 470-482

Using prismatic compass ...•••.•••.•.••.•.••...••.•.••.•... 470-482

A. To determine the compass bearing of a target........ 470-472

Off-set method ..... -..... .. .•• . .•. .•.•••••.•.••.... . 471-472

B. Laying guns with bearing determined. ... .•.•..•• . .. . 473-482

1. Lining in •.••.•.•... : •••...•.•. ~................... 474

2. Using compass as aiming point •..••.•••••.•..•. 475-482

Using aiming circle or prismatic compass and magic number method

of laying (See Chapter XXV).

CHAPTER XXII. Typical Battery Sector.

Terms, definitions and diagrams ...••..•.••........ / .

CHAPTER XXIII. Maps And Records. Of Artillery Sector. 524-543

Classes of records ..•.•..................•.......•.....•.. 524-543

A. Maps and charts ••.•.•........•••••....•..•..•.... 525-538

1. Battle maps of sector ....•......••.•.......•..•.... 525

2. Charts .•.•.•.......••..•.•...•..•.........•... 526-538

a. The firing chart' •. . • . . • • • . . • . • . . • . • • • • . • . . . . 526-527

b. Range and deflection fan .••....••.••..••.•..•... 528

c. Position chart •..•...••••••.•.•••••••..••••••.. 529

d. Auxiliary position ..•...•.••.••..•.•..••••••..• 530

e. General system of communication .• :............ 531

f. Chart of visible and invisible areas •.•.•...•.... 532

g. Chart of dead space •....•.••..••••.•.••.•.• 533-534

h. Combined charts •.••.•..••...••..•••••...•• 535-538

B. Written records •.•....•...•..•.•••.•...•••••.•• :.. 539-543

a. B. C. data book................................ 539

b. Ammunition record ..•..••....••.•..•..••....•• 540

c. Target sheet •••..••...••••..••.••..••••••••... 541

CHAPTER XXIV. Topographical Operations In Occupation Of A

Battery Sector. 544-558

General ••••....•.............•....•..•....••.•••••.........•.• 544

Gun position •..•..........••.••.•.••.•••••.•••.•••..••.•..•• 545-549

A. When coordinates of gun position can be read directly from

map •.•••••••......••.••.•••••..•.••••..•.••••••• • • . • 545

B. When gun position cannot be identified on map .•..... 546-549

1. Using geodetic point ••.••••••••.••••.• -............. . 547

2. By resection .•••.•.•.•••••••...•.••......••••••.... 548

3. By an orienting point ....••...•.•.••••••...........• 549

Topography for Field Artillery

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-xivBase point or target 550-551

, A. When base point may not be determined from map 550

B. Determination of direction to target or base point 551

Aiming point •..•..•....•..............•..•................ 552-558

. A. Determining direction to aiming point ......•............ 552

. "B. The orienting line 553-558

, 1. Two types of orienting line .......•.............. 554-556

2. Typical. case . . . . . . . . . . . . . . . .. . . 557-558

CHAPTER XXV. Laying The Guns On Base Line. 559-597

Steps performed. in occupation of a sector 559-561

Establishment of base piece on base line '..... 562-597

A. Staking out ..........................•................ 563

B. Drill regulation method 564

C. Using topographical methods 565-597

Classes of topographical methods ............•....... 566-597.

First class. Plane of sight through points located by

coordinates 567-574

1. Errors 568-571

a. First case, using direction established by

point plotted by coordinates 570

b. Second case; using a direction 571

2. Methods of checking 572-574

a. First method 573

b. Second method 574

Second class. Plane of sight determined by an

established direction 575-597

1. Direct orientation 575-582

a. Using plane table 575

b. U sing aiming circle 576-582

2. Orientation by means of an orienting line. . 583-597

a. Advantages of an orienting line 583

b. Steps to be performed .......•......... 584

I. Determination of base angle........ 585

II. Laying on base line with aiming

circle ......................•...... 586-595

First case......................... 587

Second cas~ 588-595

Method No.1. 589-590

Method No.2 :. 591-595

III. Laying on base line using a plane

table 596

. CHAPTER XXVI. The Observation Post 598-609

General facts 598

Functions and classes of O. P.s 599-602

A. Intelligence O. P.s ..............•....................... 600

B. Command O. P.'s .......................•............. 601

C.. Firing O. P.'s .•....................................... 602

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A. Reconnaissance •....................•................. ". 603 .

B. Preliminary topographical operations ..•..•••........... 604

C. Determination .of origin line ........•.••..••........... 605

D. Construction and consolidation •.••.•.••••••.•.••.. .. '.' . 606

. E. Determination of registration marks or targets .... :..... 607

Records kept at O. P. ............•....•..•....••••.•........ 608-609

Plan of observation :\................. 609

CHAPTER XXVII.

Terrestrial observation

Comparison of methods

CHAPTER XXVIII.

Locating Targets.

Duties Of Various Officers In Position

610-617

610

611-617

'Warfare. 618-625

General 618

A. Brigade commander ..•...............•.................. 619

n. Regimental commander .............•...• ~. . . . . . . . . . . . . 620

C. Battalion commander :................. 621-623

D. Battery commander ................•............... 624-625

APPENDIX.'

Appendix I. Slopes. 626-629

Practicability of' slopes 626

Practicable depths of fords .••.......•...•.••.............. 627

Strength of ice ..•.....•.....•.....•....•......•.•......... 628

Length of pace on slopes .....•..• ~......................... 629

J\ ppendix n. British Maps. 630-635

British coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . 630-631

The grid system .................•.........••..•....••.• 632-634

The North point 634

Designation of sheets ...........•..•..•.••••.•............. 635

Appendix III. Table Of Natural Functions. 636

Appendix IV. Circular Measure. 637-638

"Conversion tables ............•.....•.....•.•........... 637-638 '--

A. Mils in terms of degrees and tangents 637

B. Degrees in terms of mils and tangents •.•........... 638

.Appendix V. Reduction Of Stadia Readings. 639-641

Appendix VI. Azimuth Of Polaris. 642

Tovography for Field Artillery

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TOPOGRAPHY FOR FIELD ARTILLERY.

CHAPTER I•.~:

INTRODUCTION.

IMPOI{TANCE OF TOPOGRAPHY TO FIELD ARTILLERY OFFICERS.

1. Topography, in general, is "the exact and scientific delineation ano

rlescription in minute detail of any place or region" (Webster's New International Dictionary). Military topography delineates and describes all the

physical features of military importance of a place or region. The science

i~ used by every branch of the service in the disposition and maneuvering

of its forces, both combat and non-combatant. Topography is especially

important in the artillery, where it is used not only for maneuvering and

other general purposes, but for the preparation and conduct of fire. For

this purpose a high degree of accuracy is essential, requiring exact methods

not usually necessary in ordinary work.

2. The extensive use of topography in connection with artillery firing'is

a deve]opement of the late European War, which was largely a war of position. Batteries frequently remained for long periods of time in fixed positions, making it possible to study the terrain thoroughly and to locate positions and objectives on maps accurately and in great detail. By means of

topographical measurements on map and ground, very accurate data for

opening fire could be prepared, and the first shots dropped close to the target.

,'educing the labor of adjustment to a minimum, saving much valuable time

and ammunition, and gaining an immeasurable advantage by surprising the

the enemy with a sudden and effective fire. The advantage of this was especially apparent in crowded sectors where many batteries were firing at

the same time. Unless a battery could place its first shots close to the target it was difficult for the observer to distinguish them from those of other

batteriei. Another important use of topographical methods was found in

the designation and identification of targets for observation, both aerial a~

terrestrial.

Thus firing \vith. data obtained from the map came to be used rather

frequently. Even in rapid advances to new positions, much firing was done

on known enemy positions from the map alone. as it was sometimes impossible to seCUl'e observation in the broken and fireswept zones over which

the advance was made. Of course adjustment always was secured whenever possible by aerial or terrestrial observation, but with accurate map~

and calibrated guns, fire with considerable effect could be delivered almost immediately on the occupation of a new position. without waiting for

obsE'rvation. The value of this procedure in harassing a retreating enemy or

in surprising him at any time is very great.

3. It is by no means to be understood that the new methods of preparation a~d conduct of fire have supplanted the methods of open warfare.

Topography for Field Artillery
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These methods always will be required in rapid preliminary operatioJ'l'i and

at various stages during the combat. Where no accurate maps are available

terrestrial observation or open warfare methods must be used. However

when operations are continued for any leng-th of time in the s;J:~e tPl'l'itory,

surveys can be made and maps prepared for firing purposes. The artillery

which fails to do this is neglecting an important opportunity. A good artillery commander should understand the application of all methods, and take

the fullest advantage of every opportunity to improve the effectiveness of his

fire. To this end a thorough knowledge of topography is essential.

4. Topographical information is recorded chiefly in graphical form, supplemented by written or printed explanations and reports. Topographica.l

records include maps and position charts, roads and area sketches, panoramic

sketches, road and reconnaissance reports, visibility and dead space charts, and

any other forms of records which may be necessary to furnish the required information. The essentials of a good topographical record of any kind are:

First, it must contain all possible information of military value for the

purpose which it is designed to serve, considering first the most important,

and omitting irrelevant matters which cause confusion.

Second, it must be accurate to the degree required for its purpose.

Third, it must be clear and legible, presenting its information in such

form that it can be readily understood and used.

In conveying the desired information on maps and sketches, the top~grapher or cartographer very largely makes use of a system of conventional signs, which, in reality, are graphs of the thing represented. These

conventional signs are much the same in all services. See Chapter XI.

5. An officer need not be an expert surveyor, draftsman, or artist in order

to make use of topography. The methods used are comparatively simple,

and much of the work can be, and commonly is, done by trained enlisted men.

Where extensive surveys are required they are made by the engineers. In

training for topography, the practical value of the work should be constantly

emphasized, every step should be illustrated with practical examples, and no

subject should be left until its application is thoroughly understood.

Note: Where the term artillery is used in this text it is understood

that field artillery is meant.

TOpOgraphy for Field Artillery
CHAPTER II •

. DISTANCE AND DIRECTION. '~.

MEASUREMENT AND SYSTEMS OF MEASURE.

6. The artiller; topographer must be thoroughly familiar with the different systems of linear and angular measure used in field artillery, and must

be able to make accurate measurements. Detailed methods will be discussed

later. ,

7. One of the aims of artillery- topography is to save the waste resulting

from inaccurate methods. Hence accuracy should be striven for in all work,

and every effort made to eliminate sources of error. However, it is useless

to carry either measurements or calculations to a greater degree of refinement

than is requh'ed for the use for which the results ~e intended.

. For example, it is possible from an accurate map to' calculate site to

a minute or a fraction of a mil. If an accurate quadrant is to be used for

laying the gun, one graduated to minutes or fractions of mils, such close eal- .

calculation is d~sirable. However, with ordinary materiel graduated only to

even mils, it is useless to calculate closer than the nearest mil. Nor in any

case, is it worth while to calculate closer than the least setting of the range

~cale or quadrant of the the particular gun being used. Exceptions to this

may arise where several small calculations are to be combined, the total of

the fractions if taken together making an appreciable amount, but it is a

was~e of time to carry a calculation to several decimal places which cannot

be used, especially if there is a possible error in any of the measurements

on which the calculation is based. The result of a calculation is never more

accurate than the least accurate factor which enters into it.

Again, in measuring ranges on a map, a skilled man can measure' with

a good scale to the nearest meter, or even to fractions of a meter on large

scale maps. But if the map itself is inaccurate, due to faulty printing, shrinkate, etc., such close measurement would be needless. On the other hand,

in"performing resections or other surveying operations on a plane table with....

an accurate grid, a high degree of accuracy is possible, and every measurement should be made with the greatest care in order to make the total error

of the operations as small as possible. .

Each operation should be studied to determine what degree of accuracy

is required, always bearing in mind, first, the use for which the result of the

operation is intended, and second, the possibilities of the instruments with

Which the operation is performed.

LINEAR MEASURE.

8. The metric system of linear measure is now used by the artillery of

practically all nations, including the United States. However, our old materiel is graduated in yards, and many of our maps, manuals, tables, and

other documents to which the artilleryman must refer use the .old English

Topography for Field Artillery

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units of measure. Hence it is necesary not only to know the metric system,

but to be able to convert, readily, one system into another. It is assumed

that the old English system already is well known, so it will not be treated

in detail.

Latin

prefixes

Greek

prefixes

A. METRIC SYSTEM.

Abbreviations t*Milli- = 1/1000 or .001 mm.

*Centi- = 1/100 or .01 em.

Deci- 1/10 or .1 dm.

*Meter -= 1, Base -Unit. M.(orm.)

f Deka- = 10 times . Dm.

Hecto- = 100 times Hm.

*Kilo- -- 1000 times Km.

Myria- 10000 times Mm.

*Units in most common use .

. Note that the abbreviations of the units larger than the meter are capitalized, while small letters are used for the smaller units. The standard

abbreviation for meter is a small "m", but in artillery work a capital "M"

should be used to distinguish it from the sign "tft" for mil. •

9. Care should be taken to distinguish the Greek prefix "deka", 10 times,

from the Latin "deci",(pronounced "desi"), 1/10. "Deka" is sometimes

spelled "deca" (but pronounced "deka"), especially in France, so the only

certain means of distinction is in the "a" and the "i" and in the pronunciation.

These prefixes are used more frequently in the gmde system of angular

measure than in linear measure. .

B. CONVERSION BETWEEN ENGLISH AND METRIC SYSTEMS.

10. Base Equivalent: 1 meter = 39.37 inches (practically exact).

This is the most important equivalent to remember, as any conversion

can be made through it (reducing English distances to inches and metri~

distances to meters) and any other desired equivalent can be derived from it.

11. The length of the standard international meter has been fixed with

great precision, but the authorities dit1'er slightly as to its equivalent in

English measure. The above value of 39.37 inches is the legal standard equivalent for the United States, by act of Congress, July 28, 1866. The official

British Board of Trade equivalent is 39.370113 inches. Other values have

been determined by different scientists, some larger and some smaller than

89.37, but the variation between them is very slight. 39.37 is so close to the

average that it may be accepted as a practically exact equivalent. It differs

from the English standard by only .000113 inch, or a ratio of about 1 unit

in 350,000, which is negligible except for the most delicate scientific measurements.

Note: The standard meter is 1/10,000,000 of the quadrant of the

earth measured along a meridian.

12. Following are other useful equivalents derived from the base equivalent.

Centimeters to inches;

Topography for Field Artillery

1 em. .3937 in. =
 
-5-

This is practically exact, being simply 1/100 of the base equivalent.

Inches to centimeters: 1 in. 2.54 em.

Practically exact. Derivation: 1 M. 100 em. 39.37 in.

1 in.=100+-39.37=2.540005 em:, or 2.54 within a negligible error .

. Meters to yards: 1 M. 1.09-1 yds.

Sufficiently accurate. for aU artillery purposes. Error amounts to about

+.00039 yd., or a l"atio of 1 in 2800 :M or 3.6 in 10,000, negligible for artillery

work. If closer results are desired use 1.0936.

Derivation: 1, M. 39.37 in. 1 yd. 36 in.

1M. 39.37 +- 36 1.093611 or 1.094 yds.

Yards to meters: 1 yd. .914 M.

Sufficiently accurate for all artillery purposes. Error amounts to about

.0004 M., or a ratio of 1 in 2500 M or 4 in 10,000, negligible for artiller)'

work. If closer results are desired, use .9144.

Derivation: 1 yd. 36 +- 39.37 .9144018 or .914 M.

Meters to feet: 1 M. 3.28 ft.

Sufficiently accurate for all artillery purposes. ~Error amounts to about

.00083 ft., or a ratio of 1 in 4,000 M or 2.5 in 10,000, negligible for artillerr

work. If closer results are desired, use 3.2808.

Derivation: 1.•ft. 12 in. 1 M. 39.37 +- 12 3.28083 or 3.28 ft.

l<'eet to meters: 1 ft. .305 M.

Sufficiently accurate for all artillery purposes. Error amounts to about

+ .0002 M., or a ratio of 1 in 5,000 M or 2 in 10,000, negligible for artiller)'

work. If closer results are desired, use .3048.

Derivation: 1 ft. 12 +- 39.37 .304800 or .305 M.

13. The foregoing abbreviated values are the same as those published a~

standards for general use by the U. S. Bureau of Standards.

Mistakes in making conversions can be avoided by checking all results

by inspection, first deciding which factor to use, and then obtaining an ape

proximate result by a quick mental calculation.

For example, in converting yards to meters, the result in meters will

be smaller, because it will take fewer meters to reach the same distance (a

me~eJ;;being longer than a yard). Hence use the smaller equivalent, .914, not

1.094. One of the most common mistakes is in taking the wrong equivalent.

l'rom this equivalent it appears that the result in' meters should be about

9/10 of (or 1/10 less than) the amount in yards. Thus, 1000 yds.X:914

==914 M., which checks with the approximation.

Again, in converting inches to centimeters, the result will be larger,

, because it will take more centimeters to reach the same distance. Hence

use the larger equivalent, 2.54. not .3937. From this equivalent it appears

that the result in centimeters should be about 2 1/2 times the amount in

inches. Thus, 2 in.X2.54=5.08 em., which checks with the approximation.

14. In order to cultivate facility in thinking and estimating distances in

metric units, it is convenient to bear in mind the following approximate

relations.

1 meter about 40 inches, which is 4 inches, or, about 1/10,

greater than a yard.

Hence distance in meters is about 1/10 less than distance in yards

Topography for Field Artillel')'

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(since it will take fewer meters to reach the same distance). To get meters

from yards. subtract 1/10.

Conversely, distance in yards is about 1/10 greater than distance in

meters. To get yards from meters, add 1/10.

1 centimeter about 4/10 inch.

10 centimeters (1 decimeter) = about 4 inches.'

1 inch = about 2~ centimeters, or 25 millimeters.

1 foot = about 30 centimeters, or 3 decimeters.

1 millimeter = about 2/3 of a sixteenth of an inch.

1 kilometer = about 5/8 mile.

The above equivalents are close enough for rough approximations,

such as estimating distances in open warfare, but for all exact topographical

work the standard equivalents should be used.

ANGULAR MEASURE.

15. An angle is measured by the included arc of a circle. the center of

which is at the vertex of the angle. It is immaterial how large the circle

is or how long the sides of the angle are, because angular measure is not

a measure of distance or area, but is an expression of the proportion between the part of the circle included within the angle and the Whole.circle.

This proportion remains the same for any given angle, whatever the size of

the circle.

16. By dividing the circle into a convenient number of equal parts, a

system of angular measure is obtained. This is sometimes called circular

measure, as it is used to measure the relative size of arcs of circles as well

as angles. The artilleryman is more concerned with angles than with arcs .

.so the term angular measure is preferable.

In all systems, use is made of the

main divisions of the circle and the classification of angles based thereon. The

circle is divided into four equal parts

or quadrants, each of which is included

within a right angle.

Two right angles make a straight

angle or semicircle. Four right angles

make a round angle or complete circle.

C Any angle less than a right angle is an

acute angle. An angle greater than a

right angle and less than a straight

A- RIGJiT-AI'JGLE,QVADRANT angle is an obtuse. angle. An angle

1 greater than a. straIght angle and less 5- .sTRAI~HT.ANqL[,J[M1CIRCLE:. than a round angle is a reflex angle.

C'ROVf.JD.ANGL[ CIRCLE. All forms will be met frequ~ntly in

Fig. 1. artillery work.

'Topography for Field Artillery

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AC\lTE:AN~LE:

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OBTV,SE.ANC1LE

Fig. 2.

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REFLEX ANGLES

17. There are three standard systems of angul~r measure in common use;

the degree system, the grade system, and the artillery mil system. The mil

system is used to a greater or less extent by the artillery of practically all

naticm.. and in time it probably will replace the other systems entirely for

artillery use, on account of its greater convenience. However, it often will

be necessary to make use of surveys, maps, tables, etc., in which the other

units are used, so the artilleryman must be familiar with all systems and

be able to convert readily one form to the other.

A. DEGREE SYSTEM.~'

18. Called sexagesimal because subdivided by 60's.

Base unit: Degree 1/360 of a circle.

60" (seconds) =1' (minute)

60' =10

(degree) =3600"

90° =1 quadrant or right angle

180° =1 semicircle

360° =1 circle=21,600'=1.296,000".

This is the old standard system used by the navigators. astronomers,

and surveyors of all nations. In France and other Latin countries it has

been largely replaced by the grade system, although the old unit still is used

to s'ome extent. The old system is largely used in the British artillery.

19. Modifications of the standard subdivisions are found in the artillery of

different nations. In the French heavy artillery a unit of 1/20 degree (3'),

or 1/7200 of a circle, is used for laying certain types of guns for elevation.

On some German heavy guns 1/16 degree, or 1/5760 of a circle, is used.

The notation of seconds(") is seldom used in artillery, fractions of

mjnutes being indicated by decimals where necessary. ./

Thus: 12° 13.8', instead of 120

13' 48". . "'--

20. In calculating with quantities in the degree system, especially in making conversions, it usually is more convenient to convert the entire quantity

into degrees and decimals.

Thus: 13::13' 48" 12.+ + 3:~0 12 + .217 +'.013 = 12.23°.

Or: 12° 13.8' = 12 + 1:08 = 12.23°.

To re-convert to the regular notation:

12.23°=12° +(.23X 60') =12° 13.8'=12° 13'+(.8X 60") =12°13' 48".

The advantage of the other systems, using' decimal subdivisions, is

obvious.

Topography for Field Artillery

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E. GRADE' SYSTEM.

21. Called centesimal because subdivided by 100's.

Base unit: Grade =1/100 of a quadrant or 1/400 of a circle. (Sometimes spelled, "grad")

100......(seconds) 1'" (minute)

100'" = 1 g. (grade) .10,000......

100g 1 quadrant

200g 1 semicircle

400g 1 circle = 40,000'"=4;000,000"

The signs for centesimal minutes and seconds are inclined backward

to distinguish them from the sexagesimal notations. .

Any expression in this system may be handled as a decimal simply

by putting a decimal point in place of the ~jgn "g". Thus: 3g95'" 80" =3.958g.

It must be remembered. however, that the subdivisions are by hundredths,

not tenths. Hence if the figure for either minutes or seconds is less than

10, a cipher must be put in front of it before pointing off. For this reason

a cipher should always be p~t in front of a single minute or second digit

even in the regular notation. Thus: 3g4' 7" =3.0407g, and should therefore be

written 3g04' 07". •

This is the standard system used by French. navigatol's, astronomers,

and surveyors, although they still make use of the old degree system to

some extent.

22. The following modificatio'1s of the standard system are used in the'

French artillery:

To indicate wind direction:

1 dekagrade (or decagrade) =10 grades (Abbreviation Dg.).

10 dekagrades=1 quadrant.

40 dekagrades=l circle ..

I'~orlaying certain types of heavy guns:

1 decigrade=1/10 grade=10' (abbreviation dg.)

1000 decigrades=l quadrant.

4000 decigrades=l circle.

Note carefully the distinction between the spelling and abbreviations

of the two units.

C. MIL SYSTEM.

23. Base unit: MiI=1/6,400 of a circle. Abbreviation "1!1-".

1,6.001jt=1 quadrant.

3,2001jt.=1 semicircle.

6,4001ft=1 circle.

There are no subdivisions of the mil. Fractions or decimals are used

where required.

24. The size of the mil unit was determined by taking the angle which

subtends an arc 1/1,000 of the radius. The angle whose arc is equal to the

radius is called a radian. A true mil is therefore 1/1,000 of a radian. In

a complete circle there are 2 'II' =6.28318. radians. There are, therefore

6.283.18 true mils in a circle. This is an odd number which cannot be subdivided conveniently. The nearest number which can conveniently be subTopography for Field Artillery

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divided is 6,400, and 1/6,400 of a circle was therefore adopted as the artillerr

mil. Its value is so close to that of the true mil that in ordinary calcul~tion

the difference may be disregarded, and it may be assumed that the artillery

mil subtends .001 of the radius or distance. However, if an instrument

graduated in artillery mils is to be used for stadia measurements or other

fine work, the exa.ct value 9f the arc subtended by the artillery mil should

be taken as the basis for computing tables or other calculations. This value

is:

6~~~;8 X.001=.0009817 of the radius.

25. The Rimailho mil s:rstem takes 1/6,000 of a circle as the working

mil, called the R-mil. Its value is not so close to that of the true mil as

1/6,400, and it is little used.

26. The advantage of the -mil system over others for artillery

work is that angles in mils, within certain limits, can be calculated directly

from linear distances. For small angles, up to 330 mils, the arc subtended b~

the angle is practically equal to its tangent, maki,'lg it possible to use the

tan~('nt, a straight line, in connection with. the radius, as a measure of tht,

angle, instead of the arc. The great majority of angles requiring such calculation in artillery work are less than 330 mils. For an explanation of the

reasons for this limit, see par. 37, under Expression of Angles by Tangents.

27. To illustrate the mil graphically, in fig. 3 let OA=l,OOO of any linear

unit, say meters, and arc AB=l meter. Then angle AOB=l mil. Tangent

f'

----,:-

I

[' 4.t;'ETER5

--:--r I

2.ME:TERS _-1_i_

o D

Fig. 3

AB', perpendicular to OA, is practically equal to the are, and may also be

taken as one meter long. If another mil is added, making the angle AOe, 2

mils, then arc Ae or tangent AC' is 2 meters, and so on within the defined

Ii••lit. If the sides of the angles are extended to 2,000 meters, at D, then ar~

DE or tangent DE' of the 1 mil angle is 2 meters, DF or DF' of the 2 mil

angle is 4 meters,. and so on, the arc or tangent always having a length or

1/1,000 of the radius for every mil of the angle.

28. The mil relation may be expressed in three ways, with which everr

artilleryman must be familiar. In fig. 4, let tjJ be any angle in mils within

W{l60)

L(800)

Fig. 4.

Topography lor Field Artiller)'

,
-10-

the limit of 330 mils, L any radius or length, and W any tangent or width,

perpendicular to L. Then:

W ( • • 1,000 W) (1) 1ft 1/1,000 L sometimes wrItten -L--

For example, let W=160 meters and L 800 meters.

160 160 .

Then 1ft 1/1,000 X800 -:s = 200 mIls.

L . . 1ftX L

(2) W 1ft X 1/1,000 (sometimes wrItten 1,000 )

This is the most common form, being used constantly in calculating deflection

offsets, deflection differences, site, etc. The other two forms may be derived

readily from it by transposing the terms. This equation may be used for

find~ng the linear width of a target when the angular width can be

measured or estimated, and for similar purposes. For example, using the

above figures, W=200X1/1,OOOX800=200X.8=160 meters.

. W . . 1,000 W

(3) 1/1,000 L = ---:;;-(sometimes WrItten L = --,.-1-) 1,,, \ ,,~

Used principally in calculating ranges to targets or other objects of known

linear width whose angular width can be measured, etc.

For example, 1/1,000 L= 160 =.8, and L=800.

200

Some artillerymen prefer the forms given in parentheses, but most

find it simpler to use the form::::first given, always thinking of L in units of

1,000. Thus, 800 meters=.8, as above; 4,600=4.6, etc.

This method of calculating angles and distances may be called the

tangent method, since it is based on the tangent ratio. See par. 32, under

Expression of Angles by Tangents.

29. The same method may be applied, though less conveniently, to the degree, grade, or any other angular unit, by taking, instead of 1,000, the length

Fig. 5.

of radius at which the unit considered subtends a tangent of 1. For the degree this length is 57.3. Applying this in the same way as 1,000 was applied

for the mil, we have the following relations for the degree, fig. 5.

Topography for Field Artillery

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= =-

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W 57.3W

(1) Deg. 1/57.3 L (or -L-)

, Deg.XL (2) W Deg. X1/57.3 L (or 57.3 )

W 57.3 \V (3) 1/57.3 L. Deg.' (or L Deg.)

L is thus considered to be divided into irnit lengths of 57.3 instead of

1,000. In calculating with grades, use 63.66, the length of radius at which

1 grade subtends a tangent of 1. To find this length for any angular

umt, take the reciprocal of the tangent of that unit.

1 Thus: Tan l,jz .001. :ooI 1000.

1

Tan 10= .0174551. .0174551= 57.2899or 57.3.

1

Tan Ig = .0157093. .0157093 63.6567 or 63.66.

The limits for these forms of calculation are .about 11 degrees or 15! grades.

These limits are somewhat less than the artillery mil limit of 330 mils. For

an explanation of this, see par. 38-39 under Expression of Angles by Tangents. The inconvenience of these forms of calculation as compared with

mil calculations, using even thousands, is obvious. They are useful, however,

for calculating slopes in degrees or grades directly from distances and altitUdes. although it is practically as convenient to calculate the angle in mils

and convert to degrees or grades by means of the equivalents.

D. CONVERSIONS IN ANGULAR MEASURE.

Base Equivalents:

;jOt 1 Circle=3600=400g=64001ft.

1 Quadrant=900=100g=16001/ ••

Any desired equivalent can be derived from the above, if the subdivisions are known. Following are the special equivalents which will be

found most useful:

Degrees to mils: 1°=17.781/1.

Close enough for all artillery purposes.

Derivation: JO=6400+360=17.777 •.• 01' 17.781/t.

Mils to degrees: 11/.=.05625° exactly.

Derivation: l1/t =360+6400=.05625 0.

Minutes to mils 1'=.296,/1.

Close enough for all artillery purposes.

Derivation: 90°=5400'=16001/1. 1'=1600+5400=.296296 ... 01' .2961/t.

Mils to minutes: 1,/t=3.375' exactly, or roughly 3 1/3'.

Derivation: 1,/1=5400+1600=3.375'.

, Frequently used in calculating site in minutes. For all ordinary work

it is close enough to calculate in mils and multiply by 3 1/3.

Grades to degree or degrees to grades: Ig=.9° exactly.

Derivation: Ig=90+100=.9°. To convert grades to degrees multiply

by .9; degrees to grades, divide by .9.. This is easier and more accurate than

using 1°=1.111 •.• g.

Grades to mils or mils to grades: Ig=16,/. exactly.

TOpOgrllPhy for Field Artillery

=

=

= =

= =

=

~
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Derivation: 100g=1600, 1g=1600+100=16tjf.

To convert grades to mils, multiply by 16; mils to grades, divide by 16.

This is easier than using 1tjf=.0625g, which, however, is also an exact

equivalent.

The above equivalents will meet practically all the needs of artiller,'

work. Others may be derived in a similar way for special purposes if desired. All angular conversions should be tested by mental approximations.

the same as described for linear conversions, par. 13.

31. The following true mil equivalents are given for purposes of comparison and for exact conversions from the tangent form of mil calculation

to other units, the limitations of which are shown in par. 40 and the table

in par. 42. Such conversions will seldom be necessary in general artilIer}'

work. but occasionally may be required for exact computations.

6400 ., 1 true mil = 6283.18 = 1.0186 or 1.02 artillery mIls.

6283.18

1 artillery mil 6400 -.98174 or .98 true mils.

360

1 true mil 628J.HS .057~96or .0573° 3.438'.

6283 18

360 17.4530 or 17.45 true mils.

E. EXPRESSION OF ANGLES BY TANGENTS.

To illustrate the tangent graphically, fig. 6, construct a right triangle ABC, of which angle A is the angle of which the tangent is desired.

The sides of the angle, AB and AC, form the base and the hypothenuse of

the triangle. which is completed by dropping the perpendicula':' BC from the

hypothenuse to the base at any point. The size of the triangl~ is immaterial.

since the ratios of the sides will remain the same for any giYen angle. Then

tangent A=~~, or, in general, considering the two sides of the triangle which

form the' right migle, the tangent is the' ratio of the opposit,~ f:' ide over the

adjacent side, or the vertical side over the base. Expressed in linear units.

the tangent gives the length of the vertical for a base of 1.

Topography for Field Artillery

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33. . The most common application of the tangent is in calculating slopes

from a map, where the vertical distance. BC, can be obtained from the contours, and the horizontal distance, AB, measured with a scale. For example

let BC=160 meters and AB=800 meters. Then the tangent of the slope AC,

or of the angle -1, is =.2, see fig. 6.

34. There are thteeforms' of the tangent relation, the same as the mil

relation :,!,

(1) ". BC Vertical I. an A = AB' or Tangent = Base •

This form is. used in calculating the tangent, as illustrated above.

(2) BC=AB>< Tan A or Vertical Base X Tangent.

For example. using the. above figures, BC=800X.2=160 meters.

Be . Vertical

(3) AB Tan A or Base Tangent.

160 .

For example, AB = :2 800 meters.

c

:CM.

Fig. 7

35. To plot the above angle by its tangent layoff a base AB of any convenient length, say 10 centimeters, fig. 7. At one end, B, erect a vertical, BC,

the length of which is equal to the base multiplied by the tangent, 10X.2=2

centimeters. Draw the hypothenuse A C. The angle A between base and

hrpothenuse is then the desired angle which was expressed by the tangent

2. It must be equal to the original angle from which the tangent was ob-

• 2

taIned because the tangent ratio of the sides of the plotted triangle, 10' has

been lnade the same as the ratio of the corresponding sides of the original

.'''' 160

trIangle, 800 • making the triangles similar and the corresponding angles

~q?al. An angle of any size can be expressed by its tangent and plotted in

hIS way without the use of a protractor. .

36. The similarity between the calculation of the tangent and the calCUlation of mils, degrees, or grades. as described in par. 29, is apparent .. The

tangent in the illustration, fig. 6, was =.2. The calculated angle in

mils 0. 160. . . 160

IS 1/1,OOOX800=200 mIls (I,OOOXthe tangent), In degrees. 1/57.3X800

::::11.46°(57.3 X the tangent); in grades, 1/63.~~~'800 -12.73g (63.66X the tan-

~ent). The calculation in each case is based on the .tangent ratio, simply

lntroducing the proper factor to convert the tangent ratio into angular units.

37. A Comparison. The reason why the calculation of the angular value

Topography for Field Artillery

~~~

=

= =

=

'

~

~~~
D!../OO

/O-c Cl-/O

lOGO B

TRVE MILS.

Fig. 8

-14-:'

based on the tangent ratio is limited to small angles, while the tangent itself may be used for any angle, is that the angular value is to be used in

an entirely different way from the tangent value. The angular value ,obtained from the calculation is to be used like any other angular measure,

with instruments graduated in a circle, _while the tangent value is to be

used, either in calculation or plotting~ as a ratio between straight lines, in

the same way as it was originally calculated. Angular measure is represented by the arc of a circle. The tangent is represented by a straight line

tangent to the arc. The tangent form of calculations can be used for angular

measure only within the limits where the tangent is practically equal to the

arc. This is true only for small angles. As the angle increases the tangent

becomes longer than the arc and cannot be used to represent angular measure.

38. To illustrate graphically the relation between the tangent value and the

actual angular value of an angle, construct a right triangle ABF', fig 8,

TA~J.

r~330

with base AB=:=l,OOO and vertical BF'=330, divided into smaller triangles as

shown. Then, since the base is 1,000, arc BF and its divisions give the actual

angular measure, and tangent BF' and its divisions the tangent value, in true

mils, of the corresponding angles at A. In angle BAC' the arc BC and tan ..

gent BC' are practically equal, both having a length of 10, so the angular

measure is practically the same as the tangent value, 10 mils. Of course in

reality the tangent is slightly longer than the arc, but the difference for

such a small angle is negligible. In angle BAD' the tangent BD' has gained

perceptibly over the arc BD, but the difference is still slight, only .3 true

mil. But when angle BAE' is reached, with tangent value of 250 mils, the

tangent BE' is 5 mils ahead of the arc BE. This, therefore, must be taken

as the limit for using the tangent calculation of true mils, or the similar

calculation of degrees, grades, etc., as described in par. 29. In 'the angle

BAF' the tangent exceeds the arc by 11.3 mils, entirely too great an error

for artillery work. Thus it is seen that the tangent calculation gives practically exact values for small angles, but that as the angle increases the

gain of the tangent over the arc causes an error in the tangent calculation

as compared 'with the actual angular value which is positive and which in-

, crea;;es progressively from the start.

39. The relation between tangent and angle with the artillery mil, howTopography for Field Artillery

~
-15-

ever~' is not the same as with the true mil. The relation shown in the foregoing illustration is true only where the angular measure is taken in the

same unit as that on which the tangent calculation is based. In fig. 8 the.

tangent calculation was based on a length of 1,000. the exact length at which

a true mil subtends a width of 1, and the arc. representing the ac-,

tual angular value, was me:::tsured in true mils. Similar results would be

obtained if the tan'gent values had been calculated in degrees on a length

of t7.3, or grades on a length of 63.66, and the angular value's measured in

true degrees or grades. However, if the angle or arc be measured in a different unit from that on which the calculation is based, it is evident that the

relation between arc and tangent will be changed. By taking a unit slightly

~maller than the one on which the tangent calculation is based, the error

In that calculation may be offset to a considerable extent for practical purposes.

This is just What is done in using the artillery mil. To illustrate, construct

a triangle BAH'. fig. 9, of exactly the same dimensions as triangle ABF' in

fig. 8. Measure the arcs, however. with artillery mils instead of true mils.

, TAN:';:

~~3JO

ARTILLEI1'Y MILS.

Fig. 9

40. Since the artillery mil is smaller than the true ~il, it will take more

of them to measure a given angle. Hence for the small angles where the

angular value in true mils was practically the same as the tangent, the

artillery mil value will be greater than the tangent value, and the tangent

calcwlation will therefore have a negative error at the start, instead of

Positive error as with the true mil. ..For small angles this negative error is .

practically negligible. For angle ABC', with a tangent value of 10 mils the

actual angular value in artillery mils is 10.2, making an error of -.2 mil, in

the tangent calculation. This error increases in the negative direction,

simply because the quantities are increasing and the increase in the tangent

Over the arc has not yet commenced to make itself felt, up to angle DAF',

Which has a tangent value of 145 mils and an actual angular value of 146.8

artillery mils, making an error of -1.8. At this point the tangent begins

to gain, and at 237 mils, angle BA C', it overtakes and exactly neutralizes

th~ negative error, the tangent value and angular value in artillery mils

?eIng exactly equal at this point. From here on the, error is positive and

Increasing, the same as with the true mil, though to a lesser degree. For

angle BAH', with a tangent value of 330, the actual angular value in artillery mils is 324.7, making a positive error of 5.3 mik 330 mils, therefore,

Topography for Field Artillery

~
-16-

has been taken as the limit for fairly accurate artillery mil calculations (F.

A. Drill Regulations, Par. 1044).

U. If the angle be measured in a larger unit than that on which the tangent calculation is based, the effect, of course, will be opposite to that produced with a smaller unit, and there will be an exaggerated positive error

in the tangent calculation at the start, increasing rapidly with the angle.

fhis is the case with the R-mil, making it very inaccurate for calculating'

angles above 100 mils by the tangent method.

-12. The following table shows the relation between the tangent calculation

and the actual angular value for the degree, true mil, artillery mil, and R-mil.

Values for grac1es may be found by converting either degrees or true mils by

the proper equivalents, as the basjl) of angular measure and tangent calculation is the same for all three units.

TABLE

Showing accuracy of tangent calculation of angular values.

Error in Tangent Calculation II Tan. IITia~Fo~n:f~:~I:-Il

II II 0' I Mils 1\ 0'

Actual Angular Value II

\ 1w: I ~~t~I :iis II , I True

Mils I Art. I R. Mils Mila

11.010II 34.41 10. II 34.41 10. I 10.21 9.611 0.01 0.0 1- .21+ .411

11.050II 251.91 50. 11251.81 49.97\ 50.91 47.711+ .11+ .031- .91+ 2.311

Wn.0875f1 500.7187.5Tf500.01 87.3 I 88.91 83.3If=F-.-71+ .2 1~1.4-1+ 4.2:\

(2) 11.100II 543.81100. II 542.71-99.7 1101.5195:211+ 1.11+ .3 1-1.51+ 4.811

11-145II 818.41145. II 815.31144.1 1146.81137.611+3.11+ .9 1-1.81+ 7.411

11.200111127.51200.111118.61197.41201.11188.511+ 8.91+ 2.6 1-1.{1+11.511

11.237111334.61237.111320. 1232.7 1237. 1222.211+14.61+ 4.3 I 0.01+14.811

(3) 11.250111419.31250.111402.1f245. 1249.5:233.911+17.2-/+ 5. 1+ .51+16.111

11.300111711.21300.11164~r29m296.81278.311+2~21+ 8.5 1+3.2H-21.711

(4) 11.330 111854.31330. 111815.81318.7--,324.71304.411+38.51+11.3 1+5--:3-1+25.6]

(1) Limit for practically exact calculation in true mils, degrees, or

grades.

(2) Limit for fairly accurate calculation in R-mils.

(3) Limit for fairly accurate calculation in true mils, degrees, or

grades.

(4) Limit for fairly accurate calculation in artillery mils.

t3. It may be laid down as a general rule that for all practical artillery

purposes the most convenient method of using the tangent form of calculation is always to calculate in artillery mils, and then convert to degrees or

grades by the proper angular equivalents if desired. This saves confusion

and is close enough for all ordinary uses. For exact results with angles less

than 50 or 51g (such as slopes, most of which are small angles), it may be

desirable to calculate in true mils, degrees, or grades on the exact basis, converting to artillery mils if necessary. However, it is seldom that either the

accuracy of the measurements or the requirements of the case will justify

such refinements in 'artillery work.

H. If angular values above the limits for tangent calculation are desired,

or if absoluteiy exact values are desired for any angle, the tangent should

TOVORraphy for Field Artillery

-
-17-

be calculated' and the corresponding angular value found in a tange~t table.

4-5. To Add or Subtract Tangents. In practice, it is frequently necessary

to add, or subtract angles which are being handled by their tangents, as in

applying the angle of site in the proper sense to the angle of fall in order

to obtain the quadrant angle of fall. This can be done by tangents only when

the sum of the two angles does not exceed the limits for the tangent cal..;

culation of angular' values .. Strictly speaking",:the sum (or difference) of

the tangents of two angles is not the same as the tangent of the sum (or

difference) of the actual values, but within the limits prescribed, the results

are close enough for artillery work. To illustrate the error with angles

?eyond the limits, suppose the tangent of the angle of fall has been found

In the range table to be .500, and the tangent of the angle of site has been

calculated from the map to be -.100. Putting the two together to make the

. quadrant angle of fall, a tangent of .600 is obtained. Now, the actual angle

corr~sponding to a tangent of .100 is 101.5 artillery mils and the actual angl~

corresponding to a tangent of .500 is 472.3 artillery mils, making the sum.

or actual quadrant angle' of fall '573.81/~. The tangellt of this angle, obtained

from a tangent table, is .631, showing an error of ..031 in the result, obtained

by adding the, two tangents. Hence a tangent table must be used if the

quantities exceed the prescribed limits. .

.(6. Certain modifications of the tangent are used in expressing ground,

slopes. The most common are the gradient and the per cent.

F. GRADIENTS.

. Vertical distance . . GradIent = H' t 1 d' t reduced to a fractIon wIth anum. , orlzon a IS ance

era tor of 1. It is simply a fractional form of the tangent, in which the denominator always gives the horizontal for a rise of 1. Thus, in fig. 6, the

. BC 160 1

gradIent of Angle A or slope A C is AB 800 5 usually stated, "Ion

or in 5". To obtain the gradient. ~rom the tangent, simply convert the decimal

, 2 l' .

lnto a fraction with numerator 1. Thus,. 2 = io = "6' To obtain the tangent

1 from the gradient, reverse the process, thus, T .2.

~7."*. To plot an angle from the gradif'nt, layoff a base equal to the denomInator and a vertical of 1, in any convenient unit. "---

. '. . . . . For example, fig. 10, layoff base AB, 5

======:J,C;". centimeters, and vertical BC, 1 cen,tiI .meter. Join AC. This gives, of course,

Ar----- . the same angle as plotted by the tan5 B gent, fig. 6.

Fig. 10.

G. PER CENT •

.{8 Vertical distance . h ft. • Pel' cent =, . expressed. In t e form 0 per cen , th . • . HorIzon tal dIsta.nce. • .. . at IS" the vertIcal distance or rIse In a hOrIzontal dIstance of 100. Thus,

• .. , B C 160 20

USl~g the.same illustration as with the gradient, AB= 800= .20 100or 20%.

To obtain the per cent from the tangent or gradient, multiply by 100 and affix

Topography for Field Artillery

-

'

= =

'"

=

- c

o

'

'

=

_
I

I

-18-

the per cent sign, which thus beco~es simply a substitute for two decimal

places. Thus, .2 or 1/5X100=20%. To obtain the tangent from the per

cent, divide by 100, or point off two decimal places. To obtain the gradient.

20 1 divide by 100 and reduce to a fraction with numerator 1, thus IOU T.

49. To plot an angle from the per cent, layoff a base of 100 and a vertical

of the :0

A /00 .8

Fig. 11

j

100

c

IDO' B

Fig. 12

A

For example, fig. 11, layoff base AB 100 millimeters and vertical Be

20 millimeters. Join AC. This gives the same angle as plotted by the

gradient or tangent.

50. A common error in expressing slopes in

per cent is to call a vertical drop (that is, a

right angle, or 90°) a.100% slope, whereas a

45° or 800,!J slope is really a 100% slope. To

illustrate, fig. 12, layoff a base AB of 100 and

a vertical BC of 100, in any unit. Join AC •.

100 Then, the per cent of angle A islOO =100%.

It is evident from inspection that this angle

is half a right angle or 45°. Its tangent, of

course, is =1, which is the tabular tan1

gent for 45°. The gradient is -1-. Above this

angle the values increase until at 90° either the tangent, gradient, or per

cent is infinity.

Fig. 12 gives a good illustration of the fallacy of attempting to calculate angular values from the tangent relation above the limits laid down

100

1/1,000 X 100 =l,0001Jt. in par. 40. Calculating in mils, angle A would be

C I I. . d 100 .

a cu atmg In egrees, 1/57.3 X 100 =57.3°. Since the actual angular value

is 8001/t or 45°, the tangent calculation has an error 'Of 2001/t or 12.30.

51. It is not customary to use the gradient form of expression above 45",

since this would make a fraction with a denominator less than 1. For example, the angle of 76° has a tangent of about 4, or 400%. This would make

d f 1 1

a gra lent 0 1/4 or .25. For angles above 45° it is customary to use the

straight tangent, giving th~ rise for horizontal of 1. Among engineers this

is commonly stated, "1 to 4," giving the horizontal figure first instead of the

vertical. Thq,s "Ion or in 4" means a gradient, giving the vertical figure

first, while "1 to 4" is merely a form of stating the tangent, giving first the

horizontal figure, which, for the tangent, is always 1.

Topography for Field Artillery

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l

I ~~~

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H. CONVERSIONS IN TANGENT EXPRESSIONS AND ANGULAR

MEASURE.

52. It is often desirable, such as when a tangent or gradient is given without the angular measure, to convert a tangent expression directly to angular'

measure by means of a factor or equivalent without stopping to plot and

calculate the aIlgle .. This may be done within the limits laid down for calculation of angles by the tangent method. and with the same degree of.

~ccuracy, (par. 40 and table, par. 42), as the result of the conversion

IS exactly the same as the calculation.

Tangent or gradient to mils: multiply by 1,000.

Tangent or gradient to degrees: multiply by 57.3.

Tangent or gradient to. grades: multiply by 63.66.

For example, Tangent .2X1,000=200,!t.

Tangent .2X57.3=11.46°=11 °27.6'.

Tangent .2X63.66=12.73211=121l73" 20....

In each case the factor or equivalent is the distance at which the angular unit considered subtends a tangent of 1; that is, "'he factor is the reciprocal of the tangent, the same as the factor used in calculating angles from

the tangent ratio, par. 39.

Per cent to mils: multiply by 10 (1%=101/t).

Per cent to degrees: multiply by .573 (1%=.573°).

Per cent to grades: multiply by .6366 (1 %=.63661:>,

The factors for per cent are simply 1/100 of those for the tangent

or gradient since per cent is 100 times tangent or gradient.

It is also often desired to find the tangent of a given angle for calculation or plotting. This may be done without a tangent table by means of

the following factors or equivalents, within the prescribed limits.

Mils to tangent: multiply by .001 (the tangent of 1 mil) or point

off three places. For example, 2.001/tX.00l=.2, tangent. .

Mils to gradient: set up a fraction with the given number of mils in

the numerator and 1,000 irt the denominator. Divide through by the numerator to reduce numerator to 1. This is the same as multiplying by .001

and then converting the result into gradient form.

F 200 1 2 2 1.

or example, 20011z= -1UUO 5' gradient. Or 200t!tX.001=. 10-""6 . Degrees to tangent: multiply by .0175 (the tangent of 1°).

}1'orexample, 2°X.0175=.035. tangent.

Degrees to gradient: set up a fraction with the given number of

degrees in the numerator and 57.3 in the denominator. Divide through by

the numerator to reduce the numerator to 1. This is the same as multiplying

by .0175 and then converting the result into gradient form.

For example, 2°=572.3=~:.6' gradient. Or 2°X.0175=.035=1.~~O=2;.ti

Grades to tangent: multiply by .0157 (the tangent of .1g).

. Grades to gradient: same as with degrees. except that 63.66 is used

Instead of 57.3.

Mils to per cent: multiply by 1/10, or point off 1 place (l1/t=.l%).

Degrees to per cent: multiply by 1.75 (1°=1.75%).

Grades to per cent: multiply by 1.57 (1,=1.57%).

Topography for Field Artillery

_ = = ~
Ii ./ ,

-20-

These factors are simply 100 times those for converting to the tangent,

since the per cent is 100 times the tangent.

53. For angles above the prescribed limits for calculation, a tangent

table must be used for all these operations. If a table is available it should

be used for all angles, as it is more accurate and more convenient than calculating .

MEASURING INSTRUMENTS.

A. SCALES.

54. All measuring instruments used for exact topographical work should

be the best available, made by reliable manufacturers. No instrument, even

a government standard issue, should be 'used without being tested.

Scales, rules, or alidades may be of wood. metal, celluloid, or other

durable composition. Paper scales (except graphical scales drawn on maps)

are not satisfactory, as they are subject to expansion and contraction from

moisture.

55. A metric measuring scale for artillery work should be 25 or 30 centimeters long. and should have two edges, one graduated to millimeters, the

other to half-millimeters. If the scale has only one edge it should be graduated to half-millimeters. An English scale should be a foot long, graduated

on one edge to tenths. on the other to fiftieths of an inch. If it has only one

edge it should show both tenths and fiftieths. An. ordinary engineer's (not

architect's) scale has these graduations. A triangular scale is a good form,

since it can be used as an alidaG(" but it is harder to straighten when warped

than a flat scale, and it is seldom that more than two edges will be used

for measuring. A flat scale with folding sights makes a better all-round

instrument and is easier to carry.

56. Every measuring scale not known to be standard should be tested

by comparing it with a known standard. Wooden or metal scales made by

reliable manufacturers may usually be accepted as accurate. All other

scales should be tested by comparison with a good wooden or metal scale.

57. Tapes or chains for ground measuring should be either all metal or

fabric with wires woven in lengthwise (usually called metallic tapes). Every

woven tape. and every all-metal tape or chain not known to be standard,.

should be compared with some known I standard. Any errors discovered

should be corrected by marks on the tape or by making allowances in measuring. In long measurements where great. accuracy is required it is necessary

to allow for stretching, sagging, and expansion or contraCtion due to heat.

Artillerymen, however, will seldom be concerned with these corrections, as

extensive surveying usually will be done by engineers. In5ltructions for

making such measurements. if desired, may be found in any good engineer's

or surveyor's manual.

58. Every edge which is to be used for drawing straight lines or for

sighting should be tested by sighting along it or by laying it along an already

tested straight edge or plane surface (as a 'piece of plate glass or mirror

which gives true reflections). An edge may also be tested by drawing a

line along it with a sharp pencil, then reversing the edge along the other side

of the same line. If straight it will coincide with all parts of the line. A

scale may be slightly crooked and still be good for measuring, though it canTopography for Field Artillery
-21-

not be used for drawing straight lines. Wooden scales are likely to become warped and metal or celluloid scales to become bent, so they should be

handled carefully and tested occasionally even after passing the first test.

59. The line of sight of an alidade, whether defined by sights or by a

straight edge, should be tested to see whether it is parallel with the drawing

edge. This may be done as, follows. Lay the alidade on .a piece' of paper

fixed on a plane table..or other flat surface, and sight on some sharp, well- ,

defined point at least 2,000 meters distant. Draw a fine line with_a sharp

pencil along the drawing edge. Examine the line after it is drawn to see

that it follows the edge exactly, and verify the sighting on the distant point.

Reverse the alidade, placing the drawing edge carefully along the other side

of the same line. Then, if the line of sight is parallel with the drawing edge

it will again strike the point first sighted on. The process should be repeated two or three times to make sure of the test. Comparative err9rs in

angles between lines drawn in any particular operation may be avoided by

~Iacing the alidade so that the line of sight and the drawing edge are always

In t~e same relative positions~ but errors in orientatj':m; that is, the relation

of lInes on the map to corresponding lines on,the ground, cannot be so avoided. Hence if the alidade is inaccurate and cannot be adjusted it should be

discarded for sighting purposes.

B. PROTRACTORS.

60. An accurate protractor is harder to get than an accurate scale. A

transparent celluloid or composition protractor is the most useful type for

artillery work, though metal protractors are usually more accurate. A protractor should be as large as can conveniently be used, with a radius of at

least 10 centimeters. A mil protractor should be graduated to a least reading

of 10 mils, or 5 mils with a large protractor, and a degree protractor to

half, third, or quarter degree, (30', 20', or 15'), depending on the size of

the protractor. Closer readings are made by eye, if necessary. Circular

protractors are sometimes used, but the semicircular type with a linear

measuring scale on the straight edge is better 'for general use. The subdivisions should be numbered clockwise. In a semicircular protractor there

• should be an outer row of figures, from 0 to 3200* or 180°, for use in the

fire.t semicircle, and an inner row, from 3200~/~ to 64001/1, or 180° to 360°, for

Use in the second semicircle, with the protractor reversed. "-

61.' To test a protractor, draw two lines with a tested straight edge intersecting at about their centers at right angles, each line slightly longer than

the diameter of the protractor. The lines should be very carefully drawn

and all the right angles tested with a standard right angle form or with a

. scale or compass, as described in par. 72. Then lay the protractor over the

lines so that the center of the protractor is exactly over the intersection of

the lines and the 0 and 3200'1' or 180° marks are on one of the lines. The

16001/1 or 90° mark should be on the other line (also the 480011~or 270° mark

with a circular protractor). If the marks on the protractor do not fall

~xactly over t4e proper lines, it indicates either that the center hole of the

protractor is not at the true center, which is the most common error, or that

the graduations are inaccurate. A slight inaccuracy in the position of the

center hole may be corrected by enlarging the hole so as to make its center

Topography for Field Artillery

'B ~~ S5f
• <. -22- .

,coincide with the true center. If the error is greater than the diameter of

the hole, a new hole should be drilled at the true center, made very small at •

first, then tested, and enlarged as desir€:d. A needle broken off at its largest.

part, ground flat, then pointed, and fitted with a sealing wax or wooden t

handle, makes a good drill. If the new hole runs into the old, the old one

,should be filled with a hard waterproof cement, such as china cement. If.

the protractor has lines running to the center, these should be changed, if.

necessary, so as to intersect exactly at the true center. Before a point is

accepted as the true center, it should be tested by the middle points and ,

quarter points of the quadrants, the same as above described for the main

quadrant points. Having completed the test, using one of the intersecting

lines as the origin, turn the paper by a full quadrant and repeat the test,

using the other line as the origin, so that any possible inaccuracy in the

,drawing of 'the lines may be detected. The results should be the same using

. either line.

62. While testing the center it may be discovered that some of the graduations are irregular. In that case the center should be located so as to

give correct readings for the greatest possible number of points, especially

the quadrant point and the principal subdivisions. Having established th~

center, the accuracy of the graduations should be tested as follows. Center

the protracto~ over the intersection of the two test lines, with 0 on one of

the lines and note whether the other main quadrant points coincide exactly

with the other: lines. Then shift the protractor by one of the main sub-

'divisions, such as 10011£or 10°, keeping it centered carefully, ar.d note

whether the corresponding points in all four quadrants coincide with their

proper lines. Continue until the main subdivisions have been tested in this

way. This is usually a sufficient test, as it is unlikely that corresponding

points in two different. quadrants will both have an error in the same direction. If a closer, test is desired the right angles may be. subdivided as de-

, scribed in par. 64. Another check is to measure the main subdivisions along

the edge with a good scale to see whether they are uniform. This, however,

is not an absolute test; because the edge of a protractor may be irregular and

still measure angles accurately, and such a test could not be used with a

rectangular protractor.

,C. EMERGENCY DEVICES.

63. Other Devices. .Every artilleryman should know the length of his

shoe. his exact height, and the exact distance between some well-

. defined lines or marks ..on his hands, for use in improvising measuring devices

in case he should be without a scale. Marks usually can be found on the palm

or inside the fingers which will give an even number of centimeters or inches.

The measurement should be made with the hand held perfectly flat without.

straining. \Vhen needed, for use the measurement may be taken from the

hand by marks on the edge of a stick or piece of paper. Such measurements,

of course, are not exact; but a fair degree of accuracy can be attained. It is

convenient also to know the span of the fingers, but this is a very rough

method of measul'ing on account of the difficulty in stretching the fingers

uniformly at different times. The hand and fingers should, of course, be

. calibrated for measuring: angles in mils, as described in Artillery Drill

Regulations.

Topography for, Fie.ld Artillery

I

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D. METlio1.1S OF CONSTRUCTION.

64. To Construct a Protractor. A ""'ory accurate protractor may be improvised with a good scale and a pair of COlnp~sses. To make a mil protractor take a piece of medium weight cardboard or stiff paper with a good

p

Fig. 13

surface, about 15 by 25 em., fig. 13. Draw a straight line the full length

of the paper parallel with and about 1 em. from one side. All lines shoul.}

be drawn carefully with a very sharp, medium hard pencil, and all measurements made carefully and mal'ked with a very sharp pencil or needle point.

With the compasses, using point 0 at the middle of the line as a center,

and a radius of 102 mm., describe a semicircle ACB,. extending to the edge

of the paper. The reason for this length of radius is that 1 artillery mil

subtends an arc or chord of 1 in a length of 1,018.6. Hence by making the

radius 101.86 mm. (or 102 mm., which is close enough), 10 mils will subtend

exactly 1 mm. on the circumference, and the millimeter scale may be used

f()~ making the graduations. This makes a very convenient size of protracto~

WIth A and B as centers, and radii about 3/4 of AB, describe arcs intersecting at P. Draw PO, extending the line to the edge of the paper. This

should be exactly perpendicular to AB and should bisect the semicircle at C.

To test this, measure the chords AC and BC straight across with the scale.

The distances should be exactly equal, each 144.2 mm. (The chord of 900

or \ ---- 1600,ft is 1.414 times the radius. 1.414X 102=144.2, also, '\l1022

+1022=144.2).

~ith A. C, and B as centers, and radii a little over half of AC. draw arcs

Intersecting at Q and R. Join QO and RO, bisecting the quadrants at D

and E, forming angles of 450or 8001jl. at O. With the scale measure the

chords DA, DC, CE, and En. They should be exactly equal, each 78 mm.

~Th~ chord of 450

or 800,!t is .765 times the radius.' .765XI02=78). Simdarlv bisect the 8001jt arcs at F, C, Jl and /. making 4001ft arcs. The chords

of these arcs should also be exactly equal, measuring 39.8 mm. Adjust the

Topo~raI>hy for Field Artillery
-24-

marks if necessary to make all the divisi~J1.aabsolutely equal. These 4001'/1

arcs may now be subdivided with the E:cale. Take arc CH! Mark point K ~)D

the arc 20 mm. straight acrOSE:II'om C. This should also be 20 mm. from H,

bisecting the arc and making 2001/t divisions. With the scale mark each

millimeter along arcs CK and KH, each representing 101ft. 511t subdivisions

may be put in if desired, but this. is usually unnecessary, as readings may

be made within a mil by eye from the 101ft graduations. Graduate the remainder of the semicircle in the same way .. Make all marks lightly at, first,

inspect them to see that the graduations are uniform, and correct them if

necessary. Then go over the marks and make them permanent with a very'

sharp hard pencil or a very fine pen, pivoting the ruler at O. Pen. marks

cannot be made so fine as pencil marks, but they are darker and easier to

reati. Make the 50'1t and 1001/~ marks longer than the 101ft marks. Inner

arcs may be drawn lightly as guides for this purpose. Number the graduations every hundred or every two hundred mils, as desired, with the numbers

froIr. 0 to 3200 next the edge and from 3200 to 6400 inside. Make lines AB

and CO permanent with hard pencil or fine pen, producing OC to the edge of

the paper. Cut the protractor out along the semicircle, leaving the margin 01

about 1 em. between line AB and the straight edge. Punch a hole about U

mm .. in diameter at the center O. A small nail with the end filed squarely

off makes a good punch. Or a ~quare hole may be cut out, with the corners

exactly on the lines. Two or three coats of transparent shellac or varnish

will make the protractor waterproof and durable.

65. The method of subdivision above described, working from the whole

to the part, is the only satisfactory way to secure uniformly accurate graduations throughout the protractor. It is practically impossible to make the

graduations come out even by measuring from one end of the semicircle

clear around to the other with a scale, though a small protractor, up to perhaps 4001/1, could be made in this way.

66. If compasses are not avaiiable, take a strip of cardboard or stiff paper,

prick two pinholes in it the length of the desired radius apart, and put the

sharp point of a pencil through one hole for drawing and a pin through the

other for a pivot. The arcs can be bisected with the scale. If compasses

but no scale are available, bisect the arcs with the compasses until a 501/1

arc is obtained. Divide this carefully into 5 parts by eye. Take these marks

off on the edge of a piece of paper and use to graduate the other arcs.

67. A scale graduated in other units than millimeters such as sixteenths

or tenths of an inch, may be used in the. same way, each division representing 101/t, by taking a radius 101.86 times the unit of the scale. With tenths

of an inch this makes a rather large protractor, so the scale may be halved

if desired. .

68. To make a degree protractor, take a radius 57.3 times the length 01

the scale unit. Each unit will then represent lOon the circumference. This

makes a convenient. size with sixteenths or tenths of an inch. With millimeters the radius is too small, and the scale should be doubled. With

eighths of an inch the scale should be halved. With a degree protractor the

'even bisection,S can be carried only to 450

arcs. Divide each 450 arc into 9

equal parts each 50, with the scale, verify them to see that they are uniform,

and then graduate each part with the scale to degrees and half, third, or

quarter degrees, as desired. .

Topography for Field Artillery'

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69. To make a grade' protractor, take a radius 63.66 times the length of

the scale unit. Divide the arcs by bisection until a 25g arc is reached. Then

complete the graduations with the scale. .

70. If no instruments are available a rough protractor may be quickly

improvi~ed with nothing but. a piece of paper and a pencil, fig. 14. Medium

AV!" B

o I

I

I . I

I

I

C ------ -_JD

(a) (b) (c)

i

I

!

o

"0' C'

(e)

Fig. 14

c'

(f)

. " . ,A .. ',

r~.G""

B p 0 E: C

~e~ght "paper that will fold easily is best. Tear or cut the paper so that

It IS roughly square. 20 by 20 em. is about the right size. In folding the

paper, rub all folds to a sharp crease with the thumb nail. Whenever the

paper is unfolded, rub the creases out flat with the thumb nail so that the

paper will lie flat without distortion, leaving only the marks of the' creases.

(a) First fold diagonally along BC. The crease should be perfectly straight.

(b) Fold across the first fold, bringing C to B, taking care that the two

parts of the first folded edge BC come exactly. together along OB. ADB is

then the right angle. (As thus folded the paper may be used as a right triangle or right-angled ruler). (c) Fold A over to B, taking care that all

three folded edges come exactly together along DB. Angle EOB is then 45°

or ROO,

/t• (d) Unfold the sheet and carefully cut or tear it in two along th~

firs~ diagonal BC, creasing it again both ways if necessary to make it te~r

easlly. Rub out the folds with the thumb nail. One half, ABC, is to be used

for the protractor; the other, B'DC', for making subdivisions. (e) Take B'DC'

and fold so that crease O'F lies exactly along crease O'D. Crease and unfold.

0'/ bisects the 8001ft angle FO'D, forming two 4001ft angles. Fold 0'/ to O'D,

forming 200,!t angles with crease O'K. Unfold and fold O'K to O'D, forming

lOO1/t angles with crease O'L. Unfold and lay O'F along O'D. Mark M on O'D

So that O'M=O'F, Unfold and rub out all creases. 'With a pencil and piece

o~ paper or string as a compass, or simply by hand describe arc FM, cutting

o L at N. Arc MN then represents lOOt/to Bisect this carefully. and dividE7

each ~alf into five parts by eye, making 101ft divisions. Cut or te~r the

Paper carefully along arc FM so that the marks will come to the edge.

(f) Take the other half" of the sheet and describe semicircle PECE with

radius equal to O'F. Subdivide the semicircle by applying arc FM, transTopography for Field Artillery

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ferring the marks with a pencil, taking care that the corresponding creases

exactly coincide. .Unless the protractor is intended for constant use, it will

be sufficient to subdivide only the last segment, COCo The protractor may

be shifted if necessary in making measurements. However, a fairly accurate

complete protractor for general use may be made in this way if the subdivisions are carefully equalized. Having completed the graduations desired,

,either produce them to the edge of the sheet with the edge of a piece of paper

or other straight edge pivoted at the center 0, or,' preferably, cut or tear

the paper carefully along the semicircle.

This method is much more satisfactory than the method of repeated

. refolding described in some texts, as it is impossible. to equalize" several

folds together on account of the thickness of the paper.

71. To make a degree protractor by this method, fold the 45° segment

FO'D into three folds, carefully equalizing them. Each of these will then

represent 15°. Draw arc FM. Divide one of the 15° segments into 3 parts

by eye, and subdivide one of these parts into 5, making 1 graduations, which

may be further subdivided if desired.

C

Fig. 15

E. RIGHT ANGLES.

72. Construction. It is often

necessary in artillery topography to draw lines at exact right

angles, such as' in establishing

the first lines of a grid on a

firing board. The best methcd

is to use intersecting arcs as

described in par. 64, with intersections below as well as

above the base line, making

all dimensions as large as possible.

Where the base line cannot be extended on both sides

of the perpendicular, as in 3.

corner, proceed as follows, fig.

15. Draw a straight line, say

25 em. long, as the base of the

right angle. Mark point A,

where the foot for the perpendicular is desired. Take as a

center 0, so that OD is about

equal to AD, say 10 cm. Make

all distances as long as the paper

will allow. With radius, OA, say 15 em., describe an arc somewhat larger

than a semicircle, cutting the base at A and B. Draw a straight line through

80 cutting the arc at C. Join AC. Angle BAC is then a right angle.

Unless the work is very carefully done this method is more subject to errors

than the other. It may be made more certain by taking another point, 0',

as a center, with radius 0'A, and still another point, 0", below the base line if

possible, with radius 0"A, fig. 15.

TOpOgraphy for Field Artillery

°

"
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The method first described may be made more certain by drawing ~everal pairs of intersecting arcs below "as well as above the base line

with the same centers, A and B, but with different radii, fig. 16.

o

Q

100 o

Fig. 19

c

f

Fig. 16 Fig. 17 Fig. 18

With either method, if the perpendicular passes through all the intersections, a perfect right angle should be obtained.

73. A right angle may be drawn with a scale without a compass as follows. fig. 17: Draw straight lines AB and AC, making an angle of about

60° or 1,00011t, AB slightly longer than AC. Mark point C exactly with a

sharp pencil or needle at some convenient even distance on the scale. as long

as Possible. Then pivot the scale on C, moving it along AB until the edge

of the scale intersects AB at a point D such that CD=AC exactly. Mark D

carefully, and bisect AD at E with the scale. Join EC. Angle AEC is then

a right angle.

The test AE=ED and AC=CD is a good test of a right angle, but can

be used only where the base line can be produced on both sides of the perpendicular. The test may be verified by taking other points on the perpendicular above and below the line, as F, when AF should equal FD.

74. To draw a right angle with a scale where the base cannot be ,produced

on both sides of the perpendicular, as in a corner, proceed as follows, fig. 18.

Draw AB and AC, making an angle of about 45. Mark

point C exactly at some convenient even distance on the?

~cale, as long as possible. Pivot the scale on C, moving'

It along AB until the edge of the scale intersects AB at

point D, such that CD=AC exactly. Produce'DC to £,

marking E carefully so that CE=DC or AC exactly. Join

AE. Angle DAE is then a right angle. It may be verified by taking other points, as C' and C", above or below

the base line, repeating the same process, or by testing

as described in par. 75 below.

75. Where the test described in par. 73 cannot be used, .as in a corner,

a. right angle may be tested as ,follows, fig. 19: Measure carefully equal

dIstances OA and DB, as long as possible, from the vertex along the sides

of the angle, and mark A and B with a sharp pencil or needle. Measure AB

, I

straight across. If the right angle is true, AB= \,OA2+ OB'l, or AB=

Topography for Field Artillery

~
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1.414XOA (or 1.414XOB, since OA=OB). This is based on the fact that

the chord of an angle of 90° <>r1600* is 1.414 times the radius. If possible,

always take OA and OB as an even 100 of the unit of the scale (as millimetf'rs). when AB will equal 141.4 units. This is similar to the method fOl'

testing the quadrant described in par. 64.

A draftsman's triangle or right-angled ruler may be used for drawing

or testing small right angles, but a ruler large enough for drawing an ordinary firing board grid is seldom available. It is not satifactory to draw a

small right angle with a right-angled ruler and thE!n produce the sides:'

Greater accuracy will be obtained with one of the methods described above.

using. lines as .long as possible. Every right-angled ruler should be tested.

This may be done with a scale, as above described, or as follows:

. Lay the ruler -along a good straight edge on a piece of paper and draw

a li~e carefully along the perpendicular edge. Then turn the ruler over and

bring the perpendicular edge carefully up to the other side of the line, still

keeping one edge along the straight-edge. If the right angle is true the perpendicular edge in its new position will coincide with the line drawn. Care

must be taken not to move the straight-edge .

.'Topography for Field Artillery
CHAPTER III.

MAPS AND SCALES.

THE ELEMENTS OF A MAP.

A. DEFINITION.

76. A map is a representation (usually on a flat surface), of "the surface

of the earth, or some portion of it, showing the relative size and position,

according to some given scale or projection, of the parts represented (Web.

ster's New International Dictionary).

B. CLASSES OF ~IAPS.

~7:.. The map is the most important record of topographical information ..

•hhtary Maps may be divided into two general classes,' according to their

~es: . first, strategical and tactical maps; including staff maps, road and area

s etches. and all other kinds of maps and sketches prepared in advance 01"

made through reconnaissance for use in the disposition and maneuvering of

troops; second. technical maps, including artillery battle maps, firing charts,

~lane table sketches, etc.. used in the preparation and conduct of artillery

. reo Every military map should represent the features of the region which

~t ~ov.ers wi~h the degree of completeness and accuracy required for its use,

mlttmg ummpol"tant details. .

C. MAP MAKING AND MAP READING.

78. A thorough knowledge of maps is an essential part of the training

of every artillery officer, and, to some extent, of non-commissioned officers

and other especially trained soldiers: Applied knowledge of maps falls into

two parts, map making and map reading.

(1) Map Making.

79•. For artillerymen there are two phases of map making: first, map

makmg of an elementary sort, including the making of road, position, and

area sketches. to be used in the conduct of marches and the selection and

oCCupation of camp sites and artillery positions generally; (all officers, nonCOmmissioned officers, scouts, and other soldiers employed in reconnaissance

must be able to make sketches of this kind); second, map making for purpos~~ of exact location and orientation, to be used in the location of gun

POSltIons and targets and in the preparation and .conduct of fire. All officers

c~ncerned with the preparation and conduct of fire must be. skilled in this

kInd of map. making to the extent required by their particular duties, and

every artillery officer should have at least a general understanding of the

methods used. Certain non-commissioned officers and other soldiers employed in the preparation and observation of fire, such as instrument sergeants

and instrument operators, also should be trained in this work.

Topography for Field Artillery

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(2) Map Reading.

80. Map reading also may be divided into parts, corresponding to the two

general classes of maps: first, strategical and tactical map reading; second,

technical map reading. Every artilleryman must be able to read intelligently all maps which he may be called on to use~ A knowledge of map

making is a valuable aid to map reading, and at least an elementary training

in map making is desirable for everyone who is required to use maps, even

though he seldom may be called on to make them.

D. GROUND RELATIONS.

81. The foundation of every map is a representation of the ground. Other

features of military importance are then added as required. Every point

on the ground has three relations with reference to every other point: distance, direction, and altitude. (The term elevation is sometimes used instead

of altitude, but in artillery this should be confined to gun elevation to avoid

confusion. )

(1) Distance.

82. The distance between points as represented on a map is the horizontal distance.

(2) Direction.

83. The direction of one point from another is the horizontal angle between an established line of known direction and a line joining the two points.

(3). Altitude.

84. The altitude of a point is its distance vertically above an established

known horizontal plane. Altitude may also be expressed as the vertical

angle between a borizontal plane and a line joining the two points. Between

a gun and its target. this is called the site.

85. By means of t~ese three relations the exact position of every point

on the ground and the rdatiop of all points to each other, both horizontall~'

and vertically, can be shown on a map. Ground forms are shovm by the

altitudes of critical points, supplpmented by graphical devices such as contours or hachures, see pars. 133, 134, Ch. IV. Commercial maps usually sho',';

only the horizontal relations, distan::'p. and direction, but for most military

purposes it is necessary to show also altitudes ar.d ground forms.

(4) :\Iap Essentials.

86. The essentials of a military map may be summoned up as follows:

1. It must show distances according to a given scale.

2. It must show directions with reference to some established lin~

of known direction, such as true north, magnetic north, or grid north,

or 'Sometimes, on small local sketches, simply a line between two known

points, so that the direction between points can be determined from the

map, and so that the map can be oriented with l'espect to the ground, see

par. 175, 176, Ch. VI.

3. It must show altitudes and ground forms to the extent required

for its use, giving altitudes above an established horizontal datum plane,

usu3.11ysea level.

TOpOgraphy for Field Artillery
-31-

DISTANCES AND SCALES.

A. DEFINITIONS.

87. Distances are represented on maps by scales, usually conforming to

a r ~gular system in which th~ scale is' varied to suit the purpose of the

map ..

The scale of a map is the relation between distances on the map and

the corresponding horizontal distances on the ground. Any distance on the

map is called the map distance, abbreviated M. D. The corresponding hori-

~nt,al distance on the ground is called the horizontal equivalent, abbreviated

. E. On any map drawn to scale, all M. Do's are proportional to the corl'esponding H. Eo's. . . .

Since the surface of the ground is not always horizontal, the horizontal equivalent is seldom the same as the actual ground distance.

Horizontal equivalent may therefore be considered both as the horizon-

~~l distance corresponding to a certain map distance, and as the horizontal

t~stance corresponding to a certain distance measu!cd along the surface of

d' e ground. Methods of obtaining the horizo'ntal equivalent from the ground

Istance are given in Ch. X. (Most topographers limit the terms M. D.

and H. E. to distances between contours, but this limitation is likely to be

~~nf~sing. In this work these tprms will be applied to any desired distance.

dIstance between contours is meant, it will be so stated).

B. SCALES. :8. ~ny map scale may be expressed in three ways, anyone of which may

e derIved from the others: . .

89 . (1) As A Representative Fraction, Abbreviated R. F.

• . ThIS is the simple ratio between a given map distance and its horiZontal equivalent, expressed in the form of a fraction, whose numerator

one: For example, R. F., 20,1000 • means that M.. D. : H. E.:: 1 : 20,000.

hat IS, one unit on the map represents a H. E. of 20,000 of the same units.

.th? ground, and thus every M. D. is 1/20,000 of the corresponding H. E.

t IS IS not a unit of measure, but is an absolute ratio, which can be applied

o .any unit, provided both members of the ratio be expressed in the same

~nlh. Thus, if the M. D. between two points measured 1 em., the H. E. be~

t~een them on the ground would be .20,000 em. If it measul'ed 2 inches,

't e H. E. would be 40,000 inches. Or if the H. E. measured 20,000 feet,

1. Would take an M, D. of 1 foot to represent it on the map.

(2) In 'Vords And Figures.

90. This' is a simple statement of the map distance corresponding to some

convenient unit of horizontal equivalent, giving the 1\1:. D. in small units

Used for measuring on the map, and the H. E. in large units used on the

ground. For example, 3 inches equals 1 mile. This means that 3 inches

~: ~he map represents a horizontal equivl:!lent of 1 mile on the ground. To

rIVe a words and figures scale from the representative fraction, express

the R. F. in some definite unit of measure, and then,' convert to other units

as desired. Thus, if the R. F.is 20 ~oo' 1 em.• 1\1:. D. equals 20,000 em.

Or 200 meters H. E., and 5 em. equals '1,000 meters or 1 kilometer. To conTopography for Field Artillery

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"vert an expression in words and figures into a representative fraction,- set

up a fraction with the given M. D. in the numerator and the corresponding

H. E. in the denominator, converted into the same units as the M. D. Divide

both members by the numerator to reduce the fraction to a numerator of

1. The result is the R. F. Taking the first example above. 1 mile=63,360'

. 3 1

inches, hence the R. F. IS 63 360 21 120 , ,

(3) By' A Graphical Scale.

91. This is simply a rule or a line drawn on the map itself with divisions

marked showing the horizontal equivalents corresponding to the map distances between the divisions of the scale. The length of any desired graphical scal~ maybe determined either from the R. F. or the words and figures

scale, as will be shown. The main divisions of the scale should be large,

for measuring the even portion of long distances, with an extra division to

the left of the 0 subdivided for measuring the odd portion of any distance

down to the last reading of the scale, fig. 20.

MILE:"

YL -0

I I I

ME:Tf:R" ~oo 0 500 1000 1500 ZOOO ZSOO I ""!,, .. I I I I I

+B

Fig. 20

92. In measuring between two points, the scale is placed so that the left

hand point is opposite the center of the subdivided portion to the left of the

O. and is then shifted, if necessary, to bring the nearest even mark on the

main scale to the right-hand point. To illustrate, using the meter scale in

fig. 20, place the scale fir'sf with the middle or 250 meter point of the sub-"

divided part opposite A, then shift to bring the even 1,000 meter point to B,

making the distance 1,150 meters.

93. A graphical scale may be made on a separate straight-edge or on the

map itself. Every map should have a graphical scale. The advantage of this

is that if the map expands or contracts according to the moisture in the air,

or if it is enlarged or reduced photographically, the scale goes with it. To

use the scale, take it off on the edge of a piece of paper or a ruler and apply

to the map, or mark the map distance on the edge of the. paper and place it

against the scale. The latter' is a convenient method in measuring crooked

distances, as roads.

'94. Where a map bears a graphical scale, but the R. F. is .~nknown. the

R. F. may be determined as follows: Measure the M. D. length of the graphical c::cale,or any convenient even portion of it. Set up a fraction with the

mea~ured M. D. in the numerator and the corresponding H. E. from the scale

. in the denominator, converted into .the same units as the. M. D. Divide both

members by the numerator to reduce to a numerator of 1. The result is the

R~ . .

For example, suppose that a photographic reduction of a map has a

graphical scale for 5,000 meters which was reduced with the map, with a

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!~~~nd' showing that the R.'F. of the original map was 20 ~OO. The

scale:~~'as~~e~ 12.5"cm.:long.'" 5,000 meters~500,000 em.' Then the new R.

. 12.5 1, ,,' ,'. '. .

~. IS 500,000 4Q,000' showing that'the map wa~\ r~du~ed o~e-half

In linear dimensions.. \ ":,l f,,~\~ ;' r~,::.I!:: ; .

95. When & map,1,>~w.rsIiQ ',~c~le,"9f!"~n~'kind:':'4t~ ~c~le may be determined

by. a comparision of, Ille~sprements'))~iween knowh' poin,ts on map and ground.

Wlt~ ;a~r."c?~v'enient scah';'measure the ',M;. ,D~ between '.,tw9 points on the

map. Measure the distance between' the corresponding points on thegroun~,

reducing it to the H. E. if it is not so actually (see par. 90). This gives'at

~~ce a "words and figures" scale.,wh~c4/an be) c~mv~rted into any u'nits deIred. ,The R. F. can now be founcJfr'om this as. described under, "words and

figures scales", in ,par. 90. 'the 'poihtssei~~ted: ~hotild, be such that the horiIZio~tal,d,istance betwee~' them c~n 1;>erpeas\I,red,' and sholfld, be as far apart

!l~,CP.TIvenientlycan be l'eached.' \'The process should be' repeated with other

Points hl different directions, if possible, in' order to v~r1:fy the scale. "!",

1 For example, supp'ose the dist81ice pet.we~np'ointsA and, B measur~s

,7 ~m., on the map" and ,the hor~zontal distance between the corresponding

Points on the ground' measures' 340 meters~Then,. the ,words and figures

Scale of the map is '17 ~m.=340"m~ters, orl mm.=20 'meters. 20 meters= , 1 ,1', ,

20,000 mm so the R F 'I'S' '.0' ' . • •, 20 000 • ~"#', (.' i . ,.. I

}. ,. ....,

•~.' .:I

", MAP SCALE' PROBLEMS • ! 'I

A. CLASSES OF PROBLEMS.

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~6. Map scaJe:problems fall into' twu:,c1:a.sses:' map to ground (M. D. to

.• E.), and ground to map (H~ E./toM. D.)'~' An example of the first class

IS in deterniinihgtheH: E. for a'l\:1.'D.;me'aSured on the map with an ordinary

Scale. An example of the second class is in detetniining'the M. D. to lay

off on a map or sketch for a~certain' H. E. measured on the ground, or in

de~ermining .the length "of a I graphical scale to' read a, certain' number of

UnIts of H. E. In either case the' calculation is a simple 'one of converting

;tiis!~nces. by means, 'Of, the R. F.' or the words (artd figures' scale. , .. 1..,:" ..... 'i' .. .. .1' ,.t'-. t.', '; 'I. I .,', .~

B. SIMPLE"RULES FOR MAP'SCAiE'CALCULATIONS.

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':7:, :',t'a) , n~ ihe IL Ii.' '(~~):~~:i~i;~~:b:~i~ m~p m~asure U~i~bY' th~

Ceno~Inator of the R. F. The product is the H. E. in the same umts. (2)

onvert ,this H.: E. into anydesire,<I: grounameasute, units. ,i "f

, Example: OnastandardAmerican map,;the;scaleof'which is 3 ,inches

. .1 J' r' . n, .. ~._:-~... ~, :- te., -.,

-1nllle, R. F. = 2il2O ' the' M~D.'!rom, .point', 4, to, point B measures 5.08

~entimet~rs. What is, the' H .. E.' from "A. to B In' yards 1. I I • • I

;:i ~.;::Solution: ;'(1) ~'5..,08X~I.120t~10?.!2~9.~6'cni~'.~.;~.(1,~;"(,' . 'I

dJ, :-': :: ',;,; :,(,(2>,; .~9'7,289:,6c~'.:T;'2.~4~12,~~ m...ii;,,;,";: ;' ." I

42,240-+36=1,173.3 yards, ans. .'.;' ~:"~J

or: 107,289.6 cm.=1072.896 meters.

1072.896Xl.0936=1,173.3 yards, ans.

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98. . (b) By the words and figures scale. (1) Find number of, ground

measure (H. E.) units represented by 1 map measure unit. (2) Multiply this

by the M. D•.

Example: Same as under par. 97.

Solution: (1) . 3 inches=l mile=1760 yards. '

.3 inches=3X2.54=7.62 em.

Therefore 1 cm.=1760+7.62=230.97 yards.

(2) 5.08 cm.=5.08X230.97=1173.3 yards. ans.

Or the H.. E. represented by 1 map measure unit may be found from

the R. F.:

1 em. on map=21,120 em. on ground.

21,120cm.=211.2 meters.

211.2Xl.0936=230.97 yards.

Therefore 1 em. M. D.=230.97 yards H. E..

This method of finding the H. E. value of 1 map measure 'unit is

simply to express the R. F. in the given map measure units, and convert the

denominator into the desired ground measure units.

Complete the solution as above.. , "!

The above example might be worked through in inches instead of centimeters by converting the M. D. into inches at the start:

(1) 5.08 cm.+2.54=2 inches. M. D.

3 inches=l mile=1760 yards.

Therefore 1 inch=1760+3=586.67 yards.

(2) 2 inches=2X586.67=1173.3 yards, ans.

Or, obtaining the value in H. E. of 1 map measure unit from the R.

F.:

1 inch on map=21;120 inches on ground.

. 21,120+36=586.67 yards.

Therefore 1 inch M. D.=586.67 yards H. E.

Complete the solution as above.

(2) Ground To Map.

99. Ground to map, or H. E. to M. D. problems, are simply the reverse

of. map to ground, or M. D. to H. E. problems.

100. (8) By the R. F. (1) Convert the given H. E. into map. measure

imits•. (2) Divide by the denominator of the R. F. The result is the desired

M.D. .

'.. .Example: The H. E. from point A to point B on the ground is 1.000

meters. How-many inches M. D. must be laid off.to represent this distance

on a standard American map, the scale of which is 6 inches= 1 mile, R. F. '

~O ~60? Or, as a graphical scale problem, what will be the length in

in~hes of a graphical scale. of 1,000 meters for this map?

Solution: (1) 1,000metersX39.37=39,370 inches.

(2) 39,370+10,560=3.7 inches, ans. .

101. . (b) By the words and fig,UJrescale. (1) Find number Qfground

measure (H. E.) units represented. by 1 map measure unit, the same as in

map to ground problems. (2) Dividethis into the H. E. in the same ground

measure units.

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Example: Same 'as under par. 100.-

Solution: (1) .6 inches=l .mile=1760 yards.

1 inch=1760+6=293.3 yards.

293.3 yardsX.9144=268.2 meters.

Or from the R. F.: 1 inch on map=10,560 inches on

ground. '!:

10,560 inches+39.37=268.2 meters.

Therefore 1 inch M. D.=268.2 meters H. E.

1 (2) 1,000+268.2=3.7 inches, ans.

02 From the above illustrations, it. is evident that any map scale problem

~an be solved either by means of the R. F. or the "words and figures" scale.

or most purposes the R. F. is simpler, as it uses the absolute ratio between

map and H. E., and can be applied directly to any units of measure. How-

~"er, in reading maps with an ordinary measuring scale, the words and

gures scale is useful to get the H. E. value of the measured M. Do's. The

measuring scale becomes a sort of graphical scale rhen the H. E. value of

one of its units has been determined, though this may not be in a convenient

e~en amount. Thus, with American maps, as in the above examples, an inch

a ways equals an odd number of yards H. E. The metric system •.with the

corresponding maps having representative fractions in even thousands, has

a great advantage over the English system in this respect. For example,

a map the R. F. of which is 20,~00' 1 em. M. D.=20,OOO'em. H. E.

-200 meters H. E. The centimeter scale then becomes practically a graphi-

~al scale, on which each centimeter represents 200 meters, each millimeter

o meters. and each half-millimeter 10 meters. With such maps any metric

scale may be used as a reading scale, and most problems can be solved mentally.

103. A convenient rule to remember when using the metric system on any

map is that 1 millimeter of M. D. equals a H. E. in meters 1/1,000 of the

denominator of the R. F. (because 1 millimeter equals 1/1,000 of a meter).

.11

Thus, on a 20,000 map, 1 millimeter=20 meters; on a 21,120' map,'"1

m'W 1 1 meter=21.12 meters; on. a 80000 map, 1 millimeter=80 meters; on

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40,000map, 1 millimeter=40 meters; etc.

C. SCALE CONVERSIONS.

104. The M. D. length of a graphical scale reading in certain units, as rards, being given, it is sometimes desirable to be able to determine the

.. ength for a similar scale reading in other units. as meters, directly from the

first scale, without calculating through the R. F. or the words and figures

~cale. This is the case when the map has a graphical scale but the R. F.

IS unknown, as when a map is enlarged or reduced photographically. Proceed as follows:

105. On the given graphical scale measure with any convenient measuring

scale, the M. D. length of a convenient number, say 1.000, of the ground

measure units in which the scale reads.. Multiply this M. D. by the ratio

between the length of one of the ground measure units of the desired scale

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, and the length of one of the ground measure tmitsof the I giv~n scale. The

result is the M.' D. length of the' deSired Iscale~ reading' the, same number

of new units, that is, 1,000, a,:;'was taken! \()f the old. The new scale may

then be laid off on ,the' map ()tmad~up asa 5eparate scale.

::.,,For example, a map. is found with a' '1,000 yard graphical scale which

measures 3.4 inches. How many inches should~be laid off for a 1,000 meter

.scale for the same map'! Any M.' D~ is. proportional to the H. E. which it

represents:: Hence' thel\L, D. for ,a 1,000 meter. scale is to the M. D. for a

1,000' yard scale as 1,000 meters i's to '1;000. yards, or as 1 meter is to 1 yard,

or :as 1.0936.is to 1.(par; 112).' •. Therefore the M.' D. for th~ 1,000 meter

Be'ale,will. be 'L0936X3.4 inches=3.7 inches.' (This is the same ,as was obtained. by the complete calculation' in the example under 'par. 101.

l06.~~ The: distinction' between the 'conversion ot map scales and .the conversion of. ordina.ry linear distances from one unit to another should be noted.

In '/':'onvertingmap scales,' the M;D.' representing a: given number of one

groundurtit is multiplied by the inverse ratio between the' units to find the

M. 'D. corresponding to the same number of the second ground unit.. In

ordinary cdnversions of linear distances the given distance in One unit is multiplied by the' direct ratio between the' units to find how many of the second

unit it;,wil1:take to cover the same distance. Thus,.distance in yards is to

distance-in meters as 1 yard is to 1 meter, or as .9144 is to I, and 1,000 yards

X.9H4=914.4. ,meters, using the direct ratio .•. In the first case the distance

corresponding to a fixed number of units is sought, and the inverse ratio 'of

yards'to meters or 1.0936 is used; in the 'second' case' the number of units

in' a fixed distance. In either case mistakes 'in uSIng the 'wrong ratio 'or

equivalent '.may be' avoided by. thinking whether" the results should be larger

or smaller .than the given figure, and gross' errors in calcu:Iation may' be

avoided by making a quick mental approximation of the result. 1: I

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, .:'",: :n. T~~Es',OF ~RAPHICAL SC~LE~'" "1' I

107:" Graphical scales 'may be' diviaed Into two classes', working scales for

mapmaking iand reading scales for map reading. Some scales may be used

iorboth. 'Stride scales or mounted tim,ingscales are workirtg scales. They

cannot be used conveniently as reading scales because they are not graduated

. in any standard unit of ground' measure. To read a distance with them it

would be necessary to convert every measurement into standard units by;the

proper equivalent. A mile scale is purely a reading scale. It cannot be

used conveniently as a working' scale I:>~cause''it' is impracticable to measure

distances ~m.the ground in miles~ A yard or meter. scale is both a reading'

and a w~rking scale, because it, reads i,n stand,ard .units' with which measQ.rem~n~s.'cfnbe made on the ground. .... :,::. '.. q', 'i"';;"

," ," (1) Construction Of Reading Scales .... ,'i ,' .):.;,:

108.'~ If 'no graphical scale isavaiIable" hatizontal equivalehts may be. 'calculatedfrom'map distances; and convers'ely,.from the R>F~ or words and

figures scale. However, if any considerable amount of measuring'istb ..be

done, oro ;the' map,. a graphiCal: scale should ,:ber,corlstructed;. dete'tmining .its

length/.from the'R. F. or words and figureS'iseale, as descriBed in 'pallll09,~and

subdividing' it' as desirE:!d~.Every topographer; should, 'b'e't able" to'imake any

K"md:6f;.a, graphical scale.' ~:., ',,! r,:; ':'.... !l;, '"l I. !~I";iI ';;~J',

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109. For example, to construct a scale to read yards on a 6-inch American

map, the R. F. of which is 1~,1560' Assuming that the ~cale' at hand for

measuring is in inches, first find the M. D. In inches which must be laid off

~<j) represent some convenient.even length, as 1,000 yards. Applying the rules l,n. par. '100: .

(1) 1,000 yards=36,000 inches.

(2) 36,000+10,560=3.4 inches M. D. for 1,000 yards. .

.: .. The next problem is to divide this distance into 10 equal parts, each

?f which will represent 100 yards. Each 100 yard division wiII. then be .34

Inch. If a scale graduated to 50ths of an inch is available, it may b,e used

to ~ake the desired subdivision, since .34= inch. This is th~:most con-

~enlent method, and is also' the most accurate if the scale is used carefully,.

ui- if such a scale is not availai:>le, the subdivisions may be made. a~ follows;

see fig. 21.

Draw line AB the length determined for 1,000 yards, 3.4 'inches. At

a convenient angle with AB, preferably not Over 45°, layoff AC, the neares:

length to AB which can be divided into 10 equal parts by some ev.en graduation of a scale, say 3 inches; The length of AC should be so chosen 'and the-

',anglt'. BAC so. adjusted to make BC .about perpendicular to AC if possible'

though this is not absolutely necessary. Join BC. Divide AC into 10 equal'

:Parts with the scale by marking every .3 inch. From each of thesemark~

draw a line' parall~l toBC intersecting AB, which is thus divided into 10'

e~ual parts by the intersections.. The parallel lines may be drawn with a

tI?'ht triangle and straight-edge, .as shown by the' dotted .lines. .Lay the

trIangle with one perpendicular edge along BC •. Then lay the straight-edge

against the other perpendicular edge, holding it firmly as the triangle il'

moved along in 'drawing the lines. If no right triangle is available, draw the

Parallel lines as follows. Layoff BD exactly equal and parallel to BC. (by

the ordinary compass method or' by measuring two equal distances. straight

across), and divide it into ten equal parts, the same as AC. Join the correSPonding points on A C and BD. The lines so drawn will be parallel.

110.. The greatest care must. be used in making the measurements and

draWing the lines in order to secure accurate. results. One of the divisions

should be marked off on the edge of a piece of paper and placed against the

~th(>rs in turn .. Anyjrregularities should then be adjusted .. The .dividing'

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line~ may then be erased and the scale completed. as shown, or the whole

scale may be taken off on a straight-edge or map. To transfer the scale

to a map, prick through the graduations with a needle. or fold the paper

along the scale. place it against the desired line on the map, and take off

the graduations with a sharp pencil. A scale of any desired length may be

made simply by shifting the divided line along and taking off the marks.

111. In making a graphical scale, it is, of course, immaterial what units

the measuring scale is graduated in. A topographer should be able to make

use of whatever kind of a scale he may happen to have. For example. to

make the above scale with a centimeter scale:

.1,000 yards=914.4 meters=91,440 em..

91,440+10,560=8.6 em.

Or the M. D. could have been worked out in inches, as was done above,

and converted to centimeters for measuring:

3.4 inchesX2.54=8.6 em.

The line would then be laid off with the centimeter scale and divided

as above directed. The completed scale would, of course. be exactly the same

length as the one made with the inch scale.

(2) Working Scales.

112. (a) Stride Scales. The most common form of working scale is the

stride scale. Every artilleryman who is likely to be engaged in reconnaissance or topographical work should have a stride scale made for the R. It'.

most frequently used. He should also know the length of his stride so that

if he is without a scale, he c",n improvise one if necessary. Using the

American map system, the most useful R. F. for a scale is 1/21,120 or 3

inches to the mile, which is the scale used for road sketches. Using the

French map system, the most useful R. F. for a scale is 1/20,000, or 5

centimeters to the kilometer, which is used for road sketches and artillery

firing charts.

113. To make a stride scale, proceed as follows:

First: Determine the length of the normal stride. To. do this, pace

over a measured course of from 400 to 800 yards or meters on level ground,

preferably compact turf or dirt road, not a hard road or pavement. The

course should make a circuit or double back on itself so as to offset the effect

of any wind which may be blowing. Conditions should be as nearly normal

as possible. It is not well to attempt to determine the' normal stride when

very tired or in a high wind or when the ground is sticky or slippery. Take

a natural stride. It is inadvisable to try to change the natural stride to step

even meters or yards. This can be done for short distances, but not for long

distances. The topographer should not keep step with or pay attention to

anyone else who may be going over the course. Cover the course two or

three times on different days, if possible, and take the average. Convert

the length of the course into whatever units of measure are to be used for

laying off the scale (inches or centimeters), and divide this by the average

number of strides taken to cover the course. The result is the length of one [

average stride. It is close enough to determine the stride to the nearest inch

or the nearest even centimeter, as this will be well within the probable errors \

of striding and measuring with the scale. ,

114. Having determined the normal stride on level grou!1d and made up ,

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the scale accordingly, allowances can. be made in using the scale for slope9.

for rough, sandy, or muddy ground, for wind, for the physical condition or

the person, etc. Ability to make these allowances comes with experience.

The table in Ch. VII gives the average allowances to be made for slopes.

However, anyone with much sketching to do should take advantage of every

opportunity to determine his own allowances,:under different conditions,

pacing measured courses both up and down hill. with and against the wind,

pacing the regular. course when' tired. etc., marking on his scale the allOwances.thus determined. Mter the length of the stride has once been

det~rmined. it should be tested occasionally to see whether it has changed,

especially on moving to a different climate, terrain, or altitude.

lI5. Second: Multiply the length of one normal stride by the total number

of strides desired for the scale, as 500 or 1000. This gives the length of the

Scaleon the ground in the units in which the stride was determined, (inches

or centimeters). Multiply this by the desired R. F. The result is the length

of the scale, which may be laid off and subdivided.~s directed in par. 109.

Mark on the scale the name of the maker, the length of stride, and the R. F.

lIG. For example, to make a stride scale of 1,000 strides with an R. F. of

1/20.000: .

Suppose a 500 meter course has been covered three times, in 255, 259,

and 262 strides, respectively, making an average of 258.7 or 259 strides. Assume that the scale is to be laid off with a centimeter rule. Then the length

of the stride will be determined in centimeters. Length of whole course is

500XI00=50,000 em. Length of one stride is 50,000+259=193 em. Take the

nearest even number, 194 em. The scale is to cover 1000 strides. 1000X

1?4::::194,000 em., length of 1,000 strides on the ground. 1/20.000X194,000=.

9.7 em.• length of scale. Layoff the scale and mark it: Lt. John Smith.

Stride 194 em. R. F. 1/20,000.

117•. It is immaterial what units of measure are used in determining the

length of the scale. whether yards or meters, inches or centimeters, because

the absolute length of the stride is the same, no matter what units it is

measured in, and the length of the .scale is determined from the length of

the stride by the R. F. In the above problem, if an inch scale is to be used

~Or)aying off the stride scale. convert the length of the course, 500 meters,

Into inches instead of centimeters and find the length of 1 stride in inches'>---

The length of the scale will then be determined in inches. Or work the

~roblem through in' centimeters and convert the final result, 9.7. em., into

Inches. A course measured in yards might be used instead of a meter course.

In any case the .absolute length of the stride and of the stride scale would

be the same. It should be impressed on men learning the subject that the

scale when completed is a working scale of strides only, having no relation

to the system of measure by which it was determined. It cannot be used

as a general reading scale except by converting the strides into some standard units of measure, nor can it be used as a working scale by any. one

haVing a different length of stride.

lIS. (b) Mounted Working Scales. For mounted sketching, a 'timing

scale.is most convenient. A stride scale can be made for a horse the same

as for a person, a.nd is somewhat more accurate than a timing scale. How",:

Topography for Field Artillery
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ev~r;a timing scale is easier. to use, and gives as close results as are' usuallr

required for' mounted sketching:, , .., •,i

119.' To make a mounted timing seaJeproceed as follows: ",'

First: Find the average distance covered in 1 minute by the horse' at

the desired gait under normal conditions. To obtain good results, ,the horse

must have a uniform gait. ,.An ordinary trot is the best gait for general

work. Take' the horse over,' a' measured, course, say 2,000 meters or 2,000

yards,' noting the time carefully.' Cover' the' course two or three times o~

different days if possible, and take the, average time. Divide this into. the

length' of the 'course, giving the average distance per minute~ ,~

, The course should be the' same, kind of ground as' will~ ordinarily be

covered in actual work. usually a dirt road. The horse should be, warmed up

but not tired, and other conditions should be as nearly normal as possible.

Tests under other conditions should be made later and allowances determined.

the c;:ameas described for stride scales (par. '114). It is especially important

to 'determine the difference between traveling light and with packed saddle.

ThE"scale should be 'made on the time taken with the load usually carried.

and allowances 'made when, carrying other loads. Separate scales maybe'

made for the different gaits,' or the ratios between the gaits may be determined, and the trotting scale used for' all gaits, multiplying by the proper

ratio.. For example, the walk is usually about half as fast as the trot, so

when walking" take half as much distance on the' scale as when trotting •

• 120. Second: Convert the average distance per minute into the units of

measure (inches or. centhneters) which are to be used. to layoff the scale.

Multiply this by the desired R. F. The result is the length of the scale fOJ"

1 minute. Lay' off enough of these to make a scale of 'convenient length.

say 5 or 10 minutes, with an, extra division at the left subdivided to halves,

quarters, and twelfths (5 second intervals). Mark on the scale the name or

number of the horse. the name of the rider. the load carried, the gait, 'thE'

rate of speed per minute, and the R. F. ,.

For example, to make a trotting scale, carrying packed saddle, R•. F.

1/20,000. Say the' horse covers 2,000 meters trotting in an average time,

taken from three trials, of 10 min. 15 sec., 01"10.25 min. The average dis:..

tancf> per minute is 2,000+10.25=195 meters. Suppose the scale is to b~

measured in centimeters. 195 1\:1.=19,500 em. 1/20,000X19.500::;::.975 em..

length of scale for 1 minute. Take 10 minutes, or 9.75' em. for', the full

length of the scale. Lay this off, divide it, into 10 equal parts, and. layoff

an extra division at the left subdivided into twelfths as above directed. Mark

the scale: Horse, Bob, No. 278. Lt. John Smith, rider. : Packed saddle. Trot.

195 M. per min. R. F. 1~20,OOO.

121.' Using standard American map scales,' an ordinary inch scale divided

into eighths of an inch can be used as a trotting time scale for the average

horse .. The average horse trots a mile in 8 minutes. Then if' the' scale: of

the map is 1 inch to the mile, 1/8 inch will represent 1 minute. For other

map scales take as many eighths of an inch per minute as there are inches ['

per mile in the scale. Thus, for 'a sketch on a scale of 3 inches to the mile.

take 3/8 inch per minute. For a walking scale, take sixteenths of an 'inch,

.as the average horse walks a mile in 16 minutes.:. ~. .

122. (c) Interchange of Graphical Scales. Any graphical scale, reading

,)'opography for Field Artillery

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or working, mad~ with. a given R. F.,can,be' used with any. other R:~F.

by correcting: the readings by. the ratio. between the original R. F.- of the

scale' and th~ desired R.F. ',Thisean be' done very conveniently where the

R.,'F./s. run. in i ~ven. proportions, as in the American 'and French. standard

systems. '.

For example, to use a 1/20,000 stride scale for a 1/2,000 sketch, as

will frequently be required: The ratio of the original R. F. to the desired

R. F. is 1:10. Hence consider all the figures on the scale as if multiplied

by 1/10. Thus, if a distance is covered in 80 strides, it will take 800 stride

diVisions on the scale to represent the 80 strides on the sketch. .

The procedure is similar with reading scales. For example, to use

1 I , .

a 10560 reading scale on a 1/21,120 map. The ratio. of the original

R. F. ~f the scale to the R. F. of the map is 2:1. Hence consider all ;figures

On the scale as if doubled. Thus, if the scale shows 100 yards betwe~n two

Points, the distance on the map will be 200 yards. ~.

123. (d) Working Scale Graphs. Where a number of men are t6 make

Working scales of the same kind, the labor of calculating the length of each

scale .separately can be saved by preparing a graph. This can be done for

any kind of scale, mounted or dismounted. .

124. For exa~ple, to make a graph for a set of stride scales of 1,000 strides,

with an R. F. of 1/20,000, plate I.

First: Determine the length of the longest scale and the: shortest

scale which will'probably be required.

. Say the longest stride is 200 em. Then the length; of the longes;;

scale' will be: 200XI000Xl/20,000=10 em. . ;,

I Say the shortest stride is 140 em. Then the length of the shortest

sca1e' will be: 140XIOOOX1/20,OOO=7 em. , ;

125. Second: Calculate the number of different scales, according .to the

.units; of measure used, between the longest and the shortest. If the strides

'are measured in centimeters, take the scales every other centimeter; that is,

on the even numbers. If measured in inches, take the scales every inch.

Th13,w~ll be close enough, well within the probable errors of measurement~

etc. In this example, the difference between the longest and the shortest

scales is 200-140=60cm., making 30 double-centimeter or even numbered

diVisions, see plate I.

126. Third: Layoff AB, 10 cm. long, representing the longest scale. Draw

AC, perpendicular to AB, 30 units long, using any convenient graduation of the

~ler. The length of these units is imma~erial as long as the line is divided

Into the required number of equal parts;' being the number of scales between

the longest and the shortest, as .above determined. ,It is ::well"however, ,to

lllake these divisions as long as the paper used will.allow,So as, not to<:r~wd

the lines. (In plate I the divisions were made2.5~lnm'.,.using.~every fifth

lllark on the. half-millimeter scale). Mark the divisions carefully (>nAC., :::,.

l27. ',' Fourth: Draw. CD, 7 cm. long" representing the shortest sca.le, exactly

Parallel toAR. . Thisis done by laying offMNequal to AC, perpendicular to

An, making AM a little less than CD, and then drawing CD so' that it passes

throughN. Divide MN into equal parts, the. same as AC • .'~... .... :,::,,'.:j'

Topography for. Field' .Artillel'j'

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representing 10 strides. Draw lines across from En to FD, joining EF and

BD, and the corresponding dividing points between.

129. Sixth: Through the corresponding division points which were marked

on AC and MN, draw lines parallel to En and FD and running from line EF

to line BD. These lines then represent the lengths of the different scale8

between En and "FD. Thus FD being the scale for a 140 em. stride, the next

line above is the scale for a 142 em. stride, and so on. Number these scale

lines at the left with the corresponding lengths of stride in centimeters.

TOpOgraphy for Field Artillery
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130. The portion of each scale line intercepted between AC and BD repres;nts 1000 strides, divided into 10 equal parts of 100 strides each. The portIon of each scale line intercepted between A C and EF represents 100 strides

d!vided into 10 equal parts of 10 strides each. These extra subdivided portIons at the left are .for making close measurements, as described in par. 91.

To make a stride scale from the graph. apply the edge of the paper or rule

to the line on the graph corresponding to the previously determined length

of stride, and take off the marks with a sharppencil~ ,If desired the entire

~calemay be graduated down to 10 strides by shifting each 100 stride section

tn turn opposite the subdivided portion of the graph at the left, taking off the

marks. However, it is. very difficult to get all the divisions uniform over a

long scale, especially for men unaccustomed to drawing. It is better to

Illake the scale in the form. shown, subdividing one section very carefully,

and then using the scale in measuring as described in par. 92.

Topo"raphr for Field Artillery

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. CHAPTER IY~

, ELEVATIONS AND GROUND 'FORMS.

'HOW SHOWN.

'131. '. A map is' a picture of a portion of the' earth's surface, usually'drawn

o'na flat piece of paper, and gives a view of the earth similar to thatpre-1

,sented to an observer in the car 'of a balloon. 'As a balloon rises an observer

gradually loses sight of some of the details. He will, however; seethe surface of the earth in relief, and will be able to distinguish all the undulations

of the ground. As he rises higher the country will look. flat and he will

find difficulty in distinguishing valleys from hills. In such a circumstance,

the view from a balloon exactly resembles the picture which the map maker

endf'avors to reproduce.

It is necessary, however that elevations and ground forms be shown

on the map. This is accomplished by several methods. Those most generally used are the Bench Mark, Hachures and Contours.

A. BENCH l\IARKS, HACHURES AND CONTOURS.

(l) Definitions.

132. (a) A Bench Mark is a permanent object or marker, the. exact location and elevation of which, with respect to sea level, are known. Usually,

only the elevation is marked upon it, thus, 1167.7 would, on an American

map, mean that the bench mark in question is 1167.7 feet above sea level.

133. (b) Hachures. The appreciation of the form of an object results

from the difference of light and shadow on its various sides, so an illusion

of solidity may be procured by a suitable arrangement of shading. The

means of doing this in topography is

called Hachuring. In the absence of

Contours, which are discussed in the

. succeeding paragraph, relief or elevations on the earth's surface may be indicated by hachures, which are short

parallel, or slightly divergent lines, running in the direction of the steepest

slope. Hachures should be used only to

indicate areas which present slopes steep

enough to offer cover or become obstacles. The use of hachures is illustrated

in fig. 22.

134. (c) Contours. A Contour line

is an imaginary line Jommg points Fig. 22.

of equal elevation on a given ground form. Contour lines on the map are

TOpOgraphy for Field ArtiIlery

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--.;

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-4~-rlines joining. pQints of equal elevation above' a known datu~ plane, usually

~a level;isee figi 23. ... , r : ~, .' ;~I" .111

I. • .:, MovNTAtf\Jq,ndCONTOVR.5:: ',,:: .._~' t''. . '1, r .1, 'i . .. . . . t

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:2-;,y:, . Prisznt .5~Q uwa.,- "

1 •••• :. -Fig. 23.' . ,"

. Imagine a: submerged mountain with the ocean' receding, thus bringIng the mountain peak up out of the water. The water around the mountain

leaves a series of water marks as it recedes. These" water marks may be

l~kened to the contour lines which are drawn oil the map representing eleva-

. bons above sea' level. . A contour line,. then is a line, each point of which

has the same elevation.' Contour lines never cross except in the case uf

over-hanging. cliffs, see fig.. 24•. ': . : : ... ::., ..

, PROfILE: MAP..

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....

c-- ", .

b

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Fig; 24.

Valley contours go in pairs; .that is, there is always one contour "f

the same elevation on each side of the valley.. They form a V which opens

~ut i.n the' ?irection of w~ter flow, the point of the Y being upstream. ConFig. 25.

t?ur lines take the form' of a U for spurs with the curve of the. U at the

rIdge crossing, see fig. 25..

135. (d) A contour has no end. If it enters a map it must leave it, the

ttopognp~y ,for. Field 4rt;ill~ry

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two ends joining soinewhere off. the sheet. A contour is' a- line without a

break, a closed circuit. A contour which closes within the limits of the map

indicates either a summit or a depression. Contours always are at right

angles to the lines of the steepest slope, see fig. 23. The spacing ot the contours indicates the steepness of the slope; the closer the spacing the steeper

being the slope.

(2) Vertical Interval.

136. Vertical Interval is the difference in elevation between adjacent contours. In American maps and the new French maps the Vertical Interval

(abbreviated V.I.) changes with the scale of the map in a regular progression. A simple rule for American maps is that 60 divided by the scale of the

map, (inches to th~ mile) will give the V.I. in feet.

Thus: Scale Vertical Interval

1" equals 1 mile """,', ,..... 60 feet.

3" " 1 mile 20 "

6" 1 mile 10

. 12" " 1 mile 5 "

• On the new French maps the rule is to divide.the denominator of the

Representative Fraction by 4,000 to find the'V. I. in meters, thus:

Rep. Fraction Vertical Interval

1/40,000 •....................... 10 meters

1/20,000 ... :.................... 5 meters

1/10,000 ..............•......... 2~meters

However, many French maps show both a 5 and 2~ meter V.I., due to

the fact that the ground represented in one portion of the map is hilly or

mountainous and in another portion of the same map, quite flat. The two

V. I.s are therefore used to k~ep from crowding the contours on the hilly

portions.

(3) Critical Points.

137. Critical Points. No map can show every change of form of the gr.ound.

It is necessary only to know the critical points of the master lines of the

ground. Such points are the heads of valleys, the changes.in direction. and

the changes in slope of the drainage lines; the tops, the changes in direction,

and the changes in slope of the ridge lines; and the points at which a stream

enters and leaves the area being mapped. These critical points must be

located and their elevations determined.

B. LOGICAL CONTOURING.

138. Logical Contouring. When the critical points and the drainage net

have been established as above described, the sketcher can interpolate between these master critical points and draw in all contours by taking inu.

account the logical relation of ground forms, see figs. '26, 27, 28, 29.

.

'Topography for Field Arti11e1'7

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Traverse made and Critical Points plotted.

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Interpolation between Critieal Poiz:ats.

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CHAPTER V.

INSTRUMENTS USED IN TOPOGRAPHIC OPERATIONS:

DESCRIPTION AND USE.

139. A. AIMING CIRCLE-See Hand Book.

140. B. BATTERY COMMANDER TELESCOPES-See Hand Book.

141. C. TRANSIT-See.'Engineer Manual.

142. D. 'PRISMATIC COMPASS-See Hand Book.

143. E:' PEIGNE' COMPAss. ~.

, .. . . T.lie Piegne" compass 'is used for topographicai reconnaissance. It al-

~o\Vs,the' topographer' to measure bearings and slopes. The distances are

llleasured "by 'stri"de or steel tape.

. The Peigne' compass comprises a box in the bottom of which 'a grad •

.u~t~d dial' is set. 'The m'agnetic needle swings on a pivot standing in the

C~nteroi the box.' It 'may be clamped by means of a lever and a milled

k,n')b. The line of sight is defined by a slit sight and two wires extended in

the slot of the lid. Inside of the lid a mirror is inlaid.

( :. , One' side of the box is beveled and engraved with a millimeter scale.

plummet rotating on the pivot of the needle gives the slopes in mils.

(1) To Read Bearings.

144. The lid is kept open by means of the slit sight." The sketcher holds

the compass in his left hand, using his right index finger to release or clamp

the needle as needed. The point is sighted 'and ~heJmage of b~th needle and

graduated dial are observed in the mirror. By means of the lever,

the sketcher may check the vibrations of the needle. ,He then

screws the milled knob with his right thumb. The bearing may then be read.

It is'lbetter to repeat the operations two or three times and take the mean ""-

of the readings. , ,

(2) To Plot This Direction \Vith The Compass.

145. On a sheet of drawing pape~-'attached to a board draw a few parallel

lines in the direction of magnetic north (these lines makIng an angle with

~rue north equal to the declination of the compass) near the point representIng the place at which the hearmg was read.: Lay the box, entirely opened.

on the 'table and pivot the bevel about the station' point until the axis of the

neerHe is parallel to these lines. Draw a ray along the bevel. This ray

represents the direction as obtained with the compass.

(3) To Plot The Direction \Vith A Protractor.

146. Use a protractor the graduations of \vhich are the same as those on

the dial. Layoff a line through the station point in the direction of magnetic

north. Rotate the protractor about the station point until its zero line coin- •

cideq with the line on the paper 'representing magnetic north. Mark off a

Point on the paper that will coincide with the angle as read from the compass.

Connect this point and station point. This gives the line of known direction.

Topogl'aphy for Field Artillery

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(4) 'fo Measure A Slope.

147. Hold the box vertically, and sight the point in question. Keep the

box vertical and note the image of the graduation which is seen in the mirror in conjunction with the plummet. This gives the value of the slope.

F. THE PLANE TABLE.

. PLANE: TABLE:'

Fig. 80.

148.

o

The plane table consists of a drawing board fastened to a tripod of

. three adjustable legs, by me.aIlS

of a large hand screw. The

drawing board mayor may not

o contain a compass inlaid near

one edge of the board. The

plane table revolves on the

head of the tripod and can be

held in a fixed position by

tightening the head screw. The

plane table should be 1eve I

when in use, fig. 80.

(1) To Level The Plane Table.

149. This is accomplished bS

placing two of the legs firmly

on the ground and by adjusting the third .by bringing the

surface of the plane table on

a plane of sight in accord with

a distant horizon. When one

edge is parallel with the horizon, level the edges perpendicular to the first edge, in a

similar manner, by using one

of the other legs as the adjusting leg. Repeat to make sure

the other side has not been

thrown out by the last adjustment. The board may be leveled more. accurately in the same

manner by means of a leveling alidade or spirit level.

The declinatormay or

may not be attached to the

board, fig. 81.

The plane table is used

in connection with topographical work for running traverses,

measuring angles, and other

like operations.

Topography for Field Artillery

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. PLAN.

Fig. 81.

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G. ALIDADES.

(1) Triangular Alidade.

150. The triangular ~lidade is' a box wood rule wllich has a triangular crosssection. All three edges of the alidade must be parallel to one another. In

Using this alidade one lower edge is placed along the line drawn, or to be

drawn, while the sighting is done along the top edge. •

(2) The Sighting Alidade.

151. The sighting alidade orF. A. plotting scale is a flat ruler about 25

Centimeters long with two beveled edges. One edge is calibrated in millitneters and the other graduated to a '1/20,000 scale. On the face are placed

two folding up-rights, one at each end, so that the line of sight passing through

the 8lits in each one is parallel to the edges of the scale. This alidade can

.be used only for laying off directions and plotting poin~s. In laying off directions either edge is placed along the line drawn, or to be drawn, and the

sighting is done by lining in the object with the line of sight passing through

the up-rights. The slit with the crosshair should be placed farther from

the eye.

(3) The Leveling Alidade.

, 152. The leveling alidade. sometimes called a French aIidade, may be used

in laying off directions, plotting points, and measuring gradients, fig. 32. It

----_. ---- - -------_. -----' ----

All DADE:.

Fig. 32.

consists of a ruler 20 to 25 centimeters in length on which al'e supported a

level and 2 hinged standards. It also contains two eccentrics for leveling the

alidade. The rear standard contains three eye holes. The front standard

forms an open frame including a horse hair sight. One side of the frame

bears a graduation numbered upwards, the other side bears a graduation

numbered downwards. Each graduation consists of 40 divisions, each division being equal to 1/100 part of the distance between the two standards,

or 10 mils.

Topography for Field Artillery
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By construction, when the standards are fully raised and the level

shows the bubble between its marks: .

1. The lines of sight are horizontal. These lines are defined by:

The bottom eye hole and the bottom zero division. •

The intermediate eyehole and the division 20 of the 2 graduations.

The top eye hole and the top zero division.

2. • The horse hair stretched across the front standard is vertic~l~

The edges of the alidade bear a graduation in millimeters and a scale

of cotangents.

(a) To measure a gradient: To measure the angle of elevation or

depression to a point, the alidade must be absolutely level. This is accomplished by bringing the bubble between the respective marks by means of

the eccentrics which raise or lower one end of the alidade, as desired. In

measuring elevations. to points higher than the point at which the plane table

is Sf't up, use the bottom eye hole and the risin'g gradient, and for point,~'

lower, use the top eye-hole and descending graduation.

(b) In laying' off directions or finding direction use the alidade the

samp as the sighting alidade.

(4) Telescopic Alidade.

153. This alidade consists of a flat metallic straight edge on \vhich is mounted a telescope (similar to an ordinary surveyors transit) with a level. It

mayor may not contain a declinator. In the latter case one generally is

carried in the same box. This telescopic alidade may be used for determin- .

ing directions, slopes and stadia readings. For measuring slopes and. determining directions it is used similarly to the other alidades. To use in

measuring slopes the telescope must first be placed in a level position.

154. To measure distances with the telescopic alidade, a stadia rod is used.

On the stadia rod are graduations subtending different known distances as read by the telescope. By means of cross hairs in the telescope,

called stadia hairs, a certain length subtended on the rod may be read.

fhe length read on the rod, required to produce an image of fixed size

in the telescope, is directly proportional to the distance of the rod from the

point over which the telescope is set, see figure 33.

The length of the rod as read, therefore, may, by means of tables,

be reduced at once to distance on the ground. The distance measured is

along the gradient and this in turn may be reduced to the horizontal, if

desired, by means of tables, diagrams or stadia slide rule.

Elevation is read by taking a level sight on the rod with the telescope

and measuring on the' rod the vertical distance from the ground to the

point where the line of sight cuts the red. The elevation 'of the telescope

-above the ground must be taken into consideration in determining the difference in elevati.on between stations.

. The' degree of precision of the stadia method may be enhanced by

using it for traverses under 800 feet. using a telescope the magnifying power

of which is 15 to 25, with cross hairs that are as fine as possible, and by

taking readings during the cooler portions of the day, since excessive temperature causes refraction.

Topography for Field Artillery

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155.' (a) To'me"asure distance with the stadia. The distance to an'y point

is ,read by observing either the angle subtended by a known length, or how

tnany divisions of the stadia road are inte'rcepted by a known, angle.

1st Process, The stadia rod, Be, is 'provided with' two sighting

tnarks the distance of which, h, is constant and generally equal to 2 meters.

If the stadia rod is standing perpendicular to the line of sight, see fig. 33,

h

D = Tan a.'

. C

. h

AI~I

Fig. 33.

The micrometer of the instrument used may consist of a scale giving

distance, D, instead of angles a.. When the micrometer is' graduated in mils,

..' 2037

and the stadIa rod IS 2 meters long, D meters a. mils'

The numerator of this equation takes into account the relations of

.' 6400

artIllery mil to the true mil; that is, 2X 6283 (see par. 24 and 31).

2nd Process. The stadia rod is graduated in centimeters. The angular distance between the upper and the lower horizontal wires of the telescope is known and is generally' equal to 1/100~10 mils or 1/200=5 mils.

In the first case (1/100) the number of divisions intercepted on the

stadia rod gives the distance in meters. In the other case (1/200) the reading on the stadia rod must be doubled. .

156. (b)' Horizontal distance. Distances on the map are' the representation ()f horizontal distances. Therefol'e the readings taken on sloping ground

, are to be corrected before they are plotted. . "--.

Fig. 34.

157. If the stadia rod stands perpendicularly to the line of sight, readings

on it give actual distance on' the slope, fig. 3'4.

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The slope measured is angle CAB=i. Then the horizontal distance

AB A C X Cos i Th. . b. D D D . 2 i ) DXcos i IS equatIOn. may e WrItten (2 sm 2".

It also is applicable to the distances measured along the slope with chain or

read on a stadia rod vertically.

158. When the stadia rod is not provided with a peep-hole, the rod-man

cannot easily stand it perpendicularly to the line of sight. Then he stands

it vertically and it is read with the line of sight inclined up or down, fig. 35.

The intercept is CG instead of CF,=CG cos i. If D" is the distance read

then AC=D=D" cos i and D'=AB=AC cos i D" Cos2i. .

The equation may be written D'=D" cos2 i = D" (I-sin2 i)

D"-D" sin2 i

Tables. in appendices give the correction D" sin2 i to be subtracted from

distance read on stadia rod standing vertical. Q

H. THE ABNEY LEVEL.

159. This level or clinometer is an instrument adapted for measuring gradFig. 36.

ients, .fig. 36. It has the horizontal plane indicated by a spirit level. The

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abo\'e level consists of a tube, with a graduated vertical arc fastened to it and

a level tube with attached index arm revolving about a horizontal axis through

the center of the vertical arm. The base of the sight tube is a plane

par~l1el to the line, of sight. Under the center of the level tube is an

Opening in the sight tube inside of which is a,~:mirror occupying one half

the width of 'the sight tube and facing the eye end at an angle of 45° with

the line of sight. A horizontal wire extends across the middle of the sight

tub~ in front of the mirror. When the bubble is brought to the center,

its reflected image seen from the eye-end appears to be bisected by the wire.

The central position of the bubble indicates that the level (ube is

horizontal, and the reading of the index arm upon the arc is the angle

between the axis of the level tube and the line of sight. This reading

should be 0° when these lines are parallel. The vertical arc is graduated

eaclt way from 0° at its middle point. The index arm has a double vernier

whose smallest reading is 10' cf an arc. GradientR> of more than 45° are

difficult to measure on account of the foreshortening of the level tube as

reflerted in the mirror.

When the vernier is set at 0°. the instrument may be used as a hand

level to locate points at the same elevation as the eye. The graduations on

the inner edge of the vertical limb correspond to the ordinary fractional

method of indicating s'lopes as 1 on 2, 1 on 10, etc. This scale should be

read on the forward edge of the index arm, or in some forms on special

index marks on a shorter part of the arm.

160. To use the Abney level, steady it by resting it against some object

as a tree or fence post, sight through the eye-piece bringing the cross hair

upon the object to be measured, level the bubble with the left hand (its reflection being seen in the small mirror). When level read the angle of

slope.

161. The level ~ube is made parallel to the. sight tube by the adjusting

scrp.ws. To test and correct the 8.djustment, place the instrument on a smooth

sUrface, the more nearly horizontal the better, and mark carefully the position,of one side and one end of the sight tube. Center the bubble by moving

the index arm, and read. the vernier. Reverse the instrument, bringing th~

other side and end of the sight tube to the marks. Center the bubble by

moving the index arm and read again. Note and record for each reading

its direction from 0°, whether toward or away from the eye end of the

sight tube. Note and record also the location of the eye end in each position with respect to some fixed object, so that the instrument can be replaced

in the first positon or second position at will. .

If tbe first and second readings are the same, the adjustment is correct. If they differ, take the mean of the two and set the vernier at that

reading on the side corresponding to the first reading. Place the instrument

in the first position and bring the bubble to the center by means of the

graduating screws. For a check, set the same readings on the side corresPonding to the second reading and place the instrument in the second position.

The bubble should come to the middle.

TOpOgraphy for Field Artillery
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I. THE GRAVITY CLINOMETER.

162. The gravity clinometer consists of a circular case in which is a graduated circle controlled by a pendulum, fig. 37. The line of sight is through

Fig. 37.

peep and a glass covered opening. The ~ero line is engraved on the glass.

A m:rror near the center reflects the scale back to the peep. Looking through'

the instrument the object is seen on the zero line, and at one end of the latter

a graduation of the scale is visible. The graduations are from zero at the

horiYontal, each way to 45°, the graduations and numbers for elevation being

'in red and those for depression in black. .

A sliding bar on the outside of the case unlocks the spring controlled

stop. which, when pressed, frees the pendulum and graduated circle, and

when released stops them again.

To use, move the locking bar to free the stop; hold the instrument in

the !eft hand with the forefinger on the stop; depress stop; bring line of

sight on object and read.

J. LEVELS.'

163. The engineer's level is an instrument that does not give the angles

of slope, but is' used in conn~ction with a graduated rod and by successive

steps (with back and fore sighting) the actual elevation or depression of an

object is measured. The proce<;s is slow but accurate and seldom used in

military sketching. Its use for locating drainage lines in trenche's, emplacements, etc., is common.

In the use of the level gl'eat care must be exercised to see that it is

properly leveled at each set-up.

A type of hand level designed for slope readings is now' generally

preferred to the ~linometer. This level, has horizontal lines on the object

glass, either' reading degrees or percent. 'With the percent graduations it is

poss ble to obtain differences of tlevation without the necessity of using tables

of degrees for differences of elevation, see Abney level, par. 159.

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K. SLOPE BOARD.

Fig. 38.

held in a vertical plane, will make the same angle with the plumb line that

the klghting edge makes with the horizontal; or in other words, will indicate "-----

the colope;fig. 38.

. , The scale may be constructed by drawing an arc with the center at the

Intersection of the perpendicular and the sighting- €dge. From the perpendicular layoff each way on the arc, chords equal in length to 1/57.3

of the radius. It is convenient to take a radius of 5.73 inches or 5i inches

Scant, when the chords will be 1/10 of an inch. or to use a radius of 7 3/16

inches. when the chords will be 1/8 of an inch.

Short radial lines drawn at the ends of the chords form a graduation

hi de-grees." The scale may be drawn on the lower edge of the board by prolonifing the radial lines. The plumb line is' suspended so that when the

sighting edge is horizontal it coincides with the zero line on, the board.

165. In use, the boardis held RO that the plumb line swings freely but very

close to the board. The sighting edge is directed to the object and when

the line is steady the board, is quickly tilted so that the line draws across

the edge. The board is then turned in a horizontal. position or nearly so,

and the reading taken; or, when the line is steady, it' may be press~d against

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the board with the finger and held in place until the reading is taken. It

is better to take two or three readings and use the mean.

L. SITO-GONIOMETER.

166. The 'sito-goniometer, intended primarily for the light artillery, is a

pocket instrument for rapid approximate 'measurements during a reconnaissane-e, or at any time when more accurate instruments are not available.

The instrument is contained in an aluminum case. On one face there

is a table of parallaxes. A handle is provided, which also serves as a point

of attachment for a chord.

It is used for:

(a) Measuring the sight and determining the minimum range which

will clear the mask.

(b) Measuring angles in mils and transferring them into terms of

platf'au and tambour.

(1.) To Measure The Site And Find The Minimum Range.

161. (a) Site. Hold the instrument, edge to the front, at the height of

the eye, in such a manner as to see the site bubble, and also external ob.

jects on the right side. Incline the instrument to the front or rear so as

to center the bubble. Read the graduation seen on the height of the objective,

fig. 39.

Site Minimum Range

168. (b) Minimum Uange" At the gun position, again hold the instrument

as if to measure a site. Select a point A on the mask of the same site as

the objective. l\love the instrument so this point is seen to the left. Bring

the zero of the scale to the height of the point selected, and then read the

mimmum range at the summit of the mask. This can only be used for

distances from the mask not greater than 306 meters and with the normal

charge, (French 75), fig. 39.

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(2.) To Measure Angles And Deflections.

169. Hold the instrument horizontally, edge to the front, close to the right

eYe so as to see the deflection scales and at' the same time see distant ohject!l' over or under the instrument.

Bring one or the other of the indices at. PI. 0 on the objective, the

lower one if the aiming point is on the right of the objective. and the upper

One if the aiming point is on the left of the objective. The deflection is

then read at the aiming point in terms of plate and drum, fig. 40.

If an angle is to be measured: look over the upper edge and use the encirC'lf>dfigures with the 0 on the left.

M. PROTRACTORS.

170 A protractor is an angular scale of equal' parts used for plotting and

reading angles. Protractors may be semi-circular, rectangular, or circular

in !';hape; made either of metal or transparent organic substances; graduated in mils. degrees, or grades; in a clockwise or counter clockwise manner

or both, while the size will depend upon the purpose for which the protractor

is to be used. For methods of construction see Chapter 11.

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CHAPTER VI.

ORIENTATION.

DEFINITIONS.

171. A plane table or map is said to be oriented. when all the directions

on the map corresp.ond to the respective directions on the ground; i. e.• when

true north on the map points to true north, etc. It is evident, therefore, that

a plane table is oriented when all the lines on the board are parallel to the

respective lines on the ground and points on each line are in the same

relative positions, as on the ground.

A plane table is said to be declinated when the declination of the com- .

pass needle is known and recorded: so that when the compass needle is

brought opposite its index, the table becomes oriented. I'

An instrument is said to be oriented when the zero is on true north or

the Y-north depending on which is used as an origin.

An instrument is said to be declinated when the declination of. the

compass needle is known and recorded, so that when the declination constant

is set off and the needle is. brought opposite its index, the instrument will

be oriented.

METHODS OF ORIENTATION.

172. There are two general methods of orientation; viz. •

First. By means of a declinated instrument, or plane' table. and,

'Second. By means of a line of known direction, which mayor may

not be established in advance.

A. BY A DECLINATED TABLE.

(1.) \Vith Declinator Unattached.

173. Draw a line on the board making an angle with true north in the'

proner direction equal to the declination ,of the compass. Place the declinator

on this line and rotate the board so that the compass needle coincides or is

parallel to this line. Lock the board and verify by repeating the same operation. .

. :(2.) .With Declinator Attached.' ,

174 Place the map or griddedsheet upon the plane table so that the true

north line makes an angle with the zero line of the declinator which is equal

to the compass declination. Rotate the board until the compass needle is

opposite its index. Lock the board. Verify by repeating.

Note: For a discussion of the process of orienting with adeclinated

.instrument, see Chapter XXV.

B. BY A KNOWN LINE.

(1.) When The Plane Table Is On A Station Over One Of The Known

Points Of a Given Line.

175. Let the capital letters designate the points on the ground that are

represented respectively by the same small letters on the map or plane table.

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Assume A to be the point on the ground at which the plane table is to

be set up and B a point of known location which can be seen from A, fig. 4i.

•.. s" Set up the boald over A and bring t;> moM •.

Stac..!:l B a level position. Place the alidade on . __/--& I the line ab with the point a nearer ar.d

b farther away.

If the point B is so far from A

that. the two points cannot be plotted

on the same sheet, it will be necessary, only to have a line from a in the

Fig. 41. . direction of b.

Rotate the board until the point B falls directly in the line of sight

When sighting over the alidade. Lock the board and verify by again sightover the alidade. The board is then said to be oriented because ab of the

plane table corresponds in direction with AB on the ground.

The orientation may be verified by sighting one or more other points

in a similar manner. If the alidade is placed on ac the point C should fall

exactly in the line of sight and if on ad the point D should fall exactly in the

line of sight. If this does not occur then the en-or lies either in the point

:>1' points being improperly plotted, poor sighting, or else the plane table may

not be in station over A. Make the necessary corrections and repeat.

(2.) When The Plane Table Is Somewhere On 'rhe Line Joining Two

Points Of Known Location.

176. The plane table may be on th~

line ab extended, in which case the

. point farther 'away, will be sighted

on, fig. 42.

';l.'::/:.6.

t9Q~ La

Fig. 42. Fig. 43.

Set the p'lane table up on an imaginary line joining the two points, A

and' B., Placing the alidade on the line ab and with the plotted point a the

,.far~hest away, rotate the board until the point A falls exactly in the line

o,t'sight 'when sighting over the alidade. Lock the board. Verify. Leaving

the board locked, walk around to the opposite side of the table and sight over

the alidade on point B. B should fall exactly in the line of sight without

mOving either the plane table or alidade. If this does not occur either the

sight,ing was poorly done or else the board is not on the line An. The latter

generally' is the case. Make the necessary corrections and repeat the operation. .

Note: The process is SImplified when the direction is materialized

On the ground as in the case of a road, see fig. 43.

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(3.) By Angle Traverse (See Chapter YII).

177. Orienting by an angle traverse involves the principal discussed above .

.The last leg of the traverse is the line of known direction.

(4.) When Known Point On A Given Line Cannot Be. Occupied.

178. The case sometimes occurs when the station A cannot be occupied.

Under these circumstances the plane table is set up near point A and a

line of known direction from this new position is established on the board.

>fA

\

\ ~B

....-....-

Fig. 44.

(a) Let x be the point at which the plane is set up and x' its assumed location, fig. 44.

After the plane table is set up, orient it approximately and, pivoting

the alidade around a, sight on A. Draw the ray from a. Measure the distance from A to x and lay off ax' which gives the approximate location of the .

plane table. Pivoting the alidade at x' sight on B, draw x'B. D~op a per- .

pendicular from b to the line x'B. Let this be bb'. Draw line a,Y"~qual to

x'b'. At.Y' erect a line .Y,Y' perpendicular to the line a,Y' and equal to

bb'. Drawa,Y. At x', erect a perpendicular. The intersection of this perpendicular with the line a'y determines the point x which the plane table occupies. Orient the board by using x as one point of the known line.

179. (b) A much simpler but less accurate method than the one above

may be used for quick work. Place the table near A and orient approximately. Place the alidade on a and draw a ray towards A. Set off the station point x' at the measured distance from A, reduced to scale. While x is

the true plotting of the position which the plane table occupies, orient using'

x' as the station point.

(5.) By Resection. .

180. If more than two points are available orient approximately and resect. Solve the triangle of error and proceed as above when occupying a

point on a line of established direction.

Topography for Field Artillery
" CHAPTER VII.

TRAVERSES.

DEFINITIONS.

181. A Traverse is the process of determining a route for representation

on a map or sketch by actually proceeding over it, making the necessary

measurements on the ground.

#

A. KINDS OF TRAVERSE.

Traverses are of two kinds, open and closed. A closed traverse is one

which returns on the starting point or ends by passing through a known

Point. An open or unclosed traverse fulfills neither of these requirements.

For the sake of an accurate check, a closed traverse should always. be made

. in any topographical work involving traverses, see fig. 45.

UNCLOSE:D TRAVERSE: CLO~E:D TRAVER.s(~.

.A

b

Fig. 45.

~d

M

t\nown POln t.

B. INSTRUMENTS USED.

182. Instruments used in Traversing are either a declinated instrument

or plane table. The declinated instrument may be used either in a needle

or angle traverse described below, or in an ordinary survey. The plane

table is the usual method of recording traverses on a map or sketch. in

which event a working scale is used to layoff on the table the distances

measured on the ground.

C. METHODS OF TRAVERSE.

(1.) The Foresight-Backsight Method.

183. Methods of Traversing include the fo~esight-backsight method, needle

traverse and angle traverse. The foresight-backsight .method is described

as follows: Set up plane table at A, the starting point. Clamp the board

and plot point A on the sheet. Call the plotted point Q. Pivot the alidade

at Q until the second station, B, is sighted. Draw a light ray the full length

Topography for Field Artillery
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---><Cl

.i

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£ ':Or:~~;~ht on B

Q

--64--

of the alidade, fig. 46. Pick up the plane table and pace the distance betw\.!en A and D in the direction of the ray already drawn. Arrived at 8

layoff, on the ray already drawn. the distance ab corresponding to the

distance AD. Orient the board by laying the alidade on the rayab and turning the board until A is sighted over the alidade, fig. 47. Clamp the board. r [l,' '.. 11

/ I TABLE:'ON.B

/TABLE:'OVER-A b

Fig. 46. Fig. 47.

Pivot the alidade about b until the 3rd station C is sighted over thealidade.

Draw a light ray be, etc., proceeding by this method until the entire traverse is completed, see figure 48. .

(2) Needle Traverse. m

18... A Needle Traverse may be made in TABLE:, OVER C

order to save time over the fore sight-back 8 x.... _

sight method. Alternate stations may b~

occupied and sights taken with a declinated

instrument, to 8tations not occupied. A

rodman may be used at the unoccupie.J

stations in case these stations have no

sharply defined point to which sights may

be taken. First read the bearing from the

first occupied station to .the unoccupie(1

station: measure .the distance: thence proceed to the second occupied station, measuring that distance.. Plot the position of

the unoccupied station from the direction

and distance first measured. Set up at the second station and read the

'bearing to the unoccupied station. Draw a ray through the unoccupied station with the bearing last read, plus or minus 32001/1 (back azimuth), and

on this ray plot the second occupied station at the measured distance .

. (3.) Angle Traverse.

183. Angle Traverses sometimes are ~f value When it is desired merely

to orient at another point and the matter of distance is not important. In

such a case the orientation of the first known point is merely carried forward to the other known point.

To do this. set up the table or instrument at the fir8t point, A. 8l1rl

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-65-

°trient. Take a shot at a second point, B, and draw the direction ab, on th<"

able . , as In the case of any other traverse, fig. 46.

't Pr?ceed to the second station, B. and set up the board. Do not pause

S~measure the distance. At B orient by a back sigh.~ on the line just drawn.

,Ight on a third station C and draw a line in this direction across the line

00 P , , • roceed to C and repeat the operation.

t

Continue until the desired point is reached. The point will be reach-

{\( with an oriented board which is what is desired.

). . In this operation, as in other traverses, the number of legs must be

united, otherwise the cumulative error will be so great that the orientation

cannot be accepted. .

.

186. Tra verse. Distances passed over may be determined by the stride of

rn~n or horse, by the time taken by a rated horse. by the revolutions of a

; eel, by chain or tape, and by stadia. Distances not passed over may be

e!,ermined by estimation, by stadia, or by intersection.

- 6° 10° 15° 20° 25° 30°

UP rOWN UP IDOWN UP rOWN UP rOWN UP IDOWN UP IDOWN

~~ES ~O.4 95.6 78. 7 69.3 87.4 68.8 80.8 49.1 68'.2 ;-; 61.4

(1.) Pacing.

~87. Accurate measurement by pacing depends on the skill of the operator

In maintaining a uniform length of pace, or of stride (a stride equals two

Paces), on the care taken in determining the length of his pace, and the

accuracy with which the working scale is made and used.

t Good pacing should not be in error by more than 3% on distances up

to 600 yards. On long traverses it is better to use another method in order

o avoid a large error. It will be noticed that strides always are shorter

;n .sl~ping ground both going up and down grade than on horizontal ground.

h~CIS due to the fact that the effort of moving upward shortens the stride

WhIle in moving downward the operator checks himself. thus shortening the

strine. The length of the stride. moreover, is not the same when moving

up a given slope as when moving downward' on the same slope .

.The following table applies for an operator taking 100 paces up or

down slopes of 5 degrees and greater. The table indicates the number of

race~ to layoff with the working scale for any given slope. On slopes

eas than 5 degrees, and for distances on such slopes not greater than 200

Yards, no calculation is necessary and ground distances may be taken as

the base. In most instances errors resulting from this procedure are compen<:;ating. ..

TABLE OF PACES.

The above takes into consideration both the slope of the ground and

the difference in the length of pace due to the slope. See Appendix I. When

pacing count the number of paces between stations, apply the working scale,

and layoff the proper length of the traverse on the map.

Topography (or Field Artil\rry

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(2.) Chaining Or Taping.

188. Having set up at a given station and having oriented the board ,or

plane table, take a sight to the next station and draw a ray along tbe alidade

whUe thus sighted. Send out chain or tape men who will measure the distance between stations. Keep these men lined in by sighting over the

alidade. Apply the Representative Fraction of the map in question and

layoff the proper length of the leg of the traverse on the map. For very

accurate work the expansion or contraction of the steel chain or tape, due

to temperature, and its sag, are calculated and the measurement thus corrected.

(3.) Stadia Readings.

189. This is a rapid method of obtaining measurement of distances especially over rough terrain where the pace, chain, or tape methods are likely

to cause large errors. The apparatus consists of a transit or telescopic

alidade and a stadia rod operated by an assistant. see Ch. V.

E. SPECIAL CASE.

190. When First Station Cannot Be Occupied. (See fig. 49).

A

1', / ,

/"

I ",

/""

II "

LtJII '[BJrqo c

r

Q1 0

. B c

m n

m

Fig 49.

Set up and level the plane table at B. a point not necessarily known,

but from which the point C is visible. Orient with a compass and plot the

point a, the point (represented on the ground by A) which cannot be occupied.

Sight on A. Through a draw ray am. Pivot the alidade on a and sight

the point C. Draw this ray ao. Pace or otherwise measure the distance B-C.

This distance, laid off to scale on the ray ao, gives point o. Move to C, set

up, level and orient the table with compass as before. Through a draw an

toward C. From o. draw a line parallel to am. This intersects an at the desired point c. the station 'last occupied, thereby giving the map distance ac

wh:rh was what was desired

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F. ERRORS IN TRAVERSING.

:91. The Permissible error in traversing is 5% of the entire length of the

fav('fse. This limit applies only to the ordinary traverse. No such amount

~'l~rror is permitted in surveys. In making a closed"traverse there proba?ly

th

1• be an error of closure. Figure 50 indicates the method of correctmg IS • • t Th J> error for a closed traverse which returns on the startmg [lom. ,P

rocedure is the f;ame for a traverse closing on any kno\'lll point.

()

CORRECTING [RROR or CLOSVRE _____ ORIGINAL' TRAvERSE.

CORR(CTf:O' TRAVERSE.

.A j-

/-

/

/

e(---- ,

7r--

/

/

6~--'\

'\ -- ~=

I

I

;f 2-

/

l- I 3

/

/....

/

/

/

/

/----

/

/

I.... / ....

/

/

!'.....

/

/1..... .....

,5/

<. . ..... .....

Fig. 50.

POint A' should be at A, but due to errors in traversing does not so plot.

On a straight line O-A layoff from 0 in succession, the lengths of the

courses A-1, 1-2. 2-5, etc. From the end of this line layoff, perpendicular

,to A-O, the line A-D equal to the error in closure, A-A'. Connect D and O.

Now from each succeeding station on the line O-A, draw a line parallel to

the line A -13.

Heferring to the traverse~ draw through each plotted station, a line

fl.al'hllel to the final closure line A'.A. On each such line layoff its respectIve offset length, as determined above, giving new positions for each station.

Corn~<.'cthese new stations and the traverse is adjusted. Erase the original

t,'avPl'se from the sheet.

TO!lflll'rRphy for Fie"t Artiller)'
CHAPTER VIII.

INTERSECTION.

DEFINITION.

192. Intersection is that topographical operation by which a point on the

ground is located on the map by the intersection of rays, from two or more

known points. drawn in the direction of the unknown point.

A. PURPOSE.

193. Intersection is used to determine a point without occupying it, and

often is the only method which can thus be employed. It may be used to

locate a point behind the enemy's lines, a tree on the opposite side, of 11

stream, a mountain peak in the distance, etc.

The method may also be used to check up the accuracy in angles

and distances of a traverse. in the following manner: Before starting,

select an object on the ground that can be seen from at least three places

along the route to be followed, preferably at the "set-up" stations. While

making the traverse, after orienting the board, draw rays toward the select.

ed point from known positions. The three or more rays should intersect

at one point, if the work is correct.

B. ACCURACY.

19 J. Accuracy may be expected when the angles between at least two

of the rays is not less than 500 mils, nor more than 2700 mils, as the bad

\

\

\

\

\

x~

/ \'

/"

//"

/ \

/ /

", /

/

/

,-

/

/

/

/

Fig. 51.

etTcrt of erratic sighting becomes smaller and smaller as the angles at the

intersection of the rays approach right angles.

Topography for Field Artillery
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C. THE OPERATION.

To ~ocate A Point By Intersection:

19~. A and n are two known points, accurately located on the map (01'

~rld). It is desired to locate a third point, C, a church steeple, which can

a~ ;een. f~om both A and B. Process: Occupy A, and orient board accure y. Wlth a on the map (or grid) as a pivot, sight on C on the ground,

:n.d through a draw a rayon the map toward C on the ground. Occupy B,

l'h .' ar, an< Wlt on the map as a pivot, per orm t e same opera IOn. rlent bo d I. h b' f h t'

(> mtersection c of the two rays will be the location of the point C on th~

~ap. If there is a third point of knovln location on the map, the location

th c can be checked by repeating the operation at D on the ground. The

b ree rays should meet at one point. If they form a triangle, an error has

A

een made in sighting, orienting the board, or in plotting the location of

, n,'or D. ..

TOIlOltr8phy fnr Fit'lt.I Artillery
CHAPTER IX.

RESECTION.

DEI"INITION.

196. Resection is that topographical process (the' reverse of intersection)

by which a point on the map, corresponding to the sketcher's position on the

ground, is located by the intersection of rays drawn from points on the

ground through corresponding points on the map, after the map. has been oriented.

CONDITIONS WHICH MUST BE FULFILLED Iii' ACCUI{ATE RESULTS

ARE TO BE EXPECTED •.

197. 1. Known points must be plotted accurately.

2. Points chosen must be so located that the angles of intersection of

any of the rays drawn from them must be more than 5001/t and less than

2700,/,: also so that the points selected and the point sought should not

lie on the circumference of the ~ame circle.

3. The plane table must be level.

4. All rays should be drawn on the same side of the alidade.

5. Lines should be fine and drawn with a hard pencil.

6. Sighting should be accurate. After a ray is drawn it should lJe checked by resighting.

7. Allowable error. The error in the location of the point sought

must not exceed one millimeter of the true position no matter what scale

of map is used. Thus, on a 1 to 20,000 map this error would not be greater

than 20 meters, on a 1 to 10,000. this error would not be greater' than 10

meters, and on a 1 to 5,000 map, this error would not be greater than 5

meters.

METHODS OF UESECTION.

A. TRANSPARENT PAPER METHOD.

198. The operator' is' at point P which he wishes to determine on the map

or grid. Points 0, b. and c, exactly located on the map or grid, are visible

from this position. The plane table is SE't up and leveled. A piece of transparent paper is fastened to the board which is locked fast without being

oriented. A needle is struck in the center of the sheet. This represents p.

With the needle as a pivot, A, n, and C on the ground are sighted in

turn, rays being drawn toward each. The .rays are labeled. The transparent sheet is then taken from the board and placed over the map or the grid.

It i'i next moved about until the ray drawn toward A passes through 0 on

the map, while that to n passes through b. and that to C passes through c.

The llole in the paper made by the needle, now is over the point p which is

the map representation of the point P on the gt'ound. By pricking through

this hole, the point is recenled on the map.
-71- ::9. The proof of the above.is found in the fact that the rays. drawn on

e paper from the pin toward the various points form angles whIch corres-

~ond exactly to those actually on the ground, and that these rays can inter-

'pe~t only in one point, which is the location sought., (unless, of course, all

2~~nts are on the circumference of the same circle).

an •. ,In using the transparent paper method, it is well to remember that

u Y errors made do not show in the final result. Thus, because no error

PPears, the operator must not conclude that there is none. If accurate reRults . d h k f are sought with this method, a fourth point should be use as a c ec

a tel' the point p has been determined on the map.

D. THE TWO POINT METHOD.

201 'rh' , 't' d I' IS method reqUIres careful orienting. Thus, a very senSI Ive ec mator or a line of known direction is necessary. #

Fig. 53.

A,

\

\

\

\

\

Fig. 52,

(t.) Using A Known Liite.

The operator is somewhere on a line of known direction which ig

1'C'llI'escnted on his map, such as a railroad track. He wishes to find his

exact location.

First, he sets up his board on the track and, placing his alioade on the

Ina? representation of the track, sights along this line, turning his board

unt 1 the map direction corresponds with that of the track itself, fig. 52.

Prom his position he notes a point on the terrain which he can identify

On the map. Through a, on the map, he sights on this point A, on the ground,

~d (h:aws the ray. The intersection of this ray \vith th~ line representing

e raIlroad track is the exact location of p, which is the map representation

of the point P.

Note: The railroad is used

not only to orient the map but also

a..'i k one. of the rays drawn in a

nown direction through the point

SOught.'.

(2.) Using The Dec1inator.

~02. The declinator is used to orient the board, after which two points,

I(lentified on the map and visible from the point in qu<:stion, are selected,

fig. 53. With a, and b on the map as pivots, draw rays towards A and B on

the ground. The intersection at p will be the location on the map of the point

I).

TOl>OICfAIlhy fOf Fie)d Artilll'I'y
--72-

C. THREE: POINT METHOD.

203. Let A, n, and C be three known points on the ground which are located

on the map or plotting board, fig. 54. Orient the board as "Well as possible.

With a, b, and c on the map as pivots draw rays towards A, B, and C on the

.ground. If the orientation of the board is exactly correct the three rays will

intersect at one point. p, on the map which is the location of the plane table.

Triangle Of Error.

If the orientation is not correct a "triangle of error" 'will occur, fig.

55. This triangle may be solved in several ways.

c

I

\ /

" ~./ ~\¥~~~z~ /" \ \.

lj'

/

A

I

I

I

I

C

/

/

I

/

Fig. 54. Ie: Fig. 55.

20... (I.) If The Operator's Position Is Inside The Triangle On The Ground.

The Vertices Of Which Are A, B. And C.

(a) Solution by using perpendicular bisectors of the sides of the triangle of error, fig. 56.

to,

\

\0

Fig. 56. Fig. 57.

Draw perpendicular bisectors of the triangle of error. These meet at

a point. p, which is the location of the operator. Check by resighting.

(b) Solution by intersecting arcs. (See par. 206.)

TopolCrallhy lor Field Artillery

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205. ( ( 'rh 2.) If The Operator's Station Is Outside The Triangl..)n

Ground, The Vertices Of Which Are A, B, And C.

. (a) By the inverse triangle method.

Label the intersection of the rays to A and B as %, to Band C as 'y,

and to A and C as z. Next t\\Tist the board slightly and draw new rays to

fl, and C as b:fore. If the intersection is at o~e point, t~en, that point is

e correct locatIOn of the operator, and the tWIst has orIented the board.

(~ote: Usually the point sought will be found opposite the long side of the

~langle of error, and the twist should be in that direction.) ]f the board

. as been twisted far enough it will have moved past the true point and an

Inverse triangle of error will have been formed. Label the intersection of

the new rays to A and B as x', to Band C as y', and to A and C as %', fig.57.

. Next connect :Je and x', y and y', and % and %'. The three lines will

Intersect in a point P, which is the location of the operator on the map.

(Note: The two opposite triangles of error must be quite small to get good

results. This is because the points of intersection of the corresponding rays

~o not move in straight lines during the shift from one side of P to the other,

ut rather swing along arcs.)

20~, (b) By arcs of circles. Having resected and gotten a triangle of error,

the triangle may be solved as follows: (1) describe the circle which has

on its circumference a and b, and the intersection, :Je, of the rays therefrom;

(2) describe the circle which has on its circumference the points band c,

and the intersection,. y, of the lines therefrom; (3) describe the circle which

~as on its circumfeI'ence the points a and c, and the intersection, %, of the

hnes therefrom. (4) The three circles should intersect at a point p, which

to A I to B

~ _---.f.. ,," I ....., / I" "

Fig. 58.

is tht> true location of the point P on the map or grid. (5) Ueorient the

hoard by sighting A along the line pat (6) Check by sighting 13and C alon~

pI> and pc, fig. 58.

TOJlOlCrllphy for Field Artillery

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The proof of the above is based on the theorem in plane geometry to

the effect that all angles subtended by a given arc of a circle, the vertices

of s1.id angles being on the circumference of the circle, are equal. The angles

constructed at x, .Y, and z, by the intersecting rays, are equal to those actuallY

'Cxisting on the terrain. All other angles with vertices on the circumferences

of 1he respective circles and subtended by the respective arcs will be equal

to those measured on the terrain and constructed on the plane table. Th~

only point which will satisfy all conditions simultaneously is where the three

circlps intersect, or at p.

D. BACK AZIMUTH METHOD.

207. In using the Back Azimuth Method, it is essential that the compass

declination b-e known, par. 460, Ch. XX.

Pick three points A, B, and C which can be seen from the operator'R

position, p. and which are located accurately on the map or grid. Through

each of these points on the map, draw a true north-south line, fig. 59. ,

tOA.................

\

\ to C

Fig. 59.

With the declinated instrument take the bearing to A, n, and C and

reduce each to azimuth. Add 3200'll to the results, which will give the "back

azimuth" readings. \Vith a protractor layoff these respective readings,

usir.~ as an origin the true north lines drawn through the respective points.

The three rays will intersect at one 'point, p, which is the location of

the point, P. If a triangle of error results; some part of the work is inac'curate and should be repeated.

(Note: The point may be located in the same manner if the lines through

A, H, and C are drawn in the direction of magnetic north, grid north, or the

north of the particular compass used. See par. 469, Ch. XX.)

The value of this method lies in the fact that it may be performed in

the field without a map. It is necessary only to read and record bearings,

after which the actual work of resection may be performed in the plotting

rOO'll, or the dug-out.

E. ITALIAN RESECTION. (llessel's Theorem)

208. The fil'5t part of Italian resection is, in reality, merely a method of

orienting the board, hence the name "Italian orientation" might well be applied. The last steps are those of the ordinary two or three point I'e~cction.

Thp orienting, however, is so exact that no triangle of el'1'Ol' )'(,l'iultl'i, .

TOllOlCral,hy for Field Artillery

~
 
-75~

c)('

B

x

')(0.

A

xb

(1.) The Process.

209" . .... . : • . T .. Three points A, B, and C are selected as in the three point method. b:e cor~esponding points on the map are a, b, and c.'!:The point C (c) should

the point farthest away, fig. 60. .

e.

f

,

I

I

,

,

Fig. 60. Fig. 61.

. No attempt is made to orient the board. The sighting alidade is laid

~lth its edge on ab. Assuming that the operator is at a, he sights from a to

• "Vel' b, and locks the board, fig. 61.

With a as a pivot C is sighted at, and the corresponding ray is drawn, ,

calling it C\. The board is then unlocked,

Next, the alidade is laid along ba, and, assuming that he is at b th*:

~per~tor. sights from b to A over a, and locks the board. With b as a pivot

e 1'1ghb~on C and draws the ray C2 fig. 62.

A

'\ ,~.

\

\

Fig. 62.

Fig. 63..

The two rays, C\ and C2 intersect at a point, d.

: . From d the operator draws a ray to c. The point sought is somewhere

along this line' (see proof).

. . Unlocking the board the operator lays the alidade on the liIie de and

SIghts from J to C ovcr c. This orients the board which then is locked in

T1ol'it ion. fig. 6:1.

TOI)()J!'\'RI.hy for Fidtl Artilll'I'y

"

,

,
-76-

To find the location of the point p, on the line deC extended, it is necessary only to pivot the alidade about a and b in turn, sighting on the corresponding points on the ground and drawing the rays across dee. The intersection of the three lines is the point, p. ,

210. The location of p may be checked by sighting on a fourth point. In

fact, it is always advisable, if possible, to check any resection in this manner. In Italian resection, if the points are plotted falsely, a perfect resection,

o

o

o

Fig. 64.

I

I

I

'I :

.F'I\'T.Po.s/T/ON' 0.- -0- B

I I

I 'DR.Aw.DJI\~CTlON' I c:- - - - - - - - - - - - '- - - - - - - -1- C-Q(",

I J

, I

.Sf.COND.P05lTJot~.?- _..:. ?_ -A

I • , A I

b- - -- - _'D~ ~'EJ~.sT25~ -'--C ..b

I I

•TttlRJ).Po.slTIoN- : I

~lfNTArott> '~JTl1tltd_ _'~O.!..N IO - I

J ! - -:c -~c

'OP'f- -- - - - -.--~I~'!9'_ _ :

I

Q- ..PFtAWJ>~EC:TJO~. "'- _: A

, ,

t!>-.. - - - - I ~ptw.E!P~.!!(~' _ -:--B I

may result, no triangle of error being evident, and yet the point will be

quit~ false. A fourth sight will check this error.

211. The steps in Italian resection are illustrated graphically above.

- - - - - - - - - - ~

_

- - - - - - - -

- - - -

- - - - - -

- - - - -
212.

-77-

(2.) The Proof.

Let p (p) be the operator's position which is to be determined, fig. 65.

C~

Fig. 65.

Let A, 13, and C be known points on the ground, represented by a, b,

and c on the map.

Let d be the point where the straight line joining p and c, cuts the circle

Pa."Isedthrough pab. .

Angle ,,'=x (by construction).

Angle 31'=31 (by construction).

To prove that aCt and bCI intersect in a point d on the line pc.

Draw a circle through p, a, and b.

pc intersects this circle somewhere. at point d.

aCt intersects this circle at some point, d.,

'and bCa intersects the same circle at some point dz•

Angle x is measured by one half arc b~d (by geometry); "'--

and angle x' is measured by one half arc b~J ..

But angle x=x'.

Therefore arc bkJ.=bkJ •.

S,ince one end of the arcs, b, coincide and since the arcs are equal

,and measured in the same direction on the same circle, then the other ends

must coincide, or J and dl. are the same point.

To prove that Ja also coincides with J.

Angle 31+ angle abJ enclose the complete circle. Therefore the two

a.ngles are equal to one half of the enclosed circumference (by geometry),

Or they =1800

•

By construction 'y'+abJa=a straight angle=180° ..

Therefore 'y'+abJa='y+abJ.

But 31'=31 by construction.

Therefore abJ=abJa•

Since one side of these two angles coincide, since 'the vertices are the

Mam<,. and since both are inclosecl within the same circle: therefore, the second

TO!lOlI'raphy lor Field Artillery

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-78-

legs of the angles must coincide, and abd2 must intersect the c;ircumfcren:ce

of the circle at the same point as that of angle abd. In other words J must

coincide with J2•

And since J (by construction) was the point of intersection of the

straight line joining p and c, with the circumference of the circle, then d. and

J2 also lie on this same line and the board may be oriented by using J and c as l'ighting points for the line pc.

F. BRITISH RESECTION.

213 Three visible points of known location A, D, and C, on the ground, represented bi a, b, and c on the map, are chosen. Let P be the point occupied

on the ground and p the corresponding point on the map.

Construct a circle passing through a, band fJ as follows, fig. 66,

*

I

Fig. 66

At P with a plane tabl~ or an angle measuring instl'umcnt measure the angle APB.

Points a and b are joined with a straight line.

With the line ob as a base and point 0, as a vertex, construct the angle boy equal to APB.

The perpendicular bisector of ab is drawn.

A perpendicular is drawn to JlO at o.

The two perpendiculars intersect at r.

A circle next is constructed using r as a center and a radius ro or rb.

Points a, band p will be on this circle, and (by geometry) all angles

with vertices on the" circumference of this circle and subtended by the same

arc ab, will be equal to the measured angle APD.

Construct a circle passing through b, c and p. (as above).

The two circles intersect at two and only two points, b, being one of the two.

TOllOlnaJlhy (01' .. i•.ld Artillery
-79-

If p coincides with b then P coincides with B on the ground and in

sUch I

for a case th;re is no angle b~tween B and A o~ ?etw~en B ~nd C,. ~heree, the only mtersection which satisfies all condItIons IS p, sInce thIS IS the

only . I d pomt from which the angles will correspond ~o the ang es measure

On the terrain. ,. . ': ,;

. The location of the point p' may be checked by constructing a third

Clrel . , e m the same manner using the angle between A and C.

C. BY MEASURED ANGLES .•

214. Another method, which, like the British, makes use of the measured

~ngles in the construction of circles which intersect at the required point. p,

18 giv~n below.

At P measure the angles APB and APC. The exact location of P 18

not known, hence an assumed location is chosen.

A lin~ ap' is passed through this selected position, ~ng. 67.

Fig. 67..

, On the line ap', layoff an angle ap'b with the vertex on the line

ap and the sides passing through 0 and b; this angle being equal to the angle

tne~sured on the ground, APB.

Pass a circle through the points 0, p' and b. All angles on this circle

Subtended by the arc a1> will be equal to the measured angle APB.

Next on the line ap' layoff an angle equal to the m~asured angle APC,

~o that the legs pass through 0 and c and so that the vertex is on the line ap'.

et the angle so constructed be ap" c.

Pass a circle through op" c.

TOJlOllraphy for Field Artillery

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All angles of this circle subtended by the arc ac will be equal to the

measured angle APe.

. The only points on the circles which ~ill satisfy conditions as to both

angles will be their intersections, and of thesoe intersections, p, is the only

point which accords with the actual conditions found on the terrain. .

Therefore p, is the point on the map, the location of which is sought.

The point, p, may be checked by usin~ a third circle through band c.

TOl)OlrI'aphy for (O'leld Artillery
CHAPTER X.

MI<~ASUREMENT OF SLOPES AND 'I~LEVATIONS.

DISCUSSION.

;15. Nearly all operations by artillery involve a consideration of grounrl

borms, slopes and elevations. hence, it is important that the artillery officer

c. familiar with all methods and devices or instruments used in the deternltnation of slopes and elevations. either from the map or from the terrain.

A. INSTRUMENTS USED. .f!

Z~6.:' Slop'~s or gradients may be determined by means of the transit, th,'

~lm'ng circle, the battery commander's telescope, the prismatic compass,

evels, clinometers, alidades, the sito-goniometer, and the slope board.' .

. In most instances the aiming circle or battery commander's telescope

wllibe available; To measure a slope with the aiming circle 'or B. C. telelICOpe,level the instrument, look through eye piece and sight upon the. point,

the elevation of which is desired; level the bubble of the reading device

(commonly called angle of site device) and read the angle.

This is the angle of slope, in mils, from which the arigle in degrees.

gradients, etc., and the actual elevation may be computed. .

. In measuring slopes with any instrument that is not on an actual level

~lth the ground, a sight should be taken on .an object the height of which

~8 'l!?proximately that of the instrument being used. On long slopes the error

~s negligible but on short slopes a marked error will occur if the above rule

IR not followed.

For description and discussion of operation of the other instruments

ellu~erated above, see Chapter V.

n. UNITS IN WHICH SLOPES ARE EXPRESSED.

Z11., The amount of given slope may be expressed in several different

Ways, each of which is definitely related to the other. See Chapter II.

. (1.) Degrees And Minutes.

218. The ma~imum slope of any hill can be only perpendicular or 90"

(plus or minus); therefore any measurement made of a slope will read from

0" te 90°.

Fractions of a degree may be expressed decimally as, 6.33". 3.6°, or,

each degree being divided into 60 minutes, fractions of a degree may be

expressed in minutes, as follows; 6°,20', 3° 30'.

(2.) Mils.

219.. Slopes may be given in mils, from 0 to 1600, a perpendicular line

making an angle of 1600 mils with the horizon.

(3.) Percentages.

220. Slopes may be expressed by the percent of' rise in a given distance

TopolCraph, for Field ArtillerJ

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on the ground, i. e. the number of feet rise for each 100 ft. of horizontal

distance.

To find the percent of slope; divide the rise by the horizontal distance.

For example, assume a rise of 5 feet in a horizontal distancE' of 100 feet.

Dividing 5 by 100, the quotient is .05 or a 5% slope.

(4.) Gradients.

221. A slope may be indicated by the relation between the rise and tht>

horizontal distance such as a rise of 5 feet in 100 feet. This expressed a~'

5 on 100 or 5/100, or 1 on 20, the numerator usually being taken as unity.

Such an expression is spoken of as the gradient of the slope.

(5.) Tangents.

222. The relation between the side opposite to the side adjac'ent to an angle

of .1 right angled triangle. is the tangent relation of that angle.

Given the horizontal distance and the degree of slope, look in the

table of tangents for the tangent of that slope and multiply it by the horizontal distance. The result will be the height of the perpendicular of the right triangle.

For Complete Conn'raion Tables see Appendix IV.

223. T)'pical Problrm: Assume that with a slope board, or other slope measuring devicto', the slope of a given hill has been determined to be 4°. It i:-

desired to change this into mils, percent, gradient, or tangent values. Refering to Appendix IV the following values are found; (For a discussion of

values see Chapter II).

1°=17.78 mils or 1.75% and 1%= a gradient of 1/100 hence the equa- tions:

4XI7.78=71.12 or 4°=71.12 mils.

4X 1.75= 7.00 or 4°=7%.

1%=gradient 1/100 then 7%=7X1/100 or a gradient of 7/100=1

on 14.28 or 4°=gradient of 1 on 14.28. From the tables, 4°=a tangent of

.06993.

Assume now that the point to which the slope had been read was the

top of a cliff, to the base of which. it is possible to measure or pace off the

horizontal distance. The height of the cliff is desired.

Assumed horizontal distance=400 (60 inch) strides, 60 in.=5 feet.

Then 400 strides=400X5 or 2,000 feet.

From Appendix IV the tangent of 4°=.06993. (The horizontal distancE' times the tangent gives the altitude of a right triangle). Therefore

2000XO.06993=139.86 or the height of the cliff in feet.

C. SLOPE SCALES.

224. A slope flcale is a scale by which the slope between contours may be

read or which can be used in map making for locating the relative position~

or distances between. contours.

For American or other maps Where the V. I is directly proportional to

the scale of the map, a slope scale may be constructed that is applicable to

all such maps irrespective of the scale; i. e. if .65 in. is the 1\1. D. between

contours for a 10

slope on a map, the scale of which is 3 inches to the mile,

with a V I of 20 feet; it follows naturally that .65 in. is the M. D. for a

'fOJlOgraIlhy lor Field Artillery
Topography for Field Artillery

. -83-

f

1° slope on a map, the scale of which is 6 inches to the mile, with a V. I of 10

eet, etc.

(1.) Construction Of Slope Scale.

225. (a.) For American maps. To ascertain the ..M. D. between contourj;

wh('n the degree of slope is known, the following formula npplies:

M. D. between contours- R. F.XV. 1. (in feet) X,688 ,

6 Number of degrees of slope

88 being the number of inches horizontal distance necessary to give a rise . 1 foot on a 10

degree slope •

Proof:

IO slope=l ft. rise in 57.3 feet (or 688 inches) horizontal distance.

For 6 in, map 10 slope=10 ft. rise (the vertical distance between contours) in 573, ft. horizontal distance. But 6 in.=1 mile. Then 6 in.=5280

ft., and 573 ft.=573/5280 of 6 in,=.65 inch=l\L D. bet~veen contours for 1

0

Rlop~.

, Similarly it may be shown that the M. D. for a 10

slope with the 1 in"

3 m. and the 12 in, maps is ,65 in,

For small angles it is approximately true that the amount of rise comparpd to the horizontal distance keeps pace with the degree of the angle,

Thus if a horizontal distance of 573 feet is required to give a rise of 10

feet on a 10 slope, a similar rise would be secured in half that distance on a

2° f;lope. Or if .65 in. is the map distance between contours on the American

maps of 10 slope, then the map distance between contours will be half

,65 in, or .325 in" for a 2° slope.

Solutions for various degrees of slope for American maps give the

fOllowing: .

.65 inch M. D, (between contours) for 10

slope,

.325 inch M. D, for 2° slope,

.22 inch 1\1.D, for 3° slope,

t'l-.16 inch 1\1.D, for 4° slope •

•13 inch 1\1. D, for 5° slope. "--- Draw a line suldivided into the above units (use a ruler divided into

decimal parts of an inch, if possible, for accuracy). This scale pasted on n

triangular ruler or alidade can be used in contollring and will prove of value,

especially in road sketches.

226. (b.) l"or metric malps. To construct a degree slope scale for the

1/20,000 map with a 5 meter contour interval proceed as follows:

. For a 10 slope a rise of 1 meter is equivalent to a horizontal distanc~

of 57.3 meters, A rise of 5 meters (the distance between contours) will be

equivalent to a horizontal distance of 5X57.31\1=286.51\1=2~650cm, On a

1/20,000 scale, 28650 cm. on the ground corresponds to 1.4325 cm. on the

map

227. To construct a slope (101jl slope) for the 1/20,000 map with a :;

meter contour interval proceed as follows: For a 101jt slope a rise of 51\1corresponds to a horizontal distance of

5001\1. On the 1/20,000 map, Imm,=20l\L Therefore a distance of 500M

on the ground corresponds to 500+20=25mm. on the map.

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-84-

A 20tj, slope would have a M. D. between contours of half the above,

or 12.5 mm., and a 100'1' slope would require a M. D. of 1/10 or 2.5mm.

. (2.) Use Of Slope Scale.

228. (a) In Contouring: Only when a slope is absolutely unif~rm can a

slope scale be used for plotting contours accurately. However it can be used

with sufficient accuracy for all practical purposes of the military sketcher.

Assume that in making a road sketch a slope of 3° is measured from

the base of a hill to its crest. but by observation it is seen that the slope at .

the base is gradual, and the slope towards the crest is steeper. Then. by

. measuring the number of times the interval for a 3° slope will go into the

distpnce as laid off on the map representing the hill, the number of contours

crofl~ing the road for the distance will be known. If, in this manner, it is

found that 8 centours will cross the road, the total distance is divided into

8 'parts,. intervals near the base of the hill being wider than those near the

top. after which the contours are drawn through the points of division.

If the slope is uniform the contours will be equally spaced.

229. (b.) In reading slopes: . Place the slope scale on the map near the

slope which it is desired to me~ure. Move the scale around until one of

the divisions or. the scale corresponds to the M. D. between 2 adjacent contours and so on with the next contours until the' slope has been measured

(or. the distance desired. This gives the slope between adjacent contours

only.. . .

To get the slope between several contours the total of the slopes measured may be averaged, thus getting the average slope of. any given ground;

or the slope between the top arid bottom of the hill may be read and averaged. This should be done only where the difference in slopes between con..

tours does not exceed 1 or 2 degrees.. .

Averagefl should be taken only for plus or minus slopes, never for both combined.

'rUllOl:raph,. for .'eld Artillery
CHAPTER XI.

SI{ETCHING.

POSITION AND AREA SKETCHES.

A. CHARACTERISTICS.

Fig. 68.

230. Position and area sketches are of the same nature, including a traverlW

uPon which. as a framework, the sketcher makes' a map showing all the detailR of military value contained therein. . ..'

Such sketches must be drawn to scale; distances4J"on the ground must

b? rep~esented in proper relationship on the map, directions must be indIcated in reference to the True or Magnetic North, and where ground form~

are of value, the vertical relations must be properly represented.

A map must be capable of orientation. Thus, unless directions are

properly indicated, the sketch has little value.

. Accuracy and reasonable speed are required in making such sketches.

(The time usually is limited). .

However accuracy must not I09S lOll

b /

X985

e sacrificed for speed. The

k

x/O/4

s etcher should be careful at

first to. be accurate. Speed

will come with practice and

experience.

n. TECHNIQUE.

(1.) Whole To Part Method.

231. The simplest and best

method of making an area

sketch is known as the

"whole to the part" method,

and consists in making a traverse around the whole area,

after which the details of the

interior are located and put

on the map.

In traversing locate;

(a) every drainage line crossed or running generally parallel to the line traversed and

note the direction of drainage; (b) every building and

easily identified feature near

the route; (c) the high points

or ridge lines crossed by the

traverse. Determine the ele-
\~a9"

Fig. 69. \ North,

985

990

lOll

99"

97,5

1006

\ Mag

\North.

-86-

1095

/'X9IlS lOll:.

X 1014

}/~990

1027

985 ><

998 993

985

m

IOCJ6

vations of all these points,

without putting in any con.

tours, .see fig. 68.

This is the first step,

or sketching the "whole."

The next step is the locating

of all the critical points, with.

in the area. from which the

completed sketch can be

made, see fig. 69. The final

step is the drawing in of

these details, completing the

drainage lines, and filling in

the contours, fig. 70. (See

Ch. IV.)

For complete sketch

~E'e figuge 71.

Fig. 70.

9

TOllOlCraphy fur .'\eld Artillery
I I ,

100 0

..•.

-87-

+

AREA JH£TCH

of

NORTH Pllff and INf)/t/N'CR€~11

VICIIVlTYMELBA OXLA.

O~C. /2,19/8.

-byLt. Jotzn Smtth.

St.-

Fig. 71.

~N~9' \orth

Scal(/,

6 in.: Imil~.

,

R.F. • 7055lJ

, VI, : 10 ft., y0.5,

'00 too.w<J «.10 ~()(

Topo({raphy for Field Artillery

(2.) Determination Of Critical Points.

232. The following are critical points from which ground forms can be

fillp.d in; (a) junctions of stream lines, (b) sources of .3treams. (c) entrance

and egress points of streams(d) points of high elevation such as crests or

rid~es, (e) road crossing's or rOlld illnctions, (f) points where there is :1

marked differen('t' in the degree of slope.

~

~

~~

"

-

-
-88-

The location of these different points may be determined by traverf'-

ing through the area in one or more directions, or by intersection. If tht>

area be small. one traverse usually will suffice, the critical points being determined by intersection as the traverse proceeds across or into the area;

but if the are:\ be large or one with such natural features that the view

is materially obstructed, then it will be necessary to traverse in several di!-

ferE-nt directions. These traverses may be branches from a main traverflt'

through the area, or they may enter the area from different points.

In making the traverse of the "whole," as many of the interior critical

points should be located by intersection as is possible. With the criticnJ

poi'1ts established the contouring of the area can be done readily. Set' Chapter IV.

. (3.) Information To Be Included.

233. In the above description of the making of an area sketch, only tht'

determination of the natural features has been considered. In an area

sketch as intended for military purposes, all features that have militar~.

value must be shown. The exact purpose to which the sketch is put will

determine what features may be omitted and what must be included.

The artillery is concerned with an area sketch as it applies to artilleT)', and therefore all details must be included that will permit the artillery to use feasible roads or routes, lines of communication, and in fact

every thing that will enable the artillery commander to properly dispose of his different elements.

(4.) Conventional Signs.

234. The conventional signs used by the American service in milital)'

,..kt~t('hjn~ are iIJustrated in this chapter. See Plates II to XI.

.. ,'
-89~

Canal or Ditch ~."=

Aqueduct or Waterpipe •••••••••• •• '': ..... J.",

~:==:==============

(~~------------ . Aqueduct Tunnel ..................... , . ==--~

Canal L~ck (point up 3lream)

Metaled

............... , ...

.................. ==:==-==-~~~~

Wagon Roads ...

Good ==="'!-;-======-

Poor or Private •..........

On small-scale maps

'frail or Path .............................. ,

Railroad of any kind

(or Single Trac~)

Double Track .

I I I I I I

Juxtaposition of I I

I I I '''T"

Hailroads .

Electric ................ ~•'.'.~I •~I~III. '.11.11 ! ".'.''+,

4 I I I I I I II I I II I I 11111 11F

••••••••••••••••••••••••••••••• "'-'I~I "'I'""","~~'=~~=:;(I 'runnel

~.

.sta.am

In Wagon Road or Street ., ::r=::J:::::s::::;;t=C

:-.r

"", I I I ,- I I I I I I •

',' .' ,1

Symbol (modified below)' ; .. ".T T T T T T T T

~~ailroad Station of any kind I

Telegraph

Line .

Along road ~'r=::;:=::::;::=i=:;:::;:. :;::1;;;::;;r=-T,;:"

Along road •..•........... _-...-...--,..-.,.-..,...-,-,-

(3mall-3cale map3)

. ____~-r-J--r-r-r'

Along trail ••............. r"1

l~Jectric Power Transmission Line .. . : .:....:.:..:..•..;._:....-.:.-.---.-

. Plate II.

==========

'

"

-================

-----------

-----------

"

~

""

~ • " • ~

'

~ ~
-90-

General Symbol •.•...•...... -1

Dam •••.....•.•••••••.•.......•......•........•..

Suspension .

. Bridges. • . • . • . • • Truss ( W. Wood; S. Steel) •....••.

•••••••••••••••••••••• 1

..........................

..........................

Foot

Pontoon

Arch

Drawbridges (on large scale... . ..

charts lea'l1e channel open).

Ferries •....... : : . . . . .. 1

I

General Symbol .

(or Wagon and Artillery)

Fords. • . . . . . . . . . Infantry and Cavalry •..........

Cavalry .

Streams in General ••••••• 1 ••• ••••••••••••••••••••

Intermittent Streams .............................. ...-.......- ..._-_ ........

'.,

Lake or Pond in General •..........................

(Dlith or Dlilhout linl. Dlaterlining. etc.)

Salt Pond (bro~t'n shore line if interm;lIcnl)

Spring •..........................................

Intermittent Lake or Pond •••••••••••••••••••• II' ••• •

Topography lor .'ield Artillery

~

~

~

'

•••••••••• 1 •••••
BUilding~ in General

-91-

............................. •

o

...

•-

- RUins

Church ••••• 11." •• , •• II' ••.• II II II' ••••••••••••

+or 6

• HOS

Sshoolho use . , .

POllt Office •• •••••••••••••• ••• ••••• ••• I' ••••••.• .

'relegraph Office

Water Works fIliosPital

Windmill

•••••• II ••••••••••••••••• 1 •••••••••• 1

11 •• 1 •••••••••• 1 ••••••••••••••••••••• 1.

• P.O .

• ww .

C.lty, Town. or Village

•

Capital •......................

City, Town, or Village (generalized) ................

City, Town, or

Village .•......

(Irnall-scale maps)

County Seat .

Other Towns . o

~EM~or[f:

\,,-_.]

Cemetery .1 ••••••••• I ••••••••••••••••••••••••••

Mine or Quarry of any k' d ( ) In or open cui ., .

Prospect

Mine Tu' 1 I Opening ....•................ nne ..... Showing direction .

~haft •••.•••••••••••••••• I' .•.•••••••••...•.••. A

>- ,-.. --' ,~

Oil Wcll~ oogco 0000

Plate IV. Topography for Field Artillery

•••••••• II II •••••••••••••• : II ••••••• II ••••

# - •••••••••••••••••••••• 1.

1

•

1

••••.

• , ••••••••••••• 1 ••••••••• 1 •••••••

••• 1 ••••••••••••••• , ••••• I'

'

~

••••• II' •••••••••••••••• 1 ••••••••••••••
Oil Tanks (abbre"ialion. aT)

Coke Ovens

--92-

......... .. ••••• V/I1J. .. • ". • fI1lJA (J •• • ... ..

\Vire .

Fence of any kind ----------------.-

(or board fence)

~, Stone .

Fences Worm

eorb~d oSmootn' 'x-*-x-x-x-* ••-o-o-o-il .

Hedge

National, State. or Province Line . ------

County Line .

i

qvil Township, District, Precinct, 01 Barrio ._

Land Grant Line .

!

Reservation Line i ....................... .

• _ .._.._ .._ ..-

City, Village, or Borough .

Cemetery, Small Park, etc . ...............

Township-Section, and Quarter Section Lines .' ..

(anyone for lODJmhip line alone, and any

• 11»0 for lOl»mhip and ,eclion line,).

Township and Section Corners Recovered .

Boundary Monument . -..---

Triangulation Station .. .... .. """""""".,,. .~

Bench ~Iark .

u. S., ~Iineral Monument .

aM

x

:Z31

ToiJQlO'aJlhy for Fi..ld Artillery Plate V.

"""" """""""

~ "

~

~~~~

'"

-

'

""""""" "

" """"" " "
Contours .

(or Q3 beloD1) .

,Glaciers .

Form Lines showing flow .

Inn Shapes : ..

Contour System II •••• ••••• II 11." •••• II' .,, II ••••

Depression Contours, if otherwise

ambiguous, hachured thus , , .

I~ocky (or U3C contoun) .

Bluffs, •........ ,

Other than rocky (or U3e contoun)

Sand Dunes •••••••••••••• 11.,1•,1 ••••••••••• II .,-.

Levee • • • • • • • • • , , • , • , , , •• , , , • , • , , , •• , , • • • • • • • • • • •• ~"mmnllV""lIIll:r:l\\I:lI\~::!,llll\llll}:::

Plate VI. TOJ)Ol{raphy for Field Artillery

,
-94-

:\Iarsh in general (or Fresh Marllh)

Salt .

Marsh .

Woods or any kind (or Brood Leo\leJ Trees) ••. ••..•

Pine (or Narrorv Leo\led Trees) ••.•••.••••.•••.••••••

tr!~T IT

if ~ lllrtt (~ ~~I,et"]~' "'I'" ~, .L C (/1 "!"~ "~ I""" '. J. rc If ~''''f r

................

Plate VII.

Wooded .

Cypress Swamp

••••• II II ••••••••••• 11.,1 II •• II II ••••••• II

Woods of any kind (in green) (or os 3110rvn belorv) .

Palm

TOpt)ll'raphy for Field Artillery

_
-95-

Palmetto ...............•.........................

Mangrove .

Barn boo .......••............•..•.•..•.......•....

Cactus ••...........................................

Banana •.................•........................

Orchard .............•.............••

Grassland in general .

Tan Tropical Grass .

-'" ,\,,1{ 'flU ...." "W'

-Ill W'! "II' ""Ill ,

."" "", '4/'" 'WIII'~ ""11,"''' "'" '41"

,'\lVI "'", "", 'lH' ... ,

\I'" VI" "," ~H(

......~,: ~Il( ~'V,,'lll'

Plate VIII. To~graphj for Field' Artl11el'7

'
Cultivated FieJd14 in Keneral .

............... , , .

":r,,;

.... ',' .

-96--

.....................................

I.'

Rice

Cotton

Sugar Cane

Corn

TiJal 1"lats of Any Kind

(or a.t ,"oDIn beloDl) ••............

I

j

i

I

I

I

Shores and J'

Lo , w- ,yater mes. ., I' I

I

i

I

I

I

Hocky LedgeR

Sand

..................

Plate IX.

Shoreline

TOllOlO'aph, for Field ArtiJIt'r,

. ,. .. Surveyed ...

Unsurveyed ..-------...-......_----~

'"

"'

•••••••••••••••••••• I ••••••••••••••••••••••••

•••••••••••••••••••••••••• f

~

~ ~
I

-97-

." ••••• t" •••• ••• ••••••••••• •••••••

.. ,.

~:

.. .. "." .....

Mud

Gravel and Rocks

Coral Reefs

Sh ' ores and

Low-Wat L' er lOes

, (continued)

Eel Grass ."., .

Rock under water , , ..

Rock ~wa8h at any stage of the tide .

Rock wh 't" d b fl' ose pOSI IOn IS ou t u ....•............. ,'

ROck whose existence is doubtful .

Overfalls and Tide Rips ,.

Limiting Danger Line , .

Whirlpools and Eddies .

Kelp ,_ •• t"""" •••••••••• •••••• •••••••••••••• r~

~I

+ {f;

* (~

f;P.O

EB EO.

~//- ...

Wreck~f any kind (or Submerged Derelict) ...... "." ....

Wreck or Derelict (not ~ubmerged) .••••••..••••.......

Cable ("I1111 I or 11111 I . I ') lOut eUenng ••••••••••••••••••.•••••

. Current, not tidal, velocity 2 knots .

Flood, 16 knots ...........•.....

Tidal

~urrents, .... ...

Ebb, 1 knot ......•.•...........

Flood, 2d hour ........••.....•. or m II.

I~bb, 3d hour .

No bottom at 50 Fathoms ........... ; .

Piate X. TopoKraphy for Field Artillery

"" "" "

" " "

" -

"

~

'" " " ""

'

' ---

~

~
~l

4C~3C

50*,3C

~l

C::J

o

C:l

dII

,..

CZ'J=

'11111'1'11'

o

•

.................................

.................................

Artillery .

Sentry

Vidette •.........

Picket, Cavalr)' and Infantry ,

:\Iounted Infantry

-98-

Regimental Headquarters 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 • 0 0 0 0 •

Brigade Headquarters 0000000000000000.00.000.0.0 ••

Division HeadquaI'ters 0 0 0 • 0 • 0 • 0 0 0 0 0 0 0 • 0 0 0 • 0 • 0 0 0 0 0 • 0

Corps Headquarters 0 0 0 0 0 0 •• 0 0 0 0 0 0 0 0 0 0 •• 0 ••••••••••

Infantry in Line .0. 0 •••••••••••••• 0 •••••••••••• 0

Infantry in Column ..............•.................

Cavalry 'in' Line .. 00 ••••••• 0 ••••• 0 •••••••••••••••••

Cavalry in Column

~m

Support, Cavalry and Infantry J:. r;:;;;::J

\Vagon Train ..z-::; -:J'~

................................... @

«

ft1

(3

f!J

U

Plate XI.

Adjutant General .

Quartermaster

Commissar)'

~Iedical Corps .

Orunance _' ,

Signal Corps

Engineer Corps .

Gun Datterr .

::\Iortar Batterr .

Fort •.•... 'jTrue plan to be shown if known j . Hedoubt. . . . .

Camp .

Battle .

'{'rench ............•....•.....•.... 0 ••••••••••••••

Whcn color is w;;cd, execute the following in red.

Abattis

Wire Entanglement .

Palisades .

Contact l\lines .

ControJleu 1\ljn('~ .

r)('molitions .

Tfll.ovrsl,hy for Field Artill,.ry

~

~

0 ••••••••••••••••••••••••••••••••••••••••••

0 • " •••••••••••••••••••••••••••••

~ ~

~

~

~

0 •••••••••••••••••••••••••••••

0 •••••••••••• ' •••••••

0 ••••••••••••••••••••••••••••••••••••••••••

0 ••••••••••••••••••••••••••••••••
!

I'

., '.

• --99-

235. rn In practical sketching, if it is more difficult. 01' requires more time to

a~e the conventional sign th~n it does to write what is meant, the exper1(~nc d k h d 'I t e s etcher will write the description. A sketc IS ma e prlmarl Y

,,~ convey information.' If what is meant to be conveyed is not clear thl'

ketch, is of no use. Again, if it takes a commander too long to read a

etch he will blame the sketcher, and as his time probably will be limited

t~ may not be able to take time to read it. It is well to remember that

e sketch is being made to be read' that the convenience of the reader jg

ROU ht . , sk g , not that of the sketcher; and that it is useless to put a mark on th('

etch unless that mark has a meaning which the reader will understand.

). It is desirable that the conventional signs shall picture what they

1iI~~,'eHe~tas nearly as possible, so as' to be easily interpreted; that they b<:>

t k pIe m construction, so that they may be made rapidly; that they do not

,a p too much space on the sketch; and that they be so clear as to be readily

un{l",rsto I d' 236 . o( an not be mIstaken one fOl' anothel'. .

rna' ..The adap,tation ,of the conventi,onal signs'to the size and scale of th('

, P IS accomplIshed, m part by varymg the boldness of the pen stroke, ani

~n part by wider spacing of them. The strokes never must be 50 small a:-\

o render the signs illegible and never larger than can be made easily with

: medium pen. The object is to produce a result, which. while distinct a:-\

t~ eonventional meaning, shall not be so heavy in general tone as to catch

d' ~ye. 01', what is more important in military maps, to obscure any ad-

,~~Ions which may be made. Topographical signs should be perfectly clear

en looked for, but not obtrusive.

Practice in rapid work has developed many short cuts in making ('onb

\'('ntional signs. These convey the same information as the standard signs.

ut WI fewer pencil marks, and probably greater clearness. 'th

I' It should be noted that the cross marks on a railroad, the signs in-

(Icating the different kinds of fences, the marks along a road indicatin~

\ telegraph line, and the T representing a telegraph line across countr~',

IiIlould not be put close together. This is done principally for the sake of

c earneRs, although a great deal of time is saved by it. It is. however, an

~'xcellent rule never to put a mark on a sketch, no matter how small, that

I!'Inot necessary.

A 'culvert or bridgl', less than 10 feet long, (road length) should !.>t~

represented by two V's at right angles to the road with the point of the V':,

~P?osite each other. Dimensions need not then be given as in a largt'1'

fIdge, but the material and the condition, if poor, should be noted: ~!_Hrick.

Poor," or "Wood. bad".

Roads are conventional signs, but where possible should be drawn to

'-cale. The road lines should stand out clearly and distinctly with no line<;

~r other conventional signs crossing the roads. Fence and telegraph s~'Ill-

>018 are placed on the road lines. A hedge fence may be represented by

draWing H's across one of the road lines at the same intervals as the fence,

Sbigns. Fence or hedge signs are'the only marks which eyer should app('ul'

(.tween the road lines. Stone and wood fences, may be indicated qlliekl~' in sketching by

writing in "Stone" or "Wood" alon~ a line drawn to 1'<,pl't'sent the fence; .

TOPO\CI'Bphy (or Fil'ld Artillt'I')'

'

' '

~

~

~

~
-100-

or if along a road. on the road line, with marks indicating the limits of the

stone or wood fence. A marginal note is simplest and easiest.

Signs for single trees are drawn oblong or roughly circular in shape.

They should be spaced sufficiently so as to blue print readily. It is not

necessary to show individual trees. The sign indicates trees in that locality.

Often it is better to draw a ragged border about the timbered area and

write, "Wooded" therein. .

Houses ~re represented by blocks which are made square and large

enough to be set in the roads at the scale being used. Black blocks indicate

stone. brick, or concrete houses; and hollow blocks represent frame houses.

A row of houses occupying a certain distance along a road need not be indicated individually, but house signs covering the scale distance occupied by them should be shown.

. In order to proportion the signs to the scale used, it is convenient to

make the lines that go on or along a road, of the same length as the width

of the road. This refers to such signs as those for telegraph lines, barbed

wire, cuts, fills, bridges and culverts.

A dry watercourse should be indicated by a broken line, which should

be wavy so as not to be mistaken for the trail sign; the latter being a broken

straight line. If there is a small town along the road, it is not advisable

in a road sketch to show the individual streets, alleys, and houses. A town

sign covering the area of the town. and its name, is sufficient.

Where a conventional sign or written words can not be put in at the

place desired without excessive crowding, write a (1) at that place and insert the description in a marginal note opposite a (1) on the margin. Carry

these marginal notes by serial :lumbers. On a road sketch start them at the

bottom of the margin and run up. On other sketches start at the top of tM

paper and number them down.

Break contour lines on each side of a road, or of a conventional sign,

or of an abbreviation (as a description of a bridge).

It should be remembered that a sketch, when finished, should be ready

for blue printing without tracing; therefore all signs should be dil'tinct

enough for this purpose. All lines should be firm and clear cut.

(5.) Title.

237. Every finished sketch should have a descriptive title setting forth;

(a) the character of the sketch, (b) its locality, (c) the sketcher's name and

rank, (d) its date, (e) its lin('ar scale, its contour interval and its datum

plane. fig. 72.

Titles should be adapted in size and boldness to the size and importance

of the sheet. They should be divided into lines following mainly the subdivisions given above. The middle letter of each line should fall on a line

drawn vertically through the middle of the space allotted to the title. Lines

should be alternately long and short.

Sometimes the magnetic north direction is indicated in the title section

but usually it is found in the body of the map.

(6.) Border.

238. The sketch or drawing should be encl08ed in a rectangle, preferably

with its sides Nand S, and E and W. The border consists of two parallel

'Topograph, lor Field Artil1ery'
-101-

lin~s th .' .' h

b t

e mner one medium fine the outer one medIUm heavy, WIt a space

ew ' een them equal to the heavy line, see fig. 71.

100L • I

POSITION SffETCH

Near Easton

By Capt. wm SmithlzndF:A.

DeLc.l5, 19/tJ.

scal(Z,~

611= I mi'~. ,

o 100 200 300 400 . '00 600 700 , , , , , , , , '

V1=IO'

Datum Planf1,= CrosJ roadJ at Easton

~ds

I'

I

! '

I

j

I

I

Fig. 72,

2 (7.) Lettering.

t~9. All lettering on position sketches should be written so as to read from

b e south edge. In place sketches the lettering should be so located as to

read from the sketcher's position with the sketch oriented. In outpost

:h:l<hes ~he lettering is read faeing toward the enemy. In road s~etehe"

lettermg should be made so that it may be read by anyone followmg th ..

route of the sketcher, with the sketch oriented. . As a rule names and figures relating to points on the map are madl'"

raral1el to one side. Names and figures relating to extended features, or

arge_ areas, are disposed along the feature, or across the' area, in straight

or curved lines.

t. Ornamental lettering should be avoided. A good effeet may he oh- '----

tamed by the exclusive use of capitals of various sizes. A good general rule

o follow is to use inclined letters for all names and words on the map which

lX'elateto water, and up-right letters for those which do not. See Plates

lJ.XIV. . .

'

~

~

-
' .."CIVIL

---102-

DIVISIONS' "

States, CountilZs, Townships; Capitals and,

Principal eltie" (att capitallatteis)

I

ABCDEFCHIJ

KL lVINOPQRSIf

UVWXYZ.

Towns and Villagej (With Cap /:1itials)

, dbc d efgh ij klmnopqrjtuvwxyz

}-IYI) 110GR;\P I-IY ,

Lakes ~ RiverJ and Bay3 (all cap/l.f letter:;)

AB CDEFGI-IIJ

KLMjVOPQI~S~T

Ul/WXYZ

CreeAJ} Brook.,s) SprIngs} smaiL Lakes) Ponds

MarJluz,5 and ,6/acierj (with Cap Il7itia/~

a bed rzf917tj'lt !m 17 0PC;rJluvw xyz

Plate XII.
• I'

I

-103-

HYPSOGRAPHY

Mo un tainsJPlat~au.~, L irt ~" of Ctifr"

and Canyons (altcapitat '~ttrzrJ) I

ABC D E F G H IJ K L M N 0 P Q R S T U V

WXYZ}

smaLL Vallrt ys, Canyon.5. Istands and PointJ

. .(with Cap InittatJj~ .:

ab c de f Q hij k' m n 0 p q ,-~t u v wxyz

I

I.

I

vVORl{S

Railroads, TunnczL.s, 8ridqasJ r~rrle,.s, Wa9on-roads,

TraltsJFord.J . and DamJ (capitr,!,J onLy)

A8CD£FGHIJI1LMNOPQR5TUVW x YZ

CONrroUR NU 1"1B E IlS

/2J4567890

TO(lOlCrRl'hy (0\' Fi..ld AI1.ilh.ry

I'

I'

I'

I

lVIARGINAL LETTERING

ABC DEFGHIJKLMNOPQRSTU

VWXYZ

(with Cap Initi.at,)"

a be de fQ hi j k , m n 0 par" t u v w xy z

'234567890

PlatE' XIII.

\
-104--

LETTERING

Name3 of natural land feature3, t1ertical lettering.

Name3 of natural tvater feature3, 3lanting lettering.

Thic~ne33 of letter .!. of height. 1

Slope of letter 3 parl3 of ba3e to 8 of height.

A UTHOIUZED ABBREVIATIONS

A.

abut.

A.

b.

n. S.

bot.

Br.

br.

C.

cern.

con.

cov.

Cr.

cuI.

D. S.

E.

Est.

f.

Ft.

G. S.

giro

G. M.

i.

I.

Jc.

k.p.

L.

Lat.

Ldg.

Arroyo

Abutment

Arch

Brick

Blacksmith Shop

Bottom

Branch

Bridge

Cape

Cemeter~'

Concrete

Covered

Creek

Culvert

Drug Stofe

East

Estuary

Fordable

Fort

General StOft.'

Girder

Gri~t Mill

Iron

Island

Junction

King-post

Lake

Latitude

LandinJ{

L. S. S.

L.H.

Long.

Mt.

Mts.

N.

n. f.

p.

pk.

P. O.

Pt.

q. p.

R.

It H.

KIt

S.

s.

S. H.

S. M.

Sta.

st.

str.

T. G.

Tres.

tr.

W. T.

W. W.

W.

W.

Life Saving Station

Lighthouse

Longitude

Mountain

Mountains

North

Not fordablp

Pier

Plank

Post Oflice

Point

Queen-po:-it

River

Roundholl:-;('

Railroad

South

Steel

School HOll:-iI'

Saw mill

Station

Stone

Stream

Toll Gate

Trestle

Truss

Water Tank

Waterworks

West

Wood

Platt> XIV. -
1

I-

..

-105-

ROAD SKETCHES.

A. CHARACTERISTICS.

240 : '. . . and ~?ad sketches dIffer from area sketches In that they show the natural

Th mlht~ry features on and in the immediate vicinity of the road onl)'.

ey consIst of simple traverses that follow the direction taken by the road.

rn In drawing road sketches speed must be acquired as they should be

24;de at a rate of 2! miles an hour if dismounted, or 3 to 5 miles if mounted.

Th' Road sketches commonly are made on a scale of 3 inches to the mile.

r e sketcher should familiarize himself with a few of the common and

)

requently used units of measure so that he will not have to apply his scale

gra mg every detail on the map. He should, with practice, learn the n loc t' .

t phIcal representations of 100 and 200 yds., and the :M. D. (between conO~u1'ls),for 10, 30, and 50 slopes. He should practice estimating the degree:;;

rn

s .ope of varied terrain, checking against the reading~f an accurate instruent I thO .' h . t' . n IS way the sketcher can locate accurately and ~peedlly t e pOSItIon ,of buildings, streams. railroads, etc. on the map. He also will be able

o gIVe a better idea of slopes of the adjoining terrain.

B. TECHNIQUE.

2 . (1.) Method Of Sketching.

a~.2. The sketcher must provide himself with the following: sketching board,

p~~a~e (or triangular ruler), slope measuring instrument (or slopeboard),

cds and erasers, compass, working and slope scales. These latter two

scales should be pasted on the alidade for" convenience. The board may be

~ounted upon a tripod (becoming a plane-table) if desired. .

~' Proceed to the place of beginning, and set up the plane table, or. if

~Stng a board, set it on a fence post, stone, or on the ground. Place the

;a1'd so the general direction to be taken will correspond with the long side

o the board. Place the compass on the board and draw a line, in one comer

of the paper, parallel to the needle. Mark this line to indicate the magnetic

north. This mark or arrow can then be used for orientation.

. Having indicated the magnetic north. place a dot on the paper to "--

~'e'p1'esent the point of beginning. Insert a needle in this dot. Place the

altdade again~t the needle and in the direction of traverse. Sight along th'.!

ed~e of the alidade toward the point at which the next set-up will be made, #

U~tng the needle as a pivot, and swing the alidade until it is in direct lin<>

WIth the direction to be taken (without disturbing the original position of

~he board). Steady the alidade and draw a light ray in the new direction.

)[1;. 73. Measure the slope to the new point. Note all features in the vicinit~.,

I lace them on the sketch and then proceed to the new point just sighted.

, Again set up the plane table. Measure off, on the ray ju~t drawn, thl'

'~Istance. just traversed, orient .the board by backsighting 01' with compas~.

I lace the needle in the new point, swing the alidade in the new direction tl

he taken, and proceed as from the beginning.

Continue until the entire road distance has been covered, using tlw

Hume methods. Check the orientation frequently with the compass.

At each new set-up, after the first, all the data observed, noted 01'

meal,mr('d, will be indicated on the sketch; and contours will be drawn in

I

'

~

"
-106-

where they cross the road, as well as in the vicinity of the road. I'~speei81

attention must be given to noting' all details that have military value.

Maq,\

l~orth t

o

Fig. 73.

Time must not be wasted in actually pacing distances to buildings 011'

the road or in measuring the distance between them. Nor must time bc

~pcnt in measuring the exact size of cultivated fields, nor the distance that

streams, telephone or telegraph line!'! are from the road. Estimate th<:':-!C

distances and locate their positions approximately.

Points of importance. such as hills, villages, etc. will be located by intersection as the traverse proceeds. If their location is beyond the limits

or the sketch their direction will be indicated.

A more rapid method of making a road l'ketch is to run the tI'aVel'S(~'

entirely with the compass needle. In all lo\ketches the needle should IH\ tlsl"l

as a check to prevent gross errors of orientation.

T .... OlCrRl'hy for Jo'ield Artillery
"':-101-

(2.) Lateral Limits To Be Considered.

h he lateral limits of a road sketch are, perforce, limited to what call 2H. T

e seen readily from the road. The limits usually considered are 400 yard~

On each side.

Ill' . The lateIaI limits extend beyond this only ~hen the additional inforth:tJ.on has a military value, and then only the salient points are drawn in,

Intervening details being omitted in whole or in part. ,

')t (3.) Information To Be Included .

.. 5: A road sketch should be so complete that the military commander can

liCe at 1 . f d it' . a g ance all features of value. He must be able to tell the kmd 0 roa ;

b ,s ,slop.e and practicability for his troops; if the road is fenced; if flanked

/ cUltlVated fields and if they are fenced. also the type of fence; if there

J r? WOOdsnear the road, or other cover and concealment; if hills or high :;lnt~of observation are visible; if there is cover so tltat infantry can fire

ti ectlVely on troops on the road (effective range 600 yds.); if artillery posi;'

lions are within view (this may include up to several miles); if there are

l~es of communication, villages, buildings, water for men and animals along

t ,e route; if the ground is level on both sides of the road; the location and

o~pe of buildings. In short all information of military value must be shown

n a road sketch. Minor and unimportant details should be omitted to avoid

l.'onfusion and to save time.

Topol{raphy for Field Al1.iI1ery

'
CHAPTER XII.

ROAD REPORT.

s INFORMATION TO BE INCLUDED.

246. A road report is a series of notes taken successively and compiled into

one report covering the route traveled. It contains only the essential information gathered en route, information that will enable the person into

whose hands it is placed to determine the feasibility of that route.

247. A road report will indicate: the direction traveled; the distance between successive points on the road or between important features on eithe:

side of the road; the slopes of the road, together with the condition and tM

practicability of these slopes; oridges, giving character. condition and capacity; fords, their depth and condition; the terrain on both sides of the road

in so far as of military value, such as battery positions, observation posts.

hills. streams, wood, cover, detUade; all roads crossing or branching trOIlJ

the route traveled, including the direction of these other roads and the towni'i

or points to which they lead; watering places; telephone or telegraph linE'li;

railroads, crossing or paralleling the road.

248. For accuracy, directions should be expressed in magnetic bearingI"

However if the time is limited, or if there are long stretches of road, the

general direction may be given, as N (north) or SE (south east), etc.

249. Distance is expressed in yards. meters, strides (exceptionally), or

(preferably) by the time in minutes elapsed when traveling between adjacent

points on the road. The revolutions of a wagon wheel. 01' the readings of

a speedometer of a bicycle or motor car may be used to measure the distance.

If the time scale is used note must be made as to whether the time is to!'.

a man mounted or dismounted, and if mounted the record must show it the

travel was at a walk or at a trot.

METHOD OF PROCEDUUE.

250. A wrist pad or small note book is a convenient thing in which to make

the notes for a road report. The large form may be used although it will

prove rather cumbersome if th~ scout is mounted. If the small note book

is used all the data may be transferred to the regular form for road report:'!

at the end of the route. This latter method will prove of advantage as datu

carried in the memory also may be entered. The use of a pocket compass i:-1

essential.

251. A road I'eport reads from the bottom upward. Therefore it is made in

the same manner.

At the point of beginning note the important features on each side of

the road. measure the slope of the road in the direction to be taken and record.

Proceed forward, noting the time elapsed between different points, or the

distance traveled. Note each important feature as passed, placing it on it:o!

respective side of the road, giving the direction and approximate distanc(~
-109-

from r e road. At each change in the slope of the route, read the slope anrl th

t ecord. Also as each change in direction is made note the distance just

ara~eled and the new direction to be taken. Minor changes in direction in

WInding d . . lb' .

fi

roa are not recorded the general dIrectIOn on y, emg gIVen, see

g. 74. •

~~i~~

~~_I9IIAOt'N.1/F'.I)...._-

. ~2-Obuf.~ _~'.L~ e.//I-

~U~-a:# ;Jr$.T£mJr:.FJ?~£). .._.---

1l~AE. REPORT, from: hH_bv~~dpri:LJf!UJ!U#L/d4I1Ln;r 'p~Af) ..

.__ to~~ad ;'drJ'-~ir.r-.h--AJI/AO/)J!.-ELE2 .... ,.-- -.---

l?~;I:p~i~al d •• "'r,tlon of road.. railroad.. GraphIcal ~tion or roada. raIlroad ..

::..~~~~.~orto~:"~~i1~~:,~a~':;i~~~: ::~~~~ to~-~~h=!'~~ .. remark.. ..--roado. ..mar\<. LEFT HIGHT

Fig. 74.

Topolfraphy for Field Artillery
-110-

Sp('ed il' el'~ential; hence the scout, 01' the ~tuuent, should avo'id filljn~

up his' report with non-essential information and minol' tJetaik nrevity anI

darity always are to be sough4:, . J

When the entire route is completed the total distance tl'aveled is notel

Road 5,fl!"«h

.5az/~~"'-lml/.

Fig. 75.
/

I '

j

1

-111-

at ~h e top of the report. th If more than one sheet be used, the total of each

. (let is noted, and the grand total is indicated on the last sheet. •

Figure 74 gives a sample report.

~IAKI NG A ROAD SI{ETCH FROM A HOAD REPORT OR VICE VERSA.

252. A'" h. d' t'

I

'}' road sketch can be made readily from a road report; t e Irec lOm~

d e( on the report being laid off with a protractor, dIstances emg n( lcat I " . b •

fawn to scale, and all details being filled in by means of conventional sign::..

a

Contours drawn in on the sketch and representing the road slope will

of WIth those of the report .. However as slopes to one side or the othe\' gl'ce .

t t~e road are indicated only roughly and by estimation, or by ro?gh con.

mOUting th . I I . t on e road report, the transferred ground forms wI1 on y approxl25~ e t~ose of the actual terrain on either side of the road.

fl" rhe same method, reversed will enable the making of a road report

f om a road sketch. In preparing the report, distances will be measured

o;om the .sketch with a reading scale, and transferred (0 the report in terms

m ~~rd8 or meters. Directions will be measured and noted as bearings. In

t ; mg a road report from a road sketch it is well to avoid unnecessar~' de.

al s, just as necessary, in fact, as if actually traveling over the road.

p Figure 75 gives a road sketch made from the road report given in the

J'(l('('ding figure.

ropogravhy for .1 ..IJ Artillery

j
CHAPTER XIII.

PANORAl\IIC SI{ETCHES.

CIIARACTEIUSTICS.

254. A panoramic sketch is not a land-scape sketch. It has been called

a vertical map, but it is more than a map. In addition it is a military record

containing information of value to the higher commander and also data for

use by the officer conducting fire.

255. Every artillery officer is familiar with the term "Reconnaissance and

Occupation of a Position". Customarily, however, the officer thinks of the

,reconnaissance and occupation of a position chiefly with respect to his own

position. whereas it is just as important that he reconnoiter and familiarize

himself with the enemy position, (in the sense that he secure the same

information that the enemy has). This last is absolutely necessary if the .

./ officer is to make an intelligent estimate of the situation. In fact it is n

fundamental of military operations that he, who would outguess the enemy,

must place himself in the enemy's fosition and reason from the same prem.

ises adopted by the enemy.' Hence the need of the reconnaissance of the

enemy's position, so far as is possible from a distance. This absentee occupa.

tion of the enemy position may be accomplished by systematic observation

of the hostile terrain and of the enemy's movements, and by the careful

I'ecol'ding of the data thus obtained! Here it is that the panoramic sketch

pla~rs its part, the sketch being part of the attempt to occupy the enemy'l'l

position.

256. The meaning of the above may be illustrated better by citing a simple

instance at certain field maneuvers. In the middle distance. as seen from

the friendly O.P., was a ridge. Beyond the first ridge was a second one con.

tainir.g a notch appearing about on a level with the top of the first ridge,

see fig. 76. At a certain hour the officer in charge of the O. P. noted the

I..~

~ .# rt$ 9. . i'.~~~ ~~.;y.f ->:,' ~.~ ~~, A..~~-r

t-. "'0 J...'Vr "'d.tA..'V:~.n c,.; !::>...Q/ ..... -'t',..y/ ~!:~ .t] ~/ iSOl.,.~ ~ClI")7 cf~~Oi~~~o..~

Jo J 90 I ." 1 1 1'1 r

~I~

TOP<>lCravh,. for .1eld Artillery

~ . ~

~~ ~ ~ ~ ~ ~ ~ ~

~~ ~ ~
I

I

I

,

I

I

L

-113-

~~vem~nt of an enemy battery in the notch of the second ridge, but ~he

th mp~e was so brief and the visibility so poor that he could not determme

e dIrection of the movement. A study of the map indicated that there

. ere suitable battery positions for the enemy both in front and behind the

second 'd th k t h but 1'1 ge, He noted the appearance of the fleeting target on e s e c

th Was unable to record any definite data for the target. Shortly afterwal i

th e heads and shoulders of two men were noted on the hill to the left of

1 e notch and the officer concluded that the enemy observation post was. to

,:e ~ocated on that height, As ~ret he had nothing to indicate the battery

t'osltion, .

p Sometin;e later in the m~rning the observer saw a dismounted man

• t~~ceed up the hill to the right of the notch. He drew the line of trave~ on,

\V sketch from the point of first appearance to the point where the ridge

inas. crossed, and noted the time. Immediately afterward a horseman came

ThSIght more to the right and rode in a diagonal direclion up the same hill.

l< e facts were again noted on the sketch. Then, taking his map. the ob-

'acr;er plotted the lines of travel of the horseman and the dismounted soldier

,n, prolonged them until they intersected in the valley in front of the

I'second 'd 1'1 get The observer reasoned that the intersection of t ese wo h t

,~es was the battery position of the enemy. Accordingly he prepared a

\ etch showing the enemy position, and O. P., which, with the panoramic

lo; .etch, was furnished his commanding officer. The observer was credited

\~Ith a solution of the problem. for the enemy battery was located as he had

th • n . and zone fire in the area indicated would, undoubtedly, have SIlence leaso cd d

.~".e enemy guns.

...)7. As just indicated the function of the panoramic sketch is to supplelllent the topographical map, to aid in the' identification of objects on the

~ap, to furnish information of the situation within the enem)' Jines, and j

so to provide data for the artillery. So detailed and exact should this in- ,J

fiormation be that the battery commander may rely on the sketch and open

re without using any other data.

')_ ... TYPES OF SKETCHES.

..,)8. The panoramic sketch may be made in a few minutes by one of thp.

~couts in warfare of movement; or it may be made by a scout or other ob- "--

• ~erver from a permanent observation post, in warfare of position, in whic~l

~aRe an abundance of time will be available. Whoever makes the sketch must

h:ar in mind that the sketch is to be used by another person, either by the.'

. 19her commander in his study of the sector or by the battery commander

In his conduct of fire; hence certain fundamentals as to identification, infor-

~ation and technique must be observed. .'

..,)9. The type of sketch ,that is to be made will depend upon the timp./

f'lement. In so called "open warfare", time is likely to be the all imPortant element, since the sketch must be available by the time the batter)'

COmmander is ready to open fire; hence rapid methods of calibration of the

Paper with regard to the landscape will be employed. In warfare of position

. t he f1ketcher will use instruments in making measurements of all deflections

and of all angles of site and will, accurately, place the points 1'0 mea.~ured

on the paper. according to some adopted horizontal and vertical Fcale. Such

a ~k('tch will h<>almo~t photographic in it~ exactness. TOJlO!Crlll)hy (01' FI«>ld AI1 illf"').

'

""

'

' -

~

~

"
,\

-114-

260. The French make a distinction between the sketch made deliberatel~'

with exact instruments and covering all of the terrain visible from a give.n

O. P., and the sketch made by the scout during the reconnaissance of a pmw

tion. The former is called the panorama. The latter is known as the pcr-

~pective sketch. The American service makes no such distinction in nomendature. for there really is no distinction, one sketch grading into the other

according to the time employed on it. The blank sheets 'furnished th;

l'ketcher by the field artillery, fig. 77, may be used for either type 0

,.,ketch. The:"e sheets contain a series of parallel vertical lines and a sedelof parallel horizontal lines. By adopting a certain scale for the space between the vertical lines; e. g., 100 mils, it will be possible to make aserit'l'

of sketches all to one scale, which, when pasted together end to end, will

~ive the sketcher a complete panorama. On the other hand the lines on the.

paper lend themselves to the more hurried methods of calibration as will be

f'xplained later.

ESSENTIALS.

J 261. Wbat are the esst.>ntialli of a good panoramic skt.>h'h? There are tw.o

which stand out with particular prominence; first, clearness of identification;

.:econd, information furnished. Accuracy is another essential. Dl'awin14

I'anks last in the list.

A. IDE~TIFICATION.

262. As to the matter of identification. the sketcher must remember that,

if the person using his sketch cannot identify the terrain represented, then

"'is work is valueless. Hence the sk~tcher must neglect nothing that will

add to the ('ase of identification. Of course the horizon line is likely to bl'

t he greatest aid to identification of the sector and hence should not be omitted

although the objects thereon may he far out of artiller~' rangc. Objects ill

the mid-distance and fore-ground also should be included when they will ai.1

in this step although they may have no particular milital'y value. Lustlr

the data to be ('ntered at the bottom of the page. showing the place when'.

t he sketch was made and indicating the orientation, are el'sential to the ide'!ltification of the Sf'ctor.

B. INFOR.MATION.

J ::6:1. Of' course the object of the sketch is to ('onvey information. 11('1)('1',

although the sketch may be a work of art; and although the one whopi('h~

it up may have no difficulty in identifying the sector; if that sketch (Ioes not

('ontain military information, and, in particulal', information of use to thL'

artillery officer, t.he skE'tch is valuelesl' and the sk('tch('I' mi~~ht lI('tt(,), not

han' wasted his time on it.

:W.J. That the information fllrni~h('d fiholiid ht, ac('urnl(' is sdf lo\'i,lt'nt,

oth('rwi:--e the l'ketch loses much of its value.

C. DI:A WING.

26:). While drawing is not 80 important as some other thing'S in sketching,

the oflic('r mu:-t rE'mE'mher certain fundamentals. First. the sketch must he

dear to the point of baren('l's. That is, the important features mUi't be elllpha~ized at the ('xI)('nsc of the unimportant. In oth('r words th(' sk('tch he'

T....o~rRI.h). for Fi•.ld At1 ill....y
I

~N l":

()l l115-

~----------~

.--:.... -

'----- . ~\ ~:

g

:z:

1--

CII .. .. .. lU

m

.I:

Q !

. ;

--- A Z

t

Vl

.,.A t:

~.;:;

---- .., ~'- u .... ""'-

.~!i ,,-

~...,

..-d~

4i

l' ~- p: ::1 c: . o ;3

~.~

.t.,.E;

v

ell

..... X

V)

---- 1

"- 1

~-~ ._) (--~, --)-

~:....~

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ra. Q a: :t A Q Vi :.: ~'q"

............ .t -<- '"N ,

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I- ~

~

~

~

~

~

~

~

~ ~

~ ~

~~

~

~~

~

~

~~

~~ ~
I

(2.) Consecutiv(' Cr('st Lines.

J 272. The effect of distance can be given in a mechanical way by varying

t he weight of line. Since objects seen close at hand are large anlt cleal'

and decrease in size and clearness as they t'ecede from the otll'ierveJ', this

principle must be applied to sketching. The near('l"lt f('atul'e~ must he tht'

J

-116-

''/comes a caricatur~ of the landscape. Hence it is just as important to know

what to leave out as it is what to put in. Whatever is done the sketcher

must not attempt to show the sector by a mass of shading such as would

be employed by the ordinary sketcher. Such a procedure will hide essential

details rather than emphasize them. The fewer lines that can be used to

convey the desired idea, the better it is.

266. However, the subject of drawing need not prove troublesome. AnY

man who can handle a pencil well enough to make a map or area sketch can

make a satisfactory panoramic sketch. regardless of whether or not he has

any of the instincts of an artist. More often than. not he will make a more

valuable sketch than the trained artist because he will not be tempted to

make a pretty picture and so hide military information.

267. Since the sketch must enable the user to identify the l'ieetol' quickly,

it should convey to the eye a rough picture of the terrain as it actually j:;

:-;een. To secure this picture a few technical devices should be employed.

/ (1.) Perspective. System Of Parallel Lines.

268. First of these technical devices is the principle of perspective. Thi~

jg a means of making use of the fact that distance to the eye is indicated

by the angle which an object of given height subtends at the eye. The

g-reater the distance the smaller the angle and hence the smaller the object

appears to the eye. Thus a row of objects of a given height extending into

the distance apparently will grow smaller as the distance becomes greater

lilltil they finall~' vani~h into a point on the horizon. In order to get tM

same effect of distance or depth in a sketch, the following principles of

perspective should be applied.

269. (a) Any system of parallel horizontal lines in a plane not parallel

to the plane of the observer, tend~ to come togeth('r or vanish at a point on

1 he horizon, called the vanishing point. Such a system of lines is shown in

f.g. 78. The lines of the house which are parallel and which fulfill the con'

(~itions enumerated, if prolonged, will meet in vanishing points, VI'" and VP.,

on the horizon. I

Perhaps the commonest example of vanishing of parallel lines is to be

found in the track of a railroad, a line of telegraph poles or the sides of a

I'oad. as indicated in fig. 79.

J 270. (b) Any s)'stem of vertical parallel Hnes no matter in what 1)lane.

J will remain parallel. In fig. 78 all vertical pamllel lines remain parallel.

271. (c) Any system of parallt'1 lines not horizontal, in a plane not parallel

to the plane of the observer. vanish in a point above or below the horizon.

J n fig. 80 the lines joining the top and bottom of the picket fence form the

l'Iystem of parallel lines fulfilling the above conditions. The section of the

fence AD, is inclined downward and hence would vanish at VP~, below the

horizon. The section ne, being inclined upward, vanishes at VI'. ahove the

horizon.

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(5.) Shading. J

~?7. The tendency of the average sketcher, upon completion of his sketch.

Is to attempt to add to the general artistic effect by introducing shading of

various descriptions. This course cannot be too strongly criticised. for the

only result accomplished is to. detract seriously from the cleameRs of the

Work. It should be borne in mind that the panoramic sketch iR not a landficape drawing, but is a skeleton chart, devoid of ever~-thing of no military

value, in which clearness is one of the prime essentials sought. Therefore,

unless the sketcher is thoroughly familiar with shading 'and its ul'le. it shoulti

be eliminated.

..-,121-

~rgcst and the heaviest of line, while they should become smaller and

;:hter of line until the sky line is reached, which must be the faintest of all.

th3. Figure 81 illustrates this principle. The successive crests recede from

e Observer in the order A, B,' C, D.

d The crest A tberefore, should be the heaviest line, and the lines should

t;crease in intensity to the horizon D, which should be the faintest line. in

d e sketch. The road. following this principle and the principle of perspccbve,

ecreases in weight and tends to vanish in a point during its successive

.meanders. No lines should be so faint as to be indistinguishable.

27 . (3.) Broken Lines. .

fi f. Dy refraining from actually joining intersecting crest lines, as A:, v

\ t g. 81, a further technical means is employed of giving the effect of deptn

. the sketch. This gives the effect of haze found on distant slopes.

2 (4.) Ground Slopes And Form1

. n75. One of the fundamental requirements of a good sketch being clearI;:s, it is essential that all useless details be omitted. On the ?t.her h~n,1

general slopes and configurations of the ground are of mIlitary ImPortance and the question arises as to how to show this ground form with

~~t detracting from the elearness of the sketch. This is effected by using.l

t c natural and artificial features that exist on the ground, drawn to conform

.,~ the principles of perspective. .

~h:' In figure 82 the ,position and shape of the road indicates a rise ovel'

crest in the foreground, a gentle downward slope to the turn. and finally

a gradual rise to the crest, where it disappears. The telegraph line brings

out the same facts as does the line of single trees.' The features represented

:;e of military importance and therefore must be shown, but, by means of

. cse features the configuration of the ground also. is indicated without

. ;ntroducing useless lines or detracting from the.clearness of the drawing .

.n the same way the form of the hills is brought out by a few lines flowing

In the direction of slope. In the case of the wooded hill the lines are short

~nd' irregular, representing the tops of trees, while in the bare hill the

In:s are smoother. The necessity for showing the form of these hills arises

prImarily for easy identification and from the fact that targets, reference'-----

hOi~ts,. ctc., may be located in a particular position on the hills which can

e mdlcated only from their relation to the ground conformation. If the

dlraw~ng of a wooded hill is difficult, smooth lines may be used and the hill

aheled, "Wooded".

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-123.-

n~ . n'h Shadmg is, however essential for one purpose; namely, contrast. J ilU • 1 IS YV en 't .' necessary to distinguish between features that are adjacent or .

perImposed. simple shading is permissible and should be used.

and' In fig. 83 the consecutive groups of trees are partiallY superimposed:

'hn ;n order to distinguish them quickly, alternate groups are shaded bj'

it aPte parallel lines. Thus groups, A, D, C are quickly distinguished ami

indo arget should be located in or between these grOUPS this faet could be

fiel~cate? clearly. When it is necessary to distinguish adjacent cultiva.ted

Ob' s, sImple horizontal shading should be used in checker-board fashIOn.

Jects of military importance c~m thus be clearly located in field E or F.

279 . (6.) Conventional Signs.

Foi' Smce simplicity and clearness is the key-note of a good sketch, the

b;Plest possible symbols to represent natural and artificial features should

('as~sed. Fo: this reason conventional symbols or si~s are used tha~ are

tif I Y and qUIckly made, and which, by slight variations. represent and. Iden.

F Y features found in any given locality. One consideration should govern.

toOl'the purpose of rapid identification of features depicted, it is necessary

n

make the conventional signs look as much like the features they represent

(s Possible.

Fig. 84.

280. .' , . lor example, fig. 84 (a), IS a group of pure conventIOnal sIgns repre. . . .

"en~l~g from left to right, a tree, a house. a church and tree in their relative

rfoSIt.1on. They tell nothing of the actual appearance of those objects, and

b t?IS group were closeloy related to other groups of similar objects it would

r~ Impossible to identify it. By making these conventional sigus more nearly

I e the particular objects they represent, still keeping them equally simple, "'---

1\ result such as in fig. 84 (b), is obtained. The group now emerges from the

reneral to the particular; identification is assured. and yet the sketch has

20Sst nothing in simplicity or clearness. . 1. Possibly the features most commonly met in a landscape are tree

groups. They should be represented by an irregular line for the tops and

lnore or less straight line for the near edge, shaded or not, as required, a:;

In fig. 85. Care should be taken to make the irregular line very irregular

Fig.' 85.

lo prevent its confusion with the lines of the sketch such as hills, crest lines,

etc. "

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282. l....igure 86 illustrates in a conventional way so~e of the most commotl

. features. No attempt should be made to draw accurately villages or clost

groups of houses. It is sufficient to indicate a general outline showing very

simply the trend of the roofs. Different kinds of trees f;hould be shown

where necessary to aid identification.

METHOD OF PUOCEDURE.

283. The inexperienced sketcher examining a landscape .is confused by tht>.

mass of details that meet his eye. Important and unimportant features' art

so numerous and mixed together that it seems a hopeless task to pick o~t

j and recognize the simple frame-work on which the whole is built. It IS

necessary, therefore, that the eye be trained to separate a landscape into it.'!

main mass groups, disregarding details, and bounding these masses by singlt>

Jines so that the relative position and size of the masses, both verticaJl)'

and horizontally, shall form the frame work of the whole. The lines bounding hills, mountains. crests, and tree groups, and their intersections with

each other, form such mass groups; and once having recognized these maW

boundary Jines, and having plotted them in their relative horizontal anti

vertical I'elation, the sketcher has a frame work that is complete, after which

important details may be inserted quickly in their correct positions. A simpJ~

method of recognizing these mass groups is to half close the eyes and examine the countQ', when these groups will become immediately apparent,

A. EQUIPMENT.

that the sk(-tcher })p f'quipped with tlw following 281. It is nf>cessary

articl('s:

1.

2.

3.

4.

5,

Compass.

Field Glasses,

B. C. Ruler.

Penknife.

1 medium hard (2h) and 1 medium soft ~b) pencil. Colored pencils may be used.

6. Eraser. .

7. A map of the terrain to be sketched, from which the names of

villages, destination of roads. and railway lines, names of rivers, stream.;

'PruJ mOl,mtains may be obtained, and ranges to prominent features measured

by scalirfg, .

8. Sketching pad of smooth paper. This paper preferably should b<> •

ruled in faint lines in some convenient manner as a guide' and aid to the

",ketcher.

J The first step necessary is to determine, by actual inspet'tion, the limit~

(If the sector. If the sector has been plotted on a map previously it is necessary for the sketcher to orient himself and determine the sector limits accuratel~' from the map, Having located the Jimits of the sector, the sketcher

j m('asures it with a B. C. ruler, or some other instrument for measurin~

horizontal angles. Since the panoramic 8ketch is drawn to a definite horizontal s('&le it is n('('('f;sary to determine this scale before proceeding. TIll'

artillerr sketching pad is divided into eight vertical zones be(ween the two

limiting nrtical lines. Hence, if the Sf'ctor measures 800 mils, the distanct.

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between any two adjacent vertical lines, will represent 100 mils; if the sect~

is 400 mils, the distance between adjacent vertical lines will represent (

mils, etc. For a pad ruled in an~r similar convenient manner the scale 0

the sketch ma~' be determined.

B. IDENTIFICATION OF THE SKETCHER'S POSITION AND THIo:

ORIENTATION OF THE SKETCH.

285. It is essential that this be done immediately, for the important reasol1 ,

that unless this information is shown, the sketch is of slight value to anyoll"

else attempting to use it. I

J Casualties among sketchers and observers are fre(IUent and it shoult

be mandatory on all sketchers to complete these data, as soon as the sector

to be sketched has been determined. The sketch thus becomes valuable at

once to others as soon as any military information appears on it, and !"'

creases in value in proportion to the completeness and accuracy of this )11'

formation.

286. Just as a map must, in order to make it of any value, have indicated

upon it the points of the compass, so must a panoramic sketch have so)111'

indication of direction. In the latter case this indication is only an appro~'

imation and serves more for identification of the count1'y than a corret"t

designation of direction.

287. An examination of fig. 77 will show that, at the bottom of the sketch,

and opposite the word,:'Place", there is a cross mark on the center vertical

ruled line. It is through this mark that the arrow indicating the magn~t!('

north is drawn. Its direction is determined in the following manner.

As shown in fig. 87 turn the sketching pad into a horizontal positioll.

Sight along any vertical line at or near the center until this line, if pro'

longed, will pass through the exact point on the landscape th,'ough which

it passes in the sketch. The sketch is now oriented.

Holding the pad in this position place a compass on it and allow the

needle to come to rest.

Through the cross-mark on the center vertical line dt'aw an al'1'O\\

parall~1 to the compass needle. Note, in the spaces indicated, the place front

which the sketch is made. the name of the !"ketcher, date, w('ather, us ft"

~ards visibility, and the hour of the day. C

288. This last is important as the visibility changes from day to day an(1

from hour to hour, hence, unless indicated, an officer who was using a sketch

of a particular sector might imagine that he was in the wrong area unlel".~

he knew that the conditions of visibility had changed. If time permits a

sketcher may choose the hour of the day when the visibility is best for thl' .

area before him. Thus the early morning is best for a sector to the eu:-t

while f,hadows of late afternoon will servc to hring out SUc('cs:-;ive ridgel'l in

an arca to the west.

C. ANALYSIS OF THE SECTOR

289. Before proceeding further. ('xamin(' the 8('dor with and without gla:-'

se1'1. The ground should be stuuied in an efTort to get a clear mental picture

of its formation and to separate it into its fundamental maSH groups; thl'

foreground mass or dcfilading scr('en, l'uccessive Cl'('sts, the background or

T"""lCra"hy (nt" Fi•.,,, AI1ilJ•.,"y
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-128-

horizon. Glasses often will disclose crests, hollows, etc., capable of hiding'

targets which otherwise might be overlooked. A little study will separate ,

the important fn)m the unimportant details and the sketcher then is read)"

to proceed, along definitely thought-out lines, to conform to the object of the

l"ketch.

D. SELECTION OF REFERENCE POINT AND HORIZONTAL

CONTROL.

290. In order to make the horizontal scale of practical \Yalue, an origin of'

horizontal measurement must be selected from the terrain and mUlSt be plot~

ted and indicated on the sketch. A sketch without a clearly indicated reference point is more useless than a map without means of indicating direc' .

tion. The reference point mayor may not be in the sector included by the

sketch. It should preferably, if possible, be in the sector, but owing to the

fact that the reference point must be a distinct, easily identified point, it is

possible that a given sector may be devoid of any point that could fulfin .

these conditions. In this case such a point should be selected as close to

either limit of the sector as possible and an arrow should be drawn im~

mediately above the sketch pointing in the direction of this reference point.

and should be so labelled. The point selected should further be described

briefly as, Reference point, lone pine tree on skY-line", etc. Under normal

('onditions a suitable point can be chosen in the sector and indicated directly

on the sketch. Since it is the origin of horizontal measurements, its angular

(:esignation will be 'zero, a fact which further identifies it .

. 291. In . the selection of a reference "'Point, the following consideration~

. should govern: (a) it should be easily seen and identified even under un'

favorable conditions of visibility, hence, not too far away (as a distan'

mountain-peak on the horizon); (b) it should be of such a character that it

('annot be entirely destroyed by artillery fire.

Owing to the prevalence of conditions of poor visibility, especially

(:uring the winter months, in western Europe, the most suitable reference

points during the late war were found in the middle distance, and preferably,

\ features of the terrain, such as; a small hill of distinctive shape, a welI-M'

fined cross-roads or road fork,' the point where a road crossed a crest, or

the intersection of a stream with a road or railroad, etc. These were found

to satisfy all conditions better than houses, towers, chimneys, trees or di~'

tant mountains.

292. By means of the plotted reference point and the vertical guide linelf, ,

a basis of horizontal control is established. By actually measuring with the

mil ruler the horizontal deflection of important points from the reference

point, these points may be plotted horizontally on the sketch in their trup

relation.

In fig. 88 the farm is 200 mils from the reference point; the intersection of crests, A, is 110 mils, the peak, C, is 300 mils, etc.

E. VEUTICAL CONTUOL.

293. Vertical control, while not so important as the horizontal must be

considered by the sketcher if he would avoid distortion'. Thus, unless Borne

line of vertical control is adopted a sketcher often will enlarge the vertic~1

TOJJOgral,hy (or l"ield Artillery

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scale of one side of his sketch, due to the amount of detail which appeaJ1'

there. while the other side, being without military features, may be co~'

pressed. Usually it is customary for the sketcher who is not using Instruments to choose a vertical control line to which he will refer all other

<>levations, the reference being wholly by eye. Since the sketcher is concerned chiefly with military features at mid-artillery range. it is customary to

choose a line at about the level of the eye and at mid-distance, such as tM

top of a prominent ridge, the top or bottom of a line of trees, as line AD.

figures 89, 90, 91.

~94. In choosing the vertical control line for the sheet it is well to remember that the targets at artillery ranges are the ones with which the artiller).'

man is concerned and hence this line should be placed so as to leave the

greater part of the area of the sheet for the showing of these mid distance!'-

To properly portray the various horizontal lines of the ordinary terrain and

the mass of detail, a certain amount of exaggeration of the vertical relationfl

is desirable. otherwise successive crest and tree lines will be so crowded all

to make the picture obscure. Ordinarily the sketcher who has adopted fl

vertical control line need not concern himself with the need of exaggeration.

since he will, unconsciously, exaggerate in the course of his drawing.

If, however, the sketch is to be a true panorama in which the site of

each target is desired. the vertical relations of the several points to be

noted may be obtained and the p.>ints plotted on the sheet in their proper

relation according to a determined vertical scale. Some schools advocate

a vertical exaggeration of two to one. This amount is excessive and tbe

sketcher should be cautioned against too great an exaggeration, lest b~

. make his sketch grotesque and add to the difficulty of identification.

F. DRAWING IN FRAMEWORK. A COMPARISON OF METHODS.

295. With the horizontal and vertical control established, there are tW(I

methods of drawing in the framework of the sketch.

Assume that fig. 90 shows the terrain in which the sector occurs and

that the points represented under the arrow-heads indicate the limits of

the sector.

By measurement it is found that the sector is 800 mils in widt'h

and consequently the distance between vertical lines on the pad will represent 100 mils. The reference point indicated in the figure is selected because it is a sharply and clearly defined point. Horizontal control is now

established.

For vertical control, the horizontal line established by the crest

and tree line All, gives a well marked base line. and since this line runs approximately through the center of the sector, the center horizontal line of

the pad will represent it.

Figure 91 shows only that part of the ruled sketching pnd within

which the sketch must be drawn both vertically and horizontally.

(1.) First Method.

296. This method consists simply of plotting a few impol'tant or critical

points by means of the horizontal and verticnl control. With these point:'

established, the framework can then be drawn in through them by referencf'

to the terrain.

TOpOgraphy tor Field Artillel7

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Be t Since the reference point is slightly to the left of the center of the

c or 't . 'u h I. IS plotted sHghtly to the left of the center of the sketch, and at it: .helght ahove the Hne Ail as the eye estimates it to be above the /

8Uagmary line AD in: the sector. This point must be plotted first. By meath rement the chimney of the house is found to he 100 mils to the right of

Ue. reference point. It is also sHghtly below the imaginary Hne Ail, fig. 90.

ri s~g the pre-determined scale of the sketch, measure off 100 mils to the

thg t of the plotted reference point, and, moving vertically downward below

Ii e hne A il. plot in the location of the chimney such a distance below thi,

pn~ as to be relatively correct, fig. 91. In a similar manner, enough critical

.t~Ints are plotted to the right and left of the reference point to estabHsh

bye framework of the sketch. A few such points are indicated jn fig. 91

h crosses. Typical critical points are crests of hills. intersections of crests,

pI t Iml mg pomts of roads, Hmits of tree groupS, etc. Through these OUses l' 't' .

o ted points draw the outline of the terrain.

Th' 8t IS method is the most accurate but'is slow on account of the conthant necessity of identifying the plotted points with the points in the terrain

ey actually represent.

(2.) Second Method.

~97. lly holding the sketching pad vertically in front of the eye and looking

t;er the top of the pad at the landscape, and at the same time moving

I' e. ~ad to or from the eye, a point will be reached at which the two

,nYlIb.ngvertical Hnes of the pad will intersect. if prolonged, the correspond- tg hmits of the sector. Figure 92 shows the pad in this position for the

d

andscape and sector shown in fig. 90. Holding the pad here the sketcher

sk s. m raw . l' h 19 tly, in the one inch space at the extreme top of the sheet, the

Y •hne and as many other important points as possible, comparing the

;~~Ime directly with the country as he glances over the top of the pall.

IS procedure automaticallY locates the framework horizontally. Wh<>n

;ompleted. the pad is lowered into a comfortable horizontal position and the

r~mework so drawn is carried down into its proper position on the sheet,

especial attention being given to locating the framework correctiy by means

of the vertical control. . "---

This method is much more rapid than the other and after a little

rractice equally accurate results can be obtained with it. It has the advan-

,age of eliminating constant identification of plotted points with correspond-

~~g grounds points, and the consequent loss of time.' . 98. The frame work drawn by either method should be done lightly WIth

0. hard pencil. If time permits it can be gone over later and corrected where

necessary. More attention can then be paid t~ characteristic shapes and formations, and to relative vertical relations. The principles of perspective

also should be applied. Note 1: Dy using a sheet of transparent .celluloid, the same sizc

v

as the sketching pad blank, ruled in the same manner as the blank and

a~tached at right angles to the pad, the sketcher may calibrate his sketch,

fHmply by looking through the celluloid, and noting on which line or in

which space each feature falls. It is a simple matter, then, to sketch these

features in the same areas on the paper. •

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all N~te 2: Another mechanical device, the most rapid and accurate of ,/

wid ConsIsts of two mirrors arranged in a small hood. two or three inches

p :' and two or three inches long, very similar to the hoed of a trench

o:r~sc~pe. Instead of being placed parallel the mirrors are set at an angle

On t 2~ to each other so that the image seen thr(>ugh the peep hole appears

th he sketching pad placed below and in front of the device. In order that

In e sketcher may see the pad and his pcncil, and so trace the image of the

I' ndscape, the lower mirror is made semi-transparent by a series of fine

d rough the mercury back. The degree of vertJca exagg Ines cut th I t' era Ion

a~t;red to secure by inclining the sketching pad away from the plane parIll'~ to the lower mirror. Calibration of the sketch may be secured by a

I scale on one of the mirrors.

G. FILLING IN.

~:9fi :Vit~ the framework established it is a compar¥tively simple operation

p 11In With those details, the importance of which is governed by the purt~=e of the sket~h. Tim~ being a factor. and the object being to l~cate, targe~s,

th framework IS suffiCient and no time should be spent on filhng m, whIle

the fr~mework itself should be only a rough appl'oximation. Hence time and

knc obJcct sought govern the amount of detail shown, and it is here that the

o ~wledge of what to omit makes itself manifest. Tbis last can be gained

3~OY by actual experience. p Speed and simplicity are gained in locating details by plotting limiting

po~nts on the frame work and then drawing in the details bet,\'een these

Pomts. Points where roads. telegraph lines, fences, etc. appear and disapt ear over crests, horizontal limits of tree groups and settlements, are fear?res that can be located this way. Simple points may be located by referJng them to points on the sky-line under which they are vertically situated.

With the soft pencil the sketcher should go over the drawing and

vary the weight of the lines in it, bearing in' m1nd that the weight of line

and Ii SIze O,fobjec~s decrease uniformly as they recede from th? observer. the

ghtest lmes bemg the objects seen farthest away. No tIme should be

7asted on the foreground. A simple heavy line showing its general conormation is sufficient. "---

H, DESIGNATION OF TARGETS AND IMPORTANT POINTS.

30~. In order that the sketch may be of value to others beside the sketcher

po~nt8 of identification must be indicated and data provided as to these

POInts. First in importance of the targets is the ridge line which will afford

~elte: ~or the enemy, and on which the artillery officer I.s likely to fire.

ext In Importance will come roads where they cross such fldges, rords and

~~u.tes of travet, battery and battalion areas, tree lines, streams, and In- //

IVldual targets. As fast a~ such a target is plotted on the sketch the data .

~oncerning deflection ard range, as well as the target designation, should .

e entered in an appropriate place on the sheet. This must be done so that,

should the sketcher be interrupted, his sketch will be valuable so far as he

has gone.

302. In identifying targets they are referred to the reference point as to

deflection, and to the sketcher's position for range. Figure 93 shows th"

Topography for Field Artillery

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l"II)(»)(raphy for Field Artillery
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~.thOd of accomplishing this. Vertical lines are drawn from the top of the'

th ~et ~nd terminate in an arrow head in the exact point on the sketch where .

li e pomt in question is located on the ground. Directly at the top of the

cne the description of the point. so located is written diagonally, so that it.

f an be l'ead with the sketch held in a normal position. Conventional sign~

~\~rgets should not be used. Tbey serve only to add unneces~ary detail

tar • ~k.tch and destroy clearness. Since, in the artil1cry, t~e rJ~ht of the

I

, ?et lS,the point on which firing data are computed, the vertical lme should ndlC

t 'd t'r t' ill a e the location of the right of the target, and if further I en I Ica Ion

th necessary, its width in mils may be indicated. This would mean then, that'

toe arrow-head locates the right of the target, and that the target extends

303the l:ft of this point so many mils'. .' '. j

d~fi' , .SImplicity in designation of tal'gets can be accomplished by usmg

'rt:~ltely understood abbreviations; e.g. "I" for infantry deployed, "A" for

II I lery in position, etc. The reference point always should be indicated a~

fiUCh.and may further be given its correct name' if kno;n. For quick identit cabon the line to this point may he made heavy or doubled. Accordin~

't~ the judgment of the sketcher and the purpose of the sketch. any inform aron may be shown, such as names of hills, mountains, farms, villages, deso T~.tion of roads and railroads, location of bridges, trestles, culverts. etc.

h. e sketcher is governed only bv consideration of the relative military im- !'ort • . 304 ance of the points shown or omitted.'

p .' On the artillery sketch, directly under the description of the indicated

oOInt or ob,iect. should be shown its l'ange. The range is either estimate,J

r measured. If the latter, it is underlined. By reference to fig. 77 it i::

~:n that at the top of the sheet are five horizontal zones marked at the

t~ t, DF, DD. 51, KR, and RN. These zones are solely for firing data and

ese data are filled in before and corrected after firing. The firing data.

refer' d . ring t'0 any partIcular target, should be written across the 'Ve Ica m~ . rt' Ir

~sIgnatjnff the target. and be in the correct zone. ,-

It is evident, therefore, that a third range occurs. This range, after

actual firing and correction. is the gun range to that particular point. Hence I

On tIle complete sketch there will be shown estimated ranges, measured

~a~g?S determined hy instruments, or from the map, and gun ranges de-,'--

<'Imined by actual firing. ~o;). Immediatel~' below the five horizontal zones for recording firing data,

g. 77, is a one-inch space before reaching the upper horizontal limit of the /

~k.tCh proper. This space is used solely for recording angular deneetions. v

he deflection in mils of the particular point indicated, right or left of th,,'

:eference point. is placed directly on the vertical reference line, as indicatetl

In fig. 93. The deflection of the reference point is, of course, zero. which

further identifies this point. With a reference point within the sketch, defI?ctionR will increase to the right and left of it. With the reference point

WIthout the sketch. deflections will increase throughout the sketch to the

l~ft or right, depending on where the reference point is, ta the right or left

of the sector. Deflections are habitually indicated to the nearest multiple'

of five, as no closer measurement is possible with a mil ruler.

TOJlORT8phy for Field Artl1\(Ory

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Topography for Fil'ld Artillery
-139-

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I. SUnSKETCHES.

306. In certain cases the sketcher may wish to show the terrain surroundiP;

any particular point in more detail than is possible on the main sketc .

This may be done by means of a subs ketch, see A, fig. 93. .

307. In conclusion the sketcher must remember that he is busied in makJ~~

. a map, a military record which is to be used by others. Therefore he shou.

\ ask himself constantly the question, "What value has this sketch at thJ~

moment to another person"? With this question before him the sket.che1

should be able to resist the temptation to draw unessentia]s, and so put doWn

only data of value, recording such items in turn according to their. im"

portance.

MAP AND PANORAMIC SKETCH.

308. Plate XV is a section of the military reservation of Fort sm, Okla.

On it is marked a sector to be sketched from a given point, A. Fig. 94 is th~

panoramic sketch made of this sector from the desired point. A study 0

the map and an examination of the sketch will show the comparison between

the two and also will indicate the immense value of a sketch for showipg'

how the country actua)]y looks from the customary point of view. No matter

how great the topographer's knowledge or ability to read a m~p, it is jlll"

possible for him to get an accurate mental picture of the country simplY'

from a study of the map. The sketch bridges the chasm between imagina

tion and reality; and with both at hand, intelligent and exact action maY

be planned even though the country is entirely new and strange.

TOVOtl'raph,., for Flel:l. Artillery. \

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CHAPTEH XIV.

VISIBILITY AND DEFILADE.

DEFINITIONS.

:~~ ,In the discussion of this subject no' attempt will be made to explain

ibilit ~;t~ods other than those pertaining to Topography. The term, "vif!-

Rerv~" IS used ordinarily with reference to our own or the friendly obr . Ion posts. "Invisibile Area", then, is the area invisible from the

,rlcndly O. P.

('ne The term, "defilade", I"elates primarily to whathnay be seen, from the

the rn~ Observation posts or lines. with a view 'to obtaining concealment from

l\h('ltvlew of the enemy. Howev"er the term also is used in connection with

, er from the enemy fire.

at' Defilade is given, usually in yards or meters in order to determine

lllo once What kind of defilade is obtainable, i. e., materiel, dismounted.

unted, fla~h, dust, smoke, etc.

310. VISIBILITY.

the' 1here are several methods by which visibility may be determined.

more common of :which will be considered below.

311 A. SIMILAR TRIANGLES.

bel. 1he first method to be considered is that of similar triangles given

ow.

Co • Find from the map the elevations of the observation post, of the point

o/l'ns~dered in the enemy's lines, and of the inte'rvening crest suspected of

1'herIn?, defilade to the enemy, together with the ranges between these points.

ttriangles to be solved will be formed as shown in fig. 95.

I I

fIT,.~=:=--=-30()()YD.s~OO(LV~ --j ~~-----------r~-----tr

1~ lito -1; I..!

I~(~~ {;~. IL

. v~@i)1 ~'ll/llt. ,tQ •• I, :1 . I I ~J' II 0

F

• 91': ''fARGt'T'.,~.~ Jg. D. ~Il

1'h The line of sight from the observation post falls 30 feet in 5000 yards.

S C Intervening crest is 3000 ranis away. By proportion, 5000: 3000::30:x.

O~ving, it is found that the line of sight at the crest will pass through a

')OInt 18 feet below the level of th~ O. P. In other' words, the line of sight

the crest will have an elevation of 1112 feet. Since the crest has an eleva-

)I,onof 1120 feet the line of sight, between O. P. and the enemy's line will

lUSH 8 feet below the top of the crest. Hence the enemy position cannot be

seen.

TO\lolCraphy for Field Artll\(lry

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B. WITH AN ELASTIC BAND.

312. An adaptation of the similiar triangle methcd, based on the fact tbld

a piece of rubber, in most cases, will stretch uniformly, is given beloW. aI

Take a strip of rubber band and mark it in 5 or 10 units of e<Jl1

length. Ten units is preferable, because this will permit of the use of tbe

decimal system, in the computations which follow, fig. 96.

Figure 96 shows the map of the terrain considered in the operatioJ}!

outlined above; the O. P., the crest, and the target all being indicated.

> fff'}'+'}1Tffp

Fig. 96.

Read from the map the elevations of the O. P., of the crest, and of the

target. Next apply the rubber, stretching it between the O. P. and the target. All subdivisions will stretch uniformly. .

At the crest read the subdivisions, or fraction thereof, indicating what

decimal part of the whole the distance from the O. P. to the crest may be.

In the above figure the subdivision, 6, touches the crest. Therefore the

line of sight at the crest should show an elevation below the O. P. which i~

.6 of the total difference in elevation between the O. P. and the target.

The target is at an elevation of 1100 feet. The O. P. is situated at

contour 1130. The difference between the two is 30 feet. .

30X.6=18 feet, which is the amount the line of sight between the O.

P. and the target has dropped in the distance to the crest.

1130-18=1112 which is the elevation of the line of sight at the crest.

The elevation of the actual crest, however, is 1120 feet. Therefore the crest

hides the target.

C. ANGLE OF SITE.

313.. A comparison of angles of site affords a third satisfactory method of

determining visibility. In this method the angle of site to the intervening

crest is compared with the site to the point considered in the enemy's linc!.

Find from the map the elevations and ranges as in the similar triangle

method. Reduce the difference in elevation to yards or meters and the dis'

tance to thousands of yards or to kilometers. In the problem above, fig.

30 95, the angle of site of the point in the enemy's line is :r +5=-27/1. The

10

angle of site of the intervening crest is a +3=-17/1, approximately, 'I'M

line of sight to the objective considered, therefore, has a steeper downward

Topography for Field Artillery

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;~~{. than the line of site to the crest. Therefore the objective is invisible.

of thOpposite is true in case both crest and objective are above the elevation

p. ohservation po~t.

314. T D.. GRAPHIC METH~?D.

('on~t,. he question of visibility also may be settled by means of profiles. To

\\'hie~ ~ct a p~ofile apply a piece of cross section paper. or any other paper

alld th as ~onzontal lines equally spaced upon it, to the line joining the O. r.

of th e POInt considered in the enemy's line, see ray 13, fig. 97. On the edge

line. eJaper mark wi~h its elevation each point where a contour crosses. the

of th umber the honzontallines of the paper to correspond to the elevatIOns

the Ie .several contours crossing the. line between O. P. and the target: From JOInt . , hOti' s on the edge of the paper drop perpendiculars to the corresponding

and zon~al lines. (Note. It may be more convenient to use a straight edge

map at rIght angle triangle and so drop the perpendic~lars directly from the

mat I"~ 0 .the proper parallel line. without bothering to spot points on the

gm of the paper.) •

of th Consider the points spotted on the parallel lines as limiting points

aee e profile desired. Join these points with a smooth curve, taking into

tlUl:un.t the character of the ground forms as shown on the map. The rePOint.lll be a vertical cross section of the terrain between the O. P. and the

lD question. See Profile B, fig. 97.

to th ?n the profile draw a straight line from the observation post, tangent

In,,' lDtervening crest. If the point considered is below this line is will be

8ig~~1 Ie, and all terrain between the crest and the point where the line of

touches the ground, also will be invisible.

Wh'l In this method the horizontal scale of the map must be preserved.

mol e the vertical scale generally is much exaggerated in order to bring out,

re clearly, the ground features. .

tio It must be remembered that if the observer is placed on an observagr n tower, or in a balloon, the line of sight must be drawn. not from the

to ound elevation of the o. P., but from a point sufficiently above, according

ob the vertical scale of the profile, to maintain the proper relation between

server and objective sought.

E. VISIBILITY CHARTS.

31y.5: In preparation' for the occupation of a position, a chart called the'

o~~lbility chart is prepared, showing all areas invisible and visible from all

p,se;vation posts likely to be occupied. The invisible areas of different O.

b B.,I! appearing on the same chart, are marked in different colors. It must

pC remembered, however that no matter hoW carefully this chart is prel

't~l'ed from the map, it ~ust be verified by a careful study of the terrain

self a . b' d 316 s soon as the observatIOn post can e OCCuple • .

>. This chart is prepared on a transparent sheet from profiles as follows:

t' l)lace the sheet of transparent paper on the map. From the observaIOn }lost draw a f'eries of radiating lines, A. 13, and C, fig. 97, through the

Hecto r r an across the points most in doubt. These rays will be extended as d

tr as required into the enemy's territory. The number of the rays to he

( l'aWn will depend on the grou'nd itself and the accuracy desired.

On (Otl<'hray construct a profile of the ground and mark the points on

TOJlOll'ravh1 for Field Artillery

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the profile, X • .Y. and z, profil~ n, fig. 97, which limit the invisible areas~ . J.p'

ply the paper again to the line on the chart, and by means of perpendiculars,

transfer the points to the chart. After marking all the rays on the map in

this manner an irregular area Ol' areas will be indicated by the dots. See

points x', 'y', .and ;:' of ray A, and x", 'y", and z" of ray C. Connect thcse dot~

and hatch the area enclosed with diagonal parallel lines, using different

colors or cross hatching to distinguish hctwecn'invisibility caused by ground

forms and that due to masks, such as trees, buildings. etc. Objects situated

TOllogravhy (or Field Artillery

.~

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TOPollrapby for Field Arti1!('ry

1\(:,0

-tr---t---t-;--l,5~-r;,--- .. tMYO.P.

1 I 4 rfr' \ .,~ ~~tfl--

I I\~O \\ ') ~f!i&"'" I

I ~<;. S' .~ ~~j~~ I

OEflLAOJ ,5'" ,~1i'..r;.v .;. :,j,\!9, S'~..@ifoi~; 1"00

PO)1TI0 ~':.-_-1- ------------.::1-

.," II~ ._ -=--=SOl)()yo~(JO(~o:> -:: -=~ --4

Fig. 98.

o 1160-1100=.60 feet=20 yards=the difference in elevation between th"'-

. P. and the position.

th 1160-1130=30 feet=10 yards=the difference in elevation between

e O. P. ar.d the crcst. .-

The angle of site' of the position=20-=-5= --4,/,.

the angle of site of the crest=10-=-4=--2.51/'.

-4-( -2.5) =-1.5'/'.

l.S,/,X5=7.5 yards=defilade of the position.

(2) Measured l'rom Covering Crfst.

319. The amount of defilade. also may be found from the map, by the same

calculation generally used wben it is possible to occupy the position and the

crest with cngle measuring instruments.

d From the map determine elevations and ranges as bolore. With thi,

ata compute the angle cf site of the enemy O. P. measurcd from the crc:it,

and the angle of site cf the crest measurcd from the gun }:csition or the

. --145--

elf' In in .. b ~ISI Ie areas. the tops of which are visible, also should be indicated by

T~~gmg in" with a different color, see the smoke stack indicated in fig. 97.

1>Ollslast .is important as it often happens that a line of trees or telephone

a es proJecting upwmd from. an invisible area will indicate the presence of

road or other objective for the artillery.. .. 1'1 These charts, as constructed above, are prepared for each observation

\Vh t'ost or aUXI 'II.~ary observation post and transmitted to superIor comman ers . d

bat~re. they are consolidated and used in assigning missions to the v~rious

se t enes, and in assigning the various observation posts of a partIcular

c or. See Chapter XXIII.

317. DEfILADE.

sirn"l As. m the case of visibility, defilade may be computed by means of

I ar trIangles, by angle of site, and graphically.

A. ANGLE OF SITE.

31 (1) Measured From The Enemy O. P.

CI,8. Obtain from the map the elevations of the enemy O. P., the covering

f:st, and the proposed route or position; also the ranges between the dif.

tor~nt elements. With these data compute the angles of site to the crest. anJ

al he ~osition, as measured from the enemy observation post. Subtract

pog~~ralCallY the angle of site cf the crest from the angle cf site of the k.t1tlOn, and multiply the result by the distance, in tho~sands cf yards or

b1 orneters, from the enemy O. P. to the position or road. The result will

e the defilade in yards or meters, see fig. 98.

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road. The 'amount of defilade is obtained by subtl'acting the site of the' ob-'

servation post from the site of the crest, and multiplying the remainder by'

the distance. in thousands of yards or in kilometers, from the position to the

'crest, see fig. 99.' I

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1160-1130=30 feet=lO yards, or the difference in elevation': between crest and O. P.

1130-1100=30 feet=lO yards. or the difference in elevation between

the crest and the gun. . :,)

, 10-7-4=2.5,!l=the site to the O. P.

10-7-l=10,!l=the site to the crest.

10-2.5=7.5,!l.

7.5Xl=7.5 l'ards= amount of defilade at, the position.

. n. PROFILES. . , , ,

:320. Defilade also may be determined by means of profiles, as follows: ,J

From the enemy observation post draw a profile or series of' profile~

of the terrain including the propoRp.d position or roadway. The method of

construction is the same whether visibility or defilade is sought. ,

Draw a straight line, representing the line of sight from the observ~-

tion post, tangent to the covering crest, see fig. 100. At the position measure

the vertical distance from the surface of the ground to the line of sight,

drawn as above. This distance, according to the vertical scale of the profile,

is the amount of defilade of the position.

Fig. 100.

C. TABLE OF DEFILADE.

321. Although usuaJly determined by a personal inspection of' the terrain.

the following kinds of defilade may he determined from the map:. ;. ,;

TOllOlCraphy for Field Artillery

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.~. ro, Materiel Ilefilade, where the materiel is just below the plane of de.-

filade.

toio

w

Dismounted Defilade, where the level of the ground is 1.8 'meters

the plane of defilade.' . . tIi.' Mounted Defilade, where the level of the ground is 2.5 meters below

plane of defilade. .' . fill Dust Defilade, where the pieeo is far enough helow the Iplane ofdeT

) a~e. that the dust, caused by firing, will not be visible from the enemy

t OSitIOn. :This last val'ies with the weather and the terrain and is difficult

p

o ~~tainexcept in swamps, along watercourses, and by wetting down the

oSItion. .

.an I A eonvenient tahle showing amounls of defilade required for smoke

( Hash defilade in light and heavy artillery is given below: .

Defilade 75 mm.' ~\~.:..~~::. _~_'----

Flash, .,4 .meters 8 meters

Smoke 8 meters

15 meters'

_____ -::- __ 5000~~400OYD-;:--=--nJ

T r---=.-------------:-- t~lMV OP.

... ,: ./,.- <~;\~

lI.. \~ -r . /' ,~7wr; o I'" . _0' • 'lil\t-N-~ .,!) H lito .' '.' .Ic ::ixir{~'i/

:: ~~'.GR(~ ~~I.$~~",~~,,~\~~. •

: D(f1LAD.4 ~O,.~. :' ~;'IV""H' .

PO.5ITIONPIiOb Fig. 101.

4000: 5000:: 40:x.

x=50 feet. 60-50=10 feet =amount of defilade at the position.

(2) Second Problem.

324. To find the amount by which a mask must be rais('d to ..ecure ('on-

('('alm('nt from the enemy's "jew.

322. I , D. TYPE PROBLEMS. . .. '.

th ?y!'es of problems conceming defilade and methods of solubon, uSing

U prmclple of similar triangles. foll"w. Any of these types may be solved tng either of the other methods explained for computing the amount of

(efilade of a position.

323~ . ..... (1) First Problem. ..' . th' To compute the amounl of defilade of a pos,t,on. Havmg found from

'the m~p, the elevations and ranges, as shown in fig.' 101, construct and solve

.e tnangles indicated. The line of sight which falls 40 feet in 4000 yards tllfall 50 feet in 5000 yards. Since the difference in elevation between

lihe enemy's observation post and the position is 60 feet, it follows that the

Ine of sight will pass 10 feet above the position, or the position will have

10 feet of defilade. .

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Find from the map the elevations and ranges as shown in fig. 102-

Construct and solve the triangles indicated. Since the line of sight passcs

48 feet below the level of the enemy's observation post and the top of the

mask is 50 feet below, it follows that the mask must be raised 2 feet, flUS

the amount necessary to secure the kind of defilade required; i. e., the amount

.necessary to give 6 feet for dismounted defilade, 9 feet for mounted defil~d~

etc. I S()()() YO .... ---..J r--;:..::.---~40(lO YO-S - - --JUGO -t---~--------------- 7

, • ~~,,~.. MYa.p. t <0 ~~!~\'"

o t _ 'Iv.~

'f 1,~~--- I ~~\I

, v- I ,"~M . 1100 , t'Col fu ~~~1JJj~I/1

p(j IT ON'" Fig. 102.

5000: 40CO:: ~O : x.

x=48 feet.

116~1110=50 feet=the amount the ground level at the crest is below the enemy O. p.

50-48=2 feet=amount the mask must be raised to reach the line of sight.

6 feet at the position will give dismounted defil::tdc. 6: x:: 5000

4000. x=4 4/5 ft., distance above line of sight at the crest, which will give

dismounted defibde. Therefore 2+4 4/5=6 4/5 ft., the height necessary

to raise the mask.

(3) Third Problem.

325. To find 'he height to which an Observation towl'r or balloon must be

raised to overcome the defilade of an enemy's position. Find from the map

the elevations and ranges as shown in fig. 103. Construct and solve the

ind:cated triangles. The line of sight' from the enemy's position passes over

the crest at a height cf 30 feet above the enemy positicn. Since this is the

rise in 1000 yards, the line of sight will rise 150 feet in 5000 yards, to which

height it will be necessary to raise the observer. Dut since the ground at

the observer's pcsition is 40 feet above the enemy position it will be necessary only to raise the tower or balloon by the difi'erence or by 150-40=110

teet.

1000: 5000:: 30: x.

x=150 feet.

150-40=110 feet=height balloon or tower must be raised above the ground.

Topography Cor Field Artillcr"7

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TOpOllr8\,hy for l~il'1d Artillcr~

CHAPTER XV.

MINIl\IUM ELEVATION, l\UNIMilll RANGE.

AND DEAD SPACE.

326. " . GENERAL. .'

th ~hmmum elevahon is the lenst quadrant angle of elevahon at whlcl.

qle irajectory will clear the covering mass or mask. It is a range scale or

la rant setting on the gun.

tn" Minimum range is the actual range to the point of fall for the

IiInlmum I t' I' e eva lOn. t IS a mcasurement on map or ground 0 t e s orl .. r h h

nut of fire.

b. Dead space is ground which cannot he reached hy fire. It is caused

{j"first, the covering mass or mask immediately in front of the hattery

i': Ich, also fixes the minimum elevation); second, ohstruetions be)'ond the

medIate cover which may protect the enemy from artillery fire.

e The first class of dead space begins at the crest of the immediate

::.~~r, under the ascending branch of the trajectory, and extends to the

el

InImum range. Its limits are determined in connection with minimum

, evat' d Ion and range. The second class of dead space is usually nnder the

3~;cending branch of the trajeclory, and must be determined separatelY.

d" Accurate information as to minimum elevation, minimum range. and

ead space is of the highest importance to the artilleryman. The executive

end gunner must know the minimum elevation at which they may lay thf

!fUns, but need not know the minimum range, except SO far as the tern

range" may be applied to the range scale setting. The battery'commande.

must know both the minimum range and the minimum elevation, because h~

~ust know both the short limits of fire on the ground and the elevations to

ke given the guns for targets at those limits. IIigher commanders mu~t

now the minimum ranges and the boundaries of all other dead areas tor

reference in assigning targets to batteries.

. In open warfare the minimum elevation and range arc determined

Immediately on occupation of .a position by measurements made on the

f{0und (F. A. Drill negulations, Par. ~168-~176; Art., Firi~g, Par. 66-58),

Dead space of the first e1ass is determined In eonneehon WIth the process,

cad space of the second class cannot be determined without a map, unlesf:

~he ranges, elevations, and slores of protected enemy terrain are aceurateb'

nown f~'om previous reconnaissance. In position warfare. as soon as the location of the guns has been

?etermined, and citen before the actual occupation of the position, all this

Information is determined from the map, and tables and charts are prcparerl

shOWing it in detail, for the use of the various commanders.

3~8. Every fixed obstruction of any considerable size which may stop 01'

d!vcrt the passage cf a projectile or cause it to explode is taken into conSIderation in determining minimum elevation, minimum range, and dead

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space. Thus trees and buildings may be obstructions, as well as hills and

ridges. Tables and charts should show the nature of the obstruction by

notation or by some graphical device. It is assumed to be ground unless otherwise noted.

DETER1\IINATIO~ OF' l\UNIlUUM ELF;VATION AND I~ANGE.

329. In position .warfare a table s~ould be prepared showing thf minimuJl1

devation for each gun for at least' every 200 mils of the sector from the

right limit to the left limit.: If the covering crest is vel:y irregular, closer

intervals must be taken. Minimum range .is determined at the same time.

It may. be. recorded in special columns in the minimum elevation table or io

a separate table, and it will also be, plotted on the dead space chart. Separat~

tables must be made for each different projectile, charge. and fuse wherever

. there is an appreciable difference in the t.rajectol'Y." ,:. ,

330., The object of any calculation of minimum elevation and range is, first,

to) find the minimum elevation to clear the crest, and then to find a point on

the ground be~'ond, $uch that the,quadrant elev,ation required to,. strike it ;5

equal to the minimum elevation. This is the actual point of fall 'for th~

ini!1imum elevation. Methods differ in their details, but, all are based sub.:'

stantially on the, above principles., The following is the usual procedure.

"A. STE\S: OF CALCULATION.

331. 1. petermine the minimum elevation in angular measure (mils -or

degrees ,and. minutes, etc.) 'to clear the ci'est as follows: Find from the

range- table the elevation for the range. to the crest, and add,to this the

Bite of the crest, calculated from, the map. This is the quadrant elevation

for the crest. If the' guns are close to the crest (within 300 meters with

the French 75, normal charge), the drop in the trajectory is negligible. and

the site may be taken as the minimum elevation. The minimum elevation

should be recorded in the table. in angular measure as calculated, and the

corresponding range setting (not map range), in yards or meters should also

be entered if a range scale is used on the guns.

2.. Find from the range table the map range correspond ing to the

minimum elevation. This gives the range to the horizontal point of fall,

where the projectile would strike if the ground were level with the guns.

Call this the first trial range.

3. Find from the map the altitUde .of the ground at the first trial range.

If, it is the same as the altitude of the guns, the trial 'r~nge is the

actual minimum }'ange. (Example 1. fig. 104).

If it is higher than the guns, the actual minimum range is short of thi~

first trial range. (Example 2, fig. 105).

If it is lower than the guns, the actual minimum range is beyond thl~ first trial range. (Example 3, fig. 106).

4. ,Where the altitude of the ground at the first trial range has been

found to be different from that of the guns, a further calculation is necessary

to determine the actual minimum unge. In such calculations two things

must be taken into consideration: first. the general altitude of the ground

.at the first. trial range; second, the form of the ground, whethel' level, un!:

TOJ'KllCraphy for Field ArtiJIe..,.

'

-

-
-151-

fOrml.' .. , ei" y slopmg, or' irregular. ,The methods of calculating under different

r Umst,ances will now be taken up in detail.

;," D. EFFECT OF GROUND FORMS.

33'> '. (1) Level Terrain.'!:

tlt~d":.th the ground at 'ftrst trial range level, or approximately so, (at.

foIl e~l~her higher or lower than guns) find the actual minimum range as

. .ows:' :

;he : Calcuhite the site of the ground at the first trial range. 'Find from

equ ; auge table the }'ange change corresponding to 'a 'ch:mge in elevation

di'p~ ,to the site. In some tables this is given in special columns showing

acement in point of fall for variations in angle of site or elevation.

lhe If, not so given it can be found from the main' table by subtracting

tli. angle of elevation equal to or just below the minimum elevation from

to t~e,xt Iiigher elevation, thus obtaining the, elevati6n change corresponding

~alu e ra~ge inter~al of the table, usually 100 meters. Add the range change

lhe' euOf,t~e a~gle of site to the first trial range if the ground is lower than

lh g ns. Subtract it from the first trial range if the ground is higher than

lll~.gun~. The result is the range to the actual point of fall, the de.ired

a n1mum range.

33. Ho 'f h d

a

n wever, 1 t e range change is oyer 100 meters, thIS metho IS not

'-Curat 'b . ele e, eeause the }'ange change value of a mil or other angular unit of

ex vati?n decreases rapidly as the range increascs. In case of a range change

el.. ~e~mg 100 meters. test the new point of fall by calculating its quadrant

ee atlon. If this is equal to the minimum elevation the range may be acfi~ edas ~he minimum range. If it is not equal to the minimum elevation,

eh the, d.fference between the two elevations and make a furlher range'

'l'hange'in the proper direction equal to the range value of this difference.

it e

h

second, range change will usually give the, actual minimum range, but

if s ould be tested by its quadrant elevation, and a still further change made

f

necessary, After a little practice allowances can be made by estimation

~' th' , IS change in the range value of an angular unit.

(2) Irregular Terrain. "'----

• 334 W'th . . 1 the ground at first trial range slopmg or Irregu aI', t e gcnt>rl1 I (h I

a\erage altitude being either higher or lower than guns) the actual minimuM.

sit ge cannot be found by a range change conespondmg to the \'Blue of the ~n'

e, because the site of the ground at the new range would not be the sam'?

as at the fin;;t trial range where the site was calculated. The quadrant el~-

\'ation of any point depends on two things, range and site. Both are change;l

wfhen the range is changed on inegular or sloping g.'ound. lIenee the effect

•. holh mu,t be taken into consider:,tion in calcula~io~ o~ such ground.

hl~ can be done very readily on a UnIform slope, but It IS a htUe more (lJffi.

cult 4 on inegular slopcs or broken ground. Proceed as follow.. (Examples

3 and 5, figg~ 107 and 108). . 3;). 'Calculate the quadrant elevation of the ground at the first trial range,

~nd fi~d 'the difference between this and the minimum elevation. At the

l~'t tn:,1 range this difference is the same as the site of the ground, because

e hOJ'lzontal range corre!'ponds to the minimum elevation. ,This difference

" '

"

'

'

'

"" ' '

~

" "

~

'
-152-

is to be made up by a combined change in range and site. Make a range

chenge of some convenient even amount, say 50 or 100 meters. in the proper

direction. Call this new range the second trial range. .Calculate the quadrant elevation of the ground at this range. If it is equal to the minimum

elevation, accept the range as the actual minimum range. If not, find th~

difference between the quadrant elevations of the ground at the first an

seccnd trial ranges. Divide this difference into the difference in range be' .

tween the two ranges (that is, the range change which was made). The

result is the range change' corresponding to one angular unit of elevatiol'l

(mil or minute, etc.), taking into account the effect of both the range change

and the change in site due to the slope. Multiply this by the difference

between the quadrant elevation at the second trial range and the minimunl

elevation. The result is the new range change (including the change .lIt

site) necessary to make up the difference in elevation still remaining after

the first change. Make this range change in the proper direction from the

second trial range (forward if the quadrant elevation is less than the mini.

mum elevation, back if it is greater). This will usually give the actual

minimum range, but the quadrant elevation should be verified and a furtheJ'

change made in the same way if necessary.

Apply the same methcds cn irregular slopes or broken ground, makin'

allowances by estimation for the changes in slopes. It may be nccessar)'

to make one or two more range changes than on uniform slopes before tllf

actual minimum range is found.

(3) rfTcct Of SlopcE..

336. In making range changes on slopes. it should always be remembere'J

that if the ground at the point of fall slores upward from the guns (9Pposite

to the trajectory), a smaller range change will be required to make up :l ,

given difference in elevation than if the ground is level, because the change

in site affects the .elevation in the same sense as the range change. Thaf

is, an upward slope works with the range change in ch::mging the quadrant

elevation. If the ground slopes downward from the guns at the point of

fall (in the same direction as the trajectory), a greater range change will

be required than if the ground is level, because the change in site afrecb

the elevation in the opposite sense from the range change. That is, a downward slope works against the range change in changing the quadrant

elevation. These statements are true whether the general altitude of th£-

ground is higher or lower than the guns, and whether the range change i~

made forward or backward.

C. ACCURACY.

337. The degree of refinement to which calculations should be carried deper.d~ on the acuracy of the range tables', the map. the measurements, and

on the least reading cf the quadrar.t or range scrle cf the gun. It must b<.

determined by Circumstances of each case. No hard and fast rule can be

laid down. A practical rule which will apply in ordinary work is: calculau

mils to the tenth of a mil, degrees and minutes to the minute; nr.d yards or

meters to the nearest yard or meter, finally adopting the next nearest multiple of 5 above.

TOJlOllraphy for Field Artillery
9"1

401/1

33 . -153-

tic~bl All results should be recordcd in the tables as closely as it Is pracAll \ to calculate them, so that they can be cbecked at any time if desired.

batt:: culations should be based on existing conditions, Icaving It to tbe

ance y commander when he computes his firing data to make such allows as may be necessary for margin of clearance, safety of troopS, etc.

3 D. TYPE PROBLEMS.

c39. F 11 . 1 0 owmg are typical examples of minimum elevation and range

a l'Ulations.

Example 1.

Point of Fall on Level 'Vith Guns.

rlNIMVM r:L[VATION

QllADRANT [LI.VATION Of (R~T>.

~~tNv~110NFOR :/ TRAJr:CT{)R~1 41.. Of CR,l:ST .. ..- .. .._.~~.

~ITt Of. CRE5T•••••• ....'1 "cRi'~LT.42.0M. ............POINT OFG

.~-: !;,';i; I~/~~", '-.,fAllALT.

VN ,""l~~\N ""I %:::\~/~II 400M. /£L,-_-:::::-~'!$.r~ \ .,.,..... \

"'-"'~\\\I~' {.\'¥O~M I HORIl.ONTAL--evNttV~I/<'~~~~!~~~~~~-fiI-

'''(''-,IILjf/l .-_~ . :!::17 r"",\' I

1-------- 1~:;OM.MINIt-1VMRANGE---------i

POINT Of fALL ON GUN LEVEL

Fig. 104.

cre t 75 mm. gun, II. E. Shell, Normal Charge, Short Fuze. Range to.

s, 500 meters. Altitude of guns at muzzle, 400 meters. Altitude of

crest, 420 meters. .

(a) Elevation for range of crest, 500 1\1.,

(from range table)

S

. 20

Ite of crest, --:r;

Minimum elevation (quadrant elevation of crest)

(b) Corresponding horizontal range (from range

table by interpolation) 1950 M. "--

. Layoff this range on the map. It is seen that the grour.d at the

pomt of fall has' an altitude of 400 meters, the same as the guns. ThE'

actual minimum range is therefore 1950 meters.

Example 2.

Point of fall on level ground higher than guns.

340. Other data same as examrle 1-

(a) Minimum elevation. same as examrle .1, 49",.

(b) Corresponding horizontal range, 1st trial rangt', 1950 M.

(c) From the map the altitude of the ground at the 1st trial rang«'

is seen to be 410 meters, or 10 meters above the guns.

Si~e at this point: i~~5 =+5.1",.

Range change per mil of elevation at 1950 M.. (by interpolation from

range table), 27.9 1\1.

'

_

~ -

__ _ ~ -

- =

-
44.2//1

29.71/1

43.31/1

+5.61/1

48.91/t

.1//1, hence 1785

Fig 105. 5.1X27.9=142 1\1.

Subtract this from the first trial range, since the ground is higher than the guns:

1950':'-'142=1808 1\1., second trial range.

The range change being more than 100 meters from the 1st trial . range,; verify the quadrant elevation:

Angle of elevation for range 1808 M.

. 10

Site (AltItude 410 l\1.)r:s 5.6//1

;.,' , Quadrant elevation. 49.8//t

. .This' is .811t above the minimum elevation, and hence is beyond the

tru~ minimum range. The ground still being level, come back to the range

change value of .811t elevation.

Range change per mil at 1808 1\1.

.8X29.7=24 1\1.

1808-24=1784 or 1785 1\1.

Verify quadrant elevation:

Angle of elevation for 1785 1\1.

10

~;it~, 1.78 = Quadrant elevation

This differs from the minImum elevation by only

meters may be accepted as the actual minimum range.

-154-

Required'range change to make up difference of . .. . ad- 5.11/t between qu t

rant elevation at 1st trial range and minimum elevation (same as site.~ i

1st trial range).

LEVEL GROVND ABOVE GUN Lr:VEL

Example 3.

Point of fall on level ground lower than guns.

3 tl. Other data same as example 1.

. '(a) Minimum elevation. same as example 1. 491/t •

. '(b)' Corresponding horizontal range, 1st trial range. 1950M.

(c) From the map' the altitude of the ground at the bt trial range

is seen to be 390 meters, 10 meters below the gun level.

. 10

. ,Site.: 1.95 -5.1///.

Range change per mil of elevation at 1950 M., 27.9 .1\1.

TOI>Olfraphy {or Field Artillery

=
.'.. -:155-

"an; "FeqUired range change to make up difference of 5.111' between quad1st t~:lvation at 1st trial. range and minimum elevation (same at

•..... . r.,

LEVEl GROVND BELOW GVN'LEVEL

Fig. 106~

~"~S' ~dd this t? the 1st trial range. since the ground is lower than the

~50+ 142=2092 or 2090 M,. secondiria! 'range.

'ange • be. range change being more than 100 meters from the 1st trial

, ve!lfy the quadrant elevation:

Angle of "elevation for range 2090 1\1. 53.7111

Sit' ...!.2-- e, 2.09 _4.81/t

I . ,Quadrant elevation 48.9111

hlet This differs from' th~ minimum eievation b~; only .1'/1. Hence 2090

erg m . ay e accepted as the minimum range. b 'it. The !'eason why a single range change corresponding to the angle ,of

exa.;ave neal'll' the exact minimum range in this example, while in the ~r~t

ele ~le another change was necessary, is that the range valne of a mIl ,n

'l'h~a~lOn ran true for a longer distance' above than below the first trial range.

Ilh:"s due simply to the way the range table figures are calculated. and em.

,h' Sl7.es the need for, verifying quadrant elevations wherewr the range

ange is over j 00 meters. . '----

Example 4.

:112. I'oint of ),'all below guns. Ground sloping upward ..

Other data same as example l.

(a) Minimum elevation, same as example 1, 49111

(b) Corresponding horizontal range, 1st trial range, 1950~1.

i, I '(c) Altitude of ground at 1st trial range. 390 meters. )0 mele,'s

/ ow the gun level. Hence the actual point of fall is beyond the first trial

ange. Determine the range changes as follows: .

Angle of elevation, 1st trial range 49. III

S't1 e (altitude 390 1\1.) T:%10 = -5.1 'I'

Quadrant elevation, 1st trial range 43.9 'It

The diffc"cuce 'of -f•.l 'I' between this quadrant ele,'ation and the

))lnimul11 plevation is no\\' t6 be made up by a combined change of range and

"

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-156-

site. In this case, since the slope is upward, the site change works \\'it~

the range change, and the 'required range change will be less than on leve

ground, as in example 3.

52.,/,

-3.1/'

49.1/1

the point of fan had been

-2.4 1/1

50.1 1/t

elevation for the 1st trilll.

POINTl)f fALL lRAJECTQR.'t._ .. .. .. IF GROVND wrR!.

~,,,,~T-Al 1.420M. ......., ABOVE GUN IXva

.. -" Y(l'~'~lyt .... ~,;,.f.I ~VN :-.--- ~2i~'~..ttQ.l\.~ TAJ::"Cll'.!i.hr;y~l,:,,~I..4..QR.~'$~~': _' Ac~\V' r -?/Ii ";> .. ,. 7Ju~ \

'~\ ....~\~~0 I .' 1111'<\-'1"/. tlORllONTAL POINT Of fALl. I • g, ~. f,'j ..J r- --500 M.-~ ,,' .;c-')~J7I<~1~t11~~ ~I;-~J,~~ ~,~

r-19S0M. RANGl:TOtlORIZONTAl POINT Of fALL---t 1~;3

,---- ---" 2035 M.MINIMVMRANGE.--------I~~

RI~ING GROVND BELOW GVN LEVE.L

Fig. 107.

. Now make a range change of 100 ~eters, (increase, because. the aetu91

minimum range is beyond):

1950+100=2050 M., 2nd trial range.

Angle of elevation, 2050 M., 52.5 111

Site (altitude at 2050 M. range, estimated at about 395 1\1.),

5

2.05=

Quadrant elevation, 2nd trial range.

Difference between this and the quadrant

range:

50.1-43.9=6.21/',

which is the elevation change produced by a range change of 100 meters.

including the change in site due to the slope of the ground .

. Then the range change per mil. is:

100

62 16 M.

The difference between the second trial quadrant elevation and tbe

minimum elevation is:

50.1-49=.1.1,//.

The range change required to make up this difference is:

1.1X16=17.6=18 1\1.

Subtract this, because' the seccnd trial elevation was greater tbarl

the minimum elevation, showing that the range was over:

2050-18=2032 1\1. Taking the next multirle of 5 above use 2035 a~ Srd trial range

Verify the quadrant elevation:

Angle of elevation, 2035 1\1.,

6 Site (altitude at 2035, 394 1\1.) 2.03

Quadrant elevation, 3rd trial range,

Hence 2035 is the actual minimum range.

If the general altitude of the ground at

TOJ>OlO'aphy Cor Field Artillery

_ __

-- ~

,

~ , ~~ ~

~

=

=
higher . -157- .

the Instead of lower than the gun level, the procedure would have been

the 1sarne t ,.except that the range change would have been made back from

s trIal range instead of beyond it, as shown by dotted lines in fig. 107.

I Example 5. ~:

Point of fall below guns. Ground sloping downward.

49 '/1

-5.1,/-

-

43.9'/1

-6.8,/.

-45.7,/-

Topolrraphy {or Field Artl11ery

=

Now make a range change of 100 meters, the same as in example 4:

1!)50+100=2050 M., 2nd trial range.

Angle of elevation, 2050 M., . 52.5,/.

Site (altitude at 2050 M., estimated at about 386 M.).

14

2.05

Quadrant elevation, 2nd trial range.

FALLING GROUND BE.LOW GVN LEVlL

Fig.1G8.

343. Other data same as example l.

(a) Minimum elevation, same as example 1, 49,/_

(b) Corresponding horizontal range, 1st trial range, 1950 M.

the (c) Altitude of ground at 1st trial range, 390 meters, 10 meters below

Dcte~:'level. Hence the actual point of fall is beyond the first trial range.

me the range changes as follows: .

Angle of elevation, 1st trial range,

... Site (altitude '3nOJO 'IIII') .u~., J.Q... 1. ~5 = Quadrant elevation, 1st trial range

(Note that this is the same as in examJ:le 4).

tn" The difference of -5.1,/1 between this quadrant elevation and the

8i~nlrnum elevation is now to be made up by a combined change of range and

Pred In this case, since the slopc is downward, an incrcase in range will

pa~te a dccrcase in sitc, tnd vice versa. The change In site will thus

th Y offset the effect of the range change on the quadrant elevation, and

3.e required range change will be greater than on level ground, as in example

'

•
'~158-

Hie'1st

., .". : .~ i .: ..1 •

meters,

Difference between this a~d the quadl:ant eievation 'foi,

range:

45.7-43,9=1.81/1.

which is the elevation change produced by -a range change of 100

including the change in site due to the slope of the ground.

Then the range change per mil is:' .

100

1.-8 = 55 M.

The difference between the second trial quadrant elevation and the

minimum elevation is:

49-45.7=3.31/1. ..

The range change 'required to make up this difference is:

3.3X55=180 M. . ....,

Add this, because the second trial elevation was less than' the minim.uJ11

elevation, showing. that the range was short:

. 2050+180=2230 M., 3rd trial range.

Verify the quadrant elevation:

Angle of elevation, 2230 1\1., 59.21/1

Site (altitude estimated at 379 1\1.), 2~~3 -9.41/1

Quadrant ele,'ation, 3rd trial range, 49.81/1

This is .81/1 greater than the minimum elevation, showing that the

range change per mil of 55 meters was a little large. It would have bee~

all right for a range change not exceeding 100 meters, but beyond. that It

was too great, on account of the yariation in range value of a mil as the

range changes.

Compute a ne\v range change value pel' mil:

Difference between 3rd quadrant elevation and 2nd:

49.8-45.7=4.11//,

which was produced by a range change (together with a site change) of

180 1\1.

Then the new range change per mil is:

180

4.1 44 M.

This is probably still a little large for the far end of the l:ange, since

it is based on a change of 180 meters, and the range value of a mil decrea.;;e~

rapidly as the range increases. Hence take 40 meters as the range change

per mil, by estimation.

The difference in elevation between the 3rd h'ial elevation and the

quadrant. elevation still l'emaining to be made up is:

49.8-49=.8'11.

The range change required to make up this difference is:

.8X40=32 or 30 1\1.

Subtract this, because the 3rd trial quadrant elevation was greater

than the minimum elevation, showing that the range was over:

2230-30=2200 M., 4th trial range.

Verify the quadrant elevation:

Toriol{ral'hy (or Field Artillery

i~~~

~ ~

-

=

=
j',

-159-

'Angle of. elevation for 2200 M. . 58.' t/I

Site (altitude shown by contours to be 380'1\1.): i:~== -9.1'/1

. Quadrant elevation, 4th trial range, 48.9111

:i, th This is within ,1,/. of the minimum elevation, so 2200 may be accepted

344.' e actual minimum range. . logicalThe~e e~ample" illustrate the method of selecting trial. ranges ,bY

a, the est~matJons, usmg the information gained through each calculatlOn

a ln'l baSIS for the next range change, Knowing that the range value 01

'ho~ld (or other angular unit), decreases as the range increases, allowance;

tha be made for this by estimation wherever the range change is greater

one meters. In example 5 such an allowance could have been made n 100' :

tak' step sooner, shortening the range change from 180 to 150 meters' and

rie~ng 2~00 meters as the third trial range, but the calculation .was carlow out m order to illustrate the point: In this exa.,..TUpIe. the ground bein~

'rheer than the guns, the first 100 meter range change was an increase.

ove; :h~n the range valae per mil, calculated from this change, was applied

the n mcrease greater than 100 meters, it was found to be too, large. If

re'v ground had been higher than the guns the situation would have been

ere' roughout. The first 100 meters change would have been a de- erRed th .'

decase, and if the range value per mil so calculated were applied over a

'rh' .' grea er an 100 meters it would have been found to be too sma . rease t th II

19 should be l'emembered in making allowances by estimation..' .. ;.

a l't Facility in making calculations and estimations will be acquired after

lIis; tIe ~raetice with map and range tables. A slide rule is of great nsra ance m making calculations. Of course it is possible simply to take trial

e'In~, arbitrarily, testing their quadrant elevations, until one is found

\Vi~a to the minimum elevation, but the calculation methods above desc~ibed

be sav~ much time and labor as soon as a little facility in using them h~s

en gamed.

III Note: The combined tangent metbod discussed under Cases nand

b i. ~e~d Space, pars. 363-370, may be used in figuring minimum range,

t~ It IS more laborious than the methods given above, because it requires

lhe calculation of ground slopes and quadrant angles of fall in addition t~

e elevation and range calculations.

3 DETERMINATION OF DEAD SPACE.

t

45• Dead space of the second class under the descending branch' of th'e

of Jcetory, IS determmed by comparing the quadrant angle or slope of fall ta'

g the projectile with the slope of the ground, Wherever there is 'a ridge, .roup of trees, or other obstruction with a reverse slope, steeper than the

oPe of fall. there will be dead space behind it. See figs. 111 t~ 117.

3 A. LIMITS OF DEAD SPACE.

t ~6. The dead space begins at the point at or ne'ar the top of the obstruc- l:~7~here the slope first commences to be st..ep~r th,an ,the slope of fall,

R lS called the gazing point, where the prOjectile Will Just graze and J{O

OVer. The dead space extends to the point of fall of the projectile on the

f~ound ~clow, ,Eve,ry peint to which the slope, in a, st~aight air-line from

, e grazmg pomt, lS greater than, the slope of fall IS In dead space. The

" ~

'

" '
)

'(.

-160-

point at which the slope from the grazing point is just equal to the slope ~f

fall is taken as the actual point of fall, or far limit of the dead space. ThIs

makes no allowance for the curve of the trajectory, but that is not necessarY

except for long dead spaces, as explained in par 356.

It is clear that the actual ground slope at the point of fall must ~e

less steep in the same direction, than the slope of fall, or the projectile

could not strike the grour.d. Every dead space includes an upper portio~

next to the gazing point where the ground slope is steeper than the slope 0

fall and a lower portion next to the point of fall, where the ground slo~e

is less steep than (or perhaps opposite to) the slope of fall. Therefore It

is not sufficient simJ:ly to measure the ground slope which is steeper that!

the slope of fall. This shows where the dead space 'begins, but not how far

it extends. The test for the far limit of the dead space is not the groun,l

slope, but the air-line slope from the grazing point. And, as previouslY

explained, the air-line sloJ:e will have to be modified to accord to the trajectory, if the dead space is very long.

n. DEAD SPACE CHARTS.

347. The problem in determining dead space is to find the grazing point

and the point of fall, the near and far limits, a1cng sevelal rays drawn o.n

the map from the gun position, through each obstruction. The first ray 18

drawn through the steeJ:est slope of a ridge or through the highest point of

a vertical obstruction, such as trees or buildings, and the limits of the dead

space are determined and marked on this ray, see fig. 109. Other rays are

1 ,,&.JtC.1 y,t

.,,,AJtC.TO~Y ,

_.,e,

A Dr-AD JPAce I

t~-=-~-~:_-~-~::_:_~_~~~~-:-=-=:~~- '\

VtI\TI~AL .5l::CT10N IN THr..PLANr:. OF.HIE.. TI\AJtCTOI\y (je,

Fig. 109.

then drawn successively on either side of the first, and the dead space is

determined for ('ach, until a ray is found on each side where there is nO

dead space. The more irregular the ground, the closer must be the rays.

Some slopes will require rays every ten mils; some only every hundred.

The corresponding points. marked on the different rays are then connected

with a smooth curve, completing the boundary of the dead area, fig. 110.

The area should be hatched lightly with a colored pencil. Dead space caused

by ground may be hatched in red, that caused by trees in green, that

caused by buildings or other constructions in blue. The hatchings for different kinds of obstructions should run in different directions so that theY

can be distinguished in case they overlap. If no colored pencils are available

the direction of the hatching will be sufficient distinction. Where de~

spaces for different charges are shown on the same chart, the area for the

greater charge will always cover and exceed the area for the lesser charge.

The two areas may be distinguished by making all the hatchings for one

charge heavier, by double-line or broken-line hatching, or by cross hatching.

TOpOgraphy lor Field Artlllel'J'
.\ 1 -161-

•hOWi xp ammg the hatehmgs and any other graph,eal dev,ees used, and egend e l... . .

ng the charges. projectiles, etc., for which the dead spaces were de-

.J)ATTtrrX

S~

,tk.1V\AL.C.HM~r., czj

. ~tDVCtD ~~4t. t::ZJ -

TOllOgral1hy 'or Field Artillery

Fig. 110.

term. tr med, always should be put on the chart. The chart is usually made on

If~n:Parent paper laid over the map, but nlay be made on the map itself.

t made on the map reference should be made to the map used.

C. METHODS OF DETERMINATION.

:US Th it' e methods of determining the limits of dead space may be divided

n 0 two classes, calculation and graphical rlotting. In the instructions and examples which follow the methods are taken

in detail, with full explcnations and proofs where required. Orientation

J leers and instructors in topography should be familiar with the entire subeet, so that they may understand the application a'nd the limitations of each

~ethed, and may be prepared to answer any questiens which nlay arise,

b owever, it is seldom practicable for line officers 01' enlisted men, who may

. e called on only occasionally to compute dead space, to go into the subject

In such detail. Such men should study the general instructions. the level

"

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-162-:.

kro'u~d method (Case I) • .'thealt-round method' (Ca'se IV), anci the slope ~;

fall chart method (example 2, under Graphical Methods). The ability to u~

these methods will be sufficient for all ordinary work.

D. COMPARISON OF ANGLES.

349. With any method except the graphical, some calculatiot\ and CO~l'

parison of angles of fall and of ground slopes is necessary. i Where t :

angle of fall is less than 330 mils, all calculations may be made throug I

mils. It makes no difference whether some of the gi'ound slopes are tOO

steep to be calculated in mils. In such case it is seen at once that the,

ground slope is steeper than the angle of fall, and it is not ne~essar)' to

find its exact value in mils. /

When the angle' of fall is over 330 mils, the ordinary mil calculatio~

of slopes is inaccurate, par. 37, and all angles should be handled in tangents,

that is. the absolute ratio of the vertical distance divided by thehorizont~l)

Since a considerable portion of the angles of fall will be greater than 33(

mils, especially with howitzers, .it is just as, well to become accustomed to

using tangents for all angles, ~mall as well as large. Paragraphs 32 to 45

.on the use of tangents should be studied in c'on~ection with dead space c~I'

culation. , '/! I

350. Tangents of angles of fall' are given in French range tables in the

column headed, "Tangent" or "Slope of Fall". If the angle in mils is not

given, it may be obtained very closely by multiplying the tangent by 1000,

provided the tangent is not over 330, pars. 52-53. The old American rang';!

tables do not give tangents directly. For angles less than 330 mils. take

the value given in mils and point off three places, which gives the tangent

within a very small error. For angles greater than 330 mils use a' tangent

table. The "Slope of Fall" column in American range tables gives the

gradient, or fall of 1 unit in a certain horizontal distance. Thisl is simply a

fractional form of tangent, and may be converted 'into the regular decimal

tangent by dividing the figure given into 1, par. 46~51. However the table

gives only two digits of the gradient for angles above 100 mils, so this con'

version is not accurate above the first decimal place. .

351. In handling tangents is should be remember~d that angle's cannot be

added or subtracted by means of their tangents. pars. 52-53, For examI'J~,

the tangent of the :quadrant' angle of fall cannot be found by taking the

tangent of the angle of fall from the table and adding or subtracting the

tangent of the angle of site. The angle of fall must be taken in .an'gular

measure (degrees or mils), and then the site added if: below the guns 01'

subtracted if above' the guns, thus giving the quadrant' angle of fall. The

tangent of this angle can then be found from a tangent table or by fnter'

polation in the tangent column of the range table. See par. 362, f;'xample 1,

Calculation Method.

(1) Tang('nt Slope Scalt.'.

352. A tangent slope scale will save much labor in calculating slope tan'

gents, which frequently are required in locating probable dead Rpace, grazing

points, and points of fall. Such a scale can be made casily for any map scale

as follows. Diyide the vertical interval between contours on the 'map by

the H. E. in the same units of measure, corresponding to the least l'eadin;r

TOI)"Kraphy (or Field Artillel'y

~ "

'
of --163--

the scale Th' . . . adjacent . IS. gIves the tangent for the slope when the M. D. between

M. D b contours IS equal to the least reading of the scale. Then, when the

ft"'t i etweeu contours is twice the least reading, the tangent is 1/2 the

i. 1/;ngent; when the M. D. is three times the least reading, the tangent

the h ~he first tangent, and so on; because the tangent varies inversely as

lIa'in0rlZontal'distance, as long as the vertical distance remains constant.

Ona g computed the tangents for the desired length of scale. make a table

lIIeasu . s l'lp 0 paper showmg the tangents correspondmg to success narrow t' f' .' . n e

a "a;,em~nts from the least reading up, and paste this on the scale. On

. Po.ite e wIth small subdivisions it is impossihle to put the tangents opneces each of the smaller graduations on the edge of the scale, so it may be

.sary t d h fOr th 0 rea t e M. D. or H. E. on the scale and then refer to a table

need e corresponding tangent. For dead space work such a tangent scale

not co culaled b vel' over 150 meters, because longer dead spaces must be cal353 y the minimum range method. . . ~or example, it is desired to make a ta~gent scale for a map of which

the • . IS 20 It F' ,J. . . iJoo ' wIth a V. I. of 5 meters. Take an ordmary centimeter . .

ncale. , 10 In fladuated to half-millimeters, each of which represcnts aa II. E. of

lcast eel's •. The half-millimeters can be bisected readily by eye, making the

, readmg one-fourth millimeter, or an H. E. of 5 meters. Take this as

the b . aSlS for the tangent table. The tangent for this distance will be -6-5

I; the t .. 5 "'.5' a angent for a half-millimeter. or an H. E. of 10 meters. will be 10

, nd so on. Make up a table to paste on the scale as follows:

TO)lol(ral1hy for f'1t'1l! Artilll'l'y

5 10 I_l~

.5 .333

800 I An~le 475 328

Mils:

n.E

Mete~s'

-_.- .

20 I 25 i 30 I 35 i 40 I 45 I 50

.25 !-:;-1~167'1:1~1.~~i-';;11~

-2~ !20IrI6~11;51-1271- 112 . ;~;

f The table should be continued in the same way up to 150 meters, or

aurthcr, if desired. It is not necessary to put the M. D. in the table, because

anYone familiar with the scale will read directly in II. E., using the scale

s~ a graphical scale. For maps not made on metric scalcs the tangent table

o ~~1d be made for the ]'egular graphical scale of the map. If made for an :(tary measuring scale the M. D. should appear in the tangent table as

. e 1 as the H. Eo, which will be in odd figures.

(2) Use Of Tangent Scale.

3:).1 T . h d' 'th b' 0 use the tangent scale or table, measure t e Istance on e mai'

d

?tween two adjacent contours and find the ta!1gent correspon<ling to this

th e m e table. Interpolate If measuremen s are ma' e c oser an lstanc . th . t 1 I th

e least reading of the table. Sometimes it will be necessary to measure

OVer several contour intervals, as 'wh<"rea number of contours are so c1os~

' '

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' '

=

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-164-

together that it is impossible to measure accurately between them, orli~

measuring the air-line slore between a grazing point and a point of !~

which are several contours apart. To obtain the tangent for such a measu~;

mente multiply the t~ng(nt corresronding' to the distance in the table d

the number of contour intervals and fractions thereof which were include

in the measurement. .

355. The angular values in mils, degrees, or grades corresponding to t~e

tangents may be taken from a standard tangent table and put on the sca e

as shown, so that the scale may be used to measure angles as well as tand

gents of slopes. Howe\'er, measurements for angular values must be limite

to one cont9ur interval, unless the scale is made specially to cover more tbaF

one. The tangent varies directly as the vertical distance, so that if the V. i

is doubled by measuri~g over two contour intervals, in the same horizontat

distance, the tangent is doubled, and so on; but the angular value does nO

vary in the same proportion. see par.' 52-53, on tangents. If it is desired to

measure angular values over more than one contour interval, make up S

special table showing the tangents for the desired number' of vertical intervals and the corrcspcnding angular values taken from a tangent table.

Then in using such a scale to measure angles, always measure over tM

number of contour intervals for which the table was-' prepared. Such scates

are sometimes m~de covering four contour intervals for general map reading.

An angular slope scale is ccnvenient for general work, but its use in d~-

termining dead space is limited to the comparison of ground slopes with

angles of fall in locating probable <.lead space an<.l grazing points. It cannot be used conven:ently for locating points of fall on account of its limitation to a fixed number of contour intervals. A tangent scale is best for dear)

space work.

E. ALLOWABLE LIMITS.

:J56. In determining <.lead space it is not necessary to make any allowanc~

Cor the curve of the trajectory, unless either the vertical or the horizonta.

d;stance from the grazing point to the point of fall, is over 150 meters.

The quadrant angle of fall at the grazing point is taken as the basis lor

calculation or plotting, nrd the trajectory is £ssumed to continue at th:lt

angle in a strnight line to the point of fall. This locates the point of laU

slightly beyond the true point, but for short dead spnces the difl'erence is

negligible. In average roll:ng country the majority of dead spnces, under

the descending branch cf the trajectory. will be less than 150 meters.

357. If the distance from grazing point to point oC fnll, either verticallY

or horizontally, is greater than 150 meters, allowance must be made for the

curve of the trajectorr. Locate the grazing point as described in par. 359.

Calculate the minimum elevation for the grazing point, and the minimurTl

range, as described in palS. 331-337, thus locating the point of fall by

means of the minimum range. Theoretically nny. dead space might be cat.

culated by the' minimum range process, but this docs not give accurate re- sults in practice for short dead spaces. .

In the examples which follow, all tangents of ground slopes are cat.

culated from the contours and <.listances scaled on the map. In actual practice this should be done with a tangent scale if nvailable, as described abo\'e.

'fopogrBvhy Cor Field Artillery
TOpojtfaphy 10f Field ArtlllefY

3'8 . F. ACCURACY. .

d~p' The degrcc of refinem.ent to which calculations should bc carried

ends th and th on e accuracy of the map,- the aceu,'acy of the mcasuremcnts,

licular e least setting of the guns. It is difficult to dcterm

ine

, in any par.

tncnt case, thc amount of thc crrors of the map and the errors of meas

urc

nea' Angular measure should be takcn to the ncarcst tenth of a mil or the

llrr mu c. angcnts should bc calculatcd to three dcclm rest m. t T . . I I . a P acc•.

tan::: ?ot exceeding 2 per cent of the tangent may be disregarded. Dis'

tnet m calculations should be taken to the nearest tenth of a yard of

to t~ where they are to be multipl.ied. but the final results should be taken

e nearest unit. . I. to l:hatever meth~d .of det~rminlng dead space is use~, the fi~st step

eau cate, by a rapId mspectlOn of the map, all J)bstructlOns which mal.

se dead space, and mark them for calculation or I;!otting.

G. CALCULATION METHOD. COMBINED TANGENTS.

3

. (1) Steps To Be Taken.

»9 ( ,",: a) Locate on the map, by estimation, a trial grazing point on the

th:rse s!ope s~leete~ for calculation. If the top of the slope breaks sharply,

POinfr~~mg pomt WIll be at the break. If the top is flat or rounded, the

CuI t 111 be some distance over, where the steeper slope commences. Cal.

Ve~.e the tangent of the slope just above the trial point; that is, divide thc (r: Ical drop (obtained from the contours) by the horizontal distance

th easurcd with a scale), carrying the result to three decimal places. In

e same way calculate the sloJ:e just below the trial grazing point.

P

. (b) Measure the range and calculate the site of the trial grazing

OInt. p' (c) Find, from the range table, the a;;gle of fall at the trial grazing.

,;:mt in angular measure (mils or degrees). Thi. gj,'es the nngl

e

of fall

q ensured from the plane of site. It must be reduced to the horizontal or

buadrant angle of fall before it can be compared with the ground slope,

t eeause all grourd slopes are measured from the horizontal. Ilence sul>,_

~act, algcbrsically the angle of site from the sngle of fall; ThuS, if the

s,:c 1. plus (above the gun level). it will be ."btractcd, srithmeticslly; if

~InUS (below the gun level) it will be added, arithmctical1Y. The result

IS the quadrant. angle of fall. . (d) Find the tangent of the quadrant angle of fall, in order to com-'

i~ro it. with. the tangents of ground slopes in locating the grazing point a~d

rn~ pomt ot fall. The tangent, correBponding to the angular measure ,n

11. or degrees, may be found from a tangent table or range table. If the

range'table does not give the exact value, interpolate between the two nearest values. See par. 362, example 1. . (e) Find the grazing point (the near limit of the dead space). Com.

Pare the quadrant angle of fall with the ground slope. calculated above r

nd below the trial grazing ~oint (both tangents). The ground slope beow the trial grazing point should be greater than the slope of fall of the

)...' ,-165-

slide r I . terpola . u e .IS a great labor faver in calculating. cspeciallY in making in.

bons m the range tables.

'

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-166-

trajectory. while'it should be less than the slope of fall above the trial point.

If this is not the case at the first trial grazing point, try other points, calculating and comparing the slopes in the same way, until the true grazing

point is found. If no ground slo'pe is found steeper than the slope of fall,

there is no dead space.. ,

, The grazing point need not be located any closer than~ twenty-five or

thirty meters. 'Unless the true grazing point is some distance from the first

trial grazing point, the same quadrant angle of fall, calculated for the first

trial point may be used for the true grazing point. The test is whether there

is a., difference in the quadrant angle of fall between the two points, large

enough to make an appreciable difference in the point of fall. Ordinarily

a change in the slope of fall of less than' five mils is negligible. Unless' the

true' grazing point differs from the first trial point by at least 5 mils in

site or. 50 meters in range, or a combination of both sufficient to make a 5

mil change in the slope of fall, it is not. usually, worth while to calculate

a new. slope of fall. ,N0 hard and fast rule can be laid down for. this. on' account of the variety of conditions which may be met, but a rough estimation

in each c3:se will tell whether a re-calculation is necessary.

(f) Find' the point of fall, the far limit of 'the dead space. This

may be done with a tangent scale by measuring from the grazing point to

successive trial points beyond, until the nearest point is found where th':?

tangent' of the air-line slope from, the grazing point is equal to the tangent

of the, quadrant angle of fall. If no tangent scale is available the tangents

~nd distances are calculated as in the following examples.

(2) ,Type Cases.

CASE I. LEVEL GROUND.

360. The' simplest case of dead space calculation is whel'e the ground 'i3

level at the point of fall, as is often the case behind trees or buildings, and

sometimes behind steep ridges or cliffs. Proceed as follows:

(a)' Locate the grazing point and find the tangent of the quadrant

angle of' fall for this point as, directed in par 359.

(b) . Calculate. from the contours, the vertical height of the grazing

point above the level of the ground where it is estimated the point of fall

will be.

(c). Divide this vertical height by the tangent of the quadrant angle

of fall. The result will be the horizontal distance from the grazing point

to the true point of fall or far limit' of dead space on the level groun~.

If a tangent scale is used, substitute ,for (b) and (c) the following::

Measure from the' grazing' point to successive trial points beyond

until the nearest point is found where the tangent of the air-line slope from

the grazing point is equal to the tangent of the quadrant angle of fall.

Mark this as the point of fall.. .

E~ampIe 1. Trees' On' Level Ground. , ., ,

361.' '.75mm.gun, at altitude 550M, H.' E. shell, reduced B. C. charge, short

fuse.": Obstruction: trees 10M high; range to far edge of trees, 4,000M, altitude o~ground at foot of ,trees, 500M, fig. 111.

'.', .. Topography for Field Artillery

'

--

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'
--:-,167-:-

~1c 30'=382*

10//1

(a) Grazing point, C, is at the far edge of the 'tree tops. Altitude

{}f grazing point, 500+ 10=510M, 401\1below battery.

-40

Site: -4- = -101//

Angle of fall' for. 4,000M,

Plus the site, (being below guns)

Quadrant angle of fall for grazing point' 3921!1

Tangent of this angle. from tangent table~ .405.

For a similar calculation using degrees and minutes throughout, see

€xample 1. Graphical Method .

.......... ':to QUADRANT; ~, ........."'1/

ANGLE OR! :ANCiLf. """!:!!.~ro

, .sLOPE. : : (If f ALL -.......;;.~

~~~~~ L-~~!~.:==-----:---~~.........~....

, HORIZONTAL

RANGE:

62111

392111

10

62

.394

.466

.072

210

30'=382'11

'250 =444111

Proportional difference

Angle of fall of 4,000M,

Next higher angle; 4,500M,

Tabular difference between angles

Quadrant angle of fall,

Tangent for 4:000M, 382111(Slope of Fall column)

Tangent for 4,500M, 444111

Tabular difference between tangents

10/62X.072=.012

.394+.012=.406, tangent of 392*, quadrant angle of fall.

This is only .001 greater than the exact tangent taken from the tan~ ,

gent table, a negligible error in calculatirig dead space. The error should

not exceed .002 in any case. if the interpolation is correctly made.

The interpolation could be made' siiriilarly in degrees and minutes if

t,he. angles were handled in those units .. .'

-'In' applying the, above. method to a ridge, where: the ground beyond

Figure 11l.

(b) Vertical height, CA, of grazing point above level of point of

fall is 10M.

(c) 10+.405=24.7 or 25M, horizontal' distance, AF, 'from grazing

point to point of .fall, .far limit of dead space.

362. Note: If no tangent table is available, the tangent of the quadrant

angle of fall may be obtained from the range table by interpolation as follo&.v8 :

Topography for Field Artillery

-

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-168-

it is level, find the true grazing point as above. Calculate its vertical height

above the level of the estimated point of fall, as if this level were produced

back under the grazing point. Proceed otherwise as in the above example.

CASE II. GROUND SLCPING DOWNWARD.

363. If the ground at the point of fall is sloping instead of level, the slope

of the ground, as well as the slope of fall, must be taken into consideration

in locating the true point of fall. This can be done very readily if the slope

is fairly uniform. For irregular ground, see Case IV. below.

For ground sloping down (same way as trajectory) at point of fall,

proceed as follows:

(a) Locate the grazing point ,and find the tangent of the quadrant

'angle of fall, as directed in par. 359.

. (b) Locate by estimation a trial point of fall on the uniform slope

beyond the foot of the obstruction. Calculate or measure the tangent of

the ground slope at this point.

(c) Find the vertical height of the grazing point above the plane

of this slope produced back under the grazing point. In the case of trees

or buildings on a uniform slope, simI=ly take the height of the trees or

buildings above the ground. If the' ground slope does not run uniformlr

back under the grazing point (as in the case of a ridge or cliff); multiply

the horizontal distance from grazing point to trial 'point of fall by the tangent of the ground slope at the latter point. Subtract this product from

.. the vertical height of the grazing point above the trial point of fall, if the

ground slopes downward, and add it, if the ground slopes upward. The

. result. is the desired vertical height of the grazing point above the slope

produced back, see examples 3 and 5.

(c) Since the ground is sloping down, subtract the tangent of the

ground slope from the tangent of the. slope of fall. Divide this difference

into the vertical height of the grazing point above the plane of slope, 'found

under (c). The result is the horizontal distance of the true point of fall

from the. grazing point. (For ground sloping up, the tangents are added

instead of subtracted, see case III and examples thereunder).

Example 2. Trees On Downward Slope.

364. Trees 10M high on contour 500. Slope. uniform down to contour 49:>,

........... 11/4

-......:..:... J~c.,.

QVADRAN~"~

ANGLE. OR . . ..........

_~Q.Pf. LA.h('; HORIZ.ONTAl 1

)

l.... .',sLOPE ......................

aROUND I :: Of fALL ............ • .

;~ #"'" ~;'~~fi,~\~, ,500, .."-.; .. ,~=<;\ i/~ ~';:,b;;\' ..........

HORIZONTAL .....Ir,,~i1,~..i:1 )~ Of" ............f C•..1~ ---.----- -1._.1 , ',""',,\"";:)'~,9i1Wi,~

H ;.: -,3 G M, DEAD .sPAC.E. -"t f"'( ",~\;,:~ . .. 40 M.,- -,--.;

Figure 112.

and for some distance beyond. 40 meters horizontal distance between contours. Other conditions same as example 1. See fig. 112.

Topography for Field Artillery

~

"" . "

"'"" ~~ __ -------- ~ " - - - - - - - "" ~ ~- - - - - - - - - - - -
•. "-:'169- .

(a) Grazing point, G, at far edge of tree tops, same as example 1,

Case 1. Tangent of quadrant angle or slope of fall same, .405.

(b) Take point, C, tm contour' 495 as trial point. of fall. Tangent

of ground slope at this point equals vertical interval divided by horizontal

distance to next co~tour, 5+40=.125.

(c) Vertical height, GA, of grazing p6fnt above plane of ground

slope, 10M (height of trees above grour.d). •

(d) Horizontal distance to true point of fall:

Vertical Height, GA

HF Tan Slope of Fall--Tan Slope of-Ground

10

A05-.125 ~5.7or36 M.

........... .

Proof:

365. GA=GH-AH ._'

GH=HFXTan Slope of Fall.

AH=HFXTan Slope of Ground.

Hence GA=HFXTan Slope of Fall-HFXTan Slope of Ground.

=HFX (Tan Slope of Fall-Tan Slope of Grour.d).

Transposing, HF = Tan Slope of Fall~:an Slope of Ground

Example 3. Downward Slope Beyond Ridge.

366 Top of ridge drops off to steep slope at contour 510M taken as grazing ,

point. Drop from 510M to 4951\1or 15M in 10 horizontal. Gentler uniform

slope commences at 495M. Drop from 495M to 490 M or 5M in 30 horizontal.

Same from 4901\1:to 485M~ Other data same as in example 1, Case I. See

fig. 113.

... ...... r. 510 "~fu$~~F-.:::..--- I .f'~;! ••-....

I :i" ..-......\

: t<l .~"-"'''' i.!2 '&';~ :::1/ .•~t:c

,~, 2 AI '~ii ~/ ..--.z:9.~

: 1:~Td:~~952/ ..-.... ~. I ~"""~ ~.,,1ik.0 GROVND -.. •• : ~I~ .\~'1 -JF""~z" ,L.'i1';% '(!j ",. -.... ••

1.r, ;;;1<:7 I "), LJ T:> '''i'~!I~~c( ~,,~ -4~ ",:::: ••

--r- ---T--r-:-&1~------ ~"liit«~lfiJ1!f~\\_\v~~)~~I.::~' -... .... ____ t!.: l-J_.5i.~y...2~z..QN...!~ J~~~~~/I.~, "''1'

I I • I ""'<i~:l~'

I ~--~OM.e>ETWELN CONTOVR6'"j • '.%'lJj I

l-c-------- 40M.--,.------t i r------ ------SGM. DEAD5PACE.------;----1

Fig. 113.

(a) I The grazing point has been located at G, as directed in par 359,

the slope above G being less and below being greater than the quadrant

angle of fall. Tangent of quadrant angle (or slope) of fall, .405, same a!o;

in example 1.

(b) Take point, C, 'on contour 490 as trial point of fall. T;he slope

is uniform above and below this point, a drop of 5M in 30, as measured

'5

from the contours. Hence tangent of slope of ground 30 =.167.

Topography for Field Artillery

'

=

=

~~

_

'

_

'

~ ~

~ ~~

----

=
. -170- ,.

(cL .Find vertical height, CA, of grazing point, C, above the plane of

~his ground slope produced back, CA:

GA=FCB-AB,

J.~'.'. 'CB=;:20M, (from contours),

Hori~ontal distance, BC, from grazing point, C, to trial point, C, scal~s

40M.AB.=:=BCXTan Slope of Gl;ound, CA, (angle BCA) =40X.167=6.7

M. Hence CA=20-6.7=13.3M.

(d) Find horizontal ,distance, HF, from grazing point, C, to point of

fall, F:

HF=

13.3

.465~.167

point of fall.

GA

Tan Slope of Fall-Tan Slope of Ground.

55.9 or 56M, horizontal distance from grazing point to

CASE Ill. GROUND SLOPING UPWARD.

367. The procedure with ground sloping upward, (opposite to the trajectory) is exactly the same as with ground sloping downward, except in finding the. height of. the grazing' point above the slope, and in combining the

tangents in:.:the' final. step,' :where the quantities are added instead of subtracted.

1:,:"" . I' Example .4. Trees On Upward Slope.

368. Same data as in example 2, Case II,. except that slope is upward.

Tre~s on. contour 500. Next contour beyond, 505. 40M horizontally from con-

,tour 500: ,.,see fig., 114.

I

C-505

~; (~\ I~~f"

I

'j

,I

CA=CH+AH,

.CH=JfFXTan Slope of Fall,

(a) Grazing point, C, at far edge of tree tops, same as in example

1 and 2. .Tangent' of quadrant angle of fall same, .405.

(b) Take po~nt, C, on contour 505 as trial point of fall. Slope is

. 5

upward, 51\1 in 40 horizontal. .T~~.gent of slope of ground= 40 =.125.

(c) Vertical height, CA, of grazing point above plane of ground ,

slope is 10M (height of trees: above ground).,

. (d) . 'Horizontal distance: from grazing point to true point of. fall,

'Vertical Height, GA 10 . . .

HF TanSlope 'ol--Falf+TanSlope ofGround ,= .405+.125 18.901'19M.. .• .•. -,; I, • ( • ..,

1.- Proof:

369.

Topog~'aphy: ;for, Field ;-\rtillery.

~~

_

I

~

= " = ~ , ~ , . , j

"
---171-

'AH=HFXTan Slope of Ground.

Hence:' GA=HFXTan Slope of Fall+HF Tan Slope of Gro~md,

, =HF (Tan Slope of Fall+TanSlope of Ground),

And: HF Tan 'Slope ~rFall:~n Slope Of 'Gr~und:'

Example 5. Upward Slope Beyond Ridge.

370. Same data as example 3, Case II, except that slope beyond steep ridge

is upward. Uniform slope commences at 495M contour. rising uniformly

5 M in 30 horizontal, fig. 115.. . ,

---..

l;

(a.) Grazing point located .at G, as in example 3.. Tangent of quadrant angle of fall, .405, same as in preceding example.

(b.) Take point, C, on contour .500 as trial point ,of fall. The slope

1s uniform above and below this point,. a rise of 5M in, 30, as measured from

the contours. .., .

Tangent of slope of ground= ;0- =.167.''-

(c,), . Find the vertical height, GA, of grazing point, G, above the plane

of this ground slope produced back, CA:

GA=GB+AB, ..

CB~10 M (from contours), ,

Horizontal distance, BC, from, grazing point, G, to trial 'point, C, scales'40 M,~

AB=BCXTanslope of ground, CA (angleBCA),

=4QX.167=6.7 M.

Hence GA=10+6.7=16.7 M.

,(d.) Horizontal distance from grazing point at true point of fall:

HF "GA !16.7 M

, : ~,Tan Slope \1f F,all+Tan Slope of Ground -;- .405+.167 = 29.2 or 29

Proof: Same as example 4. , '.

CASE IV. ALL-ROU'ND METHOD FOR REGULAR OR IRREGULAR GROUND •

.371. The, preceding methods are not practicable on irregular ground, either

where: the slope is not, uniform or whel'e the ground is rough and broken.

In such cases the following method must be used. This'method may. be

.applied on level ground or uniform slopes, even more easily than on irregular ground, and is a good method. for men inexperienced at calculations, to

use for all purposes. (On level ground it is' exactly the same as the method

Topography for. Field Artillery

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given in C~se I.) However~ an experienced calculator can save much work

on uniform slopes, especially behind trees and other vertical ob~trnctIons.

by using the methods given in Cases II and III.

Example 6. Rolling Ground Beyond Ridge •

.......... ~. G-510

~\ ~:_~I'}; -;---

t I'GtJf!};t- .•

I I 1Jr~~t\\. """'-.;

I I 1"/1\ ..............,~

I I I ~t*. -...:..:i..,,!J~C7'. I. i I ., :~\~1 ..o!{y

L 0 I ~~/;ft ••

C\.I I /~t~. ~"

I I ~1t ~v:95 aROVND , """'-.. I I I ~j~~_';j~/ ""~/ .~ 0c~~'*--'t.tM;.:t;ft/ '. I _L...t\' .:~~~::::.~~~~\~~~~~-4~Q.:.~~---~O ,i:' ~-WT l__~ ~_~L_~~I"~~ +__~ ~IJ~ .

I. tlORIZONTAL7Jr.1.)'\\[lt:;c.-1Z1\':~\\~ 'fIJll I /, .. ,~_.~?4-;~- t------------- 49 M. :.LL.lil;{'_"-'" I

!-J.----------S5 M.DEAD.5PACE---------j

Fig. 116.

372. (The procedure is the same with trees or any other obstruction.) .See

fig. 116.. Same data as in Examrle 3, except that the ground is rolling.

(a.) Locate the grazing point at, G, and calculate the tangent of the

quadrant angle of fall, which is, say. .405, the same as in the preceding

examples.. ..

(b.) Take the average' altitude of the ground beyond the obstruction

in the region where the point of fall will probably be found. In this case'

the average altitude appears from the contours to be 490 1\1. Calculate the

vertical drop of this altitude from the grazing point: 510-490=20 1\1: (distance, GA). .

(c.) Assume that the ground is level at this average altitude. Calculate the horizontal dist'ance, AB, from the grazing point, G, to the point of

fall on this level, B. the same as in example 1:

. GA 20

AB '- Tan Slope o'f Fall .4u5 49 M.

(d.) Layoff this distance from the grazing point on the map, making

point, B, as the first trial point of fall. It would be the actual point of fall

if the altitude at B were exactly 490 1\1. However, it is seen from the contours that the altitude at B is somewhat below 490; hence the actual point

of fall must be beyond B. (If the altitude is above the level for which the

trial point was calculated, the actual point of fall will be short of the

trial point.)

(e) Having located the first trial point of fall,/ the remainder of the

process is to take other trial points in the proper direction from the first,

taking into account the difference in altitude and the srope of the gl'Nmd

determined by estimation, and calculate or measure the tangent of the airline slope to each point from the grazing point. until a point is fourt} where

this tangent is equal to the tangent of the slope of fall. The same rule

obtains in calculating dead space by this method as in calculating mirimum

range: if the ground at the trial point of fall is rising, the range change

Topogi'aphy for Field. Artillery

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~

~ ~ '

0 '"'-"-... "

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to the true point of fall will be less than on level ground; if the ground is

falling, the range change will be greater. See par. 336 and example.; ,.1 and

5 under Minimum Elevation and Range.

373. In the above case, assume the dtitude at a, estimated from the contours, to be 486 meters. It is seen that the ground rises to contour 490 a

short djstance beycnd 13; hence the actual point of fall ITust be somewhere

between 13 and this contour, since 13 W2S calculated for 21titude 490. Take

point F, about half way between 13and the contour, as the next trial point of

fall. Measure the horizontal distance, HF, from the grazing point, G, which

is. say, 55 meters. Estimate the 2ltitude at F, which is, say, 488 meters,

making a vertical drop of 22 meters -from G. Then the tangent of the air22 line slope, GF, is: 55 =.400. This is only .005 less' than the tangent of the

quadrant angle of fall, .4.05, which is close enough, bei'1g within an error of

2% so F may be accepted as the actual foint cf fall.

374. If a tangent scale is used, this problem may be completed with the scale

either after (a) or (b). After (a), simply measure from the grazing point

to successive trial points beyord until the nearest point is found where the

tangent of the air-line slope from the grazing point is equal to the tangent

of the quadrant angle of fall, as in Case 1. However, it is usually quicker

to carry the calculation through (b), thus locating the approximate point of

fall, then finish the work with the tangent scale as above directed.

H. GRAPHICAL ~lETHOD.

:375. Dead space may be determined by graphical plotting as well as by

calculation. Example 1 which follows gives the graphical method in detail.

but in practice much of the wOlk is saved by the use of prepared charts of

slope of fall, as shown in example 2. The graphical- method is useful in

teaching the subject to beginners, and is also good for practical use by men

inexperienced at calculations. An experienced calculator, however: can .obtain more rapid and more accurate results with the calculation method than

with. the graphical methcd.

Method.

:376. The general procedure with the graphical method is as follows:

(a) Plot the profile cf the ground as described for visibility profiles,

par. 314, from the top of the obstruction to the probable point of fall, making the profile long enough so that both points will surely be included. The

vertical scale of the profile should be exaggerated from 5 to 10 times. This

is not absolutely necessary when wOlking with very large angles of fall and

steep ground slopes, but it is necessary in order to secure accurate results

with the majority of angles and slopes which will be handled in practice.

The exaggeration may be varied if desired, using a lesser factor for larger

angles. However. it is more convenient to use the same factor throu:;hout

any rarticular problem. Any factor between the above limits will do for

practically all dead space work~

The exact vertical exaggeration of the profile must be known so that

the tangents of the quadrant angles of fall can be exaggerated to the same

degree. If accurately ruled profile paper is available, mer sure its vertical

exaggeration as follows: Assume that the vel,tical interval between two of

. Topography for Field Artillery

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the horizontal lines on the paper is to represent the vertical interval. between

two contours on the map, which is, say, 5 meters, the R. F. being 1/20,000.

One interval on the paper will be too small for an accurate comparison of

measurements, so take 20 intervals, representing 100 meters vertically, and

measure them carefully with a scale. Say this distance measures 50.8 mm.

Now take the distance required to represent 100 meters horizontally, 'which

will be 5 mm., with the above R. F. Then the vertical exaggeration of the

profile paper is the ratio between the vertical and the horizontal measurements: 5~8 =10.16 times. (This is the exaggeration of 1/10 inch .profile

paper with a 1/20,000 map, since 50.8 mm.=2 inches, covering twenty 1/10

inch intervals). If the exaggeration' of the paper as ruled is found to be to?

great, let each interval on the paper represent two or more contour intervals,

ruling extra lines between if desired. If too small, take two or more inter-:

vals on the paper to represent a contour interval.

377. If no prepared profile paper is available, it may be ruled with any de:

sired exaggeration. A' hard pencil shoud be used, making fine lines. 'Care'

must be taken to make the measurements accurate and the lines exactly par~

allel. For example, suppose it is desired to make profile paper with an exaggeration of 8 times for a 1/20000 map, having a 5 meter contour interval:

The M. D. on the map scale to represent 5 meters horizontally will be ..25

mm. The vertical interval between the horizontal lines on the paper should

then be 8X.25=2 mm. Vertical lines may be drawn as guides in bringing

down points from the map. Paper ruled horizontally without any .vertical

lines. may be used, bringing down the points from the map with. a right-:

angled ruler held firmly against a straight edge which has been laid parallel

to the horizontal lines. It is easy to rule in the vertical guide lines, either

with the right-angled ruler or by constructing one perpendicular line, par. 72,

and drawing others parallel to it at any desired interval, say 2 to 5 mm~

~part. The interval between the vertical lines. should correspond, to some

convenieht unit of the map scale, as 10, 20, or 25 meters, to facilitate, measuring the length of dead spaces. Care must be taken to make the v~rtical

. lines exactly perpendicular to the horizontal lines and parallel with each other.

378. (b) Locate a trial grazing point by' estimation as directed in par;

359, .and mal'k it on the profile. Draw a horizontal line through this point,

taking care to make it exactly parallel with the horizontal lines ofth~ profile

paper.

379.. (c)' Calculate the tangent of the quadrant angle of fall for the trial

grazing point, par. 359. Multiply this by the vertical exaggeration of the

profile.

380. (d) Plot the' slope of fall by means of this exaggerated tangent on

the horizontal line at the trial grazing point, par. 35. If this slope of fall

line goes through the ground profile at the trial grazing point, eit shows

that that point is ~ot the true gl'azing point. Draw a new slope of fall line

exactly parallel with the first so that it just grazes the ground profile. 'Mark

the 'point where'the new slope of fall line grazes the profile as the tn~e

grazing point. Produce the new slope of fall line until it intersects the

ground profile beyond and below the grazing point. Mark the intersectiol'i

as the' point of fall. If the difference between the second grazing point, and

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the' 'first 'trial point exceeds-the limits given"in pal'. 359 (e); so that the

(liffer'ence in quadrant ~levations would cause an appreciable difference in

the location of the point' of fall, a

C new quadrartt angle of fall' must be

calculated and plotted at the second

grazing point. Usually,' however, it

is close enough to take the -line

drawn parallel to the first slope of

fall line. .

B

510

,I'

505

.. '500

~~_. A

495

, .

490

.-1:

485

Fig,' 117.

Example i.

381. To illustrate the graphical method in detail, take the problem given in

~xample 3, Case II, under the Calculation :M~thod.

(a) Suppose the slope in that example; fig. 113, to be shown by con-

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tours on a 1/2,000 map with 5 meter ,contour intervals. (Most artmer~r

work will be on 1/10,000 or 1/20,000 maps, but the large scale is used here

to make the' illustration clearer.) The M. D. for 5 meters horizontally on

this scale is 2.5 mm. Then for a vertical exaggeration of 5 times. the vertical

intervals on the profile paper should be: 5X2.5=12.5 mm. Rule the profile

paper with horizontal lines 12.5 mm. apart and vertical guide lines, say !j

mm. apart, representing 10 meters horizontally. Only a small section of the

paper will be required for this profile. but enough should be' ruled at a tiine

for all the profiles which may be needed, taking advantage of the full size

of the paper and the full length of the ruler. Mark off a sufficient section

of the paper for this profile, say 10 by 15 cm. Mark the horizontal lines at

the left of the section with the contour numbers which are to be included in

the profile, from the lowest, 485, to the highest, 510. Plot the profile, fig.

117.

(b) Select a trial grazing point, say at P. Draw a horizontal line,

AP, through P.

(c) Calculate the quadrant angle of fall at P. The range to P is

seen to be very nearly 4,000 meters, and the altitude about 513 meters, or

37 meters below the guns. Calculating degrees and minutes (for similar

calculation in mils, see exam:rle 1, Calculation Methcd):

Angle of fall for 4,COOM 21°30',

Plus the site (being below guns), 37X.86

(from Table I in Range Table) 32',

Quadrant angle of fall 22°02'

Tangent of quadrant angle of fall, from tangent table, .4047 or .405.

(This quadrant angle of f211and tangent are actually slightly less than

in examples 1 and 3, Calculation Method, because P in this example is 3

meters higher than C in the other examples, making a smaller angle of site

to be tdded. However, the diffe~ence is so small that the tangent to the

third place of decimals is the same in both cases.)

Multiply the tangent by the vertical exaggeration:

405X5=2.025, exaggerated tangent.

(d) Plot the slope of fall by this exaggerated tangent. Layoff, PH,

some convenient evend:stance, as long as the paper will allow, say 3 em.

Erect a perpendicular at B, and layoff on it BC equal to the base PB multiplied by the exaggerated tangent: 3X2.025=6.075 em. If this distance

runs off the top of the paper, fasten it over another sheet 'with pins or

thumb tacks until the :rlotting is completed. Draw, CP, the slope of fall.

It is now seen that CP goes through the ground profile at P. Hence P

is not the true grazing point. Take a ruler, and holding it parallel to PC,

move' it until it just grazes the profile at C. Mark C as the true grazing

point. Measure the distance straight across from C to line CP prcduced.'

, Mark off CD the same d:stance, and draw DC, which is thus made parallel to

CPo Produce DC until it intersects the profile below at F, which is the point 1

of fall.,

The horizontal length of the 'dead space is HF, which measures 23 mm., I",

corresponding to an H. E. of 56 meters, the same as calculated in example

3. The shifting of the grazing point from P to C was too small to have any

appreciable effect en the quadrant angle of fall ..

Topography for Field Artillery

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QUN

MCTER0 BELOW GUN

. , .

5CALE=,o,ooo

/0

2/;:

3a

'In;

sa

60

70

80

90

VERTICAL EXAGGERATION =..5 TIME0

$

Plate XVI. Note: .This graph should be on transparent paper.
-177-

Proof.

382. The proof of this may readily be derived from the proof in example

2 under the Calculation Method. In that example, see fig. 112, it was

proved that: '!:

GA

HF Tan Slope of Fall-Tan Slope of Ground

Now in plotting with a vertical exaggeration of 5 times all vertical

distances, including GA, have been multiplied 5 times. The tangent of the

ground slope has also been multiplied by 5, because:

T

Vertical Distance

angent Horizontal Distance'

par. 34, and all vertical distance have been multiplied 5 times. while the

horizontal distances remained unchanged. The tangent of the slope of fall

was increased 5 times by measurement in plotting. ~hus all three factors

of the right-hand side of the above equation were increased 5 times. Substituting the exaggerated values, the equation reads:

HF' 5 GA

5 Tan Slope of Fall- 5 Tan Slope of Ground'

from which the 5's may be eliminated by cancellation, so that:

HE' ~~~----2A--~ .

Tan Slope of Fall-Tan Slope of Ground

Hence the value of HF, the horizontal length of the dead space, is exactly

the same with the exaggerated values as with the original values.

1. GRAPHICAL METHOD WITH SLOPE OF FALL CHART.

383. The complete graphical method sho"rn in par. 381, is too slow for

practical use. The following adaptation of the method. using a slope of'

fall chaI't, is much quicker, since it eliminates the calculation of the quadrant

angles of fall, but is less accurate on that account. This method uses the

angles of fall on the gun level, just as they are given in the range tables.

making no allowances for site, as is done when the quadrant angle of fall

is taken. The result, where grazing point and point of fall are above the~

gun level, is to make the plotted dead space a little shorter than the actual

dead space, because the slope of fall at the gun level is a little steeper than

the slope at both grazing point and point of fall. Where grazing point and

point of fall are below the gun level, the plotted dead space will be a little

longer than the actual dead space, because the slope of fall at the gun level

is less steep than at the grazing point and point of fall. Where the grazing

point is above the gun level and the point of fall below, the slope of fall at

the gun level will be steeper than at the grazing point and less steep than

at the point of fall. .Hence if the relative distances happen to be correctly

proportioned, the slope of fall at the gun level will represent the average

slope between grazing point and point of fall, and, the plotted dead space

will give the true value. Otherwise it may be slightly greater or slightly

less. In any case, wherever the grazing point is a~ove and the point of fall

below the gun level,' this method will give closer results than where both

points are above or below. It is not necessary for the user to make allowances

for these conditions, but he should understand them in order to know the

Topography for Field Artillery

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limitations of the method. A practical rule to remember is: . Do not use this

method where the site of the point of fall, whether above or below the gun

level, exceeds 20 mils. This method is also subject to the same limitation

as the others: that where the vertical or horizontal distance fl'om grazing

point to point of fall exceeds 150 meters,' the dead space should be calculated

by the minimum range method: Within these limits this method gives results which are close enough for most practical purposes. In average country the majority of dead spaces under the descending branch of the trajectory come within the above limits.

The following example illustrates this method.

Example 2.

384. (a) Prepare a slope of fall chart on tough transparent paper as follows, fig. 118. Layoff a base line representing the gun level. On this mark

GVN LlVLL

RANQE

TANGENT

ANGLEOF FALL

EXAG G ERATED

5 TIMt.s

3500 4000' 4500

.J 83 .232.288

.915 I.IG 1.44

C

---.5l0PE~ OFfAl~

Fig. 118.

the ranges every 500 meters from the shortest range likely to be used, say

2,000 meters, up to the maximum range of the guns. Find from the range

table the tangent of the angle of fall for each range. Multiply this by the

vertical exaggeration factor which is to be used for the profiles. Plot the -I

slope of fall by the exaggerated tangent for each range on the gun level ,

line, extending the slope 3 to 4 em. above and below the gun level line. This

chart may be preserved and used for determining dead space at any time

for the same scale of map and the same gun, charge, etc., for which it was

made.

(b) Plot the profiles as described in example 1 above. O~ each

profile draw a line showing the gun level, and mark the nearest 500 meter

range on this line.

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(c) Lay the slope of fall chart over the profile so that the gun level

line and the range marks on the transparent chart. coincide with the corresponding line and ~arks on the profile. If none of the slope lines on the

chart happens to just graze the profile, draw a line by interpolation between

the two nearest lines, as shown. This is done b'y measuring first, A G and

A'e, straight across, then measuring off points, D and E so that the corresponding distances are proportional to AG and A'G, and connecting DGE.

which is the desil'ed interpolated slope line. Grazing point, G, and point of

fall, F, are then pricked through onto the profile with a needle.

385. Instead of interpolating a new slope line, the following method, which

is somewhat quicker, may be used: . Slide the chart along until the nearest

slope line. on one side, say the 4,000 meter line in this case, just grazes the.

profile. Mark on the profile the grazing point and point of fall thus located

as first trial points. Then slide the chart back until the next line on the

other side, in this case the 4,500 meter line, ,just gI1.zes the profile. Mark

the grazing point and point of fall thus located as second trial points. Then

mark the poin~ midway between the two trial grazing points as the actual

grazing point, and the point midway between the two trial points of fall as

the actual point of fall.

If the profile is very close to a slope of fall line, say within 50 meters,

it is not necessary to interpolate between the slope lines. Draw a line parallel to the nearest slope line, or slide the chart along until the nearest slope

line grazes the profile. It is a mistake to attempt to make a slope of fall line on such a chart

correspond to the quadrant angle of fall at the grazing point by laying the

gun level line of the chart along a line drawn from the gun position to the

grazing point on the exaggerated profile. This method affects the tangent

by an amount which is out of all proportion to the true value of the site.

The only way to show_ the quadrant angle of fall graphically, except with

special charts, is to calculate and plot it on it: horizontal line as shown in

example 1.

J. GRAPHICAL METHOD WITH SPECIAL CHARTS.

386. Special graphical charts by which the angle of site and the curve

the trajectory are allowed for are sometimes prepared and issued, with

directions for their use. Such charts are very convenient when available, but

the preparation of them usually is too complicated for the ordinary artiller~'-

man in the field. Such graphs should be prepared at corps. headquarters

and issued to each battery.

Topography for Field Artillery

(1) Description Of The Graph.

387. , The method employed with this graph is simply that of a rapid projection of a given trajectory to the surface of the ground as represented by

the map. And since the method is one projection, all that is needed is a

. series of trajectories drawn to the same horizontal scale as the map and to

any convenient vertical exaggeration.

Since the method of projection is to be used in handling the graph, it

is necessary first, that a series of parallel lines be drawn representing

ground elevations above and belov; the gun position. A 10 meter interval

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and a total difference of 100 meters above and 100 meters below the g'un

is sufficient for most terrain.

"With a zero plane of site construct a series of trajectories for the

particular gun and charge used, on the determined scale of vertical exaggeration. Note: It will be necessary to construct each curve separately as an

attempt to draw in trajectories of lesser range by revolving one of greater

range which has been exaggerated vertically will result in a diagonal ex-'

aggeration of the lesser trajectories. These trajectories should be drawn

in for every 100 meters. For points between, interpolation of curves can be

made by estimation as the need arises in the consideration of ground forms.

Divide each of the parallel lines representing the ground elevations

above or below the gun level, into a series. of intervals representing the

horizontal distance which a given projectile will travel while dropping 10

meters at that particular range and elevation. These divisions afford a rapid

method of determining grazing points although not actually necessary to

the graph, since the trajectory curves. alone may be used for the purpose.

See Plate XVI.

(2) Use Of The Graph. ,

388. To use the graph draw a ray through the gun position and the area

being considered. From an inspection of the map determine the point most

likely to mark the near limit of the dead space and note the elevation of this

point.

Place the graph on the map so that the horizontal line, corresponding

to the elevation above the gun, just noted, lies along the ray, CPB, drawn

from the gun, see fig. 119. and so that the perpendicular line with zero range

passes through the gun position.

Q ,I

V I 0 0 t q-

.....J"s~

6(

.....Jo ,G B 3

2C

10

() I

l

3

Fig. 119.

To determine if P is the grazing point take the trajectory passing

through P and follow it down to a point 10 meters below. Project this point

upward to the ray considered by laying a ruler across this' point in the trajectory, at right angles to the parallel lines, and note where the rule crosses the

line of fire on the ray CPB. By reading the contours it will be noted that

"Topography for Field Artillery

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the rule crosses CPR between contours 325 and 330 or at a point about 12'

meters below P.

However the trajectory in this same horizontal distance has fallen

only 10 meters. Since the ground has dropped 12 tneters, the surface of the

terrain cannot be reached by fire and is dead spa~e. Evidently then, P is

the grazing point. Should the slope of the ground and that of the trajectory

be found to be exactly the same, P should still be considered to be the grazing point and the beginning of the dead area.

.If there were another 'contour showing above P, a point would betaken on that contour and would be examined in the same manner for a

possible grazing point.

Having determined the near edge of the dead space, or the grazingpoint of the trajectory, the next step is to determine the far limits of the

dead area. This can be done merely by moving the ruler to the right along

the trajectory,' (keeping it perpendicular to the paratIel lines) and noting

the point where the ground elevations, read along the ray, CPR, correspond to

the elevations on the horizontal lines.

Thus at a point 30 meters below the level of P, or on a line marked

10 (10 meters above the gun level) it will be noted that the ruler, where it

crosses CPR falls between contours 305 and 310. In other words while the

trajectory has dropped 30 meters, the ground has fallen away 33 meters.

When the ruler has been moved to the gun level (the line marked 0)

the ruler crosses the ray between. contour 300 and 305. That is, the trajectory has fallen 40 meters while the ground has dropped but 37. Therefore

the point. considered last is in beaten area and the limit of the dead area

must lie between the two points considered.

Moving/back to x, a point 5 meters above the gun level, it is noted

that the ruler crosses CPR at the corresponding elevation, or at contour 305,

which may, therefore, be taken as the far limit of the dead space on this

, particular ray. Instead of projecting upward from the trajectory, some find it easier

to project downward from the contours, as they cross CPR, to the corres-

. ponding horizontal lines and note whether the points so projected are~

above or below the trajectory. A point below the trajectory is in dead

area; a point above is in the beaten zone.

389. To use the horizontal intervals marked on the parallel lines as aboveo I{) Eg~ ;ti ..".tr') tr')tV

'.~ \ '" t .. I Pill i I P'i I: ,I I U

~ /i\\'

Fig. 120.

B

for the purpose of determining the grazing points proceed as folows, fig. 120:

Assume that ray CPR is being examined and P is selected as a possible

Topography for Field Artillery

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grazing point. From a comparison of contours it is seen that point P is 20

meters above the gun. Therefore the graph is laid over the ray CPBso that

the line 20 meters above the gun level coincides with the ray in the manner

already described.

By a comparison of intervals with the contours crossed, it is seen that

in the interval representing a drop of 10 meters in the trajectory, the ground

falls away but 7 meters. Evidently P is not the grazing point. It remains

then to try a second point. Let the second point considered be pi on contour'

310 which is 10 meters above the gun levet' The graph must be moved

vertically upward until the line numbered 10 corresponding to the ground

level considered, lies along the 1'ay CPB.'

If this is done it will be found that the two contour intervals correslng to a 10 meter drop in ground elevation, lie within the interval used. 01',

the ground drops nearly 12 meters while the trajectory is descending 10.

Therefore the area is dead and pi may be conside1'ed the grazing point.

In using this method of determining the grazing point it may be

necessary to move the transparency to the right- 01' left slightly until the

limits of one of the intervals coincide with a contour line. Care must be

exercised in doing this because such a movement changes the range on the

graph and a change of range changes the interval for a 10 meter drop. It

is safer and even more rapid to set o~, on a pair of dividers, the 10 meter

interval taken from the map, and apply this interval to the graph for th0

I'ame range and elevation.

The above graphs should be made on sheets of light celluloid for each

projectile and carried with the battery plotting board where they will take

up no appreciable room.

The advantage of the graph is that it is a time saver compared to the

ordinary graphical method since it is not necessary to construct profiles.

Compared to the computation method it is more rapid while its accuracy is

quite satisfactory, variations between ,the two methods being in most instances less than the probable enol' of the gun.

Tovography for Field Artillery

,

:.

I ,

I

.

,I

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CHAPTER XVI.

MAP PROJECTIONS.

DEFINITION.

390. As has been stated elsewhere. a map is a representation, to scale, of

a certain portion of the earth's surface. Its purpose is to afford information.

Therefore maps are of varied sorts' depending on the information desired.

Moreover a map usually is a plane or flat surface while the surface of the

earth is in the shape of a spheroid. It will be seen. therefore, that certain difflculties ~are met by the cartographer, in the course of map making, when projecting a certain portion of

the earth's surface, reduced in scale, upon a flat sheet of paper. The means

by which this is done is called projection. There are many types of projection involving different formulae in spherical trigonometry'. It is not the

purpose of this text to workout these fOl'mulae but rather to show the application of the various methods and to. point out the value of each fot'

certain definite uses.

The cartographer will choose the method of projection which will

least affect the accuracy of the work in hand. •

TopOlJ,'l'allhy for Field Al'tillel'y

40 20 0 fO

-~

0

,

R. /

(I F \ ) I

I ./

\ I

\ .. \ I / \ \ I / ~ ,~-r:::.. .4 , CYUNDE .-- ~""'¥-'-'--------TA'N<;E:NT M_RlDIAN Of LCNq TVDE.

TO qLoBE AT [CWi\TOR.

. Fig. 121. ,

with this projection are exact, but. beginning immediately north and south.

a distortion is encountered as the poles are approached. At the poles this

KINDS OF PROJECTION.

A. MERCATOR'S PROJECTION.

391. The oldest form of projection is the Mercator Projection, and is employed in making Navigator's charts. In this method the surface of the

earth is projected outward to the surface of an enclosing cylinder which i3

tangent to the globe at the equator. Because the line on the cylinder and

the globe coincide at the equator, distances along the equator on a map made

MERCATORj pgOJECT/ON

NORTH-POLE. .-. • .LU90 lUo .....i=: .:t- \ ex.ti

\ C3:--J

-" J:~V.M~QR

' ~ ~ __

_

~

~ ~ __ __ _ _ ~

- -
POLYHEDRAL PROJECTioN

MfRIDIAN,5 OF LONqlnJOE.

Fig. 122.

-184-

is the greatest, for the pole has been projected outward in all direction::;

until it becomes a line represented by the circumference of the top of the

cylinder, and is as great as the equator itself.

Thus the Mercator projection creates noticeable distortion in maps of

North America and Asia.

The navigator however is concerned only with latitude and longitude

and therefore can use the projection above described. This would not be

satisfactory for the person who was measuring land areas, nor-for the artil-"

leryman who wishes to measure angles and distances with precision.

Figure 121, above, shows the projection of the globe outward to the

surface of the cylinder; also the map formed when the cylinder is slit

down one side and unrolled.

B. POLYHEDRAL PROJECTION.

392. The Polyhedral is a common form of projection which may be used

in mapping siege areas and cities, since only limited areas are involved. In

this system each small area mapped is represented by an isosceles trapezoid,

the parallel sides of .which "are

equal in length to the arcs of the

corresponding parallels, while the

oblique ones are equal to the arcs

of the meridians comprised between the"se parallels.

The accurate assembling of

these small areas into a larger

whole is impossible. It only can

be done approximately by the play

of the paper, see fig. 122.

C. CONIC PROJECTIONS.

393. The most common form of projection is. the Conic of which there are

various types. In this, a cone is passed tangent to the surface of the globe

, and the surface underneath the cone is projected outward to the surface of

the cone. At the point where the cone is tangent to the globe, the distances

on the map wilI"correspond to those on the globe. Elsewhere the distortion

will increase as the line of tangency is left behind. This distortion is minimized by the application of certain mathematical formulae. The formula

to be applied will vary, according to the purpose to which the Jllap will

be applied. Figure 123 shows the cone tangent to the globe, also the same

cone after being split down one side and f~attened out to form a map.

D. POLYCONICPROJECTION.

394. The Polyconic Projection is a modification of the conic projection. It

was devised by Ferdinand Hassler, the first supel'intendent of the U. S. Coast

and Geodetic Survey', and has been applied to maps of the United States.

In it a series of cones has been passed tangent to the globe, the cones

having their apexes on the prolongation of the axis of the earth. Segments

of the cones, each with its central parallel, when unrolled, form a map which

is satisfactory along a north and south area in the vicinity of the common

meridian of origin; while the distortion east and west of the meridian inTO}lography for Field Artillery

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creases with the distance from it, due to the increasing divel'gence of the

. several segments. Such a map causes an error as great as 6! % on the

Pacific Coast of the United States, while a map of the. United States on the

PROJECTiON'!:

Fig. 123.

oK . :K :1"" ... -' -' ..... . . .

.. : : POLYCONIC

Lambert pl'ojeetion would show a maximum distortion -north and south 'of

only 2%. The figure on the left, fig. 124, shows the centres (K, K1, K2,

K3) of circles, on the projection, that represent the conesponding parallels

on the earth. The figure on the right shows the distortion at the outer

meridian due to the varying radii of the circles in the polyconic development.

Topography for Field Artillery

Fig. 124.

E. BONNE PROJECTION.

395. British and Belgian battle maps in the recent war were. made usingthe so-called Bonne Projection, another of the conic systems. The origin. of

this projection for these maps was Brussels. The earlier French battle maps

were also made using this projection taking'the town of Aurillac, Lat. 450

North, to the south of Paris, on the Paris meridian, as. the origin.

In this projection the meridian through the origin is a straight line.

All other meridians are curves, the curvature increasing with the difference

in longitude. The parallels are represented by concentric circles, with centres

at, S, north of the pole, p, the distance between the concentric circles being

equal to the lengths of the arcs of the meridians upon the globe. See fig.

- - - - - - - - - ~
 
"--186-";'

125., In this projection areas are preserved near the initial parallel and mer- .

idian; angles and distances along the initial parallel and meridian are pre-.

served in their exact relation; but departure from them brings distortions

which, at the edges of the map. of. France, reach a value of 18' for angles and

1/379 for lengths. These distortions are too great for use in computations

for artillery fire.

s

BONNE. PROJECTION

p

DISTANCE BETWEEN PARALL[L~

E:QUAL TO JlCTlLAL DI.5TANCE oN {1LClBE:

Fig. 125.

BONNE: PROJECTION Of HEMISPHERE

Dev",Lopment of conq, tangent a.long pa.raLLcz,l4SoN

160

EQvAmf.l

o

Fig. 126.

F. LAMBERT PROJECTION.

396. Because all projections, heretofore described, admitted too great a

distortion in angles and linear measurements, the French were forced to reSUlTect another projection at the beginning of the 'World 'War. The LamTopography for Field Artillery
-187~

hert Conformal Conic Projection was found to be satisfactory for artillery

Purposes due to the fact that angular and linear distortions were practically

negligible in any of the mapped areas likely to be used by artillery of any

calibre. .

This projection was evolved by .Johann Heinrich Lambert, an Alsatian

(1728-1777). Lambert was a noted cartographer and mathematician who

worked out another projection which bears his name. The one used in French

battle maps is k~own as t~e Lambert Conformal Conic Projection.

For a base map covering a zone 500 kilometers in width, or 250 kilometers on either side of the parallel of origin, 49° 30' (=55 grades) north

latitude, this projection shows a degree of precision which is unique, and

which answers every requirement as to orientation, as to direction and distance, and quadrillage (system of kilometric squares). It is admirably

adapted to a region of predominating east and west diIllfnsions, hence with

it, all the northeastern region of France, as well as Belgium and part of

Germany, can be represented on one map. It can be extended east and

west as far as desired, the projection remaining conformal throughout.

The angular distortion is so small as to be negligible and the linear

di:5tortion is no more than .05 per cent (1 meter in 2000 meters) which is

nearly negligible. It is to be borne in mind however that this is only true

within the base map, north and south limits of which, are indicated above.

In this conic projection the cone is secant to the globe instead of being

tangent to it; that is, the cone cuts the globe in two places,see fig. 127.

These two places at which the cone cuts the spheroid or globe are,

for the French battle map, along the 53 and 57 grade parallels as shown in

the figure. The origin of the projection is taken at 6 grades east of Paris

(called -6 grades longitude, since longitude east of Paris is minus and .thDt

west is plus), and at 55 grades nOlth latitude. Meridians are straight lines

perpendicular to the arcs representing the parallels~ see fig. 127.

Obviously along the pal'allels of 53 and 57 north latitude, distances en

the map will correspond to those on the globe. The arc or sector of the

globe between these parallels is somewhat distOl'ted in flattening it down

to the surface of the cone.. Two formulae may be used in caring for this

distortion, one of which is exact while the other is approximate. (See "Manual for Orienbtion Officer", "W. D. Doc. No. 648", also "The Lambert Conformal Conic Projection" by Deetz, Special publication No: 47, gov. printing

office.)

397. In summing up, the Lambert conformal conic projection preserves

angles and distances with negligible distortion within a belt whose north and

south dimension is limited to the battle area of France and Belgium, but

whose east and west dimension is not. This is the only projection as yet

devised giving these relations of the earth's surface on a plane surface Ol'

map in sufficient exactness for use in modern artillery warfare. Such a

projection is well suited for mapping the United States where the greatest

dimension is east and west.

Below is appended a chart showing the Lambert conformal conic proJection, as applied by the French in the recent war, to France, Belgium and

Germany. See Plate XVII. It will be. noted that a portion of the grid system is also shown near its origin (which coincides with the origin of the proTOPOgrallhy for Field Artillel'Y

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jection). In the chart the grid is not shown to scale, the lines being apLAMBERT '..5 CONfORMAL'

CONIC PROJE.CTION.

Fig. 127.

proximately 4 kilometers apart in place of 1 kilometer.

This grid s~rstem is discussed in Chapter XVIII.

Topography for Field Artillery

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CHAPTER XVII.

l\iAPS.

PREPARATION OF MAPS.

A. TRIANGULATION SYSTEM.

:l98. After the cartographer has adopted a system of projection for his

map, his next concern is to place on this map, the points of the ground in

their proper relation as modified by the form of the projection.

The determination of the relation of the ground#Points is the work

of the topographers all of whose work is based on the triangulation system.

This system consists of a series of triangles. the vertices of which are accurately located. This framework gives starting points from which any

detail may be plotted, see fig. 128. From astronomical observations one of

these vertices, A, may be located and one side AB, selected as base line, by

means of which the surveyor may orient himself. If this base is measured

with great accuracy. point B may be located.'

The' angles of the different triangles being measured, coordinates of

C, D •••• M, N may be determined. The operation is checked by astronomical

observations at N and the measur'ement of the base MN.

A

This skeleton is the primary triangulation. The sides of the triangles

are 40 or 50 kilometers long. Angles are measured with the greatest accuracy. The accuracy of the base measurement must be about 1/1,000,000.

399. Starting from the system just described, the secondary triangulation

is carried out within the primary triangles. Points located by intersection

constitute the third or tertiary triangl,llation. Errors on points may be as

great as 2/10 to 3/10 meters in the primary triangulation, 1/2 meter in

Topography for Field Artillery
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the secondary triangulation, and from 1 meter to 2 meters in tertiary triangulations.

This network of lines and points is completed by traversings,. by means

. of a transit. Calculation then gives the location of the successive vertices of

these traverses.

With all of these determined points at hand the topographer may noW

draw on his plotting table any detail of the ground; may horizontally and

vertically locate, accurately, any critical point; and may give on the map the

representation of as many features of the area as required according to the

use for which the map is intended. This part of the survey is called

topography.

B. RANGE TRIANGULATION DETACHMENT.

400. The 'York of the Range Triangulation Detachment (detachment of

engineers) consists, in general, of keeping up to date all maps, and determining the location and elevation of a net of reference points more closely

spaced than those of the general control.

As an army advances it is the duty of these detachments to secure

all possible information of a topographical nature which will aid in preparation of firing data for the artillery.

The work done on the ground is started with kno\\>"1ldata from the

triangulation net as described in the paragraphs above.

401. Preparation of revisions of battle maps is a function of this branch

of the service. Revised battle maps are frequently printed and issued (every

day in periods of activity). Reconnaissances and topographical surveys a1'3

constantly made on the ground. and bulletins and revised maps are issued

by these detachments. Battle maps showing enemy works only are dis--

tributed down to the Battery Commander. Distribution of maps showing

friendly works is limited to a few officers, usually battalion commander~~.

These maps must not be taken into the front line. All of these maps an:!

bulletins are confidential documents and consequently should be burned when

obsolete or when capture seems imminent.

C. SERVIC:[<~OF INFORMATION.

4112. Mention has been made in this chapter of the information rendered by I.!

the engineer detachments, or Range Triangulation Detachments in prepar- ,

ing and keeping up to date, maps and list of reference points, in particular

the Plan Directeur or battle maps.

The Artillery Information Service (A. 1. S.) with which the range'

triangulation and topographic sections work for the distribution of all topo- J

graphical data that may be obtained, furnishes the artillery with valuable

. information of many sorts. The officer in charge of this service in the army

and corps is called the Artillery Information Officer (A. 1. 0.)

403. The A. I. S. should furnish promptly the necessary information for the

execution of the missions of the artillery unit such as exact positions of

enemy batterL~s, command posts, observation posts, signalling posts, camps,

dugouts and ammunition dumps. trails and roads most used, with hours of

heaviest traffic, etc .

. The most effective and active enemy batteries and the exact time

when they can be attacked most effectively is not~d in frequent bulletins.

Topog:raphy for Field Artillery

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The direct control of the work of the flash ranging and sound ranging sections and regulation of their use by artillery units, the maintenance of

communication with the:rn and prompt handling of information thus obtained, is' another function of th~ A. 1. S.

Aerial photographs are used t~ study the det::iils of objectives.. Conclusions from such a study and those drawn from other observation, or information, is here coordinated and daily bulletins are issued to the' artillery

by the service.

404. The A. 1. S. works in close cooperation with G-2 (Army or Corps

Information Service) in receiving; comparing and forwarding information .

.Important information is communicated .at once by telephone, daily bulletins

are exchanged, and frequent conferences are held where all information received is discussed and verified. For this purpose G-2 sends to each army

and corps A. I. S., an intelligence "officer, whose function is to obtain all

artillery information required by G-2. #'

Thus from every source, including prisoners and intercepted mdio and

telephone messages, the mass of information secured is compared and coordinated and is issued in the form of orders, bulletins and maps to the

artillerr In an active sector this information is rendered daily.

MAPS OF VARIOUS COUNTRIES.

A. FRENCH MAPS.

(1.) History Of French Maps.

405. (a) The 1/80,000 map, in black, is the French Staff map, reduced

from surveys on a 1/40.000 scale. This work was undertaken at the beginning of .the 19th century and was finished some sixty years later .. It

includes France and Alsace-Lorraine and was revised as to France only.

The projection used is the Bonne (Lo=50 grades north latitude, Mo=meridian of Paris). Each sheet is divided into 4 quarters extending over 20X32 ,

kilometers. The accuracy is good as to geodetic points., The error on other

points may reach 100 meters horizontally.

Ground forms are located by hachures. Elevations are marked op,.

posite geodetic points.

406. (b). The 1/50,000 in black is a photographic enlargement of the

1/80,000. Its accuracy is therefore the same. Grid lines are dra'\<'Il on.

it. The 1/20,000 battle map on the Bonne projection is a further enlargement of the Staff map with the hachures' removed. Elevations are shown

by contours in brown. French lines are in red and German are blue. This

map is provided with the Bonne grid. Some of these maps near the areas

which have been mapped under the Lambert projection also carry the Lambert grid. In the areas near the Paris meridian this map proved to be no

satisfactory firing map.

407. (c) The 1/10,000 in black are the former battle maps of fortified

towns and are the result of precise surveys made on the ground on a scale

of 1/10,000. The projection is the polyhedral. The usual contour interval

is 5 meters. but for level regions it is 2.5 meters.

408. (d) The 1/20,000 in black is a photographic reduction of the

1/10,000. Each sheet includes four 1/10,000 sheets which are not fitted

together but simply placed side by side. with intervals between them. It

Topography for Field Artillery

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follows that these maps cannot be used with accuracy for the measurement

of angles and distances.

On these 1/10,000 and 1/20,000 maps, points are accurate withh

10 meters horizontally and, on moderately rolling country, within 5 meter3

in altitude.

409. (e) The 1/50,000 map in colors is based on accurate surveys oni

1/10,000 scale in level districts and on surveys on a 1/20,000 scale in

mountainous country. The projection is polyhedral. Each sheet represents

an area 20 centesimal minutes in latitude by 40 in longitude. Altitudes

are represented by contour intervals of 10 meters, supplemented by shading.

The maps are printed in eight colors. They are in course of preparation

and therefore cover at present a very small part of France.

410. (f) The 1/200,000 in colors is derived from the 1/80,000. Each

sheet covers 128X80 kilometers. Contour intervals are 40 meters, with intermediate contours in level country at a V. 1. of 20 meters. Principal

contours are shown at each 200 meter interval by a line heavier than the

others. This map is printed in 6 colors supplemented by shading. On a

new type (1912) contours are drawn with V•. 1. of 20 meters. .

(2.) Battle Maps (Plan Directeur).

411. Battle maps are maps of large scale on which are shown enemy works

and, in certain cases, the friendly defensive and offensive organizations.

The Lambert projection is used for most of the battle maps. These maps

take precedence, to the exclusion of all other documents, for all the names

to be employed in orders, instructions and reports.

Battle maps showing the trace of the enemy lines are made, as regards scale and size, according to the following types, each of which is

adapted to the particular requirement of the commander, the staffs or of the

different branches of the service.

412. (a) On a scale of 1/20,000 (the map usually meant when the term

"Plan directeur" is used). This is designed especially for the use of the

artillery. It is used for designating targets and for conducting fire, particularly on enemy batteries. It also affords the commander a map ona

, scale which gives a complete idea of the general layout of the enemy's defense. Finally it constitutes a map of the whole into which may be combined all maps of smaller area, but larger scale. It permits this combination and insures that all have the same titles and conventional signs. It is

distributed dov."Ilto include battery commanders.

'413. '(b) The 1/10,000 is a map of greater detail, showing the traces of

the enemy trenches in such detail as cannot be put on a 1/20,000 map.

It is issued to and used by the staffs and down to and including battalion

commanders. It is used by artillery in firing on enemy trenches and works

where their exact location cannot be seen from an observation post. In general it is of more value' to the light artillery and infantry than the heavy

artiUery.

414. (c) The 1/5,000 is a detailed sketch for use in attack. It is in reality an infantry map but is used also by the light artillery in direct support

of the infantry. This map is intended to provide an accurate picture of the

terrain. On it is developed a complete representation of all known details

of the enemy trenches.

Topography for Field Artillery

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415. In general each sheet of the Plan Directeur or battle map receives a

serial number and a title. This title is the name of the locality said to be

,the most important in the vicinity. A date is plac~d upon it, the date on

which the last data were obtained for the map.

In all of the above, except for the trace of the front line. the details

of the friendly trenches are mostly omitted so that if a map falls' into enemy

hands it will be of little value to the foe.

The French, however, make a battle map on the 1/10,000 scale which

:-;howsthe friendly trenches to the last detail. This map is issued only to

a few trusted officers and is jealously' guarded.

B. MAPS OF BELGIUM .

.H6. The 1/20,000 map in black is compiled from land title (cadastral)

maps reduced to this scale and verified and filled in detail from fresh surveys.

Bonne's projection for the meridian of Brussels and the parallel of 56 grade;.;

is used. The relief is shown by contours representing vertical intervals of 1

meter on the left bank of the Meuse and 5 meters on. the right bank.

Some sheets have been magnified to the scale of 1/10,000.

The 1/40,000 map in black is established by joining and reducing the

1/20,000. The contour interval is 5 meters. A new editipn is' published

with watercourses in blue and roads in red.

The 1/100,000 in six colors is reduced from the 1/40,000. Each sheet

includes two sheets and two half sheets' of' the 1/40,000 map. The contour

interval is 10 meters.

c. MAPS OF GERMANY.

417. The 1/25.000 sheets in black are the reproduction of the original surveys intended to be the basis of the 1/100,000 map._....The projection used is

the polyhedral, and the area represented is. about 144 square kilometers.

Contour intervals are 10 meters in broken country and 5 meters for slightly

rolling'eountry, with 2.5 and even 1.25 meters on gentle slopes. Principal

contours are shown every 20 meters.

. The 1/100,000 in black is a reduction of the 1/25,000. Altitudes are

expressed by hachures. These maps have been magnified into 1/50,000 by

.the French Service Geographique.

D. BRITISH MAPS.

See Appendix II.

TopOgraphy for Field Artillery

j

~
CHAPTER XVIII.

THE LAMBERT GRID.

ORIGIN.

418. In Chapter XVI on map projections mention was made of the fact

that the origin of the Lambert projection, used in tke preparation of the

battle maps, employed in the late war, is located on the meridian of 6

grades east of Paris and at a point on it 55 grades north latitude. A plate

also was included showing the map as made from the projection, with a portion of a grid at the origin of the projection as above noted.

This grid, consisting of parallel lines forming squares one kilometer

on a side, has been called the Lambert Grid simply because it has been used

with maps made on the Lambert projection, and because the origin of th,~

grid, for the sake of convenience and simplicity, has been made identical

with' the ,origin of the projection.' The map having been made, the grid

is rolled out upon it.

COORDINATES.

419. Compared with the method of designation of a point by means of geographical coordinates or by other systems of grids, the Lambert grid is by

far the easiest and most rapid of all methods devised for .designating a point

or objective. The north and south lines of the grid are called the Y lines.

The east and west lines are called the X lines- The Y axis (central Y line

of the grid) passes through the origin of the projection and is therefore coincident with the meridian of 6 grades east of Paris.

The X axis passes through the origin of the projection also, and is

tangent at that point to the parallel of the origin (55 grades north latitude).

All X and Y lines are perpendicular to one another.

A. COORDINATES OF ORIGIN.

420: To avoid confusion the origin of the grid is not 0 for the X and 0 for

the Y, since this numbering would necessitate the handling of both negative

~nd positive values. Such a consequence precludes any "0, 0", point on terrain in the battle area. This "0, 0" point does occur, but at a point well

removed from the battle 'line, where the matter is of. no moment.

Actually the origin has been given the following coordinates: X=

500,000, Y=300,000, which means that the "0, 0," point is 300,000 meters

south of the origin and 500,000 meters west of it. With a metric scale,

therefore, a point can. be located without confusion down to the last meter

by dividing each square into 1000 parts by means of the scale. The distanc(~

from left to right along the X line or abscissa is first read, then the distanc0

upward along the ordinate or Y line is read until opposite the point in question.

B. COMPLETE COORDINATES.

421. Distances along any X line from the 0 of the system are recorded by

Topography for Field Artillery

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means of the subdivisions on that X line made by the intersection of the Y

'lines. Similarly distanc~s on any Y line from the 0 of the system are recorded by means of the subdivisions on that Y line made by the intersecting

X lines. A point is always designated 'by taking the values (XY) of the

southwest corner of a kilometric square, then reading to the right or east

from that point, thence up or north to the point itself. Complete co~rdinates are given in six figures for each axis,. the X always being given first.

see fig. 129.

X- LINES

I

pOINr-A

X-50e.200

Y-298300

000 0

°0°00

000 It") \0 I:'-- co

()\ ()\ <l' 0'

"'-J '-JO GO '-JO

°oxoooOO

_0°0'00 0' 0 l\.J er> o~ It)o ()\ 0 0 0 o.

It) 10 lO lO to, It")

Fig. 129.

C. REDUCED HECTOMETRIC COORDINATES.

PORTION or LAMBERT GRID

. ADJACENT TO ITj ORlqlN

Y-LINE.s~

0

0

0

0 ,0RIGI N

00

00 ~A

0

...

00

00

.'

,. ,... ,...

30400

30300

30,00

30100

3000

2990

2980

,2.970

2960

422. For convenience in designating targets, a system of reduced hectometric coordinates is employed. This system is sufficiently accurate for

purposes of identification and has' the advantage of reducing the number of

figures which must be sent over a wire, or which must be sent down from

an airplane. 1

Since hectometric coordinate means coordinates expressed in hundreds

of meters, the hectometric coordinates of the point A. in the above figure

would be; X=5022, Y=2983.

But even this abbreviation calls for the use of more digits than necessary; and the above may be further reduced as follows .. A glance at any

of the ordinary battle maps will show. that there will be no duplication of

the figures in the hundreds of thousand's and the tens of thousand's columns

on anyone sheet, hence these digits may be dropped. Further, there will be

Topography for Field Artillery

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~ ~ ~ ~ ~

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no duplication of the digit in the thousand's column nearer than 10,000 meters,.

and this is a distance great enough that it should cause no confusion. Thus,

in the above figure, it is seen that the lowest figure for the Y value is

296,000, the figure 6 being the value in the thousand's column.There is no

duplication of the figure 6 for the Y value in the limits shown, the other digits in the thousands column being 7, 8, 9, 0, 1, 2, 3, 4. Similarly there is nO

duplication of the digits in the thousand's column for the X values found

below nearer than 10,000 meters, the figures running 5. 6, 7, 8, 9, 0, 1, 2,

3, 4, 5. .

Therefore, if the above digits are used as the identification numbers

of a set of coordinates, the point can be recognized just as readily as if

the complete coordinates were used (within the limits of the single' sheet).

The hectometric coordinates for the above point, A, reduced in this manner.

then, will change from X= 5022 and Y=2983 to X=22 and Y=83.

However the reduced' hectometric coordinates will not be separated as

to X and Y values but will be written thus :-2283 ..

(1.) Errors Introduced.

423. As indicated above the use of hectometric coordinates brings into

being a certain amount of error. since th~ point is read to the nearest hun-

<Ired meter subdivision. The maximum error so in);roduced is 71 meters

which is within the dispersion of the 'ordinary field piece. An error of this

.size occurs only when the point in question is located at the center of a

hundred meter square, or in other ''lords, when the point is ;;;0 meters' removed from both axes. The error introduced then is \j50~+50~ =71, see

fig. 130, in which P is the true position of the point and P' is the point ac-

.cording to its hectometric coordinates.

For actual map firing the coordinates must be .read

<lown to the last meter.

47-4. In some areas of France both the Lambert and the

Bonne projection maps are used, with grids printed upon r:

them, each using the origin of the projection as the orig- g

in of ~he grid. These are cases where complete surveyfl

for the Lambert projection have not been completed, I~_-."...~_--,

hence an allowance must be made, in using the grids, 100 M

for the joininR" of maps of the h'lo systems. Fig. 130.

.D. PLOTTING POINTS.

42:>. The above discussion has referred to reading the coordinates of a point.

In plotting points to the nearest meter great care must be given to the plotting with a metric scale, or scale which is divided into 100 units of any sort.

The X should be measured carefully in two, places on the grid, at least one

grid square apart and a line drawn joining the two points. .

Similarly it is best to measure along the Y lines in two places, at

least one square apart and join these two points with a line. The intersection of the two lines will determine the point which is to be plotted, see

fig. 131.

426. For example in the figure below it is desired to plot point B, the coordinates of which are X=484,247,Y=307.751. Measure 247 meters ove!~

l'oPol!raphy for Field Artillery
-197-

from the 484,000 line at (1) and again at (2). Draw a fine light line between

(1) and (2) thus establishing the X coordinate of the point (B). Similarly

measure 751 meters from the 307,000 line upward, and plot (3) and (4). The

intersection of the lines (1)-(2) and (3)-(4) will determine B. Outline the intersection by heavy lines in soft pencil, as "8hOV\'l1in the figure; leaving the

actual intersection untouched so that the point may be pricked with a sharp

needle.

PLOTTING A POINT

30~OOO

(I)

: ... I

308000

.307000

Q0-

(3) ._~ ..

.0

In

'lit

en

N

eiF> • •• .• + .• '0' . •• . :X(4)

I

o

8

306000o

o

a

C'")

co.

'\t

Note: In

should be used.

o

g

IC1

co

"J"

,Fig. 13!.

drawing the lines a hard pencil sharpened to a chisel edge

CONVERGENCE OF MERIDIANS.

427. On most battle maps based on the Lambert projection there are arrows

indicating the relation of magnetic north and true north with the Y (Lam ..

bert or Grid) north. Since all direction on firing charts is reckoned from

Y north, such direction being known as the Y azimuth of the point, the relation. between grid north and true north or between grid north and magnetic north must be known. In case the map does not indicate this,' US0

must be made of the formula AD=(M-Mo) sin Lo, in which AD is the

angle of convergence (sometimes called angle of divergence); M is the longitude of the point in question; Mo is the longitude of the origin of the projection (likewise of the grid since they are identical for French battle maps),

and Lo is the latitude of the origin of the projection (likewise that of the

grid). Mo is -6 grades (being east of Paris), and Lo is 55 grades north

latitude as discussed in Chapter XVI on projections. The formula then beTopography for Field Artillery

- - - - - - _ -

~
-198-

comes, Angle of Convergence=(M-(-6» sin 55 grades. The sine of 55

grades is .76. The 'formula in its final form, then is AD=(M+6) .76, which

should be noted in all artillery field notebooks. A simple discussion of and

a figure showing this relation between true north and grid north,. as above

expressed, is appropriate here ..

428. By a theorem of spherical trigonometry, the divergence of the meridians from the north pole to the equator is a function of the sine of the

angle of latitude.

CONVERG[NCE: OF" M[RIDIANS

LOOKING DowNQN NORTH PoLf:

Fig. 132

PARALLE.L

\ Of 55.9:

\

\ ANCrLE.5 Of ,

CONVE.RqE.NCE I \

00"=100.9'

EQVATOR

For example, in the left hand part of

fig. 132 are shown two meridians converging at

the poles. Figure 133 portrays a development

of these same meridians showing that the angle beteen them is greatest at the pole. At the

pole the angle of latitude is 90° or 100 grades

(see right hand portion of fig. 132) and the

sine of 100 grades=1, its greatest value.

However at the equator the meridians

are parallel. At the equator the angle of latitude is 0 and the sine of this angle is O. Hence

the meridians, being parallel, form no angle.

The amount of the angles formed by mClltl:::ms

may thus be seen to be a function of tLc :::~ne

of the latitude at any given parallel, such ~~s55

grades, the one used in the formula.

429. The divergence of the true north and

grid north is identical with that for meridian::;,

since the Y axis coincides with the meridian of ~.5. POLE.

orgin. This divergence, then, is the measure of DE\)E.LOPM ENT Of

some definite angle; that is, the angle between

the meridian of origin (-6 grades), and the Tt-IRE.E. ME.RID/AN'=>

point in question, M. Fig. 133.

Assume for example, that the point on the map in question is 3 grades

Topography for Field Artillery
-199-

east of Paris. Applying t!l~ formula, Ad=(-3+6) .76=3X.76=2.28 grades,

see fig. 134. ANGLE- or CONVERGENCE .I!:

3g 4<3 59 69

303

30Z

301

30C),OOO

2.99

~98

'0

0\

ME

----

ORIGIN Or GRID

AND PROJ eTloN

t'-:-. «) 0\ 0 N (W)

0\ 0\ ()\ 0 a ,.....

't "i v '-J -'-

0 te) It) te,

0-

0

Fig. 134. Ir)

Y-AZIMUTH.

-130. A direction from grid north is called Y-azimuth and is measured in a

clockwise direction from the Y line. This is done by means of a protracto!',

see fig. :135.

Y-AZIMlITH

,,/' Y-UNE:S'-.....

Fig. 135.

Topography for Field Artillery

~ -

-
CHAPTER XIX •.

USE OF GRID IN MAP READING AND. MAP FIRING.

ADVANTAGES OF THE GRID.

431. As indicated in the preceding chapter, the grid offers a pl'ecise and

conyenient method of designating and locating points on a map or grid sheet.

In addition it also is possible to determine the direction of one point from

another, or the range from point to point, by comparing the coordinates and

making a few simple mathematical calculations. In all of this work with

the gridded sheet,' the artilleryman, who is to do map fhing, should be a:1

adept. Often he will find that the grid sheet and the rules used are not

of the standard dimensions. in' which case he will have to adopt some one of

the expedients indicated below.

A.METHOD OF PLOTTING A POINT.

432. (1.) \Vhen The Ruler Graduations are Longer Than The Distant'l-'

Between Grids.

To plot a point P, the coordinates of which aloe;

X=25,400 Y=55,400.

57000

c p c'

a' .55,000 0 0 0 C 0 a 0 0 c.$)- r-- N N N

Fig. '136. I I •

Place the zero Of the scale on one grid line, 25,000, and the 10 or

multiple of 10 on the adjoining grid line, 26,000, see fig. 136.

Layoff the necessary unit, a'=400. Repeat by holding the ruler in

• TOIlOgrRphy for Field Artillery

•

-

~
-201-

the same manner but above or below this position. Layoff the same unit, a.

Join a and a'. This line determines the X-coordinate.

In similar manner layoff the Y":coordinate, c and c', joining them by

the line, c-c'. The point P is determined by the intersection of lines, a-a'

and c-e'. Show point as in diagram by drawing four rays with a soft.pencil,

none of which should pass through the point. Prick the point with a fine

needle.

Note: This method of using intersecting lines should be used fOl'

all accurate plotting, as it at once discloses any gross errors in the use t)f

" . the rule while small errors are averaged together.

(2.) When The Ruler Grad.uations Are Too Small.

433. Determine the number of units on the scale that the scale lacks from

being equal to the distance between two ~djacent grids. Let U-is be equal to

l. Say that the X-coordinate is 25,400. Then it is necessary to allow for

(400/1000 of 1)=5 in laying off, a. This may be done by laying the zero of

the ruler 5 distance from the grid before starting measurements, fig. 137, or

else laying the zero on the grid and adding 5 to 400, fig. 138. The point, p,

must be determined by the intersection of rays, a-a' and c-c', as in fig. 136,

above ..

O()(}~C;

N

0-

o

o

o

Fig. 137.

N

01

o

o

o

o

o

o

In

N

Fig. 138.

o

o

a

'0

(\J

55000

Example: Let the point to be plotted be, X=25,400; Y=55,500. To

plot the X-coordinate, let the distance between the grids be equivalent to

1000 plus 50 units of the rule. Then 1050 units are equivalent to 1000 meters

or 1 meter is equal to 1050/1000 of one unit. To layoff 400 allowance must

be made for the proper portion of the 50 extra units, which is equal to

400/1000 of 50 or 20. This may be done either by setting the zero of th~

ruler 20. units from the grid, or else by laying off 400 plus 20 units (420)

with the. zero on the grid. The Y-coordinate is established in a simiIa!'

manner taking into consideration 500/1000 of 50 or 25units, or 525 units.

Be METHOD OF READING THE COORDINATES OF A POINT.

434. Reading the coordinates of a point is the reverse of plotting a point.

It is essential at all times to keep in mind that the distance between adjoining grid lines is equal to 1000 meters, and that it is necessary only to find

Topography for Field Artil1ery
-202-

some means to interpolate or divide this distance up in the required numbel'

of equal parts.

(1.) When The Rule Is Correctly Scaled.

Lay the zero of the ruler on the grid'line and read the units to the

point. Add these units to the thousands of the grid. For instance, the grin

line on which the zero is laid is marked 35,000, and the number of units. to the

point from the grid line is equal to 475. Then that complete coordinate would

be equal to 35,475. The same applies for the reading of the other coordinate.

(Note:. When the grid is used to 10 times the scale for which it was

originally intended, then the distance between grid lines=100 meters. This

. case often arises when using a 1/20,000 grid for a 1/2,000 chart. Make

the proper allowance in this case).

(2.) When The Scale Is Too Large.

435. Bring the edge of the ruler opposite the point and at the same time

turn, it so that the 0 and 10 coincide with their respective grids. Read the

number of units and add to the thousands of the grid. If the ruler is too

much oblique, care must be used to get the exact value, see fig. 136.

(3.) When The Scale Is Too Small.

436. Determine the number of units on the rule that is equal to the difference in length between the rule and the distance between grid lines. Let

this distance equal I, see fig. 138. 1000+1= total number of units between

grids. Let m= the units read from the grid to the point. Then the true

distance, d, may be expressed as follows: d= [m+ (1000+1) ] 1000. Add th~

value "d" to the thousands of the grid to the left .and this will give one of

the complete coordinates. The other coordinate is obtained in a similar

manner.

Exa'mple: Assume the point up" lies between the grid lines 25.000

and 26,000; that the distance between the grids is equal to 1000 units of the

rule +50 units. In other words, there are 1050 units of the rule between

adjacent grid lines. These 1050 units are equivalent to 1000 meters. Assume that from the grid line of 25,000 to the point there are 420 units. Then

420

the distance in meters would be equal to lOOOXlOOO , which is equal to 400.

Therefore the X-coordinate =25,400. The other coordinate is obtained in

a'like manner.

(4.) With Right Angled Rule.

437: A more rapid method for plotting and reading cordinates is indicated

in' the figure given below. The right angled ruler enables one to read

both coordinates at one operation~ but does not give as exact results as the

o;erations described above.

This method is close enough for reading and plotting abbreviated

'hectometric coordinates, also for preparing firing data in some types of map

firing.

C. PLOTTING DIRECTIONS.

(1.) By Y-Azimuth.

4:J8. The Y-azimuth of a line, as heretofore stated, is the angular distance

'l'ollo~'Taphy for Field Artillery

'
-203-

measured clockwise from grid north or the Y-line. Therefore, in order to

plot a line, given its Y-azimuth. "it will be' necessary to determine the direc- .'!:

ll.

tl

w

1'1

10 /I

Fig. 139.

10 •• :

q :

8 I

7 I

b I

5 I

4- :lO,OOO

J •

Z. • I ,

0- •••. I

,

Il 13

.tion of grid north by means of a line through the point from which the

direction is determined. Placing the center of the protractor at this point,

with the zero line of the protractor on the line in the direction of grid north,

layoff the clo~kwise angle equal to the Y-azimuth. see fig. 135.

(2.) By Coordinates.

439. A line may be determined by two points on it; therefore. if the coordinates of two points are drawn and plotted and these points joined, the

line is then established. Drawing a line through one of the points parallel to

the Y-grid line and measuring the clockwise angle from this line, the Yazimuth of the line is determined. Note: If the line between the two points

intersects a Y-line of the grid, as is usually the case, the Y-azimuth may be

read directly without further work.

It sometimes arises that both points cannot be plotted on the same

grid, because the map distance between the two points is greater than the

size of the gridded sheet or map.

(.to. Take a case when working with a grid with a 1/2,000 R. F. If the

distance between the two points is 250 centimeters and the greatest distance

Topography for Field Artillery

-

~
-204-

available on the grid is. 30 centimeters, it is evident that point a and point I>

cannot be plotted, fig. 140. Let point a be the station point; let b .be the

x 4e8500

y e54400

)( 4l.S500 R

Y 250400

o

\00

~\J)

V 10'

C\J

"It"

255

2.SQ900

2.53

25(>,700

254-

1..5qBOO

2.51

25Q500

252.

l50,GOO

z:50

l5q400 8

1I")Jt)

11)'

Fig. 140.

point, (250 centimeters on the map or 5000 meters on. the ground fl'om a),

which is to be sighted on in order to orient the board. The direction to thi3

point may be continued in three ways.

Let a=X=425,500, Y=250,400.

b=X=428,500, Y=2~4,400.

441. (a) By Auxiliary Points. The grid may be renumbered on a 1/20,-

000 scale for the time being and the two points. plotted, a' b'. The Y-azimuth

can then be determined from the line connecting a' b'. Through a on the

1/2,000 scale draw a line parallel to a' b'. This will give the direction to b,

~ee- fig. 140.

442. (b) By similar triangles. From the coordinates it will be seen that

the point, b, is 3000 meters east and 4000 meters north of a, fig. 140. Then

with a scale layoff 3000 units (say 3 inches) east and 4000 units (say .~

inches) north, and the point x is determined. Joining a and x the direction

of the line, ab, is determined, since similar triangles have been constructed

and x is in the same direction from a as b, see fig. 14l.

443. (c) By I~educed Similar triangles. Or by a comparison of similal'

TOPOg'I'Rjlhy for Fiel.1 Al'tilll'ry

~

~
-205-

triangles a point, p, may be established that lies on the line, ab, near enough

to a, so that a and p may be- plotted; and in this manner the direction of

line, ab, is determined, see fig. 141 below.

3000 : 4000 :: 150 : Y

600,000=3000 Y

Y=200

Then the coordinates of point p are;-

X=425,500+ 150=425.650.

Y~250.400+200=250,600.

Next plot point p and join with a, and the direction of the line, ab, is determined. •

H.t. (d) By Reversing Directions. It sometimes will happen, that the

point a is near one edge of the paper and the point b lies off the sheet.. By

revolving the direction ab, through 3200 mils, or in other words by plottin '.~

a point b, which diffel's in its coordinates from a, in the same direction and

by the same amounts as a differs from b, the direction, b'a, which is the same

as ab, is established.

Since a is 3000 meters west and 4000 meters south of b, the point b'

will be 3000 meters west and 4000 meters south of a, see fig. 142.

')..x '

l ---- 3000---- ..... !

Fig. 141. Fig. 142.

Subtracting 3000 meters from the X-value of a, and 4000 meters from

the V-value of a, the coordinates of b' are found to be, X=422,500, Y=246,

400. This point is plotted and the direction determined, see fig. ,142.

D. DETERMINATION OF. RANGE AND Y-AZIl\IUTH BY

COORDINATES .

. (1.) Range By Square Root.

Ha. The coordinates of a point. not only determine its location on a grid

but also c:1.etermineits distance and direction from other points. The distance may be found in a mathematical way by finding the east and west,

and north and south distances between the two points. Take into considerTopoJ-rraphy for Field Artillery
-206-

ation the problem stated above, see fig. 140. The two legs of the right angle

triangle are found to be 3000 M. and 4000 M.respectively. The distance

a'b' or the range from a' to b' is equal to ~3,0002 + 4,0002 :"'=~25,000,OOO

5000M.

(2.) Direction.

446. (a) The direction of a line given by two points may be detei'mined by

a brief calculation without plotting the points, when the direction

does not lie more than 330 mils off either the X or the Y direction~.

When angles are formed greater than this, the difference between

the mil and the tangent relation tends to give inaccurate results,

fig. 9.

a.

Fig. 143.

v

Fig. 144.

Example:

Given the coordinates of a, as X=25,000 Y=50,000

b, as X=25,500 Y=55,000

b is 500 meters east and 5000 meters north of a. Figuring the

angle by dividing the distance subtended, by 1/1000 of the range,

the angle of 100 mils is found. This is equal to the V-Azimuth

of the line ab, fig. 143.

Example:

Given the coordinates of c, as X=30,000 Y=60,000

d, as X=24,000 Y=58,800

d is 6000 meters west and 1200 south Y

of c. The angle made with the x-axis

is equal to 200 mils. (1200+6) The

V-azimuth is equal to 4800-200 or

46001'jt.

447. (b). When the direction lies

more than 330 mils from the X or

the Y axis. X

When this situation arises the

. V-azimuth may be determined accurately by comparing the coordinates

to determine the tangent of the angle

considered, and then by consulting

the table of natural tangents (Appendix III). Determine the corresponding angle.

UI

o

8

lOOP(

x

Example:

Consider the direction a' b', fig. 140. The perpendicular side oPPOSit:3

the angle, b' a' R, is 4000M. The side adjacent to the angle b' a' H is 3000~L

The tangent of the angle then is 4000/3000, or 4/3 or 1.333. From t.he

table it is found that this corresponds to an angle of 53°8'=955*.

The V-azimuth is reckoned from the V-line or vertical line. TherefoI'2

the V-azimuth will be 1600ljt-9551'jt=645ljt.

Topography for Field Artillery J

~
-207-

E.' TO LOCATE ON THE GROUND A POINT THE COORDINATES 01<'"WHICH' ARE GIVEN.

448. Let p= the point to be determined on the ground. Plot this point on

the plane table or map. By examination of these coordinates and coordi- .

nates of nearby control points, make an estimation of where this point would

be on the ground. Set the plane table up at this point (called x), fig. 145.

Fig. 145.

Determine by accurate resection the location of x on the plane table. Measure

the distance on the plane table between x and p and determine the relative

difference on the ground. With the plane table oriented and the alidade on

x p, p being the point farthest away, line a man in with the line of sight of

the alidade and at the required measured distance away. This should be

the point. Verify by resection and make the necessary corrections.

449. It sometimes oCCUl'Sthat brush or a crest intervenes between P and x,

fig. 146. If such a case arises it will be necessary to run a- two (or more)

,P

r

,

f

f'

,.

f

,

~-----------~ -----~

Fig. 146.

legged traverse, determi}1ing another point .Y on the plane table and gro'und.

Proceed from .Y in the san;).emanner as x in the preceding problem.

Topography fot' Field Artillery

'

. ~ ~
CHAPTER XX.

THE COMPASS.

GENERAL.

450. In modern artillery practice the compass needle plays an important

part since it affords a convenient and reasonably accurate method of determining directions, of making traverses, of intersection, resection, and of laying guns for direction. Other things being equal the longer the needle the

greater the accuracy of the direction determined. Even with a long needle

some sort of s:ghting device and some method of reading the subdivisions

of the angle set off is needed, in order to do satisfactory work; hence the

prismatic compass, the aiming circle or similar instruments only, can be

used with a satisfactory degree of accuracy.

NORTH.

451. Because the al'tilleryman is dealing with three different norths-True

North, Magnetic North and Grid North (Lambert or Y-North) it is con-

.venient to designate horizontal angles measured from these various directions by different names.

452. Azimuth. Thus in this publication the horizontal angle, measured

clockwise from true north around to a given direction will be spoken of as

the azimuth of that direction.

453. The magnetic bearing or bearing of a given direction will be used to

designate the horizontal angle measured clockwise from magnetic north.

454. .The Y -Azimuth (Gisement) of a direction is the horizontal angle

measured clockwise from Y-north or Grid nOl.th.'

Note: Actually Azimuth is any angle measured horizontally in a

clockwise direction from a given vertical plane. In some engineering manuals and in the air service, the, term is used to designate the horizontal

angle measured from magnetic north, the same angle which, in this text, will

be termed bearing.

Bearing on the other hand in some texts is confined entirely to measurements within a certain quadrant as "North North East" and always such

bearings are less than 90 degrees.

DECLINATION.

A. MAGNETIC DECLINATION.

455. The north magnetic pole is situated south of the north pole and in

the western hemisphere. Therefore the magnetic meridians and the true

meridians generally do not coincide. Magnetic Declination is the angle at

any given point between these two meridians or between true north and

magnetic north.

Since the compass needle points toward the magnetic pole it is evident that, except at a few localities it will not point toward the north pole.

Topography for Field Artillery
-209-

At certain parts of the earth's surface it will point east of the true north

giving an easterly declination and at o~hers it will point west giving a westerly declination. '!:

-156. In America there is a westerly declination in the eastern part of the

continent and an easterly declination in the western portion of the continent.

The amount of declination varies with the locality. The amount of declination may be determined from an isogonic chart, such as that included in this

chapter, plate XVIII, which, for the epoch noted, gives, by curved lines connecting points of equal declinations, the approximate declination for point~

in the area represented.

Note: "Isogonic, of, pertaining to, or noting equal angles." Hence

isogonic lines are imaginary lines joining points on the earth's surface at

which the magnetic declination from the true north is the same.

At no point is the magnetic declination a constant .. It is subject to

a number of different variations.

(1.) Magnetic Variations.

457. There are innumerable variations in the lines of magnetic force of

the earth very few of which can be computed. Following are the more important variations to which the/'compass needle is subject. Of these, the

first two only, usually are considered.

(a) The daily variation, consisting of a swing from the extreme

easterly position at about 8:00 a. m. to the extreme westerly position about

1:30 p. m.; the mean position occurring about 10:00 a. m. and 5:00 p.m. This

variation is from 5' to 15',' and the exact amount to be expected for any

hour of the day and the months of the year may be obtained from tables

that have been computed. This often is called the diurnal variation ..

(b) The secular variation, a long slow swing, covering. many years.

In the United States both east and west declinations now are gradually increasing at varying rates depending upon the locality.

. (c) The annual variation, which is very small (less than l' per year)

and need not be considered.

(d) The lunar variation, which is still smaller.

(e) Irregular variations, caused by so-called magnetic storms, un.

certain in character and not to be predicted. Such variations are sometimes

large.

(f) Local attractions. These may greatly disturb the needle, and

often come from unknown sources. The observer should have them constantly in mind and endeavor to keep all magnetic influences, such as magnetic bodies, electric wires, steel helmets, etc., at a distance from the instrument when the needle is being read. Experiments indicate that' a transit compass needle is not materially affected by large masses of metal at

.distances greater than fifty feet.

Compass Error.

(g) The geometric axis of a needle may not coincide with its magnetic axis, hence the readings of two compasses at. the same point may diffe...

slightly. This last is known as a compass error. Any variation due to

faulty construction of the compass itself is a compass error.

Topography for Field Artillery

~
j

-210-

(2.) Use Of Isogonic Chart.

458. When the artill2ry officer is ca.lled upon to run a direction or to lay

his guns, and the declination of his compass needle is not known, and cannot be determined in the time allotted, he will be compelled to use the datn

t)

'';:;

Q)

bD

ro

"@

::s

0'

.....

0

rFl

a Q)

o 0 0

ell If). l't)

(0

furnisheu by his isogonic chart and by the tables of diurnal variation, in

determining the magnetic declination which he will use. The following problem will indicate the method of procedure.

Topog-raphy for Fielcl Artillery

J

~

~

~ ~

~

~

~ ~
-211-

AMOUNT AND VARIATION OF THE MAGNETIC NEEDLE FROM ITS

MEAN DAILY POSITION.

The letters E and W indicate which side of the

mean position the needle points.

Season and Position

in Latitude.

Dec., Jan., Feb., .

Lat., 25° to 37° .

Mar., Apr., May,

Lat., 25° to 37° ., .

Jun., Jul., Aug.

Lat., 25° to 37° ., .

Sept., Oct., Nov.,

Lat., 25° to 37° .

Local mean time: Morning Hours.

6h. 7h. 8h \9 h 11Oh. \ 1~~~.:~h.

Min. Min. Min. I Min.! I Min. Min._ Min.

O.IW O.IE 1.0E 2.0E 2.2E l.IE O.5W

lo6E 2.8E 3.3E \ 2.6E 11.IE 0.6; 1.9W

::::::;:;~::J;;:\::~:\~~~:;~::

Local mean time: Afternoon Hours.

Season and Position 1-------

in~~tit~de. I OhJ 1_h._i_2hj~J~h~ t5~~ ~ . I I I

Dec., Jan., Feb., \ Min. \ Min. Min. I Min. Min. Min. Min.

Lat., 25° to 37° .. 0.5W 1.5W 1.8W l.6W l.OW O.4W O.IW

Mar., Apr., May, I I

Lat., 25° to 37° .. l.9\V 2.6\V 2.8W 2.4W l.6W O.9W 9.5W

Jun., Jul., Aug., I

Lat., 25° to 37° .. 2.8W 3.2W 3.IW 2.4W l.5W 10.8W O.4W

Sept., Oct., Nov., i

Lat., 25° to 37° 2.IVI 2.3W\l.9W\lo2W 0.7WI0.4\y 0.2W

;.:.

(From Tracy's Surveying)

Latitude of Fort Sill is about 34°-40'.

---_.- ..,.'--,"-_._---- ,---._---_ .._----_ ..-------_ -_.--------- --_._.- ---~------_ _- _._-~.- ----_._. ---_ ... ._--~_._--._-_. ._-_._-- _.,._--_._-----_ .•.-~_. ~-----_._-~.-- ~'-

459. Assume the officer is located at Ft. Sill, Oklahoma, and that he expects

to use his compass needle at 3 o'clock on the aft8l'noon of May 1, 1919.

From his map 01' from the isogonic chart he finds that on Jan. 1, 1915, th:_'

magnetic declination at Ft. Sill was 10 degrees 4 minutes east. From the

isogonic chart, Plate XVIII, he notes that the line of secular change of 2'

east per year is north of Ft. Sill and that of 3' is south of the same place.

By interpolation he finds that there should be an annual increase of easterl~~

declination at Ft. Sill of 2.6'. Since Jan. 1, 1915, four and one third years

have elapsed. Therefore the easterly declination would have increased ir

that time by 4 1/3X2.6' or 11.26'.

From the table or" diurnal variation he finds that at 3 o'clock in the

afternoon in the month of May the needle will show-a vatiation of 2.4' west

of its mean position. He acds the variations and secures the total of 10°

12.86' or a variation of 181.5811z=1821jt east.

Topography for Field Arti!l..,ry

...:

-

__

I

1

1 ------------ __ --- - - ----------

---- _.. ..- ....

-- --- __ --

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-212-

Mangetic declination as given in isogonic chait 10° 4: E

Secular change in 4 1/3 years 11.26' E

Total ...........•........................... 10° 15.26' E

Less Diurnal variation for 3 p. m. May 1 2.4'. W

Total 100

12.86' E

10° 12.86'=181.58'11=182,/1-.

B. COMPASS DECLINATION.

460. Compass Declination includes the magnetic declination, the magnetic

variations, and the error of the compass itself. NaturallY it will be different

for each compass.

Since all of these are difficult to compute, and since the magnetic

declination and the variations generally are not subject to any sudden changes

of great size in a given locality, the most satisfactory method of procedure

is to determine the compass declination by a topographical operation and

to use the value so obtained for a limited period of time.

(1.) Sighting On The Pole Star.

461. The most accurate method of determining the compass declination of

.a given instrument is by sighting on the pole star at the hour of the night

when it is in an approximately north position. This OCCUl'S when the Dippel'

and Cassiopeia are above or below the North Star.

For practical details of the observations made on Polaris, the following

will serve as a guide. Select a clear space of level ground not too near

buildings or any object which might cause local disturbances of the needle.

Drive a picket. leaving the top smooth and level, about 18 inches from the

ground. Six feet north. of the picket suspend a plumb line from a point

high en<?ugh so that Polaris, seen from the top of the picket, will be neal'

the top of the line, fig. 147. The line should be hard and smooth, and abovt

1/10 of an inch in diameter. .

Fig. 147.

The weight at the bottom of the line should hang in a vessel of

water. or in a hole dug in the ground, to lessen the vibration of the line.

Drive a second picket in line with the first one and the plumb line,

a short distance north of the latter. Make a peep by punching a hole about

1/10 of an inch in diameter in a piece of paper and hold it on top of the

first picket. Adjust the peep so that the star is behind the plumb line when

looking through the peep. Mark the position of the peep on the top of the

Topography for Field Artillery

~
-213-

first picket, and lay a straight edge or stretch a string from the point,.

touching the plumb-line, to the second picket.

Place the north-south edge of the compass box against .the straight

edge and read the needle. To find the azimuth of Polaris at the. time of th,e observation see

figure and table of Appendix VI.

Fig. 148.

(2.) Using Sun To Establish Meridian.

462. Prick a small hole in a piece of tin or opaque paper and fix it securel~~

over the south edge of a table or other surface perfectly level;-.so that the

Runlight coming through the hole will fall on a convenient place on the surface, see fig. 148., The hole may be two feet above the table 'for long day~

and 18 inches f01:-short ones. Half an hour before to half an hour aftelnoon mark the position of the spot of sunlight on the horizontal surface at

equal time intervals of about ten minutes. Draw the curve bd, fig. 148.

through the points marked, and from a point e on the horizontal surface and

in the 'vertical line through the hole, a, sweep an arc, ef ,intersecting bd in twO'

points. The line eg, drawn through from e, through a point on the arc midway between the intersections, is the true meridian. The curve, bd, illus-.

boates this method. Its form varies with the sun's declination.

The .meridian being established on the table the compass may be'

placed on this line and the declination of the needle read.

(3.) Comparison Of Azim!u.ths And Bearings.

463. Determination of the compass decli~ation may be secured "in the following manner, see fig. 149.

Select a position to work from, which is clearly marked on the map

and from which can be seen at least three distant objects,. widely separated'

if .possible, which also are clearly marked on the map. When selecting this

position, it is important to see that no metal is near which might have an

effect on the needle of the compass.

Topography for .Field ArtillelT
-214"':"

Lay the map on- a table, care being taken that it has no blank space~;

on it caused by the joints, as in some folding maps. .

Topography for Field Artillery
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Draw a line through the selected point on the map ~arallel to the

true north':'south line found on the map.

Mark the selected point carefully on the line and draw.!:rays from it

to the three indicated objects already selected.

Place a circular protractor on the map with'its center on tili\ point

where the rays meet, zero toward the north, so that the 0-3200 diameter

coincides with the true north-south line drawn on the map.

Read off the number of mils ,at which the rays to the three distant

objects cut the edge of the protractor; in other words, read the azimuths to

these objects, making a careful note of each in turn.

Set up the prismatic compass at the position on the ground from

which the azimuths have been read on the map, and read carefully the

magnetic bearings to the three distant cbjects,m2king a careful note of each

in turn as before. Th average of difference between bearings and~azimuths

will give the mean compass declination.

In figure 149 is shown a map on which a protractor is laid, giving

the azimuths to a schoolhouse, a church, and a wir.dmill , all taken from a

turn in a main road.

A compass is set up at this turn and the magnetic bearings to thes~

three objects are read. The results are tabulated as follows:

AZIMUTH

READ WITH PROTRACTOR

Schoolhouse. 450 mils

Church. . . . .. 5670'

Windmill. . .. 3880

Total

Mean

MAGNETIC BEARING COMPASS

READ WITH COMPASS DECLINATION

775 mils 325 mils W

5985 315 W

4185 305 '\V

•..•.. : •..•...•.•••.•..•.•...•••. 945 W

declination .....•............... 315 W

This mean declination can be taken as the compass declination of the

compass used for the experiment. If this is compared with the magnetic

declination computed for the particular locality ~nd particular time, the

error of the compass can be ascertained ar:d maTked on the' back for future

guidance in this locality .•

It is important to take at least three bearings to guard against pel'.

~onal error, and desirable to select objects as much as'10 or 15 miles distant.

(4.) Reading Bearings Of Sun Or Of A Star.

464. A third method of determining the declination of a particular compass needle is given below.

Read the bearing of the sun, a planet, or a bright star at rising and

~etting on the same day, or at setting one day and rising the next.'

Add these two bearings.

Take the difference between this sum and 3600

or 6400*.

On half of this difference is mean compass declination f6r the particular time and place.

The declination of the compass is east if the sum of the two readings

is less than 64001/t and west if it is greater than 6400*. see fig. 150.

465. In fig. 150 let E be the sun at the time of rising and W at sunset. Let

a be the observer's position, N the true north and MN the magnetic north.

Let A be the bearing read when the sun is rising. B, the bearing when the

Topography for' Field Artillery

_ "

~

"

"

" "

" "

"

"
-216-

sun is setting and M the sum of these two bearings. Let D be the compass

declination.

Fig. 150.

Since the sun is at the same distance north. or south of the equatorh.1.1

line at sunrise and sunset, the angles NOE and NOW are equal.

However, the bearing read to the sun position to the east, include:'

the compass declination, as does the bearing read to the sun position in th~

west. If the two bearings are added then the compass declination will have

been included twice. This is evident from the figure. The angle WOX i..,

equal to MNOE (angle A).

To the angle B add WOX (equal to angle A). This g'ives ang'le M

which is more than one complete circle by an angular amount equal tp D+D'.

5400+ 1600=7000.

7000-6400=D+D'=600.

D=1/2 (600)=30011•

Compass declination, 3001/1 west.

(5.) Declination _Constant. ,

466. The Dedination Constant, is the reading which must be set off on an

instrument in order that, when the compass needle is brought opposite its

index, the instrument will be oriented. !

For a clockwise instr~ment the declination constant is the-.same' as

the compass declination if the compass declination. is east. If the compass

declination is west, the declination constant is equal to 6400--the' compass

declination. . ;"\

467. Y-Declination, fig. 151, is the angle which magnetic north makes. with

grid north. If the Y-Declination is used in orienting the instl'ument the

declination constant is spoken of as The Magic Number. In this case th~

zero of the instrument, when oriented will point toward Y-north. : ;.i

TopOJo!,'rRphy for Field Artillery
-217-

North,

Conv~r9(2,nc<t"

Fig. 151.

USE OF COMPASS AND MAP.

A. TO FIND A MAGNETIC BEARING ON A MAP WITH A

PROTRACTOR.

468. Dnlw a true' north-south-line through the point on the map, fig. 152,

from which it is desired to take a magnetic bearing. .

Place a circular protractor on the map, with its center on this point,

zero toward the north, so that the 0-3200 diameter coincides with the true

north-south line.

Mark off the map, by a light pencil mark, the exact number of mils

that the compass in use varies from the true north; clock-wise, if the varjs,-

tion is east, counter-clockwise, if it is west.

Join this mark to the point at the center of the protractor, and the

line so made is the magnetic north-south line through the point from which

bearings are to be taken. .

Place the protractor on the map with its center on the same point

as before and with the 0-3200 line coinciding with the magnetic north-south

line just drawn.

Keeping the protractor in this position, by means of a' piece of fine

stl"ing attached to the center, magnetic bearings can be read to any objec:

on the map across which the string is stretched, by noting the number of

mils where the string cuts the edge of the protractor.

B. MAGNETIC RESECTION (BACK AZIMUTH).

To Use A Compass And A Protractor To Locate A Position On The Map.

469. When selecting a position, it frequently happens that it3 situation '.m

the map, obtained by a study of the surrounding country, is not sufficiently

exact. In order to obtain accurate bearings and ranges to objectives, it

is very important to locate precisely, on the map, the position selected.

A simple method is as follows:

Topographv foT' Field Artillery

_

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Topogr h ap y £01" F' Id Ie ~rtil1ery

-218-

Fig. 152.
-219-

Topography for' Field Artillery
-220-

"In fig. 153,P is a position ,vhich it is desired to fix exactly on the map .

. Set up the compass at P and read the magnetic bearing to a prominer.t

distant object, as W, a windmill which also is marked on the map. This

bearing proves to be 4410 mils. .

Draw the magnetic north-south line through W to agree with the

magnetic variation of the compass used, and place the protractor with it;;

center on the windmill, with zero to the north on the magnetic north-south

line just drawn.

Make a pencil mark at A on the map close to the edge of the protractor, at 4410 mils, the magnetic bearing of W from P.

Draw a line from A to Wand produce in the direction of P.

Repeat this process for another object, as C, a church to which the

magnetic bearing is 5660 mils. .

Draw the magnetic north-south line as before through C. lay the

protractor on it and make a pencil mark at B, on the map close to the edge

of the protractor, at 5660 mils.

Draw a line from B to C and produce in the direction of P until

it cuts the other produced line, A W.

The intersection of. these two lines is the point from which were read

the bearings to the windmill and church, and is therefore the position which

it is desired to locate.

Note: The above process is the same whether the operator works

with the true north and magnetic declination or with Y-north and Y declination, fig. 59, par. 207.

TopO!.l.Taphy fol' Fie"l Artille,"y

-
wayR:

CHAPTER XXI.

LA YING GUNS WITH A DECLINATED INSTRUMENT.

USING PRISMATIC COMPASS.

-t 70. In laying the guns for direction with a compass there are two steps:

First, the determination of the bearing of the direction, gun-target or

the direction gun-base point, and

Second, the laying of the guns with the bearing determined. #

A. TO DETERMINE THE CO:MPASS BEARING OF A GIVEN TARGET.

The bearing of the target or base point may be deteWlined in two

(1) If &n accurate map is available, on \vhich both gun and target

positions are shown, the bearing may be read directly from the

map with a protractor, as described in Ch. XX, or the azimuth or

Y-azimuth may be read from the map, and the bearing computed ..

(2) If the map is not available the battery commander must compute

the bearing by the offset method, analagous to the parallel method of com'puting firing data, described in Drill Regulations.

The Offset Method.

tH. Assume that the target is not visible from the gun position, but that

there is an el.~vation near at hand from which the battery commander. can

see both the target and the directing gun.

From this elevation he takes the bearing of the target and the bearing' of the gun ...c

The batte'l:y commander also measures or estimates the distance between the compass and the gun position, and the distance between the gun

pORitionand the target.

With these data he computes the angular offset for the gun position

and modifies the bearing of the target, read from the B. C. station, by the

amount of the offset. Since magnetic north is the same for both the gun

position .and the B. C. station there is no offset to be computed for that

<lir~ction, (corresponds to "P" in parallel method).

The bearing as determined by the battery commander is sent to the

executive who lays the guns accordingly.

472. The following problem will illustrate the steps taken by the battery

commandel' in computing the bearing of the target.

Let C b~ the compass position.

Let G be the gun position.

Let T be the target position.

The distance from gun to target is 4000 meters.

The distance from the compass to the gun is 400 meters.

The battery commander reads the bearing to the target and finds that

thiR is 1400 mils, see fig. 154. He also reads the bearing to the directing

Topography for Field Artillery
-222-

gun and determines the bearing of the direction, compass-gun, to be 3800

mils.

The difference of these two bearings will give him the value of the

angle TCG. If this angle is equal to 1600 mils the line gun-compass is normal

to the line gun-target . .If not there will be an obliquity factor to be.applied.

/"'N

Fig. 154.

The battery commander subtracts 1400 mils from 3800 inils and finds that

the angle TCG is equal 2400 mils. In other words it is 800 mils greater than

the normal angle, hence the obliquity factor of .7 will be used.

At range 4,000 (the distance to the target) a base of 400 meters be.

tween the gun and the compass would subtend 100 mils if the base were

normal to the gun-target line.

In this case an obliquity factor of .7 must be applied as determined

above, hence the angle subter.ded at T will be 100X.7::=70 mils. The offset

then, is 70 mils .. 1400-70=1330 mils which is the bearing of the target

as viewed from the gun position and this is the beal'ing sent to the ex..

ecutive.

B. LAYING THE GUNS WITH THE BEARING DETERMINED.

473. In laying the guns with the bearing just determined by the batter)"

commander, the executive should have..a compass which reads the same a~

that of the captain, or at least the declination of both compasses should be

known in order that any difference in their readings may be considered.

In the above case assume that the battery commander is using a compass with a declination of 180'1t east, while that of the executive has a

reading of 1701jt east. Should the battery commander therefore, send down a

bearing of 13301jt for a particular target, the executive would modify that

bearing by th~ amount of 101ft applied in the proper direction, or he wou}.i

add 101ft to 1330'1t making 1340'1t, which would be the bearing he would use

in laying the guns, see fig. 155.

On the tther hand, suppose that the battery commander should send

down the Y-azimuth of the target as measured from the map. Assume this

to be 1320,j1. Knowing the Y-declination of his instrument, for that pattieTopography for Field Artillery
-223-;- ,

ular locality, the executive would apply this in the proper direction and lay

accordingly. .b.ssume that the Y-declination of the executive's compass is

20tjl west. The magnetic bearing with which he would lay the: guns would

therefore be 1320+20 or 13401jt, see fig. 156.

G

Fig. 155.

MAQNE.TIC DECLINATION

<:~ \

N~A

!?Ii Z

t6 l0vf. Y DECLlNATIOt-J

T

Fig. 156.

Several methods may be used by the executive in laying the gun::-

with the compass, the methods varying with' the time available and the accuracy desired.

(1.) Lining In.

474. The executive places himself fifty feet or more in the rear of the

dh'ecting gun, so that the bearing, A, of the gun, see fig. 157, as read with

the prismatic compass, is the same as the magnetic bearing of the line directing gun- target, determined by the battery commander. In order to do this

the executive moves from C" to C' to C to the right or left as the case may

be while sight3ng on the gun, at the same .time causing' the piece to be traversed, until the vertical plane through ..."'1'1 M N

the sights of the prismatic compass, cor-

. responds to the line of metal. M N

The above method may be modi- t

fled by sighting on the sight shank of

the directing piece with the determined :.., e"

bearing, and causing the gunner to lay f'l\l'l

the gun with a deflection of 3200 mils. I ~/

Similarly, it also is feasible for the C' '.1 ,,/

e~ecutive to line himself in frolp a posi- I ,#~

bon in front of the guns, the only dif- //

ference being that the compass reading // .

he uses will be modified by the £.ddition //

of 3200 mils. If the compass is in front (

of the gun on the line gun-target, the Fig. 157.

gunner may lay his piece on the compass with a zero reading set on his sight.

With the gun established on the line of fire the piece is referred to s

distant aiming point and the sheaf formed.

Topography for Field Artillery

.

-

~
-;-224-

/

/

/

{

\

\

\ M '....... , ,,/ -,.._ ......

(2.) Using Compass As Aiming Point.

475. Ordinal'ily when the guns are laid by compass, the executive sets up

the instrument in the vicinity of the guns, but distant enough that. the

masses of metal do not affect the needle, and after he has made his computations, the gunners lay for direction using the compass as an aiming

point.

Let G b'~ the gun position, C that of the "compass and T the targ~t.

The executive already knows the X

bearing of the target, angle A, fig. 158. MI\J {

He reads the bearing of the gun, angle B, I

fig. 158. Now it is evident that, since the I

deflection must be computed for the gun {

position. (not the compass position) and {

since the gunner is to usP- the compass ",

as an" aiming point, that the executive I

needs to determine, not the bearing of M N

the gun as seen from the position of the

compass, but rather the bearing 9f the

compass as measured from the gun position. It is evident also, that these two

bearings will differ from each other by

3200 mils. Therefore the executive may

modify the bearing of the gun, angle B,

or the direction, CC, by 3200 mils, and

will obtain the bearing K, or the direction. GC, which is what he wants.

The angle K, just obtained, sub- /'-

traeted from the bearing of the target, /

angle A, leaves the angle, L, one side of {

which" contains the line of sight from the \ G

gun through the compass and the other \ /

side of which contains the line of, fire to ', __ ..-;/M Fig 158.

T. If the gun were provided with a sight graduated counter clockwise this

angle, L, would be the deflection. But since the American sight is graduated

clockwise the angle, M, is wanted. 6400tjl-L gives the angle M. the d~-

flection desired.

476. The steps listed above are then: The" bearing of the gun, minus 3200

mils, minus the bearing of the target, plus 6400 mils.

This is the same as saying that the deflection is equal to the bearing

of the compass. minus the bearing of the ta:rget; the bearing of the compass ,

being increased by 6400 mils if the compass bearing is less than the target

hearing. The above formula applies in all quadrants.

This also may be expressed by the following equivalent formula:

Bearing of the gun plus 3200 mils minus the bearing of the target

equals the deflE"ction. G+3200-T=D.

477. An examination of the four cases below, arising as the compass is

placed in each of the four quadrants with respect to the gun position, will

establish the ~alidity of the formula. In each of the cases considel'ed:

Topoj,rraphy for Field Artillery
-225-

let G. be the gun position,

C the position of the compass,

T the target position,

A the bearing of the target,

B the bearing of the gun.

478. First Quadrant, fig. 159.

MN

x

. I'st.

C~VADRANT.

...

Fig. 159.

Assume that A=12001jt and that B=36001/1.

3600+3200=6800=angle M which is greater than 6400l/t, by the angle K •.

6800-1200=5600=deflection D.

479. Second Quadrant, fig. 160.

,

/

I

I

\

,

.... .... ..... - ~,.

. 2.ncl' •

O\./ADPANT

Fig. 160.

Topography for Field Artillery

\

-
-226-'

Assume that A=1200t/t and that B=5500t/t.

55001-3200=8700.

8700-1200=7500t/t which is greater than.6400*, by the, angle D or

1100111.. And since 7500 cannot be set on the sights, the setting will be

1100111.,which 'is the desired deflection.

480. Third Quadrant, fig. 161.'!

MN

T

. J'rd.-

(~VADRAI'lT

Fig. 161.

Assume that A=12001/t' and that B=8001/J.

8001-3200=4000=angle AI.

4000-1200=2800=angle D=the required deflection.

, 481. Fourth Quadrant, fig. 162.

."'\N

I

I

\

\ .

\.'....... _-..,.,,,,/

M

4 th

(lvAOAANT

". Fig. 162.

Topography for Field Artillery

"

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-227-

Assume that A=120011~ and 'that B=2500*.

2500+3200=5700=angle M.

5700-1200=4500=angle D=required deflection.

482. It sometimes will happen, when the above formul~ is used, that the

answer will be a negative quantity. If such is the case, subtract the angle

obtained from 64001f~. The remainder will be the required deflection, see

fig. 163.

MN

Fig. 163..

In the figure above assume that B, is 7501jl and that A=61001j1,.

750+3200=39501jt=angle M.

3950-6100=-2150* angle X.

6400-2150=425011l=angle D= required deflection.

USING THE AIMING CIRCLE" OR PRISMATIC COMPASS AND THE

MAGIC NUMBER METHOD OF LAYING.

See paragraphs 576-582, Chapter XXV.

ropography {OJ' Field. Artil.lel'Y

=
CHAPTER XXII.

THE TYPICAL BATTERY SECTOR.

TERMS, DEFINITI01tS, AND DIAGRAMS.

483. Adjusting Point: the point used for the adjustment of the elements of

fire. The particular point of an objectke on which the guns are adjusted.

Note: Terms used in this chapter are illustrated graphically in figs.

164, 165, 166. 167, 168.

484. Aiming Point: the point on which the gunner sights when laying hi:'

piece for direction: the point which defines' the line of sight from the gun .(

485. Base Angle: the horizontal angle between the base line and the

orienting line measured in the same direction as the sight graduations.

Therefore it is a clockwise angle for the American panoramic sight.

486. Base Deflection: that deflection which, if used in layinz the piece,

will place the gun on the base line.

487. Base line: sometimes called Base Direction; the line joining the base

piece and the base point, always continued across the orienting line, if an

orienting line exists, to form the base angle. It is used as an origin fo::

direction from the gun position.

488. Base Point: So~etimes called Reference Point but having a more

restricted meaning than the reference point of the Drill Regulations; a well

defined point of the terrain or of the enemy sector, generally, but not always situated within the battery sector. It is generally shown on the map,

and usually is invisible from the battery position. Sometimes it is visible

from the obsel'vation post from. which it is simply designated on the terrain

and may not bE: shown on the map.

One base point may be common to several batteries.

A battery can have several base points in which case they are designated, "Base Point No.1", "No.2", etc.

The base point may be the objective itself if fire must be. opened immediately, or if there is but one objective.

489. Battle Map (Plan Directeur): a large scale map, (1/20,000, 1/10,000.

1/5,000) showing the. enemy works, and occasionally the friendly works.

The term is most commonly applied to the 1/20,000 map on the Lambert

projection.

490. Command Post (Post of Command, P. C.): the post from which a bat.

tery commander directs the o'perations of his battery, usually a post or dugout near the battery. Posts of command of the higher units are near roads

or trails permitting easy communication between various units of the command. The brigade command post for the artillery usually should be neal~

the division or corps headquarters.

491.. Contingent Zone (usually contingent zones Nos. 1 and 2): the zones

within the objective zone but outside the normal zone, within which the battery may be c'J.lled ~pon to fire' in certain contingencies.

Topography for Field Artillery
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492. Control Point: a geodetic point or other point, the coordinates of which

are known,' which may be used by the topographer in his topographical

operations. -'!:

493. Control Sheet: a sheet containing a list of control points, each with it:;

coordinates, for use by the battery reconnaissance officer, battery commander,

or the battalion orienting officer, in the location and development of the positIon.

494. Datum Point (but auxiliaire): a clearly visible point selected as an

adjusting point. It must be shown onthe battle map, or be capable of being'

accurately plotted. Also it must be chosen so as. to be not more than 300

mils from the objective with which it is to be used, while the range shoul;l

be not less than 3/4 or more than 4/3 of that of the objective. This limited

meaning of Datum Point should not be confused with the term. "datum

point," "datum level," "datum plane," used in surveying.. #'

495. Declinating Point: a point thl'ough which several lines pass, the Yazimuths of which lines are knovvn.

496. Deflection Constant: the deflection setting which must be set on the

sight to bring the plane of sight on a plane parallel to the plane of fire.

For the American sight it is 0, for the French 75 it is 1001!1, and for the

Schneider 155 it is 1000//1.

497. Directing Piece: the gun for which the initial data is computed, usually

No. 1 in precision fire.

498. Field of Observer: the angle between the right and left limits of observation, either with the naked eye or with an instrument. Usually the field

of observation is limited by the location of the observation post. The O. P.

should be located so that the entire objective zone is included in the field

of observer.

499. Firing Angle: the horizontal angle between the plane. of. fire and the

plane of sight measured in the same direction as the sight graduations.

For the American panoramic sight, it is the angle measured clockwise from

the plane of fire to the aiming point, and corresponds to the deflection, (except for corrections for drift and atmospheric conditions).

500. Firing Board (planchette de tir): a' board of wood, or of zinc ann.

wood, on which is mounted the firing chart or battle map, preparatory to

the measurement of the elements of fire. The term is sometimes applied to

the Firing Chart.

501. Firing Chart: a grid sheet, or the battle map itself, on which are

shown the position, the sector, objective zone, objectives, base points, regi,3-

tration marks, orienting line, and other elements used in the computation

and preparation of firing. data.

502. . Limits of Fire: the straight lines from the guns mal'king the limits

of fire in deflection, and the lines marking the, minimum range and the extreme range of the gun. Battery emplacements should be so .collstructed

that the lateral limits of fire will include an angle of at least 1600r,'~.

503. Marker: a wooden or metal stake thl'ee or four feet in height used

in materializing an orienting line. The markers used in staking out an

orienting line should be distinctive for each battalion.

504. Normal Zone: the zone within the objective zone, for which the b:lttery normally is responsible and within which its normal fire is directed.

Topography for. Field Artillery

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-230-

Usually the battery and battalion .normal zones are identical.

505. Objective Zone: the areas beyond the friendly lines within the lateral

limits of fire; that portion of the sector beyond the friendly lines.

506. Observation Post (0. P.): a post for the observation ana conduct of

fire, for the observation of a sector, and the study of obje~tives, and for the

purpose of securing information of the enemy and hi::; act;vitie:i'

a07. Observer Displacement: is the angle at the objectiv~ behveen the ob-

~erver and the battery; the angle T' of the drill regulation'-3; applied also

to the angle between the origin line a;nd the base line.

50S. Observing Line: the line joining the observer and the adjusting point

of the objective, or the point on which fire is adjusted.

509. Observing Sector: the sector subtended by the objectiY'3 as viewed by

the observer. It contains the observing line.

510. On the Base Line: A battery is said to be on the hase line (en ~mrveillance) when the plane of fire of the base piece is dil'eded on the base

point. and when the planes of fire of the other guns form a well defined

sheaf, generally a parallel sheaf.

511. Orienting Line: a line of known direction, materialized on the ground,

and located on the map, by reference to which the guns are laid .for dirf'ction.

512. Orienting Point: a point from which it is possible to orient, the coordinates of which are known, used as a starting point for ~h,~ol'icnting line

or for a traverse to locate the orienting line or place marks.

513. Origin Line: a line selected near' the center of the field of observer to

which angular measurements are referred. If the sector is very extended

several origin lines may be used. Usually the origin line is the line extending from the observation post to the base point.

514. Place Mark: a point materialized on the ground, exactly located on

the map with known coordinates' and known elevation, by referen~'~ to which

the guns may be located, on the ground and upon the map, both horizontally

and vertically.

515. Plan Directeur: battle map made on the Lambert Projection.

516. Point of General Control: control point.

517. Position: strictly speaking, the Gun Position; actually the position

includes the battery organization for combat, or all elements outside the objectiv~ zone uaed in the computation of data, the observation and conduct of

fire.

518. Range Deflection Fan: drawn sometimes for the directing piece, sometimes for the observation post, and sometimes for both; a graph composed

of rays and arcs, showing range and deflection, and drawn ~n the firing

chart, the battle map or on separate transpare:r'cies for the determination of

firing data. In many cases, the deflection arcs only will be. drawn, and the

ranges will be measured by' a range arm.

519. Reference Point: a prominent point on the terrain by reference to

which objectives may be identified.

520. Referring Point: an auxiliary or individual aiming point used by the

gunner in referring his piece.

521. Registration :Mark: Registration Point, Registration Target, Adjusting

Point, Auxiliary Target, Datum Point, Witness Point, Witness Target; the

Topography for Field Artillery

"
-231-

first term being preferred; an object within the ~bjective zone selected to

facilitate registration of fire. . 522. Sector: the area within the lateral limits of fire of the battery. These

limits should include at least 160011t.'!'

523•. Witness Point or Witness Target (see Registration mark). The French

make the distinction between Datum point and Witness point, in that whereas the former is an adjusting point which not only must be clearly visible

but must also be accurately located on the map, the latter may be uncertain

as to map position.

TO POINT OF GENERAL.: (O!'ITROL

(f4lgh PeQK, 22 KIloS.)

I

/1 ;/

To POINT Of GENERAlCONTR C'

(TOWer; 7. Kllm)

To -STEEPLE

(3- f~llos)

Fig. 164.

Topography for Field Artillery

~~~
 
I

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'I'

""AXI""VM.RA~G[.CJf::.-~__

-- -- -...............-

-----....

Fig. 165.

'l'opo,{I'I\!lhy fot' Field Artillery

-

.1
-233-

Fig. 166. \ .

Topography for Field Artillery,
-234-

Fig. 167.

Topography for I<'ield Artillery

..
/

/

/

TO POINT OF"

GE:N.CoNTRClL.

-235-

Fig. 168.

Topography for' Field Artillel'y
CHAPTER XXIII.

MAPS AND RECORDS OF THE ARTILLERY SECTOR.

CLASSES OF RECORDS.

524. One of the important duties of the battery commander is the com.,

pilation of exact records, the elaborateness and exactness of which, depend

upon the stability and importance of the battery position to which they

pertain.

Records are kept of all battery activities and of all data affecting the

battery's functioning in combat, such records being for permanent use in

the battery position, either by the original battery. commander or by his

successors. Briefs of these records are made, from time to time, for transmission to battalion, regimental and higher commanders.

Data peltaining to the artillery sector fall into two general classes;

(1) maps and charts, and (2) written records.

A. MAPS AND CHARTS.

(1.) The Battle Map Of The Sector (Piau Directeur).

525. There should be kept at the observation post and at the command

post a battle map, of the latest edition, constantly kept up to date by the

by the aid of additions and revisions published by the topographic section.

(2.) Charts. •

526. Among the several charts usually prepared are the following:

(a) The firing chart: a great saving of time and ammunition can be

effected by making use of a suitably prepared firing chart. to be used for

the computations and measurements incident to the preparation of fil'e.

A complete chart of the TJ'pical Battery Sector would show:

Preliminary topographical operations;

The Sector, which is the al'ea enclosed by the lateral limits of fire,

the maximum range and minimum range of the battery;

The Objective Zone, which is the area beyond the friendly line within

the sector;

The Position, which means strictly the Gun Position, but includes the

battery organization for combat, or all outside the objective zone which is

used for the computation of data, the observation and conduct of fire.

;~.27. The following method of preparing a firing chart has been found

satisfactory. A sheet of drawing paper is mounted on a flat surface,;'

wooden board. or zinc sheet. Squares are drawn upon it, the sides of which

are 5 em. long. The lines are numbei'ed to correspond to the grid lines of

the battle map of the sector considered. Upon the gridded sheet are plotted

the elements necessary to the calculation of map data for the conduct ot

fire. No topographic detail is really essential on a firing chart, for it always

Topography for Field Artillery

j

"
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can be obtained from a corresponding battle map. However it is usual to

draw, or pad ~e on, the enemy organizations, see eh. XVII. '!:

The ouadrillage or grid system should be drawn first with a hard

sharp pencil and, after checking, with ink. It is indispensable that its construction be precise. The error should not exceed .2 mm. in a 5 em. square.

The following method of procedure is suggested, fig. 169,

c.

... ,/

/

"

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/\

a A B b

", /

/'...

"'- /'

"-

d I

Fig. 169.

1. Dra"w the major axis, ah, approximately in the middle "of the paper.

2. Draw the minor axis, cd, perpendicular to ab, see par. 72.

3. Draw arcs with centers on the axes. The radii for the arcs from

each axis should; be in .,multiples of the distance between the lines of thf

grid (5 em. on a 1/20,000 map) and the arcs should be tangent to the proposed outer lines of the grid.

4. Draw tangents to these arcs. They will be parallei to the axes.

5. Commencing at axis cd, by means of a carefully graduated ruler, determine points at 5 em. intervals on the axis, ah, and its two parallels. Join

successively the set of three points, lining the paper in the direction of cd.

6. In the same way the paper may be lined parallel at ab.

7. Place numbers on the grid lines representing the metric coordinates of the portion of the battle map to which the firing chart corresponds.

The grid may be checked by drawing a diagonal through two intersections .. This diagonal should pass through all corresponding intersections.

The battle map is sometimes used as the base of the firing chart.

\Vhen the map is mounted upon the board by pasting, considerable angula ..

error may occur, due to the irregular expansion and contraction from wetting. Th;s error may be confined within a small area by cutting and mounting the map in sections. This, however, is a slow process and requires

great care.

528. (b)' The Range and Deflection Fan. To rapidly determine angular

relations, and map ranges to certain points or targets .within the sector, a

Topography for Field ArtilleJ'y

\

\

~ \

-

\
-238-

range and deflection fan may be prepared on transparent paper, or on the

firing chart itself. Rays are drawn usually every 50 mils, to include the

width of the field of observer when used at the observation post,. or. the

width of the limits of fire when used. for the directing piece, fig. 170. With

the. middl~ ray as zero, the rays are numbered to the right and left in mul-

<Q

Fig. 170.

tiples of 50. "Vith the O. P. or the base piece as the center, arcs are drawn

over the rays at ranges of, usually, every 500 meters to include the extremf

\

range of the gun .. These are numbered properly.

Topoj;('raphy for Field Artillery
-239-

An\Jther method, which has been found satisfactory, is the use of th~

range arm. An arc is constructed' upon the firing chart with a radius of .'!:

ci:.

Fig. 171.

Topography for Field Artiller)'
-240-

the extreme" range of the gun and is graduated to five mils. with 'zero at

the intersection, of. the base line with the arc. The range arm, made of some

non-shrinkable material, is graduated to ten meters and includes the extreme

range of the gun. The range arm is' placed upon the chart with zero at the

gun position and its edge passing through the target. The range is read

from the arm and the deflection, right or left, is determined ,by the point

where the edge of the arm intersects the deflection arc, see fig. 171.

Although it is desirable to keep the firing chart free from unnecessary

lines, there is an advantage in placing the range and deflection fan upon

the chart itself. The error due to contraction or expansion is in this ,way

324500

324600

31:4800

o

o

'0

g

'3'

~~?~~t

1\,\ / I \ / 1\\

/ /- \ \

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Fig 172.

eliminated sinct the fan expands or contracts with the chart. The deflection rays need not be continuous, only their intersection with the range arcs

need be shown. It is desirable, however, before placing the fan upon the

chart permanently, to check its accuracy by actual fire upon registration

marks.

529. (c) Position Chart. This is a chart showing the organization of the

gun position in detail. Preferably it is made on a scale of 1/2,000 and

TOpOgl'aphy for Field Artillery

~
-241-

usually shows:' (1) the position of each gun, its coordinates' and elevation',

referred to .th~ place mark; (2) tne orienting line; (3) aiming stakes for

day and night, and the direction and designation of aiming points or auxilliary aiming points; (4) avenues of ingress and egress, with notes on' hours

for their use; (5) command post, deep shelters, telephone stations, latrines.

kitchen, etc., fig. 172.

:)30 (d) Auxiliary Positions. Diagrams and charts are also prepared

showing auxiliary positions with routes thereto, and coordinates and elevations of place marks therefor.

531. (c) General System of Communication. Charts are required showthe general system of communication between elements of the battery, with

other units, and with higher command posts.

532. (f)' Chart of Visible and Invisible areas. The zones, visibl~ and invisible, from the observation post should be accurately indicated, either on

a special map posted at the observation post or charted to scale on transparent paper which may be superimposed upon the firing chart or battl~

maps of the sector. Copies of this chart are prepared for use by the battalion and higher commanders. The method of preparing the chart has been

considered in Ch. XIV.

Areas that are invisible from one O. P. may be visible from another.

By dividing' the area included in the field of observer into small squares,

the possibilities of observation from auxiliary O. P's., on areas invisible

from any particular O. P., may be indicated. The nUrriber- or numbers of

the auxiliary O. P's. which can be used are placed in the square in question,

fig. 17& • .. 533. (g) 'Chart of Dead Space. The study of the possibility and the eft fectiveness' of fire on reverse slopes and on heavily wooded areas within a

sector. is purely topographic and its value depends upon the 'degree of accuracy of the battle map. In no case, however, should the study be neglected, for all topographical conditions capable of affecting the precision of

fire must be ascertained as far as possible. Such ~harts are particularly

important for the fire of guns with a flat trajectory. The chart of dead

areas is prepared to scale, either on a special map or on transparent papel"

which may be superimposed \lpon the firing chart or battle map of the sector.

Copies of this chart are prepared for use by the battalion and higher com""

mander. The methods of computing dead space have been considered in

Ch. XV. •

534. The possibilities of fire by neighboring batteries upon the dead areas

of a particular battery should be indicated upon the chart of dead space of

that battery. This may be accomplished by dividing the field of fire into

small squares, either 1 em. or 2.5 em. on a side; inserting the number of the

neighboring battery within the squares indicating the areas upon which it

can deliver fire. The correct squares may be determined by a study of th~

chart of dead space of the neighboring batteries, see fig. 174.

535.: (h) Combined Charts of Higher Commander. The topographical

records of the battalion and higher organizations comprise information transmitted by the batteries, together with that secured from other sources. These

records consist of information relative to the organization of the gun positions, fields of fire, observation posts, ..fields of observer, objectives, and al- . -.

'rQPography for .FieldArtillery

"
-242-

lied items. The information is compiled in compact and convenient form,

much of it being diagramatic. When so arranged the battalion commandel'

46

45

44

43

4e

41

4(J

3g

38

37

36

35

:34

33 ,

32-

31

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If{

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I~

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7 ~O p~e

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za 2.9 30 :31 elZ 33 c34 ~5 36 37

Fig. 173.

Topography for Field Artillery .

.

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-243- ,",

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Topography for Field Artillery

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-244-

IS enabled to pass along,' without difficulty, all information that his successor may need to perform his duties .

.536. The artillery commander, in order to direct properly the fire of his

artillery, needl:i to have a map so arranged that he may see instantly the

possibilities of fire of each battery. . .

There are various methods of preparing such a map. Among the

most simple and most practical, may be mentioned that one that consists

of sticking into the battle map, (fastened to a. board or to the wall), pins

.01' needles at each emplacement of the batteries of the command. A colored

thread, indicating the caliber, attached to each pin, carries a mark corresponding to the limits of the range of the battery. It is, therefore, easily

seen whether a target may be reached, and if so, by what batteries.

537. To prep::i.re plans of fire concentration, the following system may be

used. Cover the battle map, 1/20,000, with a sheet of tracing paper marked

off into squares of 2.5 em., one fourth of the ordinary square, see fig. 175.

Construct the field of fire of battery A, drawing an arc, Be, representing'

the range corresponding to the maximum elevation. Indicate the dead areaJ

within the field of fire.. Mark in each square, or fraction of square that

.can be reached by fire, the number of the battery which can fire on the

square, such as, 171. Repeat the operation for each battery. The result

will be a very simple and clear document enabling anyone to make up, without difficulty, a plan of fire concentration of the command.

538. A document maybe prepared in a similar manner to indicate areag

v;isible or. invisible from any observation post of the sector. Such a chart

Offers a convenient method of rapidly determining the most suitable observation post to use in adjustment of fire within any particular area. . .

B. WRITTEN RECORDS .

.539. (a) The B. C. Data Book. The written records of a sector consist

,of the B. C. data book and certain subsidiary documents. The B. C. data

book contains the record of all accurate data pertaining to the preparation

:and occupation of the position and its subsequent activities, including initial

elements of firing data and tactical and technical problems concerning' thi~

sector and position. It is a permanent record of the position and is turned

over to the relieving battery commander. If the position is abandoned, the

book is forwarded to the chief of artillery of the sector concerned, and, in

case of close attack, it is destroyed.

540. (b) ThE' battery commander keeps an Ammunition Record and 8

Gun Diary for each gun, which diary remains with the gun throughout it.:.;

life.

541. (c) A Target Sheet is kept at the observation post upon which j-l

entered, data concerning new targets discovered, and corrections on the location of targets previously reported. ...

542. The battery commander transmits, from time to time, reports on the

general enemy activity on his front,. sometimes including exact records ot

enemy artillery fire, reports on new targets discovered, and corrections on

the location of targets previously reported. .

543. With reference to records, it is important to remember that the efficient battery commander will not permit himself to become a slave to form~

and schedules. The elabor.atjon of l'ecords is valuable only in the exact

Topography for. Field Artillery
--245-

measure that it facilitates the tactical and' technical work of the batter~:-

and increases the efficiency of the battery's fire.'!:

,

,

I

&t-

/

I~

..- 5=171

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35

34

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31

30

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, . Fig. 175.

To})ogl"Rphy for Field 'Artillcr)'

_

. ~
CHAPTER XXIV.

TOPOGRAPHICAL OPERATIONS IN OCCUPATION OF

A BATTERY SECTOR.

GENERAL.

54(. Topographical operations to be performed in the occupation of a

battery sector are dependent on:

First, the time element;

Second, on the instruments available for use;

Third, on the accuracy of the map us€:d;

Fourth. on the proximity of geodetic points or points of. general

eontrol.

The object of the topographical operations is to determine the initial

elements of fire. These operations are performed, partly during l'econnai3.'

sance, and pm'tly after the position is occupied.

The topographical steps may be pedormed: (1) entirely by the battery commander or his rec'onnaissance officer; or, (2) by the battalion orienting officer who locates the orienting line ar.d place marks for all batteries,

followed by the battery commander who completes the work for his particular battery.

GUN POSITION.

(A)" WHEN COORDINATES OF GUN POSITION CAN BE READ

DIRECTLY FROM THE MAP.

545. The simplest operations arise when the battery is located at a poin~,

which may be identified on the map so that the coordinates may be taken

directly from the sheet.

If the base point or the target also can be identified on the map the

base line, or the direction to the target, may be taken from the map, as

may the range, while the site may be computed by using the map elevations.

In such a case a line of sight may be established through a distant

aiming point, or along a line of established direction, and the guns laid a~.

cordingly; .or, the direction to the base point having been determined, th/~

guns may be laid with a declinated instrument on the base line! see Ch. XXV'

B. WHEN THE GUN POSITION CANNOT BE IDENTIFIED'

ON THE MAP.

546. In the majority of cases the position of the guns cannot be identified

on the map.

Since the position of the guns must be known before any firing data

may be computed from the map, the first topographical step is the determination of the battery location. This may be accomplished in a number

of different ways.

Topogoraphy for Fipld Artillery

'
-247-

(1), Using. A Geodetic Point

;)47. If the battery is close to a geodetic point the coordinates and elev:.ttion of the gun position may' be determined by a short traverse.

(2) By Resection.

548. If the battery is in a position from which two or more control points

can be seen, the position may be determined by resection.

(3) By An Orienting Po~nt•.

;)49. If neither of these conditions hold, it will be necessary to establi~h

an orienting point, which will be used as the starting point for fUl'thp.i.'

topographical operations. The guns are located, in this case, by:"running

a traverse from the orienting point. .'~

If the topographical operations are performed in advance of the ar ..

rival of the guns, it is customary to establish a place mark near the battery position. The coordinates and elevation of this place mark will bE'

recorded and when the battery does arrive, the exact location of the guns,

horizontally and vertically, may be determined, either by traverse, or by

determining how much east or west, how much north or south, and how

much above or below the place mark, the. gun position may be .

• BASE POINT OR TARGET.

A. WHEN THE POSITION OF THE BASE POINT OR OTHER TARGETS MAY NOT BE DETERMINED. FROM THE MAP.

550. (See Ch. XXVII).

B. DETERMINATION OF DIRECTION TO TARGET OR BASE

POINT FROM THE MAP.

551. With the gun position and the target position determined by coord~p..-

ates, the direction or Y-azimuth may be read directly from the map by

means of a protractor, or the direction may be computed directly by a comparison of the two points, see eh. XIX.

AIMING POINT.

A DETERMINING DIRECTION TO AIMING POINT.

;)52. The direction to the base point or target being known, it is nece&-

sary, before the guns can be laid, that a plane of sight should be determined,

This also may be done topographically.

The desired direction may be determined by using a distant known

aiming point, see Ch. XXV; by using a declinated instrument, see Ch. XXV;

or by making use of an orienting line.

B. THE ORIENTING LINE .

. 553. The orienting line, as the name implies, is a line of known direction,

usually materialized on the ground by means of which the battery commandc)'

can orient his guns. Magnetic north, as used in connection with a declinatcd

instrument, is such a direction, and if this direction is materialized on the

ground, it becomes a true orienting line. The direction, Gun-Aiming Point,

if materialized on the ground, also ,becomes such a line. \

Topography for Field Artillery

I

"
-248-

(1) Two Types Of Orienting Lines .. (S~e cuts, Ch. XXII).

554. In generai there are 'two types of orienting lines, viz;

(a) Those established through a knovrn point or points, and

(b) Those established with a known direction.

Magnetic north, if materialized, is of the last type. In some cases it

is easier and more accurate to estabHsh an orienting line by direction rathe:

than to l'un it through known points. If such a line is established it is not

necessary to determine the coordinates of any points on the line. The lin~

may be run through the gun position, or in front or rear of it, and in any

direction, and the guns speedily laid by means of a plane table or angle .

measuring instrument set up on it at any place visible from the guns.

555. Where the orienting line is established by direction it still is necessar~'

for the battery commander or reconnaissance officer to take the topographical.

steps necessary to determine the coordinates of the battery.

On the other hand where the orienting line is run through an orienting

point which has been occupied in the work, the two sets of operations may

be performed simultaneously and the reconnaissance. officer will reach a

point in the vicinity of the battery with all control elements determined.

Fig. 176.

556. The orienting line should be established by means of a set of COTjspicuous stakes or markers set up at such intervals that, from anyone stake

at least two others will be visible. This affords a check on direction and

Topography for Field Artillery
-249-

alignment in case a stake is destroyed. Usually the stakes or markers of

each battalion will be of a distinctive type'.~:

(2) A Typical Case.

557. Assume that the battalion has been assigned a sector, that the general

, location of gun positions and of objectives is kno\\'ll, and that' there is time

enough for the. completion of the topographical operations.

In such a case it is probable that an orienting line and place marks

would be establIshed by the battalion orienting officer after which the batter.,1

commanders would continue the work.

Assume that the battery positions are so situated that no control

points are visible therefrom, fig. 176. ,

From the hill-top, P, the battalion orienting officer i~entifie~'three control points," A, B, and C, which he uses in making an Italian resection and

so establishes an orienting point, P. The battery positions cannot be seen

from the, hill so the orienting officer l"UnSa traverse PX)}, and arrives at 11,

the coordinates and elevation of which he computes and records.

From )} he notes a distant church steeple.in the direction of the gun

positions and so decides to run the orienting line through that object. He

measures the Y-azimuth of the direction from .Y to the steeple and finds that

it is 2450*. This is recorded.'

Starting from )}, the orienting officer then runs a line with a Y-azimuth of 2450ljt past the battery positions, establishing his markers, and determining coordinates and elevations of one or more place mat"ks in the

vicinity. of the batteries, see fig. 176. , .

558.' All data secured is recorded, and the battery commanders are furnisherl

rough sketches showing the Y-azimuth of the ,orienting Jip.e and the co'.

ordinates of thE' place marks in the vicinity of. their ,battery positions. With

theRe data the~ then proceed to establish the,ir gun,s on the base "line.

"~;"

Topol{l'aIlhy for Field' Artillery

" "

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CHAPTER XXV.

LA YING THE GUNS ON THE BASE LINE.

STEPS P£RFORMED IN THE OCCUPATION OF A SECTOR.

ESTABLISHMENT OF THE BASE PIECE ON THE BASE LINE.

562. The operation of laying the base piece on the base line or the target,

falls into three general classes:

First, Staking out or Lining in;

Second, Field method of measuring angles and calculating offsets

from the B. C. Station;

Third, Topographical methods.

A. STAKING OUT.

563. Let C be the gun, T the point through which the plane of fire is to

be directed. T cannot be seen from the gun position but can be seen from

the crest between C and T (or back of C). (Note: It is not necessary that

T be the base point selected. It need only be' some visible point on the line

Gun-Base point.)

Topography for Field Artillery
. , -251-

Two men, M1 and M2 move in such a way that M1 constal).tly keeps M2

lined up between himself and T, and M2 constantly keeps Ml lined up between

'himself and C. They cause each other to move until they are on the line

CT at M/ and M/, see fig. 177. The position indicated should be marked by

stakes and the alignment verified, after which the guns may be laid on th8

CT line.

Jv1,

O~

,

,

Fig. 177.

Instead of two men, an aiming circle or other angle measuring instrument may be moved until exactly on the CT line. This occurs when the angular reading between the two points is 3200 mils.

B. USING AN AIMING POINT, AN ANGLE MEASURING INSTRU .

. MENT, AND COMPUTATION OF OFFSETS FROM THE

BATTERY COMMANDER'S STATION.

564. This method is discussed in drill regulations.

C. USING TOPOGRAPHIC METHODS.

565. Quick and accurate fire on a given point demands careful preparation.

The required data for opening fire: deflection, range, and site, may be read

off the map, after the gun, the target, and the plane of sight, aiming direction or aiming point, have been plotted. .

Topography. for Field Artillery

,
-252-.

The accuracy of these data depend on three things:

First; The accuracy of the map itself;

, Second, The care with which the topographical operations have been

'Perf();rmed;

~'.j Third, On the. precision of the subsequent measurements;

Fourth, Additional errors may also be expected if measurements arc

made from the map, due to the contraction and expansion of the paper.

These last errors, however, may be minimized by the use of the firing board.

If the Plan Directeur (French Battle Map) is used, the original errors

due to the construction of the map itself may be disregarded. If the plotting board is employed the distortion of the map, due to weather conditions,

may' be overlooked.

There remains then, the consideration of the errors likely to aris'~'

in locating and plotting points. and in measuring distances and directions'

also the consideration of the methods to be followed which will be leal:;~

likely to involve error.

CLASSES OF TOPOGRAPHICAL lVI"ETHODS.

566. In general there are two classes of topographical methods of laying

the base piece on the base line:

First, That in which the plane of sight is established by two points

which have been located by their coordinates;

Second, That in which the plane of sight is determined by an established direction~

FIRST CLASS. PLANE OF SIGHT THROUGH POINTS LOCATED BY COORDINATE!:;.

567. The simplest of all cases involving computation of firing is that

wherein the position of the gun, the target, and the aiming point all are deflnitely known. A reading scale may

then be used to determine the range,

1200 a protractor employed to compute the

deflection, while the site may be computed by determining the difference

in elevation of the gun and target

as shown by the contours of the

map, and dividing this difference by

thousandths of the range, expressed

in the same units as the difference in'

altitude.

In' fig. 178 let G be the gun

position, P, the aiming ,point which is

visible from the gun position and T,

.. , .. .:the target position, all of them being

points accurately plotted on the map .. Draw the lines, GT and GP. With

a protractor measure the' angle;' PGT. Assume this to be 950 mils .. The

firin'g"ungle .or 'deflecfion for the American sight" then will be 6400 minus

95001'5'450. '. Measure the distance GT.' Assume this to be 2500 meters. T

is. situated on contour .1200 'and 'G .is located 'at an elevation of 1225, giving

a difference of 25 meters. This elevation',' 25,. divided by the range in kilo-'

Topograph~.for Field Artillery
-253-

54501it,

: 290111,

2500M.

meters gives a site of minus 10. The data obtained from the map then become:

Deflection :

Site'

'Range

p ~'-" ............ ............ .. ", - -p -

Fig. 179.

(1.) Errors.

5€8. This. method is necessal'ily li~ited in jts use- for the reason that an

aiming point .located on the' roapor firing board by its coordinates is likely

to, involve a considerable error in deflection unless that point is more thml

2,000 meters distant."

If care if used in the topographical op~rations of' resection, of traverse, and in plotting of gun and aiming point positions, these t~') point~

shol:lld be located on the map within' 20 meters of, their true positions. If

both these errors are in opposite directions the maximum relative displacement is 40 meters, which, at a distance of 2,000 'meters, means an error of

20 mils in deflection.

Rapid preparation of fire without previous organization will involvt3

even more considerable errors when the above method is used.

569. On the other hand if the base deflection be determined with reference

to a determined direction passing through the base piece, the error brought

about by the false location of the A. P. is eliminated. There remains the

error of orien1ation, which, with the ordinary declinator, should be under ;)

mils; also the error caused by the error in the location of the gun position.

In deflection this last error is equal to the parallax of the distance by which

the gun is offset frQ.ffiits true position, as viewed from the target, and sincn

the target usually is at a great distance this angular displacement is small.

In range the displacement should be within one probable error ..~'A compari.

son of the errors resulting from the two general methods is shown below.

570. (a) First Case: (Using a direction established by points plotted by

T'" T

\

\

\

\""\

\'

\

their coordinates).' Let T be the target, Gthegurr position, andP the' aim,.

ing point in thei~ true positions:" Le~ T',- G';:~ndP'be, thesesamepositip113

TopographY' ,for ,Field. Artillery

'
-254-

as they are plotted on the map or firing board. Assume that P' as plotted

is displaced 20 meters in one direction from P, and that G is displaced 20

meters from G in the opposite direction. The total displacement is, then,

40 meters. If the distance from the gun to the aiming point is 100 meters

the total angular error, a, fig. 179, involved, is 400 mils. Because of the dis.

tance to T, the angular displacement due to the error in plotting T may be

disregarded. Therefore if the gunner lays with the deflection as measured

from the map he will set off the angle, PGT", equal to P'G'T' instead of

PGT, and his plane of fire will be passing 400 mils to the left of the target:

571.. (b) Second Case: (Using a direction). Let T be the target, G thp.

gun position, fig. 180. The plane table or aiming circle is set up in th~

Fig. 180.

vicinity and oriented. Let P be the location chosen. Let g' and t be the gun

and target positions as plotted on the plane table. GP is a definite direction

defined by the two points, G and P. Sight across g', the plotted position of

the gun, at the gun and draw the direction, Gg'P. Assume that g' is falsely

located by a matter of 20 meters and that g is the true position on the

board. On the 1/20,000 map, 20 meters on the ground is equivalent to onl~

millimeter. If the point P, where the board is set up and oriented is 100

meters from the gun, the angular error caused by the false plotting become:;

one one hundredth of a mil (the parallax of one millimeter at a distance

of 100 meters). If the plane table or aiming circle, be used as the aimiTI1~

point it is evident, therefore, that the error in the plotted direction of the

plane of sight may be disregarded entirely. There still remain the errors in

deflection caused by the error in orientation at the point P, and error, g'tg,

which is the parallax of the gun displacement measured from the target,

but the sum of these usually is within. the allowable error.

Topography for Field Artillery

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-255-

. ... (2.) :Methods Of Checking.

Fig. 181.

IG

I

/

I

I

I

/

p

572. Often it is desirable to use a plane

of sight passing through a point located by

its coordinates ar.d not at a great enough

distance to reduce the expected errors within the permissible limits. Sometimes it is

possible to check the direction of the plane

of sight by one of the following methods.

773. (a) First :Method. \Vhen it is possible to occupy the. A. P. ,Occupy the 'point

P which is to be used as an aiming point

and orient the board. Plot p on the plane

table. Plot. 'g, the gun position. Sight over

p at the sight shank of the gun and draw

the line pC', see fig. 181. If this line does

not contain the plotted gun position, g, it may

be possible to move the piece slightly from

C to C' until the sight shank falls in the line

of vision. This will bring the plotted position of the gun to g', and the direction, C'g'p,

may then be taken as the true plane of sight.

574. (b) Second method. Set up the instrument used on the line PC.

Move the instrument perpendicularly to PC until the angle, PpC, is equal to

i- _

Fig. 182.

3200 mils. or the line, PpC, is a straight line. Carefully' orient the In'stru-:-

ment or the board with the compass, or by angular traversing, and sight ovel

p. Draw the corresponding line on the plotting board or note the, readings'

if the aiming circle is used. Any error in this direction is dependent on the

orientation and not on the plotted location of the points, p and g. Assume

that the direction, PpC, does .not pass through the plotted gun position, g•

. This may be due to the errors in plotting either or both p and g. Assume

that this angular error is g'pg. If p is a goedetic point its location on the

map may be assumed as correct, in which case the plotted point, g, should be

displaced to g' and the coordinates of g' taken as the true ones for the gun

position.

If, on the contrary, the gun position, g, has been located from a geodetic point by short topographic operations, the plane of sight. should be

Topography for Field Artillery
-256--.

dravvll through g, fJ being displaced to this line and new coordinates recorded.

These last cases, in reality belong to those classes of. operations ii,

which the plan~ of sight is determined by. reference to an established direction, since it was necessary in these cases to orient the board and correCt

the direction determined by the, plotted positions.

SECOND CLASS. PLANE OF,'SIGHT DETERMINED BY AN ESTABLISHED

DIRECTioN.

,T

I

I

',' I

I

t

t

,

1

_----I G

• J

1 :~ !

(1.) Direct ,Orientation Of The Directing Piece 'Without The Use

Of An Orienting Line.

575. (a) Using plane table.' Plot the gun position, g, on the board and

the direction gun-target or gun-base, point, either by means of the coordinates of the two points or by means of the Y-azimuth of the direction.

Orient the plane table in the vicinity of the' gun position, either by resection.

by a short traverse, (not more than three legs) or by use of the magnetic

needle (the declination co~stant of which has been determined' previously).

With the alidade pivoted ~bout g, ~ight C (the panorar:'lic sight of the gun,

Fig. 183.

and draw the direction, CgP. Mea~ure '~ith a protractor'the ang'le which

thislinemakes:with:the base line~ CT. Let this be the angle a. In the case

illustrated 'in: fig. '183, subtract angle,' a, from 6400 mils. The remainder.

angle b, is the firing angle' which, with the deflection constant added, is the

deflection (see note) given the' 'gunner. With this deflection on his sight I

the gunner next lays for direction, using as an aiming point a pencil held

vertically' on the' point, p',' on' the plane table. The operation"shouP be repeated ,once or twice on account of the displacement of the gun sl~ht duthJ~ •

the process of laying, the gun being moved slightly until this is accomplished.

'\Vhenthe gun finally is laid on the CT line the gunner l'efersthe piece \rNl.ds

t.he,deflection to a more distant aiming point) and, records the deflection;

Note: The "deflection constant" is the deflection which causes the

plane of sight: to' be parallel'to. ,the plane of fire .. It is plateau 0, tambour

400'for the 75,.and deflectiot1 1000 for the 155 Schneider howitze~: ,,:,.r

Topograph~L for" Field' Arti Ilel'Y;

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-257-

576. (b) Using the aiming circle' (French). The battery commander first

measures on the map or computes from the coordinates, the 'l-azimuth of

he base line or gun-target line.

The Battery commander knows the Y-azimuth of mag'llet~~ north 01'

(declination constant) (magic number) of his instrument (the reading which

must be set off in order that, when the needle is brought oppol:>itJ its index

by the gen~ral motion, the instrument will be oriented). He sets this on the

instrument and orients. This brings the zero of the horizontal HCHle on the

Y-line. N ext he sets off a reading equal to the Y':a'zimuth of the base lin,.~,

and with the general'motion turns the instrument until the needle is opposite

its index. The instrument then will be laid so that the line of sight will be

parallel to the base line when the reading on the lower (red) scale ij. 7.el'o. ...

With this line' established parallel to the base line' it is necessary

only to turn the line of sight, using the upper. motion, to the sight of the

directing gun, note the readings, and announce it in terms of plateau and

tambour. The gunner sets off the announced deflection on his sight and

lays on the spindle of the aiming circle as an aiming point.

577. Note 1: By making use of the deflection constant the setting on th.~

gun sight 'may be read directly from an aiming circle (graduated clockwise)

by reciprocal laying methods; that is, the setting (using a French aiming

circle) must 'be Plate 0, Drum 100 for the 75; 1,000 for the Schneider 155

howitzer; and 3200 for sights graduated clockwise from 0 to 6400.

=>78. Note 2: A modification of the above method sometimes spoken of as

the magic number method is given below. Let L be the declination constant

(magic number) of the given instrument. Let V be the Y-azimuth of tlF~

base line. The deflection of the base line from magnetic north then, is L- f'

or 6,400 plus L-V if L is less than V. Set the aiming ell'cIe "at the value

determined and proceed as before.

=>79. The following problem 'will illustrate the above method, fig. 184.

The Y-declination is found from the map to be 250 mils west. This

makes the Y-azimuth of magnetic nOl.th equal to 6150 mils. In other worrh

the magic number (declination constant) for a clockwise instrument is 6150.

From the map the Y-azimuth of the target, T, measured from the gun position, is found to be 2000 mils.

6150-~000=4150 which is the deflection from magnetic north which

will place the gun on the GT line. Setting 4150 on the instrument the needJe

is brought to its index whereupon the line of sight is in the direction CT',

parallel \to the GT line. Note: When opel'ating an aiming circle use thp.

slow motion screw rather than the rapid motion if accurate results are desired. .

With the line of sight still directed along the line CT', a setting of'

3200 mils is placed on the instrument and the line of sight is then swung

around to the gu~, G, fig. 185. The 'actual angle read is xCG, measured clock-

,vise. Assume that the angle T'CG, is 1900 mils. The reading on the instrument is 5100 mils. If the deflection constant of the gun is zero, this is the

deflection given to the gunner who sets it on his sight, directs the line of

sight on the aiming circle (line GC) and lays the gun on the GT line. The

actual firing angle laid by the gunner is TGe, measured clockwise from T,

which (by geometry) is equal to x CG, measured clockwise.

Topography fOl' Field Artillery

t

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flJi. ,!o\'I'aphy for F' I Ie d Artillery

T
-259-

580. If the aImIng circle is one divided into four separate quadrants it

will be impossible to add 3200 mils in advance. Therefore the angle read

will be J/CG or 300 mils in the second quadrant which, with the deflection

constant added, is given to the gunner. If the gunner sights on the aiming

circle with this setting he will have set off the angle, CGJ/', and the gun will

be pointed along the line, GJ/'. Therefore he swings his sight through three

additional quadrants and with the same reading in the fourth quadrant lays

the gun on the GT line.

581. Since th0re is a variation in the compass readings of different-instruments, and also daily and seasonal variations it often is of advantage to

materialize either the line, CT', or the line, GT~ on the ground as a check on

the future laying of the piece. In this case the materialized direc'jon becomes a true orienting line.

A.P

T

Fig. 186.

582. In case the base piece is not in position it may be more convenient

for the battery commander to set up his aiming circle on the base line at the

selected position, see fig. Ig6.

As before he directs his line of sight along the base line GT. Having

done so he turns his line of sight on some suitable aiming point, AP, or on

a selected aiming stake and reads the deflection. If the line GT has been

materialized on the ground, it will afford a check when the gun is moved into

position, and it will be possible to move the piece forward ar..d backward

until the selected aiming point, AP, comes in the line of vision after the

gunner has set off the announced deflection.

(2) Orientation Of The Directing Piece By Means Of An Orienting Line. ,

583. (a) Advantages of an orienting line. In using an orienting line the

artilleryman will find several advantages;

TOPOgl"aphy for Field Artillery
-260-

First, Since the orienting line establishes a particular direction, the

guns are laid using a direction, thus eliminating the enol'S mentioned in

par. 568.

Second, The orienting line. being established, permits of rapid determination of firing angles since it is necessary only to set up the plane table

or aiming circle at any point on the line and read the angles to the various

pieces; ,

Third, It is a convenient method in close country where distant aiming points are not visible;

Fourth, It is permanent and affords a convenient way of checking

deflections or of re-Iaying the guns if they are moved a stort distance;

Fifth, Since the orienting line may be common to two or more batteries or even to two or more battalions, the advantages of a regular sheaf

within a battery can be extended to' many pieces.

584. (b) Steps to be performed. The establishment of a battery on the

base line, making use of an orienting line consists of:

First, The determination of the base angle or the angle between the

base line and the orienting line measured in the same direction as the sight

graduations;

Second, The establishing of the base piece on the base line;

. Third, The establishing of a parallel sheaf or a sheaf of other well

defined relation.

The last two operations usually are performed successively or sim:-

ultaneously.,

A battery with an extended field of fire often uses several base points.

The object of this is, in shifting fire. to avoid the errors incident to measuring large angles. Consequently, if a shift will carry the line o~ fire past u

base point other than the one being used, the piece should be established on

the new base line.

I. Determination of the base angle.

585. Plot th~ base piece and the basepoint on the firing board or map

by' means of their coordinates .

. Draw the base line joining the two points ..

The orienting line having been materialized either by battalion or

battery orienting officer, plot the orienting line on the firing board by its

Y-azimuth or by coordinates taken from the plane table.

With a protractor measure the base angleII. Laying on the base line u~ing an aiming circle.

586. If the orienting line passes through the sight of the base piece, the

orienting line is used directly in laying for direction.

. If the orienting line does not pass through the sioght of the base

piece, an aiming circle or other angle measUl-ing instrument, or plane table'

must be set up on the orienting line and used. .

If the orienting line has not been previously established .and materialized, the base piece is established on the base line by means of a declinated

instrument, see pars. 576-580, and the line is afterward matel'ialized. ..

587. .First .Case. Orienting line passes through sight of hase piece. In

this case the plane of sight is taken as coincident with the orienting line

Topography for Field Artillery

_

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-261-

Fig. 188.

L

L

Fig. 187.

while the firing angle becomes the same as the base angle, providing. the

aiming point is to the right, see 'fig. 187..

Convert the firing angle

into deflection by adding the

deflection constant of the particular gun used.

Lay for direction with

this deflection" using the orient- (';--

ing line (extenaed to the right

for sights graduated clockwise)

as an aiming direction.

Refer the piece to another aiming point and record the new deflection.

When the marker of the orienting line which is to be used as4an aiming point is close to the gun, care must be used to insure that the base

piece is not thrown off the orienting line while laying for direction. To

this end it is well to establish a supplementary marker on the orienting line

near the gun.

588. Second Case. Orienting line does not pass tht'ough sight of base piece.

In this case an angle measuring instrument or a' plane table is set

up on the orienting line, so that the sights of the several guns are visible, .

and the firing angles are determined. There are a number of different methods of doing this, the order of measuring the angles usually being dependent

on the manner in which the one doing the work visualizes the relations of

the angles. he desires.

i)89. Method No.1. Using an aiming circle, laid parallel to the base line.

One favorite method is to set up the instrument on the orienting line

with the zeto of the instrument pointing in a direction parallel to the base

line and then lay the guns by reciprocal laying as in par. 576.._.

Establish the aiming circle on the orienting line (within at most a

few centimeters).<

Set the instrument at the base angle ..

Using the general motion, point the aiming circle along the orienting

T T' B~(2. Pomt.

line to the ri~ht (the right as one faces the base point). The zero of the

instrument is then on a line parallel to the base line, fig. 188.

Topography for Field Artil1el'Y

'
-262-.

Note. The above applies to an aiming circle graduated clockwise. If

the graduations of the aiming circle are counter clockwise (opposite to those

of the panoramic sight) set the aiming circle at 6400, minus the base angle.

590. The aiming circle or director being established parallel to the base

line, to lay the base piece on the base line, using the aiming circle as an

aiming point. ,

With the zero of the instrument laid in the direction, CT' or paralld

to the base line take the reading to the sight shank of the base piece. Let A

be the read:ng so obtained. .'

If the panoramic sight and the aiming circle are graduated in the

! same direction, the firing angle for the piece is:

A +3200 mils, if A is less than 3200 mils:

A-320J mils, if A is greater than 3200 mils. See figs. 189, 190, 191•

. 192, for the four quadrants, below, the first and fourth occuring when the

orienting line is in front of the battery, ar.d the second and third when the

orienting line is in the .rear of the guns .

. ,..,t.

• QVAORANi:

o

Fig. 189.

L

.2, nd

QVAORANT

o

Top~graphy for Field Artillery

Fig 190.

T'
-26~-

•

. J. rd.-.

QVADRANT.

o

4.th.-

(~VADRANT

Firlng.4 ngle

o

T

T

Fig. 192.

In each of these figs., OL is the orienting line;

C is the gun position.

C is thE" aiming circle position.

CT is the base line.

CT' is a line parallel to the base line.

A is the angle measured from the base line to the panoramic sight of

the gun.

Having cietermined the firing angle in each case it may be converted

into deflection by adding the deflection constant for the. particular type of

panoramic sight used.

After the base piece has been laid on the aiming circle it will be referred to some other aiming point and the deflection recorded.

Note. If the sight and aiming circle are grr.duated in opposite directions the firing angle is:

3200 mils-A, if A is less than 3200 mils.

9600 mils-A, if A is greater than 3200 mils.

Topography for Field Artillery
591.

lows:

-264-

.Method No.2. Using an aiming circle laid on the orienting line.

Another convenient method of laying with the aiming circle is as fo]-

• Set up the instrument on the orienting line.

With the zero of the instrument laid to the right along the orienting

line (to the right as the operator faces the base point) measure the angle

(measured clockwise) between the orienting line and the sight of the gun:

The firing angle will be equal to the reading thus obtained, plus the

base angle, plus 3200 mils. If the sum of these three angles is greater than

6400 mils,' subtract 6400 mils from the reading.

Let A be the reading obtained for the angle between the orienting

line and the gun sight.

Let 8 b~' the base angle.

C is the gun position.

C is the position of the aiming circle.

CT is the base line.

T is the base point.

OL is the orienting line.

In each case the firing angle becomes A+8+3200 mils. This will

also be the deflection for the American panoramic sight.

592. First Quadrant;

.....

- ""t ..

(~VADRANT

()

L

Fig. 193.

Let angle.8+angle A+3200 mils=angle M •

•, .But angle M is greater than 6400 mils by the angle T'Cx, whereas the

actual firing aagle is the angle T'Cx.

Subtract 6400 mils from angle M, and the firing angle, rcx is obtained.

Let 8=1200 mils,

Let A =2800 mils,

Then M=1200+2800+3200=7200 mils.

7200 miIs-6400 mils=800 mils=firing 'angle.

'fopogl'llphy for Field Artillery
-:265-

593. Second lluadrant;

e..nd.

<'M~DRANT

o L

594.

Fig. 194.

Let B=1200 mils,

Let A=4000 mils,

Then M=1200 mils+4000 mils+3200 mils=8400mils.

8400 mils-6400 mils=2000 mils=firing angle.

Third Quadrant;

o

'. Jord'

GlvAD RAN T.

Fig. 195.

L

Let B=1200 mils,

Let A=5700 mils,

Then M=1200 mils+5700 mils+3200 mils=10100 mils.

10100 mils-6400 mils.:=3700=firing angle.

fopography for Field. Artillery

"
-266-

595. Fourth Quadrant;

.4.th.

(~VAoJ1ANT.

r

Fig. 196.

Let 8=1200 mils, .

Let A=900 mils,

Then M=1200+900+3200=5300 mils=firing angle.

Note. If the zero of the aiming circle is.set to the left on the Ol'ienting line when facing the direction of fire, then 3200 mils will not have !0

be taken into consideration.

Also, if the base angle is first set off on the instrument and then laid

to the left on the orienting line, the clockwise angle read to the gun gives,

the deflection directly. .

Fig. 197.

Let' 8' equal the base angle, B. Then if the operator. at C sets B on

his instrument and directs his line of sight along the orienting line to the

left toward 0, the 0 of his instrument will be pointed to the rear on a line

parallel to the base line, GT~ see fig. 197. The reading D' to the gun, then

Topography .for. Field Artillery
-267-

will be the reading from this 0 at. the rear ar~und to the gun, or it is equal

to the firing angle, D. Proof. By geometry L=L', (alternate interior angles

of parallel linEs). Therefore D=D'.

III. Laying on the base line using a plane table.

596. The orienting line and the base line should be drawn the full length

of the plane table.

Set up the plane table over the orienting line.

Orient the table by sighting on a distant point of the orienting line.

This must be done carefully so that the orienting line on the plane table

will be parallel to the same line on the ground and over it to within a few

centimeters. 'With the alidade pivoted about g. the plotted position of the

gun, sight at C, the sight shank of the base piece, and draw the liIle Cg, the

full length of the rule. ..

With the protractor measure the angle between the base line and the

line Cg, measund in the same direction as the sight graduations.

This is the firing angle' which is converted into deflection by adding

the deflection constant. see fig. 198. .

IT

/

/

/ <;:-0)

/

o-~i~

/~//

/ /.

'~/

Fig. 198.

With this deflection, lay the gun for direction, using as an aiming

point a pencil held vertically at any point on the line Cg.

Repeat this operaticn until the sight no longer moves in laying the

piece.

Refer the piece~

Record the base deflection.

Cases in the other three quadrants will be solved in a like manner.

597. Note: In all cf the above rnethcds it is better to determine the base

deflection after the guns are in position. The method of marking the position of the gun sight with a stake and sighting on that stake from tt r.carby point, or of setting the aiming circle over this ~take and computing the

deflection, should not be used if time' permits the establishment of the piece.

If used. the piece should be moved until the deflection read on the sight

checks with that previously determined, or should be checked in some other

manner, and the corrections made.

Topography for Field Artillery

~ /

~

.
~.,

CHAPTER XXVI.

THE OBSERVATION POST.

GENERAL FACTS.

598. Above all, the observation post (0. P.) should be able to fulfill its

mISSIOn.,Observation must be reliable and continuous. . Other desirable

qualities such as command, facility of construction, communication, etc.,

should be possessed if possible.

The elaborateness of the O. P. depends upon time, varying from a

tree-top, shell hole, or bare crest to a well-equipped concrete dugout. Ruins.

steel towers, windmills, chimneys, church steeples. or any objects affording

a good view of the desired terrain are employed for this purpose. The more

inconspicuous, and permanent the O. P. is, the more desirable is the positioJl.

The observer must be efficient. If he is inattentive or inexperienced,

the artillery wastes ammunition, is poorly informed. and is not promptly

responsive to calls made upon it. Men used for observel's should be thoroughly familiar with the sector and specially trained in:

1. Loc:ltion of objectives.

2. Observing and adjusting artillery fire.

3. Observing a zone.

FUNCTIONS AND CLASSES OF O. P's.

599. Artillery O. P's. are of three kinds:

1. Intelligence.

2. Command.

3.; Firir.g.

A. INTELLIGENCE O. P's.

600. The Intelligence O. P's. proper are connected directly' with the Intelligence Section (G2) of the General Staff. These are located in or near the

front line trenches. But, any O. P. is an intelligence O. P., in the proper

sense of the. word, because a repol.t goes back once' in every twenty-foul'

hours, on all observations made in the preceding period.

B. COMMAND O. P's.

601. Command O. P's. for artillery pertain to the different units, such as

battallion, regiment, "groupment", division artillery, and corps artillery.

These stations are situated so as to afford to each unit' an extended view of

the sector. and not merely the zones of action assigned to the battel'ies of

~'the, unit. The fields of view should overlap, so that all terrain can' be ob-

'~e~ved. These posts are us€d to keep commanders informed as to the situation, and indications of hostile activity. In order to take full advantage

of any information gained in the battalion or groups, their observation posts

'~ should constitute an "Observation System", which is particularly important

"¥~~~~~a~hY' for Field' Artillery

-

'
-269-. . for heavy artillery, because of theIr long range and the large areas covered.

Command O. P's. may be used sometimes for firing, as well. f~ such a case,

they should possess the properties of a firing O. P., as listed below.

C. ,FIRING. O. P's.

602. The purpose of firing O. P's. (Battery or Battalion) is to obsei've and

adjust fire, an(l to locate objectives. These posts must, above all. permit the

objective to be seen, even in most unfavorable. weather. They should be

concealed, and be as close as possible to the front lines. In addition, they

should, if possible, have some command; should afford easy commuication

with the battery firing; should be accessible in the daytime; and should be

as close to the'line of fire as possible, as axial observatiop. shoul~' be used,

when,ever possible.

METHODS OF ESTABLISHING AN O. P.

A. RECONNAISSANCE.

603. The amount of reconnaissance pedormed before occupying an O. P.

depends upon the time available and the style of warfare. In close wadare,

it is usually done first from a map, as the proposed position probably will

be behind the enemy's lines. A "visibility chart" is made of the new sector

from the most promising points. The station possessing the least invisible

area should be chosen.

B. PRELIMINARY TOPOGRAPHICAL OPERATIONS AT THE O. P.

604. These include:-

1. Determination of the exact coordinates by Italian-'resection, (or

some other accurate method), and sending same to the battalion commander,

2. Checking the visibility chart previously made from the map, and

sending copy c.fsame to the battalion commander.

3. Drawing accurate panoramic sketch of sector.

C. DETERMINATION OF ORIGIN LINE.

605. This may be determined by Y-azimuth or it may be tied to some

reference point, which point must be visible even in foggy weather. The

reference point should also be near the center of sector if there is only one

point. MeasUl'ements to targets from the origin line must be exact if the

plotting of the targets discovered is to be accurate. Observers must frequently check t::p their instruments to see if they are on the origin line.

D. CONSTRUCTION AND CONSOLIDATION.

606. Special Orders are issued concerning concealment, routes of approach,

activity around 0 .P., and observation.

E. , DETERMINATION OF REGISTRATION MARKS FOR TARGETS.

607. These are plotted on the firing board which stays at the O. P.

These various characteristics are entered' in the Observation Post

Book.

Note: This is an example of the organization of the most elaborate post,

The development of the O. P. depends largely on the time available.

Topography for Field Artiller,r '- ','-.', ..' ',<: -"; ;(~'q(l'l

-

I

'

~
.~270-

RECORDS KEPT AT O. P.

608~ Records kept at the O. P. should include:

1. Accurate visibility chart of whole field of view checked from the

actual terrain.

2. Accurate panoramic sketch of same drawn either by an officer- or

dependable man.

3. Firing chart which must be kept up to date.

4. Observation post records of observations of enemy movements,

enemy works, machine gun and trench mortar emplacements. flashes, signals

from our own and enemy infantry, aeroplane movements, balloons, with time

of ascension and descension, with azimuth and approximate locality. These

observations ar€ initialed by the observer, and the time and the angle from

the origin line or Y-azimuth both are given.

"The O. P. Record Book" also contains the standing orders before

mentioned, and the liaison system (prescribing to whom the information obtained shall be communicated. and the order of priority).

This book is passed on to the battery relieving; is destroyed if in

danger of falling into the hands of the enemy; and, in case the position js

abandoned, is sent to Chief of Artillery of the sector.

5. A record showing to whom rocket signals should be communicated

or relayed.

6. A record showing to whom and in what order gas alarms should

be passed.

Topogl"aphy for Field AI"Ulle,'y

-

-
-271-

PLAN OF OBSERVATION.

609. Taken from Plan of Employment of the 51st F. A. Brigade, March, 3

1918.

PERMANENT OBSERVATORIES

NAME Personnel Location Alternatives REMARKS

75-28

08-30

63-30

01-26

53-57

Each station will have

permanently a scissors

RENARD inst., a fir~ng boata (chart)

with hidden and visible

areas, ar.d a panoramic

sketch, and a record book

of observations. The enANCENIS listed men will live near

the station, and one man

will always be in the observatory. Daily reports

will be handed in of all

observations, and inforCAMllRAI mation of immediate interest will be telephoned

to the regimental commander for forwarding t9

the Div. ArE -'-Comdr.

RHEIMS All rockets or other sig65-33 nals will instantly be telephoned to the Bn. Comdr.,

______________ and each station will have

aiming device arranged to

locate the positions of

CASHMERE rockets fired at night. 59-38

1 Officer

1 Non. Com.

3 Eill. Men

1 Tel. Op.

1 Officer

1 Non. Com.

3 Enl. Men

1 Tel. Op.

3 Enl. Men

1 Tel:"Op.

1 Officer

1 Non. Com.

1 Officer

1 Non. Com.

3 Enl. Men

1 Tel. OPt

1 Officer

1 Non. COm.

3 Enl. Men

,1 Tel. OPt

BXO

RENARD

ANCENIS

WILSON

CAMBRAI

Aerial Observation.

The Division Escadrille at Mont de Soissons and the Division Balloon

Co. at Veilly are at the, disposition of the Battalion Comdrs. for either

adjustment or fire for destruction.

;1 I

Topography for Field Artillery
CHAPTER XXVII.

LOCATING TARGETS.

I ( TERRESTRIAL OBSERV,t\TION.

~6io..._,While the airplane and the aerial photograph afford means ,of locat- in:g ~~~v'ta~gets. terrestrial observation continues the most important observation,' method, ,hence the battery commander, to secure the most effective

use of; his aqvantages must be familiar with all methods of 'securing the

rcoordinat~s; of the targets in his sectol'. If 'a target is visible he may d'3-

~ermin'e the range and azimuth by registering on it and then swinging his

'fire to a 'registration mark, the range and deflection of which are known.

With the range and azimuth so determined he then may plot the target in

question on his firing board or battle map. It frequently is possible, by

the employment of a few simple topographical operations, to accurately locate objectives in the battery sector, thereby saving time ..and ammunition

required for the attack.- Therefore all possible use of topographical methods

should be made in the determination of the coordinates of new targets.

COMPARISON OF METHODS.

611. The ~ost co~mon method of locating objectives is by intersection, and

where two observation posts both are accurately located, and are some dis..

tance apart this method is quite satisfactory. It is necessary only to take

the Y-azimuth of a given objective as seen from the two stations and to plot

the directions on the firing board. It usually. happens, however, that where

the observation posts are some distance apart they are unable to pick up the

same objective. An auxiliary O. P. may be established near the first station,

but usually in such cases the base is so short that an intersectio;I will show

f con.siderable Hrror~n range. Therefore it is better. where it can be done,

to determine the value of t1?-eanglesubtended at the desired point by a base

of given length and thus determine range by use of the mil relation. There

hre a number of different methods of approaching such a problem .

•Case I.

612. Given' an O. P. at A, fig. 199, a reference point at T.., and a target which

it is desired to locate, at some unknown point, T'. From A, the observer

erects a perpendicular base to B. Assume this to be 100 meters in length.

The observer knows the distance to the reference point. Assume this dis-'

tance, AT, to be 2500 meters. The angle x subtended by the base of 100

meters is then 40 mils. At A the observer measures Ithe angle a. Assume

this to be 110 mils. Proceeding to B the observer meaSUl'es the' angle, h.

Assume this to be 120 mils. By geometry a+x=b+,y. Therefore a+x-b=,Y.

or 40+110-120=30 mils. An angle of 30 mils will subtend a base of 100

meters at a distance of 3333 meters, which is the distance to T'.

If the angular distance between T and T' is great, this method will

not be accurate.

TO[lography for Field Artillery

'
T

A 100 .B

Fig. 199.

~273-"

T

A 'dc)

Fig. 200.

.B

T

Fig. 201.

Case II.

613. When T' is in line with T, as seen from the observation post, A, fig.

200. Layoff the base AB. Again assume this to be 100 meters. From lJ

measure the angle .Y between" T and T. Assume this to be 10 mils. Ha,,:ing

a known base, AB, and a known distance, AT, the angle, a, is commputed.

Assume this to be 40 mils. By geometry a=x+'y. Then a~'y=x" or 40-10

=30. If x equals 30 mils and AB equals 100 meters then the distance AT'

equals 3333 meters.

Case III.

614. Layoff a base, AB, from the" O. P., fig. 201. Let this be 100 meter'5.

Assume the angle, a, to be equal to 1600 mils. At B take a back sight and

measure the" angle, b. Assume this to be 1570 mils. By geometry a+b+x=

3200 mils. Therefore x= 30 mils. Therefore the distance to T equals 3333

meters.

Case IV.

615. From A the observer reads the bearing or the azimuth to the target,

:T fig. 202. Assume this bearing, a, to be equal to 350 mils. Proceeding to

B, 100 meters distant, he reads the bearing to the point, T. Assume this to

be 300 mils. By geometry a-b=x I or 350-300=50 mils. Therefore T is

2,000 meters distant.

Case V.

616. In any of the above cases where, because the observation post is under

fire, it may be impossible to layoff a perpendicular. base. It often is possible in such cases to run a traverse down a trench line to B, fig. 203, and by

plotting this point determine the perpendicular distance, A'B, after which

the value of the angle x may be determined as before.

Topo~raphy for Field Artillery

j

"
-274-

Case VI.

617. The observer at A desires to learn the distance to a point, T, fig. 204.

From A he measures the angle between T and another visible point, T', and

MN

I

I

I

I

I

I

I.

I

I

a

Fig. 203.

T'

Fig. 204.

finds this to be x mils. (Assume a value of 50 mils). From A he walks toward T a given distance, say 100 meters. At A' he again measures the angle

. between T and T', and finds it to be 60 mils.

Note: T and T' should be of about the same range.

The angle x, multiplied by the range, A T, in thousands of meters

equals TT'. The angle .Y multiplied by the range, A'T, in thousands of

meters, equals TT'.

(AT)

x (1000) = TT'

(A'T)

y (1000) TT'

AT A'T

Then x ( 1000 Y ( 1000 )

But A'T AT 100

Substituting in the above equation

Topography for Field Artillery

=

=

= -
-275-

AT AT 100

x ( 1000 )=y (1000 1000 )

Substituting the measured values of x and y

AT AT 100

50 ( 1000 ) 60 ( 1000 ) -60( 1000 )

50AT 60AT 6

1000 = 1000 T

50AT 60AT

1000 - 1"000= - 6

10AT .- 1"000 6

10AT 6000

AT= 600 M.

\

Topography for Field ArtilleJ')'

•

=

=-

- = -
CHAPTER XXVIII.

DUTIES OF VARIOUS OFFICERS IN POSITION WARFARE.

GENERAL.

,618. This text being concerned with the topographical sid~ of position warfare, the following chapter treats only, so far as is necessary, of the topographical duties of officers. It must be kept in mind that these duties are

elastic and transferrable, due to different situations. The executive often

lays the guns to save time, the battery reconnaissance officer often picks the

position for the battery, because the B. C. is occupied elsewhere. In fact,

.every officer must be able to fill every other officer's position in the battery.

A. THE BRIGADE COMMANDER.

,619. 1. By map designation or terrain description, assigns to his regin1ental commanders;

(a) Their mission.

(b) Their command posts,

(c) Areas within which battery empla~ements must be built.

2. Organizes and subdivides;

(a) The general system of observation within the brigade sector, especially of enemy activities.

3. Must see that the brigade intelligence officer furnishes regiments

• with maps.

B. THE REGIMENTAL COMMANDER .

.,20. 1. Assigns to his battalion commanders by map designation or terrain description;

(a) Their missions,

(b) Command posts,

(c) . Areas to be occupied by battery emplacements.

2. Organizes and subdivides;

(a) The general observation system of the regimental sector,

especially with a view to the "general observation of fire."

Note: Generally done by the regimental orientation

officer.

C~ THE BATTALION COMMANDER.

621. . (1) Prior to the occupation. of the sector, (reconnaissance);

1. Assigns missions to the batteries,

2. Supervises and is responsible for the detail~d study from the map

(and from the terrain if possible) of the following;

(a) Positions for the battery emplacements.

(b ) Available location for O. P's., both battery and battalion,

(c) Visibility charts for each O. P.,

(d) Panoramic sketches from each O. P.,

.Topography for Field Artil'lery
-277-

,'(e) Chart of "dead space" for each battery,,!:

(f) "Field of Fire" chart for each battery.

622. (2) When positions have been approved, and are to be occupied;

1. Assigns to the several batteries;

(a) Their areas within which emplacements must be built,

. (b) Their C. P's.

I:: (c) .Their' O_P's.

2. Supervises preliminary topographical Qperations (usually done by

-_... ',.the Bn.Adj.); ...

(a) Locating. place marks of the O. P's;, emplacements, etc.

on the map, . #

(b) Orienting line drawn on the map, and if need be materialized on the ground,

(c) Determination of complete coordinates of the base point.

623. (3) When sector has been organized, Bn. Co. Sees that the Bn. intelligence officer (Bn. Adj.); .

(a) Furnishes the batteries with information that has been

sent down through the regiment by the Intelligence Department,

(b) Consolidates reports sent in by batteries of observations

made during period covered by the report, (usually 24

hours previous), and sends this to the regimental intelligence officer,

(c) Keeps Bn. firing chart up to date,

(d) Makes "Consolidated Visibility Chart," "Dead Space

Chart", and "Field of Fire Chart" of the sector,

(e) Takes charge of and supervises the Bn. O. P.,

(f) Supervises the training of battery and battalion observers.

~-l_. D. THE BATTERY COMMANDER.

624. (1) 'Vhen position is to be occupied, supervises the following:

1. Preliminary topographical operations;

(a) Placing guns with respect to the place mark,

(b) Locating O. P. exactly, and getting complete coordina'tes;

(c) Identifying and locating exactly upon the map, the base

point or base direction,

(d) Drawing the orienting line upon the firing chart, which

line has been given by azimuth, or materialized on the

ground or battalion board by the Bn. O. 0.,

(e) "Laying the battery on the base line" or "with base deflection."

2. Computes the initial elements of firing data in the following order;

(a) To lay the battery with base defle<;tion,

(b) To lay the battery for normal barrage,

(c) For other targets, or objectives, in the order of their im-

. portance.

(2) After the position is occupied and the sector has been fully

organized as enumerated above;

Topography for Field' Artillery
-278-

625. 1. He sees that the following records are kept up to date;

(a) B. C. Data Book,

(b) Visibility Chart.

(c) Firing Board or Chart.

(d) Panoramic Sketches.

2. Makes consolidated report to Bn. intelligence officer of observa.

tions made during the period covered by the report, (usually 24

hours),

3. Responsible that observers are well trained by R. 0., and that

they are thoroughly familiar with the sector.

Topography for Field Artillery
-279-

APPENDIX I.

. SLOPES.

TOpOgraphy for Field Artillery
-280-

PRACTICABILITY OF SLOPES.

626. Slopes from 0° to 5 are practicable for maneuvering all arms, singly

or combined.

On slopes fr0:t:n 5° to 10° all arms can still be maneuvered, but with

increasing difficulty. .

On slopes of 10° to 15° all arms can be moved up or down.

Slopes from 15° to 30° are practicable for small detachments only.

On slopes from 30° to 45° foot troops can move with difficulty. War

materiel can be dragged up any slope.

('7}~3:~~~!.1~_Lpegree I Operati~ns

--i"-on-60 --.r -1 J-m~aximum for railroads

1--on---20 I 3 -'l-ni~ixiin-umforfirst --class- "i-"oads -.-------.--

-ron-12 1--5~ ----"-practlcaole1or all arms -----------.---.,-----

-.!on ~_I~ .,- not pracHcableforheavilYloaded .~~~~les. _

1 on 6. ..1 9~.. field artillery can no longer maneuver -ion4--1-T4-15---r-majdinumuptO-\vhIcllall arms-can-m:ove--- -"~----~

1 on 3-T-I8~--I-ngh:tvclilcles can ascend

1 _.on2-!- 2-6~--' -l-r~div~_dll_~l~ ~~(r-mules <?~n-.-a-sc-e-n~ ~I~or-.~.4e~_cen~:---.--

i o"n 1 I 45 I foof troops can -ascend 01' descendalded -bOy hands----::-

627. }'ords. Practicable depth depending on current and nature of bottom, 3-3.5 feet deep for Infantry and Artillery, 4 to 4.5. feet deep f01' Cavalry, 2-3 feet deep for wagons~

628. Strength of Ice-3 inches thiCk 'will 8upportsmall group of men. 4~

to 7 inches t~ick will support caY;l.lry and light guns, 8 to 12 inches thick

will support heavy guns and wagons:.' ..•.

LEKGTH OF PACE.

629. Length of pace on slopes corresponding to normal pace on a level of

30.4 inches.

Slopes. . ...10° . 5° I 10° I .. 15°...1 20° I 25° I 30°

Length or-step asce~di;;i-= 1~-36:;rT27~6 -r24.4-r~.::f2J.-.J =r!f.1-rT'7'-8~r--i~~(r

Lengthofstep-descendiIlg-I-3(Y.4-1-2![2-128.3-1- 27.6 -~I-26-:-41-23:-6-1-19~7--

'3;'opography for Field Artjlle.1:Y;

°

_ --~-----

---

- -

- I

__

-

"

j
-281-:'"

Reduction to horizontal of distances paced on different.!:slopes ascending and descending.

ooo)OO...-lC\lcY:)~~LO~~C\lOoo~~C\l

g~~~~~~~~~~~~~~~.~~ o 0 0 ...-I ...-I ...-I ...-I ...-I ...-I ...-I ...-I C\l '<:I' '<:I' LO

oot-~'<:I'cY:)C\l...-lOoot-~~C\lOoo~~C\l

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t- '<:I' cY:) C\l ...-I 0) 00 t- LO '<:I' ...-I 00 ~.~ 0) C':l

~~~g~~~g~~~~~~~~~~ 0 t- C':l 00 '<:I' 0 LO ...-I C\l 00 '<:I' 0 C\l 00.'<:1'

g ~ ~ ~ ~ ~.~ fJ ~ cxi gi g2 g ~ g O...-l...-l...-l...-l...-l...-l...-l...-l...-l...-lC\lC':l'<:l'LO~t-oo

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I

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cY:)

o

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C\l

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;

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Topography for Field Artillery

~ ~ ~

~

~

~

~ ~

~ ~ ~

~ ~ ~

~

I
-283-

APPENDIX II.

BRITISH MAPS.

Topography for Field Artillery
-284-

BRITISH COORDINATES.

630. In the recent war a considerable portion of the front in France and

in Belgium, was held by the armies of the British Empire, and in this portion

these armies used in part, maps which varied from those used by the French

armies.

The large scale maps of Belgium are plotted from the Belgian origin

which is on the meridian of Brussels, those of the French area having been

.made to conform to the Belgian system.

The large scale maps are on three scales: 1/10,000, 1/20,000 and

1/40,000.

Belgian Area. The original maps have been redrawn both on the

1/10,000 and the 1/20,000 scale. A 5-meter contour interval has been

adopted.

French Area. These maps have been drawn on the 1/20,000 scale

and enlarged or reduced for the other two scales.

The maps are on the metric system. Each sheet (1/40,000) represents an area 32,000 meters by 20,000 meters. At the corner of each sheet

are printed the distances of the sheet lines fI'oJn the origin.

631. The basis of the British system is the 1/40,000 sheet, which is identified by a number; for example, "sheet 28", fig. 205. Each 1/20,000 sheet

covers one quarter of the area of a 1/40,000 sheet and is identified by the

letters, N.W., N.E., S.W., S.E., denoting its position on the 1/40,000 sheet

A 1/2D,000 sheet is thus called "28 N.W.", fig. 205.

Each 1/10,000 sheet again. _COY~l:S_ one. quarter of the area of a 1/20,-

000 sheet, and is identified by -the number 1;.2, 3, or 4. The northeastern

1/10,000 sheet of a 1/20,000" area is thus called "28 S.\V. 2". In addition

the 1/10,000 sheets are given -names, as ihis'provides an easy means of

reference when, as often happens, a combined 1/10,000 sheet is made. The

.subdivision of the areas as above does not change the lettering of the subdivisions found in the 1/40,000 sheets.

The preparation of combined 1/10,000 sheets made up of parts of two

or more adjacent regular sheets, has been necessary in many cases in order

to provide a sheet on which the trench line falls conveniently. These combined sheets are in general of the same size as the regular sheets.

THE GRID SYSTEM.

632. Over the 1/40,000 metric map the British cartographers have placed

a grid expI'essed in yards. This is merely for convenience in indicating localities and obviously cannot fit exactly with the sheet lines which are in

terms of meters. The grid has therefore been placed with its central point

in the center of the 1/40,000' sheet, and allowed to overlap the sheet lines as

shown in fig. 206.

The first sub-divisions of the grid are a series of large rectangles

lettered A, B, C, ~o X from left to right, there befug 6 rectangles in a row

and 4 rows. The two middle rows of rectangles are squares, the top and

bottom rows are not. Each of the lettered rectangles is further subdivided

,into a series of-1000 yard squares, which are numbered from left to right

and from top to bottom.

At the north and south edges of the 1/40,000 sheet there is an over- .

TopogI:aphi :':{or Field- Artillery

-
-':'285-

. . ..

L)YSTEM OF [)R'ITt5H 'MAPS

ON THE Wf..5TERN FRONT

/ 'l

:f DVNKIRK

--lj9--

---~=t--

i -_o-3lbA--

o

:PRE~-i& _ .

N.W. ,'.N.E_

--2..1---- .s.w. " .5.E. ,

---l19--

I --3,--

°TOVRNAI

Yz.o,OOO

}~o.ooo

.,

-.-' 3i<:>e>--

i

--5jlE-

,

----5hD--

I .

--' --Gjc-D--

AMIEN5

--:3~f,'E-- ---.-4{4--

, DOVAI '0

• 0

i. VAlE.N!I~NNE5

---7j.ll)--. --!lIrA--

.1 I • I' .•

-r, • I 0

'---~.2.B-' g ~

dU

o0T_QV NTIN ._LE

~32,000 MUER.5-{

•• .'Fig_.205: !~.... c, ,",..., '.:. r Jd

~

; ; j
-286-

lap of the gr}d which is the difference between 10,000 meters (half the width

of the sheet) and 11,000 yards (the nearest grid line). This overlap amounts

rcsp,.(OOO'~+- sP"<OOO'9+rt- sP'<OOO''7-+~P,«()()O'~-i , ~.

'+- Il T11\

\j) 1- r -a

N lL..- -1 cr:. >< $) 0 I 0 I 0

0- \j)

<

t. ...J c.l r:t:

u..I Q)

> I1.J 0 0 .c. ""0'" CI \I')

0 C5 0 et: 0 I.J 0 0

! 0' lJ)'

l/') I t. a::

IL..I

)- 11\ IL.I \j

il >..

..... 0 --;:) 0.. > ....,

0

c

\.!5' C\J'

rf) 1

01 cf.

0

If) U 0 - .. >. 3

an If) ~-

If')

u ., G)

\O~ :g1.P ;t 0\.1) t' r:: " (j') rr)1i) If) cr If) = t::: /l")

~II) t:: ".., en :R

---z+-.;-

If) N - ...... N

-+-~-' r<') -:t-2 \D ...., ~q- \o!)

;::\ N "":.; .f:f

(5) '\. N ~ft') G) !!5'-=- r- I"")

("oJ N Ii) -+J ':-rt- N cO 0 ~N co s: 2 c.!) v tl) N N

3~ :3 m I'- ~- ,.... iri (f')-r) .,...; rJ

U 0

r

m

CI

~-- a: r-- 0

lr) 0. If) I 0

t!J CI) 0. -~«. I I L 4 --r-T--lI I I I

--t--"1-_!. +-

I

, i

Q. 01. <{

a:

'-="

to 192.4 feet and appears on all large scale maps. .The diagram shows how

TOJ)Ol{raphy for Field Artillery

~

~~ ~ ~

~

~~

~ ~

~ ~ ~~ ~

~ ~ ~ ~ ~

~ ~ - ~

- ~ ~ ~ ~ ~

~ ~

~ -

~
-287-

Cf)

.0

>

o

o

o

b

d

Fig. 207.

c

a.

I

I

I

I

I

4L---l- I I

I I

--------~-~---.--

I

I

I

I

I

I

I

it appears on the 1/20,000 and 1/10,000 enlargements of the different portions of the original 1/40,000 sheet, fig. 206,'r

(a) On the 1/20,000 sheet "N.W." the full overlap of 192.4 feet appears along the northern edge, but at the southern edge, this being the

center of a 1/40,000 sheet, the grid and sheet lines coincide.

(b) On the 1/10,000 sheet, "S.'\V. I", at the northern edge the grid

and sheet lines coincide, while the southern edge shows half the overlap, i.e.,

96.2 feet.

(c) On the 1/10,000 sheet "S.W. 3", the northern edge shows half

the overlap, while the southern edge shows the full overlap. .

633. Because 32,000 meters, the distance east and west, represented on the

1/40,000 sheet, corresponds to 34,995.6 yards,' the grid, which&'is 36,000

yards east and west overlaps about 500 yards at either en'd. Thus the map

proper will show only about half of the last tiers of 1000 yard squares on

the east and west.

In each large rectangle' of the grid these 1000 yard squares are numbered from left to right, 1, 2, 3, etc. to 30 or 36, depeding upon whether

the large rectangle is in either one of the two outer, or one of the two inner

rows. This difference in number of small squares is due to the fact that the

1/40,000 sheet measures 20,000 meters from north to south limits, hence

each half is 10,000 meters. 10,000 meters is equal to 11,000 yards approximately (10,930 yards exactly). Thus the large rectangles in the outer rows

measure 5000 yards from north to south and those in the two inner rows,

6000 yards. Consequently there can be but five rows of small rectangles in

a large outer rectangle. 1000 YDj--------.

To .r e pea t, the

large rectangles are divided into squares of 1000

yards on a side which are

numbered 1, 2,~-3, etc.

Each of these squares is

subdivided into four minor squares, 500 yards on a

side. These minor squares

are lettered 0, b, c, J, from

left to right, fig. 207.

A point may thus

be roughly located as. lying, for example, within

square M. 5. b. To locate

a point within a minor

square, consider the sides

divided into tenths, and

define the point by taking

so many tenths, first from

W. to E. along the south- ,

ern side, and then from S. to N. along the western side; the southwest cor- .

ner always being taken as origin and the distance along the southern side

always being given by the first figure.

Topography for Field Artillery
-=288-

A .point may thus be described located at M. 5. b. 3. 4., i.e., three

divisions east and four divisions north from the southwest corner of square

M. 5. b." fig. 207. This gives a 50 yard subdivision or square.

By simple extension of this method, the 0

point may be more accurately located if the 9

sides of the minor squares be considered as 8

divided into 100 parts, and. the point described 7

by using four figures. 6

5

In figuring the square coordinates of 4

point C they are 6.4 on the two figure system, ;; 0

or more accurately 64,44 on the four figure sys- z.

,tern, i.e., 64 hundredths east, and 44 hundredths

north from the southwest corner of the square,

see fig. 208.

The coordinates of A are 0.8; of B, 3.0; of D, 0.3 in the adjoining

square to the right. Note that in using these coordinates the numbers 0 to

9 should be used, but 10 never should be used, as mistakes 'may occur. To

facilitate reading coordinates, special cards may be prepared graduated

along two edges into tenths and hundredths parts according to the map scale,

and by placing the corner where the two graduated edges of the cards meet,

parallel to the respective sides of the squares, the coordinates' may be read.

THE NORTH POINT.

634. In any system of rectangular sheets, as soon as a point is reached

far from the origin on which the system. is based the vertical sheet lines no

longer point true north and south. The inclination to the sheet lines of the

meridian of longitude i.e., true north, increases with the distance from the

'ori~~ .

Hence, the vertical sheet lines of the large scale map which are all

rectangular are not true north and south. On sheet 28, for instance, the

angle between sheet line and true north is 10 04'. Since the Y-axis of the

grid is parallel to the vertical sheet lines then for sheet 28 the grid north is

1

0

04' west of north. This declination must be considered when using a

compass or when computing a direction from the Y-axis.

DESIGNATION OF SHEETS.

635. As has been stated, the 1/40,000 sheets are designated. by number,

fig. 205. There are a few sheets that have the same number, but are distinguished from each other by a small letter placed to the right and a little

above, as 57c. .

I. In the upper left hand corner, is an index showing the' number of the

adjoining sheets.

Suppose that a large scale map is wanted of the northwest part of

57c. The map to get would be 57c N.W. Such a map would be to 1/20,000

scale. If a larger scale map than that is needed ahd, say, the area desired

is in the southeast corner of the 1/20,000 map, then the map to get would

be 57c N.W. 3.

Instructions regarding their use are printed on the margin of each

map.

Topograpny for Field Artillery
-289-

~.

APPENDIX III.

TABLE OF NATURAL FUNCTIONS ....~.

Topography for Field Artillery

.
-290-

636. Natural sines and tangents to a radius 1:

Arc. Sine. Tang. Cotang. Cosine.

v , 0 ,

o 00 .0000000 .000000 Infinite. 1.0000000 90 00

10 .0029089 .002908 343.7737 .9999958 50

20 .0058177 .005817 171.8854 .9999831 40

30 .0087265 .008726 114.5886 .9999619 30

40 .0116353 .011636 85.93979 .9999323 20

50 .0145439 .014545 68.75008 .9998942 10

1 00 .0174524 .017455 57.28996 -.9998477 89 00

10 .0203608 .020365 49.10388 .9997927 50

20 .0232690 .023275 42.96407 .9997292 40

30 .0261769 .026185 38.18845 .9996573 30

40 .0290847 .029097 34.36777 .9995770 20

50 .0319922 .032008 31.24157 .9994881 10

2 00 .0348995 .034920 28.63625 .9993908 88 00

10 .0378065 .037833 26.43160 .9992851 50

20 .0407131 .040746 24.54175 .9991709 40

30 .04~6194 .043660 22.90376 .9990482 30

40 .0465253 .046575 21.47040 .9989171 20

50 .0494308 .049491 20.20555 .9987775 10

3 00 I .0523360 .052407 19.08113 .9986295 87 00

10 .05524C6 .. 055325 18.07497 .9984731 50

20 .0581448 .058243 17.16933 .9983082 40

30 .0610485 .061162 16.34985 .9981348 30

40 .06"9517 .064082 15.60478 .9979530 20

50 .0668544 .067004 14.92441 .9977627 10 ,

4 00 .C697565 .069926 14.30066 .9975641 86 00

10 .0726580 .072850 13.72673 .9973569 50

20 .0755589 .075775 13.19688 .9971413 40

30 I .0784591 .078701 12.70620 .•9969173 30

40 .0813587 .081629 12.25050 .9966849 20

50 .0842576 .084558 11.82616 .9964440 10

5 00 .0871557 .087488 11.43005 / .9961947 85 00

10 .0900532 .090420 11.05943 .9959370 50

20 .0929499 .093354 10.71191 .9956708 40

30 .0958458 .096289 10.38539 .9953962 30

40 .0987408 .099225 10.07803 .9951132 20

50 .1016351 .102164 9.788173 .9948217 10

• 6 00 .1045285 .105104 9.514364 .9945219 84 00

10 .1074210 .108046 9.255303 .9942136 50

20 .1103126 .110989 9.009826 .9938969 40

30 .1132032 .113935 8.776887 .9935719 30

40 .1160929 .116883 8.555546 .9932384 20

50 .1189816 .119832 8.344955 .9928965 10

7 00 .1218693 .122784 8.144346 .9925462 83 00

10 •1247560 .125738 7.953022 •. 9921874 50 .

20 .1276416 .128694 7.770350 .9918204 40

30 .1305262 .131652 7.595754 .9914449 30

40 .1334096 .134612 7.428706 .9910610 20

50 .1362919 .137575 7.268725 .9906687 10

I Cosine. --I Cotang. Tang. I Sine. Arc.

Topography for Field Artillery
-291-,-

Natural Sines and Tangents-Continued.'!:

I I

I I Arc. Sine. I, Tang. Cotang. Cosine.

0 , 0 ,

8 00 .1391731 .140540 7.115369 .9902681 82 00 10 .1420531 .143508 6968233 .9898590 50 20 .1449319 .146478 6.826943 .9894416 40 30 .1478094 .149451 6.691156 .9890159 30 40 .1506857 .152426 6.560453 .9885817 20 50 .1535607 .155404 6.434842 .9881392 10

9 00 .1564345 .158384 6.313751 .98768E'3 81 00 10 .1593069 .161367 6.197027 .9872291 50 20 .1621779 .164353 6.084438 .9867615 40 30 .1650476 .167342 5.975764 .9E'62856 30 40 .1679159 .170334 5.870804 .9858013 20 50 .1707828 .173329 5.769368 .9853087 10

10 00 .1736482 .176327 5.671281 .9848078 80 00 10 .1765121 .179327 5.576378 .9842985 50 20 .1793746 .182331 5.4?4505 .9838808 40 30 .1822355 .185339 5.395517 .9832549 30 40 .lf50949 .18f349 5.309279 .9827206 20

50 .1879528 .191363 5.225664 .9821781 10

11 00 .1908090 .194380 5.144554 .9816272 79 00 10 .19366~6 .197400 5.065835 •. 981C680 50 20 .1965160 .200424 4.989402 .9805005 40 30 .1993679 .203452 4.915157 .9799247 30 40 .2022176 .206M~3 4.843004 .97934r6 20

50 .2050655 .209518 4.772856 .9787483 10

12 00 .2079117 .212556 4.704630 .9781476 78 00

10 .21071)61 .2151)98 4.638245 .977;)386 50

20 ".2131)988 .218644 4.573628 .9762215 40

30 .2164396 .221694 4.510708 .9762960 30

40 .2192786 .224748 4.449418 .971)6623 20

50 .2221158 .227806 4.389694 .9750203 10

13' 00 .2249011 .230868 4.331475 .9743701 77 00

10 .2277P44 .233934 4.274706 .9737116 50

20 .2306159 .237004 4.219331 .9730449 40

30 .2334454 .240078 4.165299 .972~699 30

40 .23627?9 .24311)7 4.112561 .9716P67 20

50 .2390984 .246240 4.061070 .9709953 10

14 00 .2419?19 .249328 4010780 .97029Fl7 76 00

10 .2447433 . .252420 R961651 .9<-:91)879 50 ,20 .2475627 .255516 3.913642 .9688719 40

30 .2503POO .258617 3.866713 .9681476 30

40 .25319)')2 .261723 3.820828 .9674152 20

50 .2560082 .264833 3.775951 .9666746 10 I 15 00 .2588190 .267949 37320fiO .96)')9258 75 00

10 .2616277 .271069 3.689092 .9601681 50

20 .2644342 .274194 3.647046 ". .9~44037 40

30 .2072384 .277324 3.605883 .9636305 30

40 .2700403 .280459 3.565Fl74 .9628490 20

50 .2728400 .283599 3.526093 .9620594 10

Cosine. 1- Cotang. Tang. ). Si~-'-Arc.

Topography for Field Artillerr

~

'

'
-292-

Natural Sines and Tangents-Continued.

Arc.

0-'--

74 00

50

40

30

20

10

73 00

50

40

30

20

10

72 00

50

40

30

20

10

71 00

50

40

30

20

10

70 00

50

40

30

20

10

69 00

50

40

30

20

10

68 00

50

40

30

20

10

67 00

50

40

30

20

10

Cosine.

Sine.

.9612617

.9604558

.9596118

.9588197

.9579895

.9571512

'.9563048

.9:554502

.9545876

.9537170

.9528382

.9519514

.9510565

.9501536

.9492426

.94f3237

.9473966

.9464616

.9455186

.9445675

.9436085

.9426415

.9416665

.9406835

.9396926

.9386938

.9376E'69

.9366722

.9356495

.9346189

.9335804

.9325340

.9314797

.93C4176

.9293475

.9282696

.9271839

.9260902

.9249888

.9'238795

.9227624

.9216375

.9205049

•. 9193644

.9182161

.9170601

.9158963

.9147247

2.475086

2.454506

2.434217

2.414213

2.394488

2.375037 I

I

2.355852

2,336928

2.318260

2.299842

2.281669

2.263735

Tang. I

3.487414

3.449512

3.412362

3.375943

3.340232

3.305209

3270852

3.237143

3.204063

3.171594

3.139719

3.108421

3.077683

3.047491

3.017830

2.988685

2.960042

2.931888

2904210 I

2.876997

2.850234

2.8239121 2.798019

2.772544

2.747477

2.722807

2.fl.98525

2.674621

2.651086

2.627912

2.605089

2.582609

2.560464

2.538647

2.517150

2.495966

Tang. Cotang. I I

.2~67451

.289f96

.293052

.296213 I

.299380

.302552

I

.305730 I

.30~914

.312103

.31529R

.31~499

.321706

.324919

.32R1 ~R

.3~J~6~

, .33dfi9fi

.337P~~

.341077

, .M4327

.347fi94

.350~4R

.3f'411 R

.3fi7~95

.360679

.363970

.~fi7')6R

.370572

.373RP4

.3772n~

.380530

.3P3964

.3R7205

.390fi54

.::l9~910

.397274

.400646

.40402fl

.407413

.410R09

.414213

.417625

.421046

.424474

.427912

.431357

.434812

.438275

.441747

Cotang.

Sine. ,I

I

.2756374

.2784324

.2812251

.2840153

.2f'6RC32

.2895887

.29237171

.29S1fi22

.29793('3

.3007fl58

.3C347P8

.3062492

I

.3C90170 I

.31l7R22I'

.314Fi448

.317~('47

.~20()619

.3228164 I

.3?!'\!'6R2 I

.32P~172.1

.331r6~4

.3~::l9r69 I

.3~6!)47f) I

.3392852

.3420201

.~J.47:;?1

.3474R12

.~5C2074

.3:;29~r6

.3556508

.31'\83679

.3610R21

.36~7932

.3f6~n12

.3~92('61

.3710079 I

.3746"66 I

.3773121 I

.3799944

.3P2fiP~4 I

.3R53693

.3880518 I

.3907311

.39M071

.3960798

.3987491

.4014150

.4040775 •.. I Cosine. (

Arc.

16 00

10

20

30

40

50

17 00

10

20

30

40

50

18 00

10

20

30

40

50

19 00

10

20

30

40

50

20 00

10

20

30

40 I 50

21 00

10

20

30

40

50

22 00

10

20

30

40

50

2300

10

20

30

40

50

'fopography for Field Artillery

I'

I

II

-
-293-

Natural Sines and Tan.gents-Continued ...;

Sine. ,I Tang.

I

I

Cotang. j Cosine. I

.9135455 66'00

.9123584 50

.9111637 40

.9099613 30

.9087511 20

.9075333 10

.9063078 . 65 00

.9050746 # 50

.9038338 40

.9025853 30

.9013?92 20

.9000654 10

.8987940 64 00

.8975151 50

.8962285 40

~949~44 30

.89~6~26 20

.8923234 10

.8910065 63 00

.8896822 50

.8883503 40

.8870108 30

.8Pf6639 20

.8843095 10

I

.8829476 62 00

.8815782 50

.8802014 40

.8788171 30

.8774254 20

.8760263 10

.8746197 61 00

.8732058 50

.8717844 40

.8703557 30

.86P9196 20

.8674762 10

.8660254 60 00

.8645673 50

.8631019 40

.8616292 30

.8601491 20

.8586619 10

.8571673 59 00

.8556655 50

.8541564 40

.8526402 30

.8511167 20

.8495860 10

Sine.----r- Arc.-

Topography for Field. Artillery

2.246036

2.228567

2.211323

2.194299

2.177492

2.160895

2.144506

2.12P321

2.112334

2.096543

2.080943

2.065531

2.0f)0~03

2.C35256

2.020386

2.005689

1.991J 63

1.976805

1.9h2610

1.948577

1.934702

1.920982

1.907414

1.893997

1.8P0726 I

1.867600

1.854615

1.841770

1.829062

1.816489

1.804047

1.791736

1.779552

1.767494

1.755559

1.743745

1.732050

1.720473

1.709011

1.697663

1.6P6426

1.6752C8

1.664279 I

1.653366

1.642557

1.631851

1.621246

1610741

Tang. I

.445228

.448718

.452217

.455726

.4!'l9?43

.462771

.466307

.469853

.473409

.476975 I

.480551

.484136

.4877~2

.491 P3Q

.494954

.49Pfi81

.502218

.505866

.509525

.513195

.51687fl

.520567

.524269

.527983

.531709

.535446

.539195

.54?9fl5

.546728

.550512

.554309

.558117

.561939

.565772

.56%19

.573478

.577350

.581235

.585133

.589045

.592969

.596908

.600860

.604826

.608806

.612800

.616809

.620832

Cotang.

.4067366

.4093923

.4120445

.4146932

.4173~R5 I

.4199801

.4226183

.4252528

.427RP38

.4~05111

.433J 348

.4357548

.4383711

.4409P~8

.44%927

.4461978

.4487992 I

.4513967

.41139905

.4565P(l4

.4S91665

.41'l174P6

.464~269

.4669012

.46947J6

~4720380

.4746004

.:{.4771588

.4797131

.4822634

.4848096

.4873517

.4~98897

.49242~6

.4949522

.4974787

.5000000

.5025170

.5050298

.5075384

.5100420

.5125425

.5150381

.5175293

.5200161

.52249f'6

.5249766

.5274502 I

Cosine. l

Arc.

24.00

10

20

30

40

50

25 00

10

.20

30

40

50

26 00 I

10

20

30

40

50

27 00

10

20

30

40

50

28 00

10

20

30

40

50

29 00

10

20

30

40

50

30 00

10

20

30

40

50

31 00

10

20

30

40

50

-
-294-

Natural Sines and Tangents-Continued.

Arc. Sine. ( Tang. Cotang. ( Cosine. I 0 , --o-,_~_-

32 00 .5299193 .624869 1.600334 .84f'0481 58 00

10 .5323839 .628921 1.590023 .8465030 50

20 .5~4R440 .6~2988 1.579807 .8449508 40

30 .f-372996 .637070 1.569685 .8433914 30

40 .5397507 .641167 1.559655 .8418249 20

50 .5421971 .645279 1.549715 .8402513 10,

33 00 .5446~90 .649407 1.539865 .83f67C6 77 00

10 .54707h3 .6Fl3fi51 1.530102 ,,8370827 50

20 .5495090 .657710 1.520426 .8354878 40

30 .5519~70 .661R85 1.510f35 .8338858 30

40 .554~60~ .666076 1.501328 .8322768 20

50 .5567790 .670284 1.491903 .8306607 10

34 00 .51"91929 .674fiOR 1.482561

I

.8290376 56 00

10 .5616021 .678749 1.473298 .8274074 50

20 .5640066 .6R~0(,6 1.4€4114 .8257703 40

30 .f;f>64('62 .687281 1.455009 .8241262 30

40 .5688011 .691572 1.445980 .8224751 20

50 .5711912 .695881 1.437026 .8208170 10

, 35 00 .5735764 .700207 1.428148 .8191520 55 00

10 .57591168 .7C4551 1.419342 .8174801 50

20 .57f13323 .70R913 . 1.410609 .8158013 40

30 .5807030 .713293 1.401948 .8141155 30

40 .5t'3C687 .7176!H 1.393357 .8124229 20

50 .5854294 .722107 1.384835 .8107234 10

36 00 .5877853 .7261142 1.376381 .8090170 54 00

10 .5901361 .73C996 1.367995 .807~0~8 50

20 .5924819 .735469 1.359676 .801)5837 40

30 .5948228 .739961 1.351422 .80~8;;69 30

40 .59715t'6 .744472 1.343233 I .80212~2 20

50 .5994893 .749003 1.335107 .8003827 10

37 00 .6018150 .753554 1.327044 .79P6:355 53 00

10 .6041356 .758124 1.319044 .7968815 50

20 .6064511 .762715 1.311104 .79fi1208 40

30 .6087614 .767327 1.303225 .79~~;;33 30

40 .6110666 .771958 1.?9S405 .791 f\792 20

50 .6133666 .776611 1.287644 .7897983 10

38 00 .6156615 .781285 1.279941

I

.7880108 52 00

10 .6179511 .785980 1.272295 .7f'6~165 50

20 .6202355 .79C697 1.2647('6 .7P44157 40

30 .6225146 .7954~5 1.257172 .7P260?2 30

40 .62478P5 .800196 1.249693 .7P('7940 20

50 .6270571 .804979 1.242268 .7789733 10

39 00 .6293204 .809784 1.?~.1997 .7771 Ll60 51 00

10 .63157t'4 .814611 1.227578 .7753121 50

20 .6138310 .819462 1.22('312 •• 77~4716 40

30 .6360782 .8243~6 1.213097 .7716?46 30

40 .6383201 .829231 1.20~9~~ .7(:()7710 20

50 .6405566 .834154 1.198818 I .7679110 JO

I I

Cosine. Cotang. Tang. J Sine. I Arc.

Topography for Field Artillery

......
-295-

Natural Sines' and Tangents-Continued. t~:

Arc. Sine. Tang. Cotang. I Cosine.

I I 0 ,

1.191753 I 0 ,

40 00 .6427876 .839099 .7660444 50 00

10 .6450132 .~44068 1.184737 .7641714 50

20 .6472334 .849062 1.177769 .7622919 40

30 .6494480 .854080 1.170849 .7604060 30

40 .6516572 .859124 1.163976 .7585136 20

50 .6538609 .864192 1.157149 '.7566148 10

41 00 .6560590 .E'69286 1.150368 .7547096 49 00

10 .6582516 .874406 1.143632 .7527980 #' 50

20 .6604386 .879552 1.136941 .7508800 40

30 .6626200 .884725 1.130294 .7489557 30

40 .6647959 .889924 1.123690 .7470251 20

50 .6669661 .895150 1.117130 .7450881 10

42 00 .66913C6 .900404 1.110612 .7431448 48 00

10 .6712895 .905685 1.104136 .7411953 50

20 .6734427 .910994 1.097702 .7392394 40

30 .6755902 .91 6~31 1.091308 .7372773 30

40 .6777320 .921696 1.084955 .nfi3090 20

50 .6798681 .927091 1.078642 .7333345 10

43 00 .6~199P4 .932515 1.072368 .7313537 47 00

10 .6P41229 .937968 1.066134 .729~668 50

20 .6862416 .943451 1.059938 .7273736 40

30 .6R83546 .948964 1.053780 .7253744 30

40 .6904617 .9fi4508 1.047659 .7233690 20

50 .6925630 .960082 1.041576 .7213574 10

44 00 .6946584 .965688 1.035530 .7193'398 46 00

10 .6967479 .971326 1.029520 .7173161 50

20 .6988315 .976995 1.023546 .7152863 40

30 "-).7009093 .9R2697 1.017607 .7132504 30

40 .7029811 .988431 1.011703 .7112086 20

50 .7050469 .994199 1.005834 .7091607 10

45 00 .7071068 1.000000 1.000000 .7071068 45 00

I

) I I Cosine. Cotang. Tang. Sine. Arc.

Topography for Field Artillery
.i.

-297-

• I

APPENDIX IV.

CIRCULAR MEASURE .

'fopography'f~' Fi~ld 'Artillery
-298- ,

CONVERSION TABLES.

637. 360 degrees=400 grades=6400 artillery mils.

1 degree= 17.78r/t. 1 grade=16 mils.

1 degree=l.l1 grades.

A. MILS IN TERMS OF DEGREES AND TANGENTS.

6;:8. ..~. :. f.

l'opography for Field Artillery

. ~
-299-

APPENDIX V.

REDUCTION OF STADIA READINGS.

Topography for Field Artillery
639.' Table I. -300-

I

QN""'~OOQN"",~oo Q"''''''~OOON..,jo''''OO =C'1..-j'tf.OOO=N~tDOOO I

laOlac.l ........................ NNNN NM~ MC'.~~ ""l!l~~<iIIdl~~lQlQlQlt':lW t-oC'l -,..;,...;

...

... OlO ......r:-C'lOO~o)lO.,..... ~C'lOO..:>O>laO<OC'lt- C'f.'O)~oco ......r:-~OO~o 00 ....

~~~~~~t-:~CX1~ ~oO~"""C'Jt:I?O':)~-.::t4 ~~~t-:t--:~~C?O:~~ > 0000000000 0"';"';-:"';"';-:"';"';-: ~""'''''''''''''''''.-t''''''''''''''''C'JC'J 0 ................................................ ................................................ .....................................................

CD ... ..... 000 r:-u=tlOO':)e--J ..... O OOr:-(,Cl~CX'e-l ..... c:Door:- LO~C¥:l .....OOOr:-tD~C'l':) ..... la 0> 0 r:- r:- t- l- r:- t- r:- CJ:) W c.o

00000000000000000000 ocia6ocia6ocioca6ooaOaO 000000 oooooooooc 0000 00 0>0>0'>0>0>0>0>0>0>0> 0>0>0>0>0>0>0>0>0>0> O)(T.lO')cn~C')O)C)cnCDCD

-,.

... 00 ""'Ola ...t-":>oo "",0 1O .... r.-C'I':)OO""d40LO ...... r- ... ..:>00 """0 la ...t- C'I00 ° 1-0) ..... t,gt-oooo 0) Q')o 0 .....C.J :--J C":I C!':) IQ t.e tQ t- r:- ooooooO ..........C'JC'JIX'~ <II ~~-! aOooaOaOaOaOci"';"';"'; .,.;.,.;.,.;.,.;.,.;.,.;.,.;.,.;.,.;.,.; "';"';"';00000000 0 > ........................................ It) ~~C'J ..... OCDOOr:-""LO ""''':>'''00>00 t-<Ola ":>"'0 0>00 t-<o"",..:>C'I'" laO>"'" ... C\JC'JC'JC'JC'1 ....................... ....................000000 0000>0>0>0>0>0>0>0> 0 .,.;.,.;.,.;.,.;.,.;.,.;.,.;.,.;.,.;.,.; ci~eieieieioiai~ai aieicicx:ioooooOoooooooO t-:~~ 0>0>0>0>0>0>0>0>0>0> CDQ)Q)C:lC')~(J)cncno 0>0>0>0>0>0>0>0>0>0>0>

, -_ .•.._._~.--_. ---'--

... <OC'lt-":>O>laO<OC'lOO C"':l~LO""tDC'JOO~O')lO .....r- t'1 oo~o~ ~r:-"",oo <0000 ...

(,/ O:~~~~~~~~~ lQlOCoOt-t-OOOO0'4Q')O ...........C\1NO':)~~l.QlOc.ctQ ~q.-:

> <Ot-t-t-t-t-t-t-t-t- ~r:~~~~~~~aO a6aOoOocaOaOaOooooaOaO 0

... ......... Oc::nOOI:-COt.ClLO-.::f'I ..:>N ...Oo>oooot-<ola "'1''':>C'I'''oo>oot-<Ola'<t' laOla "I:::I'''I:'J'~'''l:jl0':)~0':)0':)0':)0':) ":>C':lC':lC':lC':lNNC'lNC'IC'I 0 0>0>0>0>0>0>0>0>0>0> "';"';"';"';0>"';"';"';"';"'; aia)o)aiaiaiaiaieDaiai ~::;~ 0>0>0>0>0>0>0>0>0>0> 0>0>0>0>0>0>0>0>0>0> 0>0>0>0>0>0>0>0>0>0>0>

--,---"---------

...

... ..:>oo"'1'O<OC'lt-":>O>la Oc.oC'JOO~o)LO""'r:-CI':l OO""l1'O('o ......t-~oo-.::t'O(,Cl la<OOO (,/ C"C'JO':)""l::f4~LQI.Qt.Ct.Ct- ooooO')c:nOOf"""lC'lC\l~ Ct:)~Lr.)l.Qtetet-t-OOQ)G')

> ..Q.o.o.o.o.o..Q..Q.ou:i ..Qu:iu:iu:i..;..;..;..;..;..; ..;..;..;..;..;..;..;..;..;..;..; 0

C't:lC'J~~oO')C)oooot- <O<Ola"'1'..:>..:>NN ...O 0> 0> 00 t- <0 <0 la ..:>C'I.... laOla ... t-t-t:-t:-t-teC"o;lt.Ct.Ct.C c.ct.C~t.CtClt.Ct.C~t.Ct.C I.QLQLQLQLQI.QLQl.QlQLQLO 0 .,.;.,.;.,.;.,.;.,.;.,.;.,.;.,.;.,.;.,; ~oi~ciai~aima)oi .,.;.,.;.,.;.,.;.,.;.,.;.,.;.,.;.,.;.,;.,.; t':5:; 0>0>0>0>0>0>0>0>0>0> 0> 0> 0> 0> 0> 0> 0> 0> 0> 0> oC)c:nc:nc::n""-:lC':lc:nQ)cnc:n

... O>laO<ONoo"'1'Ola ... t-C':)00"'1'0<0 C'I00":> 0> LO.,....t.Ce--l00~Ct.llO ....r:-e¥'3 ":>"'1'la ... ~lQt.Ctet-t-OOo)o)O O_""""C'lC'l':I~~~1.Q1.Q t.Ct:-t-OOOOc:nO)O,..... ....C'J <II cQcQcQcQcQcQcQcQC':i~ ~~~~~~~.ou:iu:iu:i 0 > IN OOt-t-t-<O<Olala"'1'"'1' C't:lc:QC'Je-.1...-(~oocncn oooot-t-<O<Ola'01'"'1'C':lC':) laOla 00000000000000000000 oooooooooooooooot-t- t-t-t-t-t-t-t'-t-t-t-t- 0 aiaiaiaiaiaiaiaiaiai maiaiaiaiaiaiaiaieD aiaio)~oioieDoiaioiai ~5~ 0>0>0>0>0>0>0>0>0>0> 0>0>0>0>0>0>0>0>0>0> 0>0>0>0>0>0>"'0>0>0>0>

... "",O<ONoo"'1'o>la .. t- ":>00 "'1'0 <0 N t-":>O>la 9""'lt"--C'lOO~Ot09""'lt-~Ct.l C'1..:>..:> t-ooOOc:ncnOO-Ne-.1 CQet:)~l.QlQ~t.Ct:-t-oo O':lO')OO9""'lC'!C'J~CQoo:::tt-.::ll

> ...:,..;,..;~ ..... C'iC'ie-.ie-ic.i C'iC'iC'iC'iC'iC'iC'iC'iC'iC'i C'iC'icQcQcQcQcQcQcQcQcQ 0

..-4 t-t-t-t.C~tOCOLQI.QI.Q la"'1'"'1'"'1''':>'':>C':I..:>NC'Ie-.1 .......... 000CDO':lo,)OOOO laOla ... 0>0>0>0>C::> 0>0>0>0> 0> ~~~~O:O>~~~~ C':lO':!.C)C)C)O)oooooooooo 0 "';"';"';0>"';"';"';"';"';"'; 0>0>0>0>0>0>0>0>0>0> .,.;.,.;.,.;.,.;.,.;.,;.,.;.,.;.,.;.,.;.,.; ~5~ 0>0>0><:>0>0>0>0>0>0> G')c:ocnc:nQ')Q)cnc:n<J)O) 0>0>0>0>0>0>0>0>0>0>0>

-------~"----------

... OCOC"Jt-C'I':)O')109""'lr:-N oo~ot.C9""'lt-C":lo,)l.Q ..... tClC'100~OlO ..... t-C'l':)c:n~ ......C'I ... ~~.-;-:C'!~~~~~ ~u::r:-:t:~~~~5:; ......C'JC'J~-::fl~LQLQc.cc.cl- <II ~...:,..;~~.....t...;,...:,...:...;~

0 > 0 0000000000 0000>0>0>0>0>0>0> 0') 0')00 0000 0000 00 r-t-t- laOla ... 0000000000 OOOO)c:nO)CDcnc:nc:n wolCDO)c:nc:ncnQ)O')CDc:nC) 0 0000000000 000";"';"';"';"';"';"';0>.,.;~.,.;0>.,.;.,.;.,.;c>.,.;.,.; 0000000000 ::::::;:;c:nCDO)Q')c:nc:nc:n 0>0>0>0>0>0>0>0>0>0>0> ?'"'t ......... .-tf"""l"""" .-t.,....

I

CN.'-=QO:::~=::;~ ON. CDO'.:lOC'l. c,cOO ON~~OOON~U'OOO I

laOlac.l NNN NNM~C'f:)""C' ""'''''''''''"'1'"'1'lQlQlQlQlQ~

Topography for Field Artillery

-I

~

"'"

~~~

"'" ~~~~~~~~~~ ~~~~~~~~~~~ ~~~ ==

-

"'" ~ ~

"'"

==

~ ~~~~~~~~~~ ==

------

~~~

~ ~

==

---- ~-----

~~~ ~~~~~~~~~~

~

==

~~~

==

-- -----------

~~~

~~~ == ...........

~ ~~~
-301-

I QN~~Q()QC'1""~r:I) =N~tt:>OOOIN~C:>OO ON"'I!1lc.oetJOC"~c.oOOO

"I

OOOll:>

.-t .... ..-I_ ~NNINCNMC'?C'I:lC'?~ 'ot:f'''''d'l'll$ll~~~'nlt:)~l.0~ t-:::;~~

t: C'l~C'l00..,00..,00..".'" ~CD'"d"Oll:lOl.ClOt.O....4 ~.....-4(J:> C'OC'1r-C'1r-e--lt- ~..,'" Q)cnOO.-;~C'JC'J~C'O ~'"d"l.Q~('c)l-l'-OOOOo) ~OO,....j_C'lC'lC'l?C'?~~ ~C'!"! QI -:"";C'iC'iC'iC'iC'ic-iC'iN C'i C'i C'i C'l C'i C'i C'i N eN C'i C'i~t:.~et':iC'l'5~Cf5C'Ocr,;c.-5~ 0 > C'lC'lC'lC'lC'lC'lC'lC'lC'lC'l C'lC'lC'lC'lC'lC'lC'lC'lC'lC'l C'lC'lC'lC'lC'lC'lC'lC'lC'lC'lC'l

..-4 ~""'CDt.O-.::tl ..... c:n(,O~~ OO~C'OOOOlOC'lOt-~ e-.1o)U:> ...~"""OOl:.CC"':)Ot-..o ..,r-- .....

00 00 00 00 l- r-- L- t.O~~t.Ol.OLQlOLO.qi~ oo:::I"C'OC"?~C'QC'JC'1C'JC'1~"'" t--:~~ 0 ~.;.~~~.;...;.....;....;....; ~....;~....;....;~~....;....;....; ....;....;....;~~...;....;....;....;~....;

t! ~C')~Ol.ClOt.O ..... t.O ...... ~C'lr--..,OO"'OO"""''''' O')lf:)Olt::>Oc'o....-ll:.C ..... l':'"'C'I u>C'ltC"-'C'O"I:2"lQlQtOtOt-r:-OO OOQ:lQ)OO ..... ~C\lC'JC':l ~:;:55:~~~55::; -:~~ QI 0060000000 000-:"";"':"':-:"':""; 0 > C'lC'lC'lC'lC'lC'lC'lC'lC'lC'l C'lC'lC'lC'lC'lC'lC'lC'lC'lC'l C'lC'lC'lC'lC'lC'lC'lC'lC'lC'lC'l

N

.... OOLO~"""OOt.O~ ..... o)t.O ~""'O':lc.o~C'1O':1t-~C'l O)r-~C'lCDr-'"d"C'JC':lt-~ ",OOC'l

t.O(,ClWWLQLt:LQl.O"d4"14 "IId4~C'r?C"OC'QC'OC'.JC'JC'JC'J ....................OOOOC';lQ:lC) ~o:~ .= u.;~tOu.;LC.r;;lO"'Ou-;)...; lo~lt5..oaa"OlL-5..ou:;~ ..o..o..o..ou-;;lt:itOU-;~"";";

mCD~c:n~a.Q)(J)CDcn c:n<:Hc:n~Q)0')c:nc:nc:n(j;l 0>"'''''''''''''0>'''''''''''' .

--_._._--~._-_.-----_. -_._---_.-

t: ~OO~C')lOOLO .....(,O ...... ~C'lOO"'OO"""''''''OOO o to .....t.~ C'l t-C'l 00 C'O 00 0001.0

t-t-ooooC')oO .....~C'J C'lC'Qcv:.'l~'"d"LOlQ(,CIt-t- ooooa:.c:nOO .......... C'JC'lC'O ""':C'!~

Cll oooOoooooo",cicicici ~~~aic:nmcia)cici c)~oi~oocooc-)o 0 > ,...-t ......'I""'"'l~'I""'"'lC\lC\JC\JC'JC"JC'Jc..J

..-4

to C"l 0':1 r-LO C'Q....-4 00 ""'C'I",r--1.O..,OOOU>.., ....-4o,)~~C"JO':Ir-LOe-lOOO C'Q 00 C"1

C'OC"':lC"':lC'JC"JC'lC'lC'l'l"'""'i'l""'"'l ,......~ooooOC')~O:l ~~~~oot-:t-:t--:t-:r:-:~ t-:a;C'!

0 r.i to~ ~..; e.c tor; tD U:>~~~~~~~l.";LO to l~ LQ LO~ LC L":! l~ l!: It:l ..... ",,,,a.,,,,,,,,,a.,,,,,,,,, Q";l~OiI~m~O}Q)~~cn

-_..--------_.----------_._ .. .. ._-----_ ..... _- ----_.-_._--

...: ou:>-,e.oC"Jr-C'Ooo-.::r~ LOO~-'tOC'Jr-C"':lOO"'dt 0') 0 lO ......to ,......r- C"l 00 CI':) ""'oc .., 'I""'"'l.-lC'JC"J~O?...q;~lOlQ C.D t-t-OO 00 0')0)00 1"""'1 t""""4C':aC'QC"':l~"o::::i'LQlOC.D~t- .-;~.C'! tal ....:r-:~r--=~t-=~r--:~t-= r:..:~r:-:~t-r..:~oooOoo oOoooooCoooOoOoooo~oo

0 > 1"""'l 1"""'1~-' .................'I""""'I 'I""'"'l-' .............................. 1"""'1...., '1"""1

C>

..-4 00.,,"" C'I 000u>"",C'l 0 OCtO ~C"J oootO~C"l 0 t- 1.0 ....-40') t-1.Q C"10 00 to "",00'"

0 Q) 0') 0') 0') 00 00 00 00 ex> t-1:-t-t-t-t.CltOtCtCtC lOL.?lOlO~'"d'-.:::r"'Q4"'l::Te:t:ICO t--:a:~ e.ot.-:5~~w~~e.O~e.O cDc.oe.O~e.O~c.Oe.Oe.Oe.O e.Oe.OtOtO~~~c.Otdt.Ce.O

:--i ....

.-

...: 1.I':I~c.e-N",,-e:t:IOO~e:t.ll.O Oc.o"""'t-C"lOO~0':I""d40 1.O .....u>C'I~..,OO""''''ooO""d4lQlCCD,.:;lt-r-OOOOO':l OO ............C'lC"lCQ~""d'lLQ ~~~t-:t-:~~o:o:q~ C'lu> .....

~~~,~~~~~~~

e.Oc.Pe.Oe.OtOe.Ot.Or.OtDcD Cll C,ClC,CltOtC<.Oe.otCtOcor-r- ~.-;~

0 > ....,....-l-:-i .-i'l""'"'l ...... 1"""'1 ....-l ...-4 1"""'1'1""'"'l'l""'"'l

LQ~NOOOe.o~~ ...... O) r-lO~....-4O':100C'O""d4NO octO ~N 0 ooe.o~e-.) 000

101I:~lOlQ~~""d'l~""d'lCQ C't:lC'.':!l:":lCQC'JC"JC'JNC"JC\1 ...-4'1""'"'l 'P""'iOOOOO~ ""''''.., 0 ~t-~~~.....:r:..:r..:r-.:t--="": .....:....:r--=~r--:r--:r:..:~....:r:..: r--:....:r:--:r---=r:..:....:r..:....:r..:r:..:c.e t-:~~ 0')~Q')~0)Q)0';l0"0l0':l0) "''''''''''''''''''''''0>'''

t: OO""''''1.O .....u>C'lt-..,OO ""d401O....-4t.Oe-.lt-C'l':'e:t.l""d4 01.0 ....u>C'lt-'"00 "'"0>0 .....>0 00

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-302-

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Topography for Field Artillery

""'"

~

'"

~ ~

_

......

~~~

--

'"

- ~~~

==

~ ~~~

~
-303-

. .

In general, stadia wires are set so that the horizontal distance with

the line of sight level will be 100 times the red reading. In this case the

horizontal distance at any. observed angle will be the Hor. tabular number

multiplied by the rod reading, to which must be added the value for c for

.that angle as shown at bottom of table. The vertical height will be the

Vert. tabular number for the given angle multiplied by the rod reading with

the value for c added. If the wires are set for a different proportion. the

result must be modified in like proportion before adding c which will not

be affected.

Example: Rod reading=5.27 at 70

37'; c=1.00.-

Tabular numbers are 98.25 and 13.14

5 27 5 27

~775- "-9198

19650 2628

49125 6570

. 517.7-775 -69.2478

c .99 .13

Hor. Dist. 518.8 69.4 Vert. Ht.

The use of the oldinary slide rule in connection with this table will

allow results to be reached with little labor to the nearest foot in distance

or tenth in elevation. which will be sufficiently close for many purposes.

640. Table II.

D~ 90 1

100 110 1

120 1130 1140 1150 1160

i Mils

80 I M.21 M~l MAl MAl M.51 M.51 M.61 M.6jM!i1~~-.M-.9~I-M-.9-'I-M-1-.0

.-!.QQI_,.41 _.51_.61 .71_.91_1.01~~11_1.21~.31-h41~51~1~

129_1 _.'l:>L~_1 _.~1~01~11_1~21_!.-.41_1.d>l~.:..61-.!.-81~.91_2.01_2~

.-l4~L!:Q1 :...-1.11 1.31 1.5j 1.71 1.91_2~1~1_21>1_2~'71_2-,-91~

nl"~_~1 1.?~~~1_2.21 2.41 2.ril 2.91 3.21.3.4\ 3.7U-:9 _ !gOI 1.3.fL.1.61 1.91 2.~1 2.51 .2404.3.11 3.~1 3.71 4.01 4.3! 4.~1 4.9 20U1 1.51 2.0 2.31 2.' I 3.01. 3.ul 3.81 4.21 4.41 4.91 5.31 5.' I 6.1

_~?OI1.-81-2.31-2_&I-=-3.2J -3.71- 4.21- 4.61-5.01-5.51-6,0H6.5\-6.91-7A •

2401 2~2.71 3.3\ 3.81 4.4 4.9 5.41 6.01 6.51 7.1 7.61 8.21 8.7

-2"6012.61 3.2 3.81 4.4\ 5.11 5.8 6.4\ 7.01 7.6rs:s1-8~919])1 10.2

~28013.01 3.11 4.6\ 5.1u.:m..-!>".~1 7.2\ 7.9\ 8.61 9.31 10])1 10.71 11.~

3001 3.4 4.21 5.1 5.91 6.71 7.61 8.41 9.3 10.11 10.91 11.81 12.71 13.5

20 ~.8 4.8 [I:, 6.7 76"I"K6 9.5 10.5 11.5 12.4 13.4 14.3 j1).3

Example: The distance read off on the stadia rod is 120 meters. The slope

is 112 mils. What is the horizontal distance? At the intersection of line 100 ar.d column 120 the correction read is 1.3 meters.

1.6-1.3 .3X 12

Variation for + 12 mils: --20 X 12= 20 .18=.2

Total correction=1.3+.2=1.5 meters ..

The desired distance is 120--1.5=118.5 meters.

Topography for Field Artillery

= =

__

=
641. Table. III.

.-304-

. 2037.

D Meters a. mils

, Mils I 0 I 1 . I 2 I . 3 . I 4 I 5 I 6 7 I ~_!L

'0 co 2037 1018-1679 '509 L!07 I 339 291 255 226

10 204 185 169 156 1~5_LJ:~6-U~7 119" 113 fO.'I

20 102 97 92 88 84 81 78 7~73 70

30 68 66 64 62 60 I 58 56 5m3 52

40 1=11 -.r9 48 47 46145~44 -43-y42 41

50 41 40-'-39 3'8-' 38r37 36 361-3-S-'-34

_~,O_I_34_,_I._?~ I. 33 . '~2_J-.-?2' '-?l -=31_. ~~=F-r0 J__

~~-H~-I ~~-HH~'~~~-'Hi~t-~}-1-~}--~.~ .-90,23 2'W22 22 I 21-' -21121 21 20120

Example: The angle intercepted b)' the two meter stadia rod, standing perpendicular to the line of sight, is 64 mils. What is the distance

from the instrument to the stadia rod? The desired distance is

read at the intersection of line 60 and column 4. It is equal

to 32 meters.

Topography for Field Artillery.

=

~~

I~~+~~
30n .

APPENDIX VI.

AZIMUTH OF POLARIS.

Topography for Field Artillery

- - ~
Lat. 51°-53°, 6/10

Lat. 56°-57°, 7/10

Lat. 58°_59°. 8/10

Lat. 60°_61°, 9/10

-306-

642. The table below shows the azimuth of Polaris in different positions

with respect to the pole. Epoch 1911; polar distance 70'. Latitude 0° to

18° north. This table may be used until 1930.

Fig. 209.

, Clock Reading of- Azim- Clock Reading of- Azimuth Clock Reading of- Azimuth --- uth 5 Z 5 , Z of 5 Z of

Cassio- Ursae of Cassio- Ursae Polaris Cassio- Ursae .Polaris

peia Major Polaris peia Major peia Major

XII:30 VI:30 18' IV:30 X:30 049' VIII II 358059'

I VII 35 V XI 35 IX III 358 50

1:30 VII:30 49 V:30 XI:30 18 X IV 358 59

II VIII 61 VI:30 XII:30 359 42 X:30 IV:30 359 11

III IX 70 VII I 359 25 XI V 359 25 --- ~-_.- ---

IV X 61 VII:30 1:30 359 11 XI:30 V:30 -359 42

For higher latitude add to the small azimuths or subtract from the

large ones, as follows:

Lat. 19°-30°, 1/10

Lat. 31°--37°, 2/10

Lat. 38°-42°, 3/10

Lat. 43°-46°, 4/10

Lat. 47"-50°, 5/10

It is well to keep track of the position of Polaris by noting it frequently and taking the corresponding clock time. Then if on a cloudy night

a glimpse of Polaris is' had, the observation m~y be taken even though the

other stars can not be seen.

Topography for Field Artillery
;-1\

INDEX.

---. "."f.

A

Abney level ................•.............•..............•. 159-161

Abbreviated coordinates 422

Abscissae. .; , 0#' 420

Accuracy

Computation of minimum range and elevation .. 0" o. 0'0 337, 338

• Dead space calculation' 0 • 0 •• 0 •• 0 • 0 •••• '-0' •••• 0 •• 0 • • • 358

Intersection 0 •••• 0 •••••••• 0 •••••••• 0 •••••••• 0 0 •• 0 • 0 •• 0 194

Road report 0 •••••••••••••••••••••••••••• 0 0 0 • • • • • • 248

Topography 0 • '.0 0 0 •••••• 0 • 0 0 ••• '. '. 7

Acute angle 0••••••••• o. 0 ••••••••••• 0. 0 •• 0 ••• o. 0... 16

Adjusting point 0 0 • 0 ••••• 0 • 0 •• 0 •••••••••• 0 0 0 •••••• 0 0 ••• 0 • 483

Advantage of

Orienting line .. 0 • 0 •••• 0 •• 0 •• 0 0 •••• 0 •• 0 ••••• 0 0 •• 0 ••••• 0 • • • 583

Aerial photographs ... 0 •••••••• 0 ••••••••••••••• 0 •••••••••••• • • 403

Aiming

Circle 0 • 0 0 ••••• 0 ••••• 0 • • • • • • • • • • 139, 576-582, 586-595

Direction 0 0 •••••• 0 • 0 0 •••••••••••••••••• 0 • 0 • • • • 552-558

Point 484, 552-558

4.1idade .", ,. 0 ••• , .•••••••••• 0.. . . • . . • . 54, 150-153

French 0 0 ••••• 0 •••• 0 •••••••••••••••••••• 00 ••• ••• 152

Leveling"~ •............. , . . . .. . o ••• 152

'Sighting ."'" , .. ,., 0 •• 0 •• • 0 ••• 151

Telescopic ,., .. , 0 •• ••• •••• •• •• 153

Tests of 0 ••••••• ••••• •••••••••••••••• 0 • • • • • • • 59

Triangular , , 0 ••• ••••••• •••••• 0 •••••••••••• 150

Altitude ..... , 0 ••• 000 ••••••• 0 • 0 •••• ••• 0 •• • ••••• 0 •••••• 0 ••• 84

Ammunition record o. 0 0 •• 0 •••• •• • ••••• •••••••••••• • 0 • 0 • • • 540

Angle

Acute .. ,........ . .... 16

Base : 0 • ••••••• 0 0 •• 0 •••••••••••• ••• 0 • • • • • • • • • • 485, 585

:',",Definition .. 0 •• 0 ••• 0 ••••••• •••••• •••••• •••• ••••• 0 ••• 15

Expression of-, by tangents 0 •• '.................... 32-45',

'Firing . 0' •••••••••••••••• ••••••••• ••••• •• , 0 ••••••• '. • • • • 499

-of divergence .• , , , , ,.. 427-429

-of fall ..••......•• ,."., ,., ..• .. ,',...... 383

-of observer displacement , •... ,."" ,... 507

..--of site ',' 313, 318, 319

Reflex ... 0000 •• 0 ••••••••••••• ••••• •• 0 ••• ,.. • • • •• •• • •••• 16

Right ..•. 0 •• 0 •••••••••• 0 ••••••••••••• 0 •••• "."., •••• ~. 72-74

Round 0 •• 0 •• •• 0 0 •••• •••• ••• 0 ••••• ,0' •••• 16

Straight 000 ••••••• o •• 0,. • • • • •• 0 •••••••••• •••••••••• ~. 16

Topography for Field Artillery

-

~ 0 0

;

' 0 ••••••••••••••••• 0 ••••• , •••••• : .;.~

' ,

0 • • •

, '

, , , • , , .' , , , • • • • • • • • • • • • • • • • •

, ,

, , '

, , , , , ,

" , , , , ,

0 ••••••••••• , • ~ ••••• , , ••••••• 0 , , • , • •

~ , , ...... ,

, , , , , , ,

, , ,

" ~

0 0 •••••••••••••••••••••• , ••• , , , , • , • • • • •

, , ,

' , ,

, ,
-308-

To plot-using gradient ........•........................... 47

To plot-using percent •.................. '. . . . . . . . . . . . . . . . . . 49

To plot-using tangent ......•.................•............ 35

-traverse .........................•....•....... 185

Angular measure ................•.••...................•.... 15-29

Base equivalents 30

Conversions in- 30, 31

Definition .......................•.•......... 16

SYstems ...................•............. ...•............. 17

Annual variation .......................•...................... ,457

Arcs of circle . ,

Solution of triangles of error 206

Area sketches ...........•.......•....•.................... 230-239

Border ........•..•..... ...•.............•.......•....... 238

Conventional signs .......•....... . . . . . . . . . . . . . . . . . . . . 234-236

Information ...........•......•• .•...•..•..••.•........... 233

Lettering .....•..•..........•...............••.......••... 239

Title •..........................•........ :................. 237

Artillery information service •....••.....•......•••........• 402-404

Artillery sector •..........................• 483-523 ,524-543, 559-561

Auxiliary position

Chart of •..............•....•.....•.•...•.....•.. •.... . 530

Azimuth ....••...............................•...••. 451, 452, 454

Back-, resection by '........ 207, 469

of Polaris •.................•.••..•......•..•..•..••...... 642

Used to determine compass declination ......•..•.••........ 463

y.:....- ••••••••••••••••••••••••••••••••••••••••••••••• 430, 451, 454

B.

Back azimuth, resection by •....••.•..•.........•.......•... 207, 469

Band, elastic, visibility by means of 312

Base

Angle ..........................•........•.....•...... 485, 585

Deflection .................•..•..............• .•......... 486

Direction ..•............•.•.••..•..•...................... 487

Equivalents .....•...........•... '.' . . . . . . . .. . .. . . ... .. . . 10, 30

Line ••...............•.....•..............••......... 487, 510

Point .....•......... ; ..........•...•....... . . . . . 488, 550, 551

Battalion commander; Duties of 618, 621-623

Battery commander ,

Data book .....••.•..•... ....•............ '................ 539

Duties of ........•............................... 618, 624. 6.25 ,

Records .......................•.....•...•• . . . . . . . . . . . . . . . 543

Reports ..•....•.••.•.......•.......•••..•..•..•.......... 542

Battle maps .....•.......••.•...•......••....•. :. '.' . . . 411-415, ,489

Bearing 451, 453

Determination of compass declination by means of....... 463-465

Of target ...............•.....•..•........•........... 470-472

To find a bearing with a protractor ...•.................... 468

,"opography for Field Artillery

.

~

'

~ ~

~

"
-30~

Belgian maps 0 0 • 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 • 0 0 0 0 0 • 0 0 0 0 0 0 0 0 • 0 0 :!:. 0 0 • 0 0 0 0 416

Bench mark . 0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 •••••••••••••••••••••• 0 ••••• 0 0 131, 132

Bisectors, perpendicular 0 0 0 0 • 0 •••••• 0 •• 0 0 0 0 0 • 0 0 0 •• 0 0 • 0 0 0 0 0 204. 213

Board

Firing 0 0 0 0 0 0 0 0 0 ; 0 • 0 0 0 0 0 0 0 •••••• 0 ••• 0 0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 0 500

Slope •.. 0 0 0 • 0 0 0 • 0 0 0 0 : 0 0 00 0 0 0 0 0 -0. 0 0 00 0 0 • 0 • 0 •• 000 00 0 • 164, 165

Bonne projection 0 0 •••• 0 •• 0 0 •••••••••••••• ••• 0 ••••••••• 0 • 0 0 • • • 395

Book, B. C. data . 0 0 •••• : ••••• 0 0 • 0 • 0 0 • 0 • 0 0 0 0 • 0 •••• 0 ••• 0 0 • 0 • 0 • • 539

Border, position and area sketches . 0 0 0 0 0 0 • 0 0 • 0 000000 •• 0 •••••• 0 • 238

Brigade commander; Duties of 0 0.............. 618, 619

British maps ......•.•......•.•..•..••.....••• .••.•. Appendix II

British resection o. 0 •• 0 0 0 • 0 0 •••••••••••••• 0 ••••••• 0 • 0 0 0 •• 0 •• 0.' 213

c.

Calculation

Angular values above limits ....•..• 0 0 • 0 •• 0 ••••• 0 ••• 0 0 •• 0 0 0 • • 44

Mental- in -conversions . 0 • 0 •••••••••••••••••••••••• 0 0 o. 13, 30

Using tangent .. 0 0 • 0 0 ••••• 0 0 •••••••••• 0 ••••••••••••••• 0 0 • 0 43

Chains' .. 0 •• 0 0 • • • • •••• 0 0 ••••••••••••• 0 •••••••••••••••••• 0 •• 0 57

Chaining .... 0.00 •••• 0 •••••••• 0 0.0 •••••••• 0000 •.• 0000.0.0 ••• 0 188

Chart

Auxiliary position . 0 0 • 0 0 0 0 • 0 0 0 •• 0 0 • 0 0 0 •• 0 •• 0 0 0 0 ••• 0 0 0 0 • 0 • 0 0 530

Combined . 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 •• 0 0 0 ••• 0 0 ••••••••••••• 0 535, 536, 538

Dead space 0 0 0 0 0 •• 0 • 0 0 • 0 •••• 0 ••• 0 •••••••• 0 • • • • • • • 347, 533, 534

.Firing ... 0 ••• 0 0 0 ••• 0 • 0 ••••••••• 0 • 0 ••••• 0 ••••••• : •• _" 501, 526, 527

General system of communication ....•.......••... 0 0 •• 0 • • • • 531

Invisible areas .... 0 0 • 0 ••• 0 ••• 0 0 •• 0 0 ••••••••••• 0 • 0 • 0 • 0 • 532, 538

Isogonic-i_o_0 • 0 0 •• 0000000. 00' 0 •• 0 ••••••••• 0 •• 0 • • • • • • 456, 458, 459'

Position 0 • 0 ••• 0 ••• 0 0 • 0 0 •••••••• 0 ••••••••• 0 0 • 0 0 0 • 0 • 0 0 • 529

. Slope of fall 0 0 •••••••••• 0 0 •• 0 0 • 0 0 0 • 0 ••• 0 0 • 0 • 0 0 0 0 0 0 0 • 0 38~ 384

Special- for dead space calculations 0 0 • 0 0 0 0 0 • 0 0 ••••• 0 0 0 386-389

Visible areas .... 0 • 0 •• 0 0 • 0 • 0 0 ••••••••• 0 •• 0 0 • 0 • 0 •••••• 0 532, 538

Visibility . oI. 0 •• 0 • 0 0 0 0 0 0 0 0 0 •• 0 0 0 0 •• 0 0 • 0 • 00 •••• 0 o. 0 • 0 • 0 315, 316

Circle •............. 0 • 0 • 0 0 0 •• 0 • 0 0 0 0 0 • 0 • 0 • 0 0 0 • 0 • 0 •• 0 0 0 0 0 0 • 0 0 0 • 16

Aiming; See aiming circle

Circular measure 000000;.000000000.0 •• 0.00.00 ••• 0.0..... 16

Table for conversion 00' 0 0 0 0" 0.000000. 0 0 •• 000 •• o. Appendix IV

Clinometers

Abney ... 0 0 0 0 0 • 0 0 • 0 • 0 •• 000 •• 0 0 0 0 0 • 0 0 • 0000. 0 0.0.0 •• 0 •• 0 I 159-161

Gravity ..•. 0 •••••••• 0 ••• 0 •••• 0 0 0 •• 0 • 0 • 0 • 0 0 ••••• 0 •• 0 •• 0. 0 0 • 162

Combined charts .. 0 0 • 0 • 0 ••• 0 0 • 0 • 0 •• 0 0 • 0 •• 0 • 0 0 •• 0 ••• 0 • 535, 536. 538

Command

Observation post 0 •••• 0 •• 0 •••• 0 0 ••• 0 • 0 0 0 0 • 0 0 0 :0 0 0 • 0 ••• 0 0 ••• ~. 601

Post 0 0 • 0 • 0 ••• 0 • o. 0 0 0 0 0 0 •• 0 • 0 •••• 0 • 0 • • • • • • • 490

Communication of information •••...•..... ; ... 403, 404

System of general-- 0 ••• 0 • 0 •••••••• 0 ••• 0 ••• 0 0 • 0 0 0 • 0 0 0 0 • • • 531

Comparison ..

Of map and panoramic sketch •......... 0 0 •••• 0 • • • • • • • • • • • • • 308

Of methods of panoramic sketching 0 0 • 0 0 •• 0 0 • • • • • • • • • • •• .- 295-298

Topography for Field Artillery

~

~

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~

~ 0

~

~

...

..

~

~

0 ••• 0 • • • • • • • •

..
Of tangent and mil calculation ....................•. .. ,;'. : : . . 36 ."

Of tangent ratio and tangent ; . 37

Of warfare methods ••• 3'

Compass r

Declination ,460-467

Determination of 461-465

. Error . '.' . . . .. 457

. North ::.r ,. 451-454

Peigne : 143;.i47~-

Prismatic- 142

Used as aiming point .••. ; ;;......... 475-482.

Used to lay guns 470-482

Used in magnetic resection............................ 469

Concentration fire, plans of ::........................... 537

Conic projection :''': 393,

Constant ",

Declination. . . . . . .. .. . . . . . .. . . . . . . . . . . . . . . . . . . .. . 466, 578, 579

Deflection 496

Contingent zone' ...................•... ....•........... , . . . . . . . . 491.

Construction of

Mounted timing scale 119~12i

Profiles 314

Protractors ,'; '. . . 64-71

Reading scale .. ;...................................... 10S:111

Right angles 72-74

Slope board............................................... 164

Slope of fall chart ~' 384

Slope scale 225-227

Special, chart for dead space 387

Tangent slope scale 353

Visibility chart ..,' 316

Working scale ;........ 113-117

Working scale graph 123-130

'Contours 131, 134, 135, 231

-Contouring, logical 138

Control

Horizontal 290-292

Point -... 492

Point of general- 516

Sheet . , '.. . . . • .. . . . . . . . . . . . . 493

Vertical 293, . 294

'Conventional signs

Definition :........................................... 4

For panoramic sketches "\......... 279-282

For position and area sketches ..............•.......... 234-236

Use, of 4

'Convergence of 'meridian 427-429'

Conversion

Angular measure '.' . 30;~31

'Topography for Field Artillery

"

' ' '

r '" :

'

"

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-311-

:'Circular measure 30, 31, Appendix IV. ?Gradients ;.;; ; •.. ;;:............... 46, 52

Linear measure' .. .. '. .. '.'. . . . . .. . . . . . . . . . . . . . . . . . . . . 10, 12-14 t .. ,

.. Mental calculations in- 13, 30

Of degrees and minutes to decimals 20

Of angles above prescribed limits . . . . . . .. . . . . . . . . . . . . . . 53

Per cent :......................................... 48, 52

Table of slope .-..................................... Appendix I

,. Tangents ..............•............................ 36, 52, 53

True mil equivalents . .- . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 31

Cbbrdinates #-

Abbreviated '.-............................... 422

Complete ................................•........ 421

.Definition :.......... 419

,.,Geographic '. 419

H'ectometric : ;....... 422

Lambert grid '. . . . . . . . . . . . 419

.. Location of point on ground by means of 448, 449

Method .of reading ...........................•.... 421, 434-437

Method of plotting points by 425, 426, 432, 433

Of . origin '. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

Range, determination by 445

Reduced hectometric 422

To measure :; :.... 434-437

To plot a direction by ..............................•... -' 439, 440

Use of .........................•........ ;... 432-449

Y-azimuth, determination by means of .. '............... 446, 447

Correction 'i-l.._ •

Errors of closure .....................................•... 191

, Of inaccurate protractor :.... 62

Crest lines '. . . . . . . . . . .. . .. . . . . . . . . . . . 272, 273

Critical .points .............................................•... 137

Determination of ........................•............. 232

D.

Daily variation .457

Data book, B. C. . :............................... 539

Datum' point ;........... 494

Dead 'space '. . . . . . . . . . . . . . . . . . . . . . . . . . . . 326-328, 345-389

Accuracy of determination '. 358

.. Chart h" • • • •• • • • • • • • •• • • • • • • • • • • • • 347.' 533, 534

Limits of 346, 356, 357

Methods of determining . . . . . . . . . . . . . . . 348-389

Calculation . . . . . . . . . . . . . . . . . . . . . 359-374

Comparison of angles of fall and ground............. 349-351

Graphical 375-389

Slope of fall chart ,............................. 383-385

Special charts 386-389

Tangent slope scale ..................•............ 352~355

. Topography for Field Artillery

' ' ' '

'

~

~

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_

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-312-

Problems ...................•........... 360-374

Decagrade ..............•...........•..•• ...•.......•....•.... 22

Decigrade ..................•..•....•..•..•..•••..•..•.. ....• . 22

Declinated plane table; Orientation by •................ :..... 173, 174

Declinating point ..........•.................................. 495

I)eclination

Compass . . . . . . . . . . . 460-467" •

Constant r. 466, 578, 579

Magnetic 455, ,456

y- 467

Declinator ............................•..... , '...... 149

Used in resection ...........•......................... 202, 203

Defilade

Definition . . . . . . . . . . . 309

Kinds of •..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309, 321

Method of determining :...... 317-320

Angle of site 318, 319

Profiles .............................•....... '. . . . . . . . . 320

Similar triangles 322-325

Table of . . . . . . . . 321

Type problems 322-32!i

Deflection

Base :................................... 486

Constant .•.....................•..•...... 496

Fan •.................•........................•..... '.. 518, 528

To measure, by sito-goniometer 169

Degrees

Conversion for use .••......................................• 20

Limit of calculation by tangent ratio 29, 39-42

Sixteenth of ..•.....•....................•................• 19

System ...........•..•... . ;......... 18-20

Twentieth of ,................... 19

Used to express slope .....................................• 218

Designation of targets '................ . 301-305

Devices

Measuring .....•.. •......................................• 63

Technical, in panoramic sketching ......•............... 267-282

Diary, gun ...........•..............•.....•..............•.•• . 540

Directeur, plan ..•.••.•.•..•.......................... 489, 515, 525

Directing piece ........•...................................•.. 497

Direction .......••........ '. .. .....•........................•• . 83

Base ........•.................... . . . .. ..•...........•..• 487

From grid north .............•...•........ '. . . . . . . . . . . . . . . 454

From magnetic north ..•................................... 453

FrQm true north •.••.•..•..... ........•........ :- ; . 452

On road report •........................................... 248

Plotting- ...•••..•................... 438-444

Director in laying gun ....•........................ 576-582, 586-595

Displacement, angle of observer .............................••. 507

Topography for Field Artillery

~

~

~
-3~3-

Distance •.•.••.....•......... . ..•..................• ":. . . . . . . . 82

Expression on map: ............•..........•.............. 87

Horizontal ..•.....................•. .•................... 156

Map- •...........•.•.•....•.••... "0 ••••••••••••••••••••• 87

On road report ........................•........... 249

Drawing

On p'anoramic sketches 0 0 •• 0 0 0 0 0 • 0 • 0 ••• 0 0 0 •• 0 0 • 0 0 • 0 0 • 0 0 0 265-282

Duties of

Battalion commander o. o. o. o. 0 0 0" O. 00000 •• 0 o. 0 0 0 ••• 000 621-623

Battery commander o. 0 • 0 0 0 0 0 0 0 • 0 0 ••••• 0 0 0 0 0 •••••• 0 • 0 0 • 624, 625

Brigade commander .....•.....•..•..•.•.. .....•... .f.... 619

Regimental com.mander ....•.............•••.•• .•.. 620

E

Elevation

How shown ...................•....••.•.•....•.......... 131

Minimum- ....................•.....•..•............. 326-344

Engineer's level ..............•........•........•...•......... 163

Engineer's scale .......................•........•............ 55

Equipment

Panoramic sketching .. 0 •••••••••••••• •••••••••••••••• 0 • • • 284

Road sketching : ........•............. ;. 242

Equivalent .

Base •........... 0 • -. 0 • 0 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• 10, 30

. Horizontal ....•.•..............•...•..•...•... 87

True mil •...•.••.•............................ :: ',-~'. 31

Error

Allowable in resection 0 •••••••••• 0 •• 0 •••• 0 • 197

Compass"'.-. . . . . . . . . . . • . . • . . .. . 0 • 0 •• 0 457

Explanation of, in tangent calculation .•.•.•...............•. 40

In closure ...•......•.. '................................... 191

In traverse ..........•.•...•..•••......•.............. 191

Maximum, by using reduced hectometric coordinates 423

Triangle of ......•...............•....••.......•....... 204-206 .

Essentials of

Military map............ . .........•........•... ..... 86

Panoramic sketch .••..•...........•.....•............•... 261

Exaggeration in vertical control . '. . . . . • . . • . . . . . . . . . . . . • . . . . . 294, 314

Explanation of error in tangent calculation 0 0 0 • • • 40

Expression of

Angles by tangents ........................•.•...... :.... 32-45

Application ....................•....... ~.. .•. .. .. 33

Comparison of tangent and mil calculation ..•..•.. 36

Comparison of tangent ratio and tangent ••....... 0 0 • • • • • 37

Mil relation ......•.•.......••••.•...............•......... 28

F.

Fall, slope of, chart

Fan, range deflection

.................................... .. 383, 384

-518, 528

Topography for Field Artille'.')O

0 • 0

---

0 • • • • • •

-

~ 0

~ 0 • • • • • •

0 •

~

0 • •

~

0 •• : • • •

0 • 0 •

- 0 • • • • •

~

0 •••• -

0 • • • • • • -

'
-314-

Field of the observer 498

Fire .

Concentration, plans of ; .. ;....... 537

Limits of ......•........ : o. • • • • • • • • • •• • •••••••••••. -. • 502

.' Possibilities of 534

Firing

Angle 499.

Board 500

Chart 501, 526, 527

'Observation post ;...... 602

Fords _. . . . . . . . . . . . . 627

Foresight-backsight traverse '0' • • • • • • • • • • 183

Forms, ground. See ground forms

French maps '. . . . . . . . . . . . . . . . . . . . . . . . 405-415

Functions, table of natural Appendix III

G.

Geodetic point; Use of '492,547

Geographic coordinates 419,

German maps 417

Goniometer, sito 166-16,9

Grade system 21, 22

Limit of calculation by tangent ratio 29, 39-42

Tangent method applied to .. ;............................... 29

Gradients 46, 47

Conversion 46, 52

Limit of use 51

To measure 152

To plot an angle using 47

Used to express slope 221

Graph, dead space :.. 386-389

Working scale '. . . . . . .. . . . . .. . . . . .. . . . . . . . .. . . . . 123-130

Graph,ical method; Visibility 314

Dead space ....•...................................... 375-389

Graphical 'scale 91-94

Interchange of- 122

Types of 107

Gravity clinometer _............................................ 162

Grid, British . . . . . . . . . . . . . . . . . . . . . . . . . 632, 633

"Lambert. See Lambert grid.,

Ground ,forms .

Effect on minimum range and elevation ,.......... 332-344

'. :Methods of indicating :. . . . . . . . . . . . . . . . . . . 85; 131, 275, 276

Ground relations 81

'Altitude . 84

Direction . -. 83

Distance '. .. . ,............ 82

'Use' of- ,.......................................... 85

Ground 'slopes; Panoramic sketches : , : . .. . . 275, 276

Topography for Field Artillel'y

.

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~

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540

545-549

"-315-

Gun'

Diary . .

Position, location of .. ...............•.............. ,. .

H.

Hachures ; . ; . . . . . . . . . . . . . . . . . . . 131, 133

Hectometric coordinates : . . . . . 422 .

Horizontal control .....• ;. : . . . . . . . . . . . . . . . . . . . . . . . 290-292

Horizontal equivalent 87

.l.

Ice' ........................•••..•• ....• ; '; •. ~............. 628

Identification; Panoramic sketch ; . . . . . .. . . . . . . . . 262

. Information

Area sketch 233

Comm,unication' of 403, 404

On map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

On panoramic sketch 263, .264

On road report "........................ 247

'On road sketch 245

Service of- 402-404 :

Source of- , 404

Title of sketch ..•..................... . . . . . . . . . . . . .. . . . . 237

Instruments

Declinated '.':~:. . .171

l\Ieasuring '; ; .. 54-62

Oriented : .. ;............ 171

Used in traversing ...............................•........ '182

Intelligence observation post 600

Intersecting arcs in solution of triangle of error ;.. 205

In'tersection 192-195

:,',Accuracy .'........... 194

Definition 192

Location of targets by 611

Operation 195

Purpose 193

Interval, vertical 136

Irregular variation ...........................•................ 457

Isogonic chart,....................................... 456, 4,58, 459

J.

K.

Known'line I ,

Orientation by 175, 176

~, Use. ~<?f,~n two point' resection . 201

L.

Lambert grid .•....................•......................

:; ,Convergerlce of, meridian •................•.••........•

418-430

427-429

Topography for Field Artillery

' ~

~ ~~ ~~~

~ '

~

' '

~ ~~

~ ~

~

'

~

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,

239

159-161

163

-316-

Coordinates 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 • 0 0 0 0 • 419-424

Description 0 0 0 •• 0 •• 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 0 •• 0 • 0 418

Divergence.o 0 0 0 0 00000000 0.0.000000000.0 •• 0 •• 000.000. 427-429

Origin .. 0 0 0 •• 0 • 0 • 0 0 0 0 0 0 0 0 ••• 0 0 • 0 • • •• 0 ••••••• 0 • 0 ••• 0 0 ••• 0 418

Use of 00. o. 0000 •••• 0 • 0 0 0 0 0 0 0 0 • 0 0 • 0 0 00.0 •••••• 0 000000. 431-449

Y-azimuth ... 0 0 • 0 0 0 • 0 0 0 0 0 •••••• 0 0 ••• 0 0 0 0 0 •• 0 • 0 0 • 0 0 0 0 • 0 0 0 430

Lambert north 000 •••• 000 •• 00000.0 •••• 00.0 ••• 0000 •• :.0. 86, 451,454

Lambert projection 0 0 0 • 0 0 0 0 •• 0 0 • 0 • 0 • 0 • 0 • 0 0 0 0 0 •• 0 • 0 0 ••• 0 •• 0 0 0 396-397

Lateral limits

Fire •. 0 0 0 • 0 0 0 0 • 0 0 •• 0 0 0 • 0 •• 0 • 0 • 0 0 0 0 • 0 0 • 0 0 0 • 0 • 0 0 0 0 0 0 0 0 0 • • • 5U2

Road report •.....•........•..•.....••..•.•........• 244

Sector . .. 0.0 •• 0 •••••• 0 • 522

Latitude 0 • 0 0 • 0 • 0 0 0 •• 0 0 •• 0 •• 0 0 •••••••••••••• 0 • 391, 396, 405, 418

Laying guns

Compass as an aiming point o. 0 0 • 0 • 0 ••• 0 ••••• 0 0 • 0 • 0 • • • • 475-482

Declinated instrument ......•..•........•...•••••... o. . 470-482

Lining in ..... 0 •• 0 •••• 0 •••••••••••• • 0 • • • • • • • • • • • • • • • • • • • • 474

Prismatic compass ..... 0 ••• 0 •••••• 0 ••••• 0" • • • ••• • • • • • 470-482

Lettering

Position and area sketches

Level

Abney ................•. 0 0 • • • • •• • ••••••••••••••••••••

Engineer's

Limits

. Calculation of mils by tangent method . 0 • 0 • • •• • • • • • •• • 29, 39-42

Dead space 0 •••••••••••••••••••• 0 ••••••••••• 0 • • • • 346

Fire 0 ••••••••••••••••••••••• ••••••• •••• 0 • • • • • • • • 502

Gradient form of expression 0 0 •••••••••••• 0 • • • • • •• • • •• 51

Line ,

Base .. 0 •• 0 ••••••••••••• 0 •••••• 0 0 •••••• 0 •••••••. • • • • • .487, 510

Broken 0 • • •• • ••••• ••••• 0 • • • • • • • • • • • • • • • • • • • • • • • • • 274

Crest . 0 •••• 0 • 0 • 0 • 0 ••••••••• 0 •••• 0 0 ••• 0 • • • • • • • • • • • • • • • 272, 273

Observing 0 •••• 0 •• 0 • 0 •• 0 • o. . ..•. 0 • • • • • • • • • • • • • • • • • • • 508

Orienting 0. 0 0 •••••••••••••••••• 0 0 • • • • • • • 511, 553-558

Origin .0.0 ••••••••• 00 ••••••• 0 .0 ••• 0 • • • • • • • • • • • • •• • •• 0.. 513

Parallel . 0 0 •• 0 •••••••••••••••••••••••• 0 •••• 0 •• 0 • • • • • • •• • 268-271

Linear measure

Conversions in 0 0 •••••••••• 0 0 •• 0 • 0 0 ••• 0 • • • • • • • • • • 10, 12, 13, 14

Lining in o. . .•.. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

Location of unknown points. by

Computation of angles ..••............. 0 ••••••• 0 • • • • • • • 610-617

Intersection 0 ••••• 00 ••••• 0.. • •••••• 0.................. 192-195

Resection . 0 •••• 0.0 •••••••••• 0 • •••••• • •• •• •• •• • • • • • • • • • 196-214

Traverse ..•.......................•...•............•.. 181-191

Logical contouring • 0 •••••••••••••••••••••••••••••••• • • • • 138

Longitude 391, 396, 405, 418

Lunar variation ....•....... 0 ••••••••• 0. 0 0 ••• 0. • • • • • •• • • • • • • •• 457

M.

Magic number .. 467. 578, 579

• upography for Field Artillery

..

0 • • • • •

'

0 ••••••••••••••••• 0 ••••••••••••••

0 •••••• '. • • • • • • •• • ••••••••••••••••

: '

'

:

:

: • • • • •

0 0 • • •

~ 0 • • • • • • • • • • • • • • • • • • • • • • • • • • • •••

•
77

76

87

86

.-317- .

Magnetic

Bearing •...............•............................ 451, 453

Bearing from map with protractor .......................•. 468

Declination ..•.•..............•...................•.. 455, 456

Resection ..........•...... . • . . . . . . . . . . . . . . . . • . . . . . 469

Variation .. 457

Maps

Artillery sector, of the 524-543

Battle . . . . . . . . . . . . . . . . . . . . . . . . . . . 411-415

Belgian 416

British (see Appendix II). . .'

Classes of ............................•...... .........•..

Definition .. -. . . . . .. . ..• . ..........................•.......

Distance . . . . . . . . . . . .. . .

Essentials ........•..•••............. . .....•.........•....

French (see French maps).

German .....................••.... .•........•........•.. 417

Information •........•................. .....•... • . . • . . . • . . 86

Knowledge required ..•.........•...........•.•.•........... 78

Oriented ........•..•.......•.......••••......•.••.•...•..• 171

Preparation of .....•..•..•..•...•.•......•...••.•.•..• 398-404

Projections .........•..••..••....•.•••..•. 390-397

Reading ...........•.... . . . • . . • . . . • • . . . • . . . . • . . . . . . . . . . . . . 80

Revision ............................• 401

Scales ..•.............•.......•.......•....••.....••.•.. _~.87, 88-91

Slope scales .........................•..•........•..... 224-229

Mark

Place ,........................................ 5'14, 54S

Registration ':-: ....•.................... • . . . . . • . • • • • . . 521, 607

Marker ...........•.. . . . . • • . . . . . . . . • . . . • . . . . . . . . • • • . . • . . • • . • • 503

Mask; Amount to be raised to secure defilade. .. •. •..•• . •• •.••••. • 324

Measuring instruments ........••..•..••••..•••..•...•.....•. 54-62

Alidades ........•.....•.........•....•.•......•. • • . . . • • . . . . 54

Test ..........•............•..•.•...•.....•............ 59

Chains ..................•.••.•..•..........•••......•••. . 57

Metric measuring scale ...........•..•.......•....•....•..• 55

Test ............•.•................................•... 56

Protractor .........•....••...•....••••..••••.. 60, 61, 62, 64-71

Construction .........•.......•...............•...•.• 64-71

Correction ......................•.............•..•..... • 62

Test ...............•.•.....•..... , 61

Specifications .....•.•.........................•..••...•.... 54

Tapes ._...............•..•.•..••...•••...•.•.•• • . . . . • . . . . 57

Tests •................•....•••.......•...•••.....•...•..... 54

Triangular scales ..........•...•........•.. -.• . . • . . . • . . . . . . . . 55

Test .......................•........................... 56

Measurement

Of sector •.............•. : .........•..•.•............... . 284

Of. traverse ........•..•..•..••••....•...•.••.•.......• 186-189

Topography'for Field Artiller,.

~

~

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~

~

~

~

~

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-318-

Measurement of distance

~"Chaining .... ........................................• , . . . 188

',.. Pacing ............................•. ; . . . . . . . . . . . . . . . . . . . 187

: Stadia readings 189

~"When first station cannot b~ occupied 190

Mental calculations

Angular conversion 30

."'Linear conversion 13

Mercator's projection 391

Meridian

Convergence of the ..............................••.... 427-429

Meter : ,., , : '>11

Methods; Comparison of warfare .............•.................. 3

Methods of

Determining compass declination 461-465

Determining dead space ..........................•.... ". 348-389

Determining defilade 0 L • • • • • • • • • • • • • • • • • • • • • • 317-320

Determining minimum elevation and range 329-344

Determining visibility ..... '.. . . . . . . . . . . . . . . . . . . . . . . . . . . . ,.310-314

Laying guns on the base line........................... 562-597

Locating gun position 545-549

Locating targets......................................... 611-617

.Making road report ...•.............................. 250, 251

Orientation 172

Panoramic sketching ,.............................. 295-298

Plotting points by coordinates .........•............... .. 425, 426

Preparing combined chart 536

Preparing firing chart ! ••••••• ( ••••••••• '", • • • • • • 527

Preparing plan of fire concentration, 537

Procedure, panoramic. sketching, . . . . . . . . . . . . . . . . . 283-307

Reading. points by coordinates ...................•.. 421, 434-437

~,Resection •.•............ !............................. 198-214

'.: Road sketching....................................... 242, 243

~'Traverse 183-185

Metric maps; Slope scales for 226,227

M~t;l'ic measuring scale ," ! • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •. ,55

'~; Test '. . . . 56

Metric system; Length of meter, . . . . • . . . • . . . . . . . . . . . . . . . . . . . . . . . 11

Mil .

......Advantage of :.. 26

.~;Conversion :.................................. 36,52

.:', Conversion, table 30

Definition and discussion ;.. 24

?' .. Expression of. mil relation ..........•......................• '28

Limit of calculation by tangent ratio 29, 39-42

;j'; Rimailho mil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 25

System "...................... 17, 23-29 :

1\'''; pse ..of ..••• ~1 '17

~;": ~., Used to express. ~lope . ..• 219

'

'

'"
-319-

Minimum elevation 326, .327, .328, '.

Accuracy 337, 338 .

Determination .329-344

Effect of ground forms ..................•.............. 332-344

Problems ...............................•....•......... 339-344

,Steps of calculation ..•.•...•..... :.......................... 331

Minimum range '....... 168, 326, 327, 328

Accuracy 337,338

Determination 329-344

Effect of ground forms ..................•..•......... 332-344

Problems . .. .. 339-344

Steps of calculation 331

Minutes

, . Centesimal .........................•...................... .21

Sexagesimal .. . . . . . . . . . . . . 18

MQunted timing scale 118

Construction of 119-121

N.

Needle traverse ..................•............................ 184

Normal, zone .............................................••... 504

North ."...................... 86, 451-454

Grid ,... 86, 451, 454

.Lamoert 86, 451, 454

Magnetic -.",-~.86, 451, 453

On British maps 634

. True 86; 451, 452

Number;' Magi~ 467, 578, 579

O.

Objective zone 505

Observation

Of enemy's movement :...... 255, 256

Of hostile terrain ..•.....................•............ 255, 256

Plan of : '..................... 609

Terrestrial .........................................•.. 610-617

Observation post ..................•......•............... 506, 598

Classes of •............................................... 599

Command •.•.•............ : '...................... 601

Determination of origin line ...........•......... ,.......... 605

Determination of registration mark or target 607

Firing ...................................•.......... '. . . . . . . 602

Intelligence •.•............................................ 600

Plan of observation , ....•.............. '..... 609

Reconnaissance '. . . . . . . . . . . . . . . . . . . 603

Records of •.................................... . . . . . . . . . . 608

Special orders for 606

,. Topographical operations ...•.............................• 604

: Visibility charts ............................•........... 315,' 316

Topography for Field ArtiIlery

~

"

_

'

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-320-

Observation tower, height of 325

Observer

Angle ~f-displacement 507

Field of the 498

Observing

Line ;............................. 508

Sector 509 $

Obtuse angle .................................•................ 16

Occupation of position ',,' 255

Of sector '.......... 559-561

Operations. topog~aphical: See topographical operations.

Ordinate .................................................•.... 420

Orientation

Methods of 172

By angle traverse ..................•...................... 177

By declinated plane table '. 173,174

By known line 175. 176

By resection 180

Panoramic sketches '....................... 285-288

When known point or given line cannot be occupied 178-179

Orienting line 511, 553-558

Advantages of ................................•........•.. 583

Determination of :........................ 553-558

Kinds of 554

Selection of ...•.................. '. . . . . . . . . . . . . . . . . . . . 553-558

Use of

To lay guns on base line ...........•............. 583-597

Using aiming circle 586-595

Using plane table . . . . . . . . . . . . . . . . . . . . . 596

Orienting point ..........•.................................... 512

""To locate gun position '.... 549

Origin; Lambert grid 418

,',., Coordinates of '............................................ 420

di'igin line

"Definition '. . . . . . . . . . . . . . . . . . . . . . . '513

Determination 605

P.

187

639

254-257

261-281

283-307

306. 307

258-260

268-271

48-51

48

50

f'

Pacing .

Length of pace .

Panoramic sketches

Characteristics .

Essentials. . ; ..

Method of procedure .

Subsketches .

Types of sketches : '. :

Parallel lines .

Per cent : ....................................•.........•....

Calculation : .

Common error .

~

'

~

'

"

'
-321-

Conversion ............•...•............................ 48, 52

To plot an angle, using 49

Used to express slope ........•..•... '. . . . . . .. . . . . . . . . . . • . . . . 220

Perpendicular bisector ..•................................. . 204, 213

Solution of triangle of error • . . . . . . . . . . . . . . . . . . . . . . 204

Perspective . . . . . . . . . . . . . . . . 268-270

Photographs, aerial ...................................•....... 403

Place mark

Definition ...............................................• 514

Determination of ...............•................•.....• '~.. 549

Plan directeur 411-415, 489, 515, 525

1/20,000 .......................................••....•... 412

1/10,000 413

1/5,000 ..•......................................•.....•.. 414

Plan of observation .....................................•...... 609

Plane table

Declinated ......................•...............•...••... : 171

Description ..........•..•............•.............••....• 148

Oriented ...............•.•..•.....• '....................... 171

To level ............•....•.•................•.....•....... 149

Use •••...................•.•.................... 148, 575, 596

Used in traverse .....•........•...•.•.••..• '. . . . .•. ..• .•. . . 182

Plotting directions

By auxiliary points ........••••••••..•.........•..• .'& •• • • 441

By coordinates •.......•.....•..•.. ••........... .-. : • . . . 439, 440

By reversing directions •.••.••.•.•......•.....•.••..•.•••.• 444

By similar". triangles ...•...•.•••... . . . . . . . . . . . . . . •• • . . 442-443

By Y-azimuth 438

Plotting points by coordinates •..........•..•....... 425, 426,432, 433

Point

Adjusting 483, 521

Aiming •...•..•....•.•.••••..•..•.....•.... -....... 484, 552-558

Base •.•.....•.••...••••.••.••.•••......••.•.•... 488, 550, 551,

Control ...........•••..•••.••.•....••..•• '. • • . . • • . . • • . . • • • . 492

Critical ..•....•...............•.••.•..•..•.....•.••.. 137, 232

Datum .....•.••....••..•..••••••••.••..... . . • • . • . • . • . • • • . 494 ,

Declinating .......•..•.....••.•.....•..•....••..•..•.....• 495

Geodetic •.•.••....••.•.•.••..••••..•.••..••.•...••.•. 492, 547

Important-, Designation of 301-305

Location of-,by coordinates ..•..•..••.•.....•.......... 448-449

Method of plotting' . . . . . • . . • . • . • . • • . . • . . . . . . . . . 425, 426, 432, 433

Method of reading .........•............... :...... 421, 434-437

Of general control ••......•..•.....................••.. ~. .• 516

Orienting .....................•.•.••.... ;................. 512

Reference •.......................................• 290-292, 519

Registration ...........••.......•.....................••.. 521

Referring ~'.•.......•.................... .. '. 520

Witness ....•...........•. • . . . . . . . . . . . • . . . . . . . . . . . . . . • . . • 523

Polaris; Azimuth of .......................•..•................ 642

Topography for Field Artillery

~

~

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'

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~

~
-322-

Pole star, used to determine compass declination 461

Polyconic projection 394

Polyhedral projection .............................•............ 392

Position

Amount of defilade, problem 323

Auxiliary-,Chart of "............................... 530

Chart ..•..•........................•..................... 529

Definition 517

, Gun . . • . . . . . . • . . . . . . . . . . . . . . . . . .. • ..•.••........... . 545-549

Reconnaissance and occupation of ',' •.. .. . 255

Position sketches 230-239

Border 238

Conventional signs '. . . . . . . . . . 234-236 .•

Information 233

Lettering ;...... 239

Title 237

Possibilities of fire 534

Posts

Command '. . . . . . . . . . . . . 490

Observation (see observation posts) 506, 598-609

Prefixes

Latin and Greek 9

Prismatic compass 142

Compass as aiming point .............................• 475-482

Compute bearing of target .:.......................... 470-472

Laying guns \vith 473-482

Lining in '. . . . . . . . . . . . . . . . . . . . . 474

Problems

Comp~tation, minimum range and elevation 339-344

Conversion of slopes .....•......................... '. . . . . . . . 223

Dead space 360-374

Defilade 322-325

Laying guns on base line with aiming circle 592-595

Laying guns with compass as aiming point.............. 477-482

Locating targets by topographic means ..•..•........... 612-617

Map scales ....................•.....•.................. 94-103

Profile

Construction of .......................................•... 314

To determine defilade ....•......................•.......... 320

To, determine visibility '. • 314

Projections, map .................••.....•.•..............• 390-397

Bonne .••..................•.............................. 395

Conic ....................•..........•......•............. 393

Definition ................................•..•............ 390

Lambert . . . . . . . . . . . . . . . . . . . • . . . . . 396, 397

Mercator's ..........................•.......•.....•..•..•. 391

Polyconic ......• . . . . . . . . . . . . . . • . . . . . . . . . • . . . . . . . . . . . . .. . . . 394

Polyhedral ...............•..............•........•.. '0' ••• -. 392

Proof. Italian resection 212

Topography for Field Artillery

I

- ~

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Protractor

Construction 64-71

Corrections for inaccuracy 61, 62

Description :................... 60, 170

Test 61

Use of 170

Use of in finding magnetic bearing from map 468

Purpose of intersection 193

Q

Quadrant, circular measure ......... .

R.

16

255.

256

603

255

Range

Deflection fan 518, 528

Determination by coordinates :..... 445

Minimum

Accuracy ',' . . . . .. . . . . . . . . . . .. . . . . .. . . 337, 338

Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

Determination . . . . . . 329-344

Effect of ground forms 332-344

. To measure, sito goniometer 168

Steps of calculation '. . . . . . . . . . . . . . 331

Triangulation detachments 400, 401

Reading of points -' 421, 434-437

Reading scales 91, 92, 108-111

Censtruction of 108-111

Use of ...•. ",~ '.' . . . . . . . . . . . . . 92

Reconnaissance of

Enemy position .

Example .

Observation post .

Position . Records

Ammunition .............................................• 540

Artillery, sector .. '.' . . . . . . . . . . . . . . . . . . . . . . . . 524-543

Classes of 524

Elaboration of 543

l\-Iaps and charts . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . 524-538

Of O. P : '. 608

Topographical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Written 524, 539-543

Reduced hectometric coordinates 422

Reduction of stadia readings 155, 639

Reference point . . . . . . . . . . . . . 519

Desirable considerations 291

Selection of ..............•............................ ,290-292

Use of 292

Referring point ........•...................................... 520

Topo(.!."raphy for Field Artillery

"

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-324-

.Reflex angles ......•...•........••••.....•..•.••...••....•..... 16

Regimental C. 0., Duties 618, 620

Registration mark ••............ : .• ".......................... 521

Determination of •.••..........••.•.••.••••.•••...••......• 607

Relation of

M. D. to H. E .........................•.................. -.. 87

Tangent 'computation and true angular value •..•....•...••. 38, 42

Tangent computation and degrees •..•••••••....••..... 4 • • • • • • 42

Tangent computation and artillery mil ••••.•..•....••....• 39-42

Tangent computation and R-mil ..••.• '. • • • • • . • • . . • . • . . . • . 41, 42

V. I. to scale of the map •..........•.....•............•.•• ,136

Of B. C. ..•..•..•..•.•.......•.............•..•.......•.. 542

Road (see road report) :..... 246-253

Representative fraction •.....................••...•............. 89

Requirements for accurate results in resection... .. . .. . . . •• .•. • 197

Resection '. •..•..•• .•. . • . •• . . .• 196-214

Back azimuth ..........•............................. 207, 469

British ...................•......•.••..•..•............••. 213

Definition 196

Italian ..•........• 208-212

Magnetic ....•... '. 0 ••••••••••••••••••••••• .' • • • • • • • • • 469

IVleasured angles . '0' •••••••••••••••••••••••• 0 •••• 0.00. • • • • • 214

Orientation by 0 •••••••••• 0 •••••••••••••• • • • • • 180

Requirements for accurate results ......•................... 197

.Three point method .•........................•.. 0 •• 0 • 0 • • • • 203

To locate gun positions by ..........•.............. 0 • • 548

Transparent paper method ........•..•....•..•......... 198-200

Two point method ..•..............•....•.•... 0 • • • 201, 202

Revision,' battle maps ..•........•.......•..••.•............... 0. 401

.Right angles ...•.....••.••.......••.......••••...... :.......... 16

Construction of .. 0 :..................... 72-74

Test ..•.•.••..........•.••..•.....•...•••..••..••.....•..•. 75

Road report •.••••..•.....•..•..•....•..••••.•••••........• 246-253

Definition •.•...••.........••.•.•....•..•.....•..•..•...•.. 246

Direction .......•..•........•.••..•.•.•••..•.....•....•..• 248

Distance 249

l\lethod ..•.........•..•.•.....•.•.... 0 0... •.. . • •. . . 250, 251

Use to be made of ......•..........•.••..••..• 0 • • • • 252, 253

Road sketch •...•...••.•.....•..•.....•.••••.•..•.......... 240-245

Characteristics •••..•... : ...•••.•..•..•••••.• '. . . • • . . . . . 240, 241

Information ..•..••....•.•••..•.•....•••.••.••.•..•.....••.. 245

Lateral limits ....•..•.•...•....•... '.0 ••••••••••••••• • • • • • • 244

Made from road report ..........•..•.....•.....•..... • 252-253.

l\Iet~od .....•..•.•..•..•.••.•.••.•.•.••.••..••..•...•• 242, 243

S.

Scales

Computations

Topography for Field Artillery

94':103

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o~~ •

0 ••••••••••••••••••••••••••••••••• : • • • • • • • • • •• • • • •

0 •••• -.. • • • • • • • • • • • • • • • • • • • • • • ... • • • •

• • • • • •

: : • • • • •

• • • • •

• • • •

• ;

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Conversions 104-106

Graphical 91

Map ....••••.•.......•... '. ....•.......•.........•....••. 88-91

Metric measuring '. 55

Mounted timing '.. . . . . . . . . . . . . . . . . .. 118

Reading 107

Relation to V. I. 136'

Slope 224

Tangent slope scale, 25° ..•.....•....•..•....... '.' .....• 352-355

Triangular 55

Types of ............•..................................... 107

Use of .....•....•.....•.................................... 92

\Vords and figures ;..... 90

Working .................................................• 107

\Vorking-graphs . . . . . . . .. 123-130

Seconds

Centesimal 21

Sexagesimal ...•........................................... 18

Sector .............................•........•................. 522

Analysis of .........................•....................• 289

Battery i.............................................. 483-523

Maps and records .•........................•.......... 524-543

Measurement of; Panoramic sketch ~. 284

Occupation of '. • • . . . • • . . • . • . • •• . • . • • . . . . . . . . . . . . . . . . . . 559-561

Secular variations ......•..•........................•........•. 457

Shading ...........•..............•........................ 277-278

Sheet "i_.

Control ...............•..••.....•...•....•• ......•....... 493

Target .•.•....•....•.... • . . . . • . . • • • . . . • • . . . . . . • . . . . • .. .. 541

Signs, see conventional signs •....•.••....•....•. 4, 234-236, 279-282

Similar triangles

To determine' visibility •...••..•.•.•.••..•.••..••..•.•.••••. 311

To plot direction by 442, 443

Site

Angle of, used to determine defilade .••••.••••.•••••.•.•• 318, 319

Angle of, used to determine visibility •••.••.•.•...•....••... 313

Sito-goniometer .........•••.•..•.••.•••••••••.••••.•.•.••• 166-169

Use of .•.....•..••••.•••.••••••••••••.••••••••.•••••••. 167-169

Size of mil 24

Sketch

Panoramic, see panoramic sketch

Position and area ......................•...•..•..•..... 230-239

Border ........•..••.•..•..••.•.••.•. -................. 238

Characteristics ....••.••..•.••.••...•.•..•.......••.•.. 230

Conventional signs ........................•......... 234- 236

, Critical points ..•..• .••.....••••.•.•.............• <... 232

Information .•...••.. _- 233

Lettering ..........•...............•..•..•••••.•..•• . . 239

Method of making .........•••...••....•.....••.•.•. 231.,' 232

Topography for Field Artillery

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~

_

~

~

~~

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-326--

Title 237

Road, see road sketch

Slope

Board 164, 165

Construction 164

Conversion of slope, problem . . 223

Ground 275. 276

Practicability of 626

Scale 224

Construction '. . . . . 225-227

Use of ............•............................... 228-229

To measure 147, 152, 216

'Units of expression

Degrees and minutes 218

Gradient 22l

Mils 219

Per cent 220

Tangent 222

Solution

Conversion of slope, problem 223

Dead space 360-374

Defilade . 322-325

Map scale, problems 94-103

Minimum Range and elevation 339-344:

Triangle of error...................................... 204-206

Space, dead (see dead space) .

Special orders for observation posts 606

Stadia red

To measure distances..................... 154, 155, 157, 158, 189

Reduction of readings 639

Straight edge tests 58

Sun, used to determine magnetic declination 462

Systems

. Degree or sexag~sin:al : ,.... 18-20

General communIcatIOn 531

Grad or centesimal 21, 22

Map projections 390-397

l\iil ..•..•................................•............... 23-29

Tl'iangulation 398-399

T.

Tables

Azimuth of polaris 642

Conversion,- of App. IV

Defilade '. . . . . . . . . . . . . . . . . . . 321

Length of stride 629

Natural functions App. III

Reduction of stadia readings '. . . . . . 639

Slope corrections ... '. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Topography for Field Artillery

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-327-

169

626

353

38

39

57

552-558

550, 551

545-549

Slope practicability 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Tangent slope scale 0 0 0 0 0 0 0 o. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Tangents

Above' 45 degrees 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 0 0 0 51

Addition and subtraction 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,0 0 • 0 0 • 0 0 0 0 0 0 0 0 0 0 0 • 0 0 • 45

Conversion 0 0 0 0 • 0 0 0 0 0 0 0 • 0 0 • 0 0 •• 0 0 • 0 0 0 0 0 •• 0 • 0 0 0 0 • 0 0 0 •• 0 0 • 36. 52

Slope scale o. 0 ••••• 0 0 0 0 0 0 0 • 0 0 • 0 0 • 0 0 0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 • 0 • 352-355

Used to express slope 0 0 0 0 0 0 • 0 0 0 0 0 • 0 • 0 0 0 0 • 0 0 • 0 0 • 0 0 0 0 0 0 0 0 • 0 0 0 222

Tangent methods o. 0 •• 0 0 0 0 0 • 0 0 • 0 0 0 0 0 0 0 0 0 0 0 •• 0 0 •••• 0 '.0 •• 0 • 0 0'. . 0 0 0 28

Applied to degrees and grades O' 0 0 .000000000000000000.0. 00000 29

Tangent ratio, limits of calculation by .... 0 • 0 0 • 0 • 0 0 0 0 0 • 0 0 0 • 29, 39-42

Tangent values

Relation of, to actual angular yalues 0 0 •• 0 • 0 0 0 o. 0 0 0 0 0 ••• 0 0 •• 0

Relation of. to artillery mil .. 0 ••• 0 • 0 0 0 ••• 0 • 0 0 0 0 0 •• 0 0 •• 0 0 • 0 0 0

Tapes 0 0 0 0 • 0 0 0 0 0 0 0 • 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 •• 00 0 0 0 •

Target

Bearing of ... 0 0 0 0 0 0 0 0 0 0 0 • 0 0 • 0 0 0 • 0 0 • 0 0 0 0 0 0 0 0 0 0 0 ••• 0 • 0 0 0 470-472

Designation of ... 0. 0 0 0 0 0 0 0 0 • 0 • 00' 00000.0: 00000. 0 0 0 • 0 0 0 301-305

Location of o. 0 0 0 •••••••• 0 0 0 • 0 0 0 0 0 0 • 0 0 0 0 0 0 o. 0 0 0 550, 551, 610-617

Registration .. 0. 0 0 • 0 0 0 0 • 0,0 0 0 0 • 000000000000000000.00.00. 0 0 0 521

Sheet .. 0 • 0 0 0 • 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 0 0 0 • 0 0 0 0 '0 0 0 • 0 0 0 0 0 •• o. 0 0 0 541

Witness 0000000000000. 0 • 0 • 0 00000000.0000.0000000. 0000000.0 523

Telescope, battery commander's 0 0 0 00 00 ••• 0 0 0 •• 0 0 00 0 0 0 ••••• 0 ••• 0 0 140

Telescopic alidade :. 0 0 0 0 • 0 •• 0 0 0 0 0 0 0 0 0 • 00 0 0 0 0 • 0 • 0 0 0 • 0 • 0 0 0 • 0 0 • 0 • • • 153

Terrestrial observation .... 0 • 0 •• 0 0 0 •• 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 0 •••• 0 •• 0 00 610

Tests ...

Edges .. 0 • 0 0 0 0 0 0 0 0 0 0 ••• 0 0 0 0 • 0 0 0 0 0 0 0 • 0 0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 • 0 0 • 0 0 0 58

Line of sight of alidade 0 0 •• 0 0 • 0 0 • 0 0 • 0 0 • 0 0 0 • 0 • 0 0 0 • 0 0 • 0 0 •• 0 0 • 0 59

J\![easuring instruments 0 0 '0 ••• 0 0 •• 00 00 0 • 0 0 0 0 0 • 0 0 0 0 0 0 0 o. 0 00 : 0 0 54

Protractors . 0 0 •• 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 0 :0 0 0 0 0 0 0 61

Right angles 0 0 • 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 •• 0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 o. 0 00 75

Scales 0 0 0 0 0 • 0 •• 0 0 • 0 0 • 0 •• 0 0 • 0 •• 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 0 • 0 0 0 0 0 0 0 0 56

Three point method, resection by 0 0 0 0 0 0 0 0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 203

Title, position and area sketch 0 0 0 0 0 0 • 0 0 0 0 '0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 237

To lay guns on base line 559-597

Aiming circle method 0000000000000000.00000.00000000000 576-582

Aiming point method 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 564

Errors 0 '0 0 0 0 0 0 ••• 0 0 0 0 0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 O' 568-571

Method of checking 0 00 0" 0000000 •• 0 0 0 00000000 572-574

Orienting line method 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 • 0 0 0 0 583-589

Plane table method 0 0 0 0 • 0 0 0 0 0 • 0 0 •• 0 0 • 0 • 0 0 0 0 0 0 0 0 0 '0 0 • 0 • 0 0 0 0 0 575

Staking out method 0 0 0 0 0 •• 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 563

To level plane table .00. 0 0 00. 0 0 0 0 0 0 0 • 0 0 0 0000 o' 0 • 000000000: 0 0 0 0 0 00 149

To locate

Aiming point or direction 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 •• 0 • 0

Base point or target 0 0 0' •• 0 0 •• 0 • 0 0 0 0 0 0 0 •• 0 0 0 0 • 0 0 0 0 0 • 0 :

Gun position . 0 0 ••• 0 0 • 0 • 0 : •• 0 • 0 • 0 • 0 0 0 • 0 0 0 0 0 •• 0 0 0 0 0 • 0 • 0 0

To measure

Angles and deflection. sito-goniometer 0 0 .0 0 ••• 0 • 0 0 • 0 •• 0 0 0 •• 0

Topography for Field Artillery

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0 0

~

.. .. .. .. ..

~

~
400, 401

398, S99

425, 426, 432, 433

-328-

Distance, telescopic alidade 154

Minimum range, sito-goniometer 168

Slope

, Leveling alidade 152

..:.Peigne compass 147

Sito-goniometer 167

To plot

Coordinates .

Direction

Coordinates ..................•...........•.. :..... 438-444

Piegne compass ....................................•.. 145

Protractor 0. • • . • • • . • • • . • • 146

Topography

Advantages .................................••...•.........• 2

,Definition ;........... 1

Uses of ..........................•.............•............ 1

Topographical information, how recorded .....•.....•...... "....... 4

Topographical methods .• .•••.••.•....•.•..•..• : • . . . • . . . . . . . . . . . 5

Topographical operations ..•..................•.•..•••.. . . . . . . . . 544

Laying guns on base line ............•..•.•.•...•••..... 559-597

Locating aiming direction ............•••...••.......... 552-558

Locating base point ...•.••.....•.....••••..••.........• 550-551

Locating gun position ....•..•..•••..••.....•..••. • . . • 545-549

Topographical records ..•.•.•••..•••••••.•.•.••.•.•••.•••..•..•.. 4

Essentials ....•.•.•••...••.••••.•..••••.•••••••..•.•...••... 4

Transit ...........•....•..•••..•...••••.•.•••••.•...•.••••...• 141

Traverse ..••...•..•...•.•....••••..••.•••.•••••..••••.•.•• 181-191

Angle ...................••.••.•••••••.•••.••••••••••••... 185

Orientation by ..•••••.•••••..••.••.•••••••••••..•.•.... 177

Closed ... . . . . . . . . . . . • • • . • • • • • • • . • • • . • • • • • • • • • • • • • • • • • • . • • 181

Definition .......•.••..••.••.••••••••••••••••.•••••••••••••. 181

Errors in .....•.•••••.•••.•••••.•••••••••••••••.•••••••..• 191

Foresight-backsight ••••••••••••.•••.••••••••••••••••••••.. 183

Instruments used .••.•••••••••••••••••••••••••••••••••••••• 182

Measurement of distance :................................. 186

M.ethods ..•..•.••••••••••••••••••.•••••••••••••••••••• 183-185

Needle ..••.....•.•.•..••••••••••••••••..•••••.•••••••••.• 184

Open .......•..•••••••.•••••••••••••••••••••••••••••••.••. 181

Triangle of error ..•.....•••• :............................. 203-206.

Solution of .....•....•.••.•••.••.•.••••••••.••.••.•••• 204-206

Arcs of circles ........••.••.•.••..••..••.•••••••••••.• 206

Intersecting arcs 205

. Perpendicular bisectors •••••••••••••••••••••••••••••••. 204

Triangles, similar

To plot direction by ..•..•..••.•....••..•••••••..•.•.•• 442, 443

Visibility by 311

Triangulation

Range detachments ............•...•..•••.••.••.•..•..

System ............................•.•.•..••...•.....•

Topography for Field Artillery

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o
-329-

Twentieth of a degree 19

Two point method, resection by 201, 202

U.

1'.

Unknown points

Location by

Computation of angles ......•.... .

In tersection ...•........................... .

Resection .....•..................................

Traverse ....••............. ;

610-617

192-195

196-214

181-191

Use of

Abney level ....•.•.................................... 160, 1'61

Aiming circle ..•.............................. 576-582, 586-595

Declinator .....•.............•........................ 202, 203

Elastic band 312

Engineer's level 163

Gradient ..............................................• 47,' 221

Graphical scale . 92

Gravity clinometer 162

Grid 431-449

Ground relations 86

Isogonic chart r. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 458, 459

• !{no,vn line 175, 176, 201

Orienting line 585-597

Origin line ; :: ~-:". 513, 605

Panoramic sketch ........•................................ 257

Panoramic sketch pads 260, 287

Peigne compass 144, 145, 147

Plane table '. . . . . . . . . . . . .. . . . . .. . . . . . . . . . . .. 148, 575, 596

Prismatic compass .....•............................... 470-482

Profiles ...........•................................... 314, 320

Right angled rule •..........•............................ ".. 437

Similar triangles ..............•........... 311, 323-325, 343, 344

Sito-goniometer ...•....•...........•.................. 167-169

Slope board .•.....................•..•.................... 165

Slope scale •.•..•.....•................................... 229

Special chart, dead space ••..•..•....•...•..........•.. 388, 389

Stadia .....•..•............................ '.' .• 155, 157, 158, 189

Tangent slope scale ....•.............................. 354; 355

Telescopic alidade •....•..............•............... :.... 154

Visibility chart ..•.•......•.....•.......................... 316

v.

Variation, magnetic ..•.••...........••...• ... . . . . . . . . . . . . . . . . . . 457

Vertical control ;.......................... 293, 294

Exaggeration 294, 314

Vertical interval ; ,..... 136

Visibility •................... ;............................. 309-316 \

Charts 532, 538, 315, 316

Topography for Field Artillery

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231,

22

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Construction' 0 •• o •• 0 316

Definitions and limitations 0 •• 0 • 0 0 0 • 0 0 ••••• 0 ••••••• 0 • • • 309 ..

Methods of determining 0" 0 •• 0 •• 0 0 ••• 0 •••••••• 0 ••••• ; • • 310-314

Angle of site o' 0 0 0 0 0 0 • 0 •• 0 0 •• 0 0 0 • 0 0 0 • 0 ••••••• 0 • • • • • • • • • 313'

Elastic band .. o ••••• 0 ••••••••••• o •• o •• 0.0 •••• 0 '0' ••••• 312

Graphic method 0' ••• 0.0.0.00000 •••• 00 •• 0 o. 0 0.0......... 314

. Similar triangles .00 •• 0 0 • 0 •• 0 • 0 0 0 0 0 • 0 •••••••• 0 ••• 0 • • • • • 311

Wo

Whole to part method

Wind direction 0 •••• 0 ••••••••••••••••••• 0 0 0 ••••••••••• ••••••••••

Witness

Point 0 ••• 0 .00 •• 0 •••• 0 •• 0 •••••• 0 •••••••• • • • • • • • 523

Target 0 •• 0 •• 0 • • • • • • • • • • 523

Word and figure scale .. 0 0 ••••••••••••• 0 •• 0 •• 0 •• 0 ••••• 0 •• 0 0 • • • • • 90

Wol'king scales 0 ••••• 0 •• 0 •• 0 •••• 0 •••••• 0 • '.' •••• 0 ••• 0 • • • • • 107

Construction of 0 0 •• 0 •• 0 •• 0 •• 0 •• 0 •• 0 •• 0 0 ••• o ••• 0 • • • • 113-117

Graph 0 0 ••••••••••••• 0 0 ••• 0 .00 ••••• 0 ••••••••••• 0 • • • • • • 123-130

l\1ounted 0 • 0 0 •••••••••••• 0 ••••• 0 •• 0 0 •• 0 •• 0 • • • • • • 118

Stride 0 ••• 0 ••••• 0 ••••• 0 ••••• 0 •••• 0 • 0 • 0 • 0 • • • • • • • • • • • • • • 112

Xo

"x., line ......................................................

Yo

419

"Y" azimuth ..... 0 •• 0 •• 0 •• 0 •• 0 •• 0 •• 0 •• 0 •• 0 • 0 0 •• 0 •• 0 • • 430, 451, 454

Determination by coordinates 0 •• 0 • • • • • • • • • • • • • • • • 446, 447

Plotting direction by 0 •••• '. 0 • 0 ••• 0 •• 0 0 • 0 •• 0 0 •• 0 • • • • • • •• 438

"Y" declin3.tion 467 .

"Y" line 0 •••••••••••• 0 •• 0 • 0 0 • 0 0 •• 0 •• 0 •••••••• 0 ••• 0 • • • • • • 419

"Y" north 0. o •• o' •••• o. • • • • • •• • • • • • • • • • • • • •• • • • • • 451, 454

Zo

Zones

Contingent .. 0 ••••• 0 •••••••• o ••••• 0 •••• 0 0 0 0 ••• o. 0 •••• 0 • • • • 491

Normal 0 •••• 0.0 ••• o. 0 •••• 0 ••••••• 0. 00000. 0 o. 00 •• 0" 0... 504

Objective 0 ••• 0 0 0 •• 0 0 • 0 •• 0 • 0 0 •• 0 •• 0 •• 00 ••• 0 ••••••• 0 505

Topography for Field Artillery

"tj

• • • • • • • •

-

0 •• 0 •••••••••••••••

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~