# Tm 3-34.55 (Fm 5-233/4 Jan 1985)

## Construction Surveying August 2012

Publication of TM 3-34.55, 3 August 2012 supersedes FM 5-233*, Construction Surveying,* 4 January
1985.  This special conversion to the TM publishing medium/nomenclature has been accomplished to comply with TRADOC doctrine restructuring requirements.  The title and content of TM 3-34.55 is identical to that of the superseded FM 5-233. This special conversion does not integrate any changes in Army doctrine since 4 January 1985 and does not alter the publication's original references; therefore, some sources cited in this TM may no longer be current.  For the status of official Department of the Army (DA) publications, consult DA Pam 25-
30, *Consolidated Index of Army Publications and Blank Forms,* at http://armypubs.army.mil/2530.html.
DA Pam 25-30 is updated as new and revised publications, as well as changes to publications are published.  For the content/availability of specific subject matter, contact the appropriate proponent.

DISTRIBUTION RESTRICTION: **Approved for public release; distribution is unlimited.**

## Headquarters, Department Of The Army

This publication is available at Army Knowledge Online https://armypubs.us.army.mil/doctrine/index.html.

This manual contains copyrighted material reproduced by permission of the American Railway Engineering Association and the Macmillan Publishing Co., Inc.

Technical Manual No. 3-34.55 (5-233)
Headquarters Department of the Army Washington, DC, 3 August 2012

## Construction Surveying Contents

Page

PREFACE........ vii
Chapter 1
SURVEY OBJECTIVES ........ 1-1
Duties of the Construction Surveyor ........ 1-1 Accuracy of Surveys ........ 1-1 Field Notes ........ 1-1 Metric System ........ 1-2
Chapter 2
ROAD SURVEYING ........ 2-1
Section I - Reconnaissance Survey ........ 2-1 Preparation and Scope ........ 2-1 Collection of Data ........ 2-2 Use of Maps ........ 2-2 Section II - Preliminary Survey ........ 2-3 Preparation and Scope ........ 2-3
Personnel........ 2-3 Section III - Final Location Survey ........ 2-4 Preparation and Scope ........ 2-4 Running the Centerline ........ 2-4 Reference Stakes ........ 2-4 Profile and Cross Sections ........ 2-4 Section IV - Construction Layout Survey ........ 2-5 Preparation And Scope ........ 2-5 Alignment ........ 2-5 Setting Grade Stakes ........ 2-5 Setting Slope Stakes ........ 2-7 Culvert Location ........ 2-10 Drainage ........ 2-10

DISTRIBUTION RESTRICTION: Approved for public release; distribution is unlimited.

## Acknowledgements

Acknowledgement is made to the following associations and companies for their permission to use in this manual the text and tables listed below. Pages 3-25 through 3-28 and table A-9, Functions of the Ten-Chord Spiral, from A.R.E.A. Manual, Volume I. Copyright 1911 and 1950 by the American Railway Engineering Association. Reprinted by permission of the American Railway Engineering Association. Table A-7, Deflections and Chords for 25-, 50-, and 100-Foot Arcs, from Route Surveys and Constructions by Harry Rubey. Copyright 1956 by Harry Rubey. Reprinted by permission of the Macmillan Publishing Co., Inc.

## Preface Purpose And Scope

This manual is a guide for engineering personnel conducting surveys in support of military construction. In addition to mathematical considerations, this manual offers a comprehensive analysis of problems which are typical in military surveying. It may be used for both training and reference.

## Application

The material contained in this manual is applicable without modification to both nuclear and nonnuclear warfare.

## User Information

Users of this publication are encouraged to recommend changes and submit comments for its improvement. Comments should be keyed to the specific page, paragraph, and line of text in which the change is recommended. Reasons will be provided for each comment to insure understanding and complete evaluation. Comments should be prepared using DA Form 2028 (Recommended Changes to Publications and Blank Forms), and forwarded directly to the Commandant, US Army Engineer School, ATTN: ATZA-TD-P, Fort Belvoir, Virginia 22060-5291.

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## Chapter 1 Survey Objectives Duties Of The Construction Surveyor

1-1. In support of construction activities, the surveyor obtains the reconnaissance and preliminary data which are necessary at the planning stage. During the construction phase, the surveyor supports the effort as needed. Typical duties of the construction surveyor include


Determining distances, areas, and angles.

Establishing reference points for both horizontal and vertical control.

Setting stakes or otherwise marking lines, grades, and principal points.

Determining profiles of the ground along given lines (centerlines and/or crosssection lines) to
provide data for cuts, fills, and earthwork volumes.

Preparing large-scale topographic maps using plane table or transit-stadia data to provide information for drainage and site design.

Laying out structures, culverts, and bridge lines.

Determining the vertical and horizontal placement of utilities.

## Accuracy Of Surveys

1-2. The precision of measurements varies with the type of work and the purpose of a survey. Location surveys require more accuracy than reconnaissance surveys, and the erection of structural steel requires greater precision in measurement than the initial grading of a roadbed.

1-3. The officer or NCO in charge of a project usually determines the degree of accuracy. The surveyor makes a practical analysis and chooses appropriate methods and procedures for each type of measurement. The surveyor must consider the allowable time, the tactical situation, the capabilities of construction forces, and the current conditions. The best surveyor is the one who runs a survey to the order of precision which is required by the job with a minimum of time, not the one who insists on extreme precision at all times.

1-4. Surveyors must always be on the alert for probable cumulative or systematic errors, which could be the result of maladjustment or calibration of equipment or error-producing practices. Laying out the foundations for certain types of machinery and establishing angular limits for fire on training ranges are examples of conditions which might demand a high degree of precision from the surveyor.

1-5. For the most part, the construction surveyor will not have to work to the most precise limits of the equipment. However, the surveyor should recognize the limits of the validity in the results. The surveyor cannot expect resultant data to have a greater degree of accuracy than that of the least precise measurement involved. The surveyor must analyze both angular and linear measurements, which are a part of the survey problem, in order to maintain comparable precision throughout.

## Field Notes

1-6. The quality and character of the surveyor's field notes are as important as the use of instruments. The comprehensiveness, neatness, and reliability of the surveyor's field notes measure ability. Numerical data, sketches, and explanatory notes must be so clear that they can be interpreted in only one way, the correct way. Office entries, such as computed or corrected values, should be clearly distinguishable from original material. This is often done by making office entries in red ink. Some good rules to follow in taking field notes are


Use a sharp, hard pencil (4H preferred).

Do not crowd the data entered. Use additional pages.

Keep sketches plain and uncluttered.

Record numerical values so they always indicate the degree of precision to which a measurement
is taken. For example, rod readings taken to the nearest 0.01 foot should be recorded as 5.30 feet,
not as 5.3 feet.

Use explanatory notes to supplement numerical data and sketches. These notes often replace sketches and are usually placed on the right-hand page on the same line as the numerical data they explain.

Follow the basic note-keeping rules covered in TM 5-232.

## Metric System

    1-7. The military surveyor may work from data based upon the metric system of measurement or convert
    data into metric equivalents. Tables A-13 and A-14 in appendix A, pages A-168 through A-175, provide
    metric conversions.


## Chapter 2 Road Surveying Section I - Reconnaissance Survey Preparation And Scope

2-1. The reconnaissance survey is an extensive study of an entire area that might be used for a road or airfield. Its purpose is to eliminate those routes or sites which are impractical or unfeasible and to identify the more promising routes or sites.

2-2. Existing maps and aerial photographs may be of great help. Contour maps show the terrain features and the relief of an area. Aerial photographs show up-to-date planimetric details.

2-3. The reconnaissance survey must include all possible routes and sites. The reconnaissance survey report should summarize all the collected information, including a description of each route or site, a conclusion on the economy of its use, and, where possible, appropriate maps and aerial photographs.

## Design

2-4. Design and military characteristics should be considered during the reconnaissance survey. Keep in mind that future operations may require an expanded road net. A study of the route plans and specifications is necessary. If these are unavailable, use the following as guides.


Locate portions of the new road along or over existing roads, railroads, or trails, whenever possible.

Locate the road on high-bearing-strength soil that is stable and easily drained, avoiding swamps, marshes, and organic soil.

Locate the road along ridges and streamlines, keeping drainage structures to a minimum. Keep
the grade well above the high waterline when following a stream.

Select a route as near to sources of material as practical, and locate the road along contour lines
to avoid unnecessary earthwork.

Locate the road on the sunny side of hills and canyons, and on that side of the canyon wall where the inclination of the strata tends to support the road rather than cause the road to slide into the canyon.

Locate roads in forward combat zones so that they are concealed and protected from enemy fire.
This may at times conflict with engineering considerations.

Select locations which conserve engineer assets, avoiding rockwork and excessive clearing.

Avoid sharp curves and locations which involve bridging.

## Roadway Criteria

2-5. To insure satisfactory results, study the engineering specifications of the road to be built. If these are
not available, use the information provided in table 2-1, page 2-2.

|                                                        |    | WIDTHS                                                | SIGHT DISTANCES    |
|--------------------------------------------------------|----|-------------------------------------------------------|--------------------|
| One-way road11.5 feet or 3.5 meters minimum.          |    | Absolute nonpassing minimum200 feet or 60 meters.    |                    |
| Two-way road 23 feet or 7.0 meters minimum.           |    | Absolute passing minimum350 feet or 110 meters.      |                    |
| Shoulders (each side)4 feet or 1.5 meters minimum.    |    |                                                       |                    |
| SLOPES                                                 |    |                                                       |                    |
| Clearing6 feet or 2 meters each side of roadway.      |    | Shoulders34 inch per foot (in/ft) or 6 percent.       |                    |
| GRADES                                                 |    |                                                       |                    |
| Crown {gravel and dirt)12 to 34 in/ft or 4 to 6 percent |    |                                                       |                    |
| Absolute maximumdetermined by the lowest maximum      |    |                                                       |                    |
| gradeability of vehicles using the road.               |    |                                                       |                    |
| Crown (paved)14 to 12 in/ft or 2 to 4 percent.          |    |                                                       |                    |
| Normal maximum10 percent.                             |    | Cut and fillvariable, but normally about 1 12 to 1    |                    |
| Desired maximumless than 6 percent; on sharp curves,  |    |                                                       |                    |
| loss than 4 percent.                                   |    |                                                       |                    |
| DRAINAGE                                               |    |                                                       |                    |
| HORIZONTAL CURVES                                      |    |                                                       |                    |
| Take advantage of natural drainage.                    |    |                                                       |                    |
| Desired minimum radius150 feet or 46 meters.          |    | Locate above high waterline near streams or creeks.   |                    |
| Absolute minimum radius80 feet or 25 meters.          |    | Grade at least 5 feet or 1.6 meters above groundwater |                    |
| table.                                                 |    |                                                       |                    |

## Vertical Curves Traffic

Minimum length on hill summits125 feet or 40 meters par 4 percent algebraic difference in grades.

Overhead clearance14 feet or 4.3 meters minimum.

Minimum length in hollows100 feet or 30 meters per 4 percent algebraic difference in grades.

Traffic volume2,000 vehicles per lane per day.


Load capacitysustain 18,000 pound equivalent axle load.

Turnouts (single laneminimum every 14 mile or 0.4 kilometers recommended.

## Collection Of Data

2-6. Upon completion, the reconnaissance survey should support the routes surveyed and provide a basis of study showing the advantages and disadvantages of all routes reconnoitered. Typical data collected in a reconnaissance survey are


Sketches of all routes reconnoitered.

Reports of feasible routes. Data on clearing and grubbing.

The number of stream crossings involving bridge spans exceeding 20 feet or 6 meters.

The approximate number of culverts and spans less than 20 feet or 6 meters.

Descriptions and sizes of marsh areas and other natural obstacles.

Unusual grade and alignment problems encountered.

Anticipated effects of landslides, melting snow, and rainfall.

Soil conditions and stream and substrata conditions at proposed bridge sites.

Discrepancies noted in maps or aerial photographs.

Availability of local materials, equipment, transportation facilities, and labor.

Photographs or sketches of reference points, control points, structure sites, terrain obstacles, and any unusual conditions.

## Use Of Maps

2-7. The procurement of maps is a very important phase of the reconnaissance. The surveyor should locate and use all existing maps, including up-to-date aerial photographs of the area to be reconnoitered. Large scale topographic maps are desirable because they depict the terrain in the greatest detail. The maps, with overlays, serve as worksheets for plotting trial alignments and approximate grades and distances.

2-8. The surveyor begins a map study by marking the limiting boundaries and specified terminals directly on the map. Between boundaries and specified terminals, the surveyor observes the existing routes, ridge lines, water courses, mountain gaps, and similar control features. The surveyor must also look for terrain which will allow moderate grades, simplicity of alignment, and a balance between cut and fill.

2-9. After closer inspection, the routes that appear to fit the situation are classified. As further study shows disadvantages of each route, the surveyor lowers the classification. The routes to be further reconnoitered in the field are marked using pencils of different colors to denote priority or preference. Taking advantage of the existing terrain conditions to keep excavation to a minimum, the surveyor determines grades, estimates the amount of clearing to be done on each route, and marks stream crossings and marsh areas for possible fords, bridges, or culvert crossings.

## Section Ii - Preliminary Survey Preparation And Scope

2-10. The preliminary survey is a detailed study of a route tentatively selected on the basis of reconnaissance survey information and recommendations. It runs a traverse along a pro-posed route, establishes levels, records topography, and plots results. It also determines the final location from this plot or preliminary map. The size and scope of the project will determine the nature and depth of the preliminary survey for most military construction.

## Personnel

2-11. The survey effort establishes a traverse with control and reference points, or it may expand to include leveling and topographic detail. Normally, obtaining the traverse, leveling, and topographic data are separate survey efforts, but this does not preclude combining them to make the most efficient use of personnel and equipment.

## Traverse Party

2-12. The traverse party establishes the traverse line along the proposed route by setting and referencing control points, measuring distances, numbering stations, and establishing points of intersection. The party also makes the necessary ties to an existing control, if available or required. When no control is available, the party may assign a starting value for control purposes which can later be tied to a control point established by geodetic surveyors.

## Level Party

2-13. The level party establishes benchmarks and determines the elevation of selected points along the route to provide control for future surveys, such as the preparation of a topographic map or profile and cross-section leveling. The level party takes rod readings and records elevations to the nearest 0.01 foot or 0.001 meter. It sets the benchmarks in a place well out of the area of construction and marks them in such a way that they will remain in place throughout the whole project.

2-14. If there is no established vertical control point available, establish an arbitrary elevation that may be tied to a vertical control point later. An assigned value for an arbitrary elevation must be large enough to avoid negative elevations at any point on the project.

## Topographic Party

2-15. The topographic party secures enough relief and planimetric detail within the prescribed area to locate any obstacles and allow preparation of rough profiles and cross sections. Computations made from the data determine the final location. The instruments and personnel combinations used vary with survey purpose, terrain, and available time. A transit-stadia party, plane table party, or combination of both may be used.

## Transit-Stadia Party

2-16. The transit-stadia party is effective in open country where comparatively long, clear sights can be obtained without excessive brush cutting.

## Plane Table Party

2-17. The plane table party is used where terrain is irregular. For short route surveys, the procedure is much the same as in the transit-stadia method, except that the fieldwork and the drawing of the map are carried on simultaneously.

## Section Iii - Final Location Survey Preparation And Scope

2-18. Prior to the final location survey, office studies consisting of the preparation of a map from preliminary survey data, projection of a tentative alignment and profile, and preliminary estimates of quantities and costs are made and used as guidance for the final location phase. The instrument party carefully establishes the final location in the field using the paper location prepared from the preliminary survey. The surveyor should not make any changes without the authority of the officer-in-charge.

## Running The Centerline

2-19. The centerline may vary from the paper due to objects or conditions that were location not previously considered. The final center line determines all the construction lines. The surveyor marks the stations, runs the levels, and sets the grades.

2-20. The centerline starts at station 0+00. The surveyor numbers the stations consecutively and sets them at the full 100-foot or 30-meter stations. The surveyor also sets stakes at important points along the centerline. These may be culvert locations, road intersections, beginnings and ends of curves, or breaks in the grade. When measurements are made in feet, these stations are numbered from the last full station
(+00). They are called plus stations. A station numbered 4+44.75 would be 44.75 feet away from station
4+00 and 444.75 feet from the beginning of the project.

2-21. When using the metric system, the total distance from the beginning of the project would be 135.56
meters and would be numbered 135.56.

## Reference Stakes

2-22. Referencing of stations is described in TM 5-232. The control points established by the location survey determine the construction layout. Therefore, these points must be carefully referenced. The surveyor should set the control point references far enough from the construction to avoid disturbance.

## Profile And Cross Sections

2-23. After the centerline of the road, including the horizontal curves, has been staked, the next step in the road layout is the determination of elevations along the centerline and laterally across the road. The surveyor performs these operations, known as profile leveling and cross-section leveling, as separate operations but at the same time as the elevation of points along a centerline or other fixed lines.

2-24. The interval usually coincides with the station interval, but shorter intervals may be necessary due to abrupt changes in terrain. The plotting of centerline elevations is known as a profile. From this profile, the design engineer determines the grade of the road.

2-25. The cross-section elevations make it possible to plot views of the road across the road at right angles.

These plotted cross sections determine the volume of earthwork to be moved. The surveyor establishes the cross-section lines at regular stations, at any plus station, and at intermediate breaks in the ground and lays out the short crosslines by eye and long crosslines at a 90-degree angle to the centerline with an instrument.

2-26. All elevations at abrupt changes or breaks in the ground are measured with a rod and level, and distances from the centerline are measured with a tape. In rough country, the surveyor uses the hand level to obtain cross sections if the centerline elevations have been determined using the engineer level.

## Section Iv - Construction Layout Survey Preparation And Scope

2-27. The construction layout is an instrument survey. It provides the alignment, grades, and locations which guide the construction operations. The construction operations include clearing, grubbing, stripping, drainage, rough grading, finish grading, and surfacing. The command must keep the surveyors sufficiently ahead of the construction activity in both time and distance to guarantee uninterrupted progress of the construction effort. Note the following suggested distances.


Keep centerline established 1,500 feet or 450 meters ahead of clearing and grubbing.

Keep rough grade established and slope stakes set 1,000 feet or 300 meters ahead of stripping
and rough grading.

Set stakes to exact grade, 500 feet or 150 meters ahead of finish grading and surfacing.

## Alignment

2-28. The surveyor must place the alignment markers ahead of the crews engaged in the various phases of construction. The surveyor may do a hasty alignment, marked by flags and rods, suitable for guiding the clearing and grubbing operations. However, a deliberate location of the centerline is necessary for the final grading and surfacing operations.

2-29. The surveyor marks the curves and minor structures concurrently with the layout of the centerline.

Major structures such as tunnels and bridges involve a site survey. The general demarcation of the site boundaries is carried on with the establishment of the route alignment. The layout of the site proper is a separate survey.

## Setting Grade Stakes

2-30. Grade stakes indicate the exact grade elevation to the construction force. The surveyor consults the construction plans to determine the exact elevation of the subgrade and the distance from the centerline to the edges of the shoulder.

## Preliminary Subgrade Stakes

2-31. The surveyor sets preliminary subgrade stakes on the centerline and other grade lines, as required.

First, the surveyor determines the amount of cut or fill required at the centerline station. The amount of cut or fill is equal to the grade rod minus the ground rod. The grade rod is equal to the height of instrument minus the subgrade elevation at the station. The ground rod is the foresight reading at the station. If the result of this computation is a positive value, it indicates the amount of cut required. If it is negative, it indicates the amount of fill.

2-32. For example, given a height of instrument (HI) of 115.5 feet, a subgrade elevation of 108.6 feet, and a ground rod reading of 3.1 feet, the grade rod = 115.5 feet -108.6 = +6.9 and cut or fill = 6.9 -3.1 = +3.8, indicating a cut of 3.8 feet. The surveyor records the result in the field notes and on the back of the grade stake as C38 (figure 2-1, page 2-6, example a).

2-33. Sometimes, it is necessary to mark stakes to the nearest whole or half foot to assist the earthmoving crew. In the example given, the surveyor would measure up 0.2 foot on the stake and mark it as in figure 2-1, example b. If at this stake a fill of 3.8 feet was required, the surveyor would measure up 0.3 foot and mark the stake as in figure 2-1, example c. Figure 2-1, example d, shows a case where the actual subgrade alignment could be marked on the stake. The number under the cut or fill represents the distance the stake is from the road centerline. The surveyor normally makes rod readings and computations to the nearest 0.1 foot or 0.01 meter.

2-34. During rough grading operations, the construction crew determines the grades for the edges of the traveled way, roadbed, and ditch lines. However, if the road is to be superelevated or is in rough terrain, the survey crew must provide stakes for all grade lines. These would include the centerline, the edge of the traveled way, the edges of the roadbed, and possibly, the centerline of the ditches. The surveyor sets those stakes by measuring the appropriate distance off the centerline and determines the amount of cut or fill as outlined. The surveyor offsets the stakes along the traveled way, roadbed, and ditches to avoid their being destroyed during grading operations. The construction foreman, not the surveyor, makes the decision as to how many and where grade stakes are required.

## Final Grade Stakes

2-35. Once the rough grading is completed, the surveyor sets the final grade stakes (blue tops). The elevation of the final grade is determined and the value of the grade rod reading is computed. The surveyor uses a rod target to set the grade rod reading on the rod. The rod is held on the top of the stake. The stake is driven into the ground until the horizontal crosshair bisects the target and the top of the stake is at final grade. The surveyor marks the top of the stake with a blue lumber crayon to distinguish it from other stakes.

2-36. The surveyor should provide blue tops on all grade lines. However, the final decision as to what stakes are required lies with the construction foreman. To set final grade, the surveyor normally makes rod readings and computations to 0.01 foot or 0.001 meter.

## Special Cases

2-37. Where grade stakes cannot be driven, as in hard coral or rock areas, the surveyor must use ingenuity to set and preserve grade markings under existing conditions. Often, such markings are made on the rock itself with a chisel or a lumber crayon.

## Setting Slope Stakes

2-38. Slope stakes indicate the intersection of cut or fill slopes with the natural groundline. They indicate the earthwork limits on each side of the centerline.

## Level Section

2-39. When the ground is level transversely to the centerline of the road, the cut or fill at the slope stake will be the same as at the center, except for the addition of the crown. On fill sections, the distance from the center stake to the slope stake is determined by multiplying the center cut by the ratio of the slope (for example, horizontal distance to vertical distance) of the side slopes and adding one half the width of the roadbed. On cut sections, the surveyor can find the distance from the center stake to the slope stake by multiplying the ratio of slope by the center cut and adding the distance from the centerline to the outside edge of the ditch.

2-40. In either case, if the ground is level, the slope stake on the right side of the road will be the same distance from the centerline as the one on the left side of the road. On superelevated sections, the surveyor must add the widening factor to determine the distance from the centerline to the slope stake. This is because the widening factor is not the same for both sides of the road, and the slope stakes will not be the same distance from the centerline.

## Transversely Sloping Ground

2-41. When the ground is not level transversely, the cut or fill will be different for various points depending upon their distance from the centerline. The surveyor must determine the point, on each side of the centerline, whose distance from the center is equal to the cut or fill at that point multiplied by the slope ratio and added to one half the roadbed width for fills, and the slope ratio multiplied by the distance from the centerline to the outside of the ditches for cuts.

2-42. A trial and error method must be used. The surveyor will soon attain proficiency in approximating the correct position of the slope stake, and the number of trials can generally be reduced to two or three.

The surveyor will mark the cut or fill on the slope stake and record it in the notebook as the numerator of a fraction whose denominator is the distance out from the centerline. Three-level, five-level, and irregular sections present this problem. Figures 2-2 through 2-5, pages 2-8 through 2-10, illustrate the procedure involved in setting slope stakes on sloping ground for three typical cases.

## Cut Section

2-43. The cut section in figure 2-2 has the level set up with an HI of 388.3 feet. The subgrade elevation at this centerline station is set at 372.5 feet for a 23-foot roadbed with 1.5:1 side slopes, 4-foot shoulders, and 7-foot ditches. The "grade rod" is the difference between these two elevations or 388.3 -372.5 = +15.8 feet. The rodman now holds the rod on the ground at the foot of the center grade stake and obtains a reading of 6.3 feet, a "ground rod." The recorder subtracts 6.3 from the grade rod of 15.8, which gives +9.5 feet or a center cut of 9.5 feet. On slope stakes, the cut or fill and the distance out from the centerline are written facing the center of the road. The backs of the slope stakes show the station and the slope ratio to be used.

2-44. The recorder estimates the trial distance by multiplying the cut at the centerline (9.5) by the slope ratio (1.5) and adding the distance from the centerline to the outside edge of the ditch (22.5).

2-45. The rodman now moves to the right at right angles to the centerline the trial distance (36.8 feet). The rod is held at A and a reading of 9.1 is obtained, which, when subtracted from the grade rod of 15.8, gives a cut of 6.7 feet. The recorder then computes what the distance from the centerline to A should be. This is done by multiplying the cut of 6.7 by the slope ratio and adding one half the roadbed width, which gives 32.6 feet.

2-46. However, the distance to A was measured as 36.8 feet instead of 32.6, so the position at A is too far from the centerline. Another trial is made by moving the rod to 32.6 feet from the centerline (B), where a reading of 8.9 is made. The cut at B is now 15.8- 8.9= +6.9, and the calculated distance from the center is 6.9 x 1.5 + 22.5 = 32.8 feet. The distance actually measured is 32.8 feet. Therefore, B is the correct location of the slope stake and is marked C69. Since moving the rod one or two tenths of a foot would not materially change its reading, greater accuracy is unnecessary. After a few trials, the rodman locates the slope stake on the left in a similar manner. The instrumentman verifies the figures by computation. When placed in the ground, the stakes will appear as in figure 2-3.


## Fill Section (Hi Above Grade Elevation)

2-47. Figure 2-4 illustrates a fill with the HI of the level set up above the subgrade elevation of the 31-foot roadbed. In this case, the grade rod will always be less, numerically, than rod readings on the ground. The grade rod in this problem is +2.8; the rod reading at the center stake is 6.5; and the difference is 2.8-6.5=
 -3.7 feet. The minus sign indicates a center fill. The rodman finds the positions of the slope stakes by trial, as previously explained.

## Fill Section (Hi Below Grade Elevation)

2-48. Figure 2-5, page 2-10, illustrates a fill with the HI of the level below the grade elevation of the future roadbed. Therefore, the grade rod has a negative value. Adding the negative ground rod to the negative grade rod will give a greater negative value for the fill. For example, at the center stake, the fill equals (-2.40 meters) + (-2.35 meters) or -4.75 meters. Otherwise, this case is similar to the preceding ones.

## Culvert Location

2-49. To establish the layout of a site such as a culvert, the surveyor locates the intersection of the roadway centerline and a line defining the direction of the culvert. Generally, culverts are designed to conform with natural drainage lines. The surveyor places stakes to mark the inlet and outlet points, and any cut or fill, if needed, is marked on them. The construction plans for the site are carefully followed, and the alignment and grade stakes are set on the centerlines beyond the work area. Thus, any line stake which is disturbed or destroyed during the work can be replaced easily.

2-50. The surveyor should also set a benchmark near the site, but outside of the work area, to reestablish grades. Figure 2-6 shows a typical layout for a culvert site. Circumstances or practical considerations may dictate that certain types of surveys will be eliminated or combined. For example, the location and construction surveys may be run simultaneously. (Refer to TM 5-330.)

## Drainage

2-51. The construction of drainage facilities is an important part of any project. The surveyor must anticipate drainage problems and gather enough field data to indicate the best design and location for needed drainage structures. (Refer to TM 5-330.)
2-52. The problem of adequate drainage is important to the location, design, and construction of almost any type of military installation. Proper drainage is of primary importance with respect to the operational requirements and the desired useful life of an installation. Inadequate drainage causes most road and airfield failures. The surveyor must see that these and similar facilities are well drained to function efficiently during inclement weather. Temporary drainage during construction operations cannot be ignored since it is vital to prevent construction delays due to standing water or saturated working areas.

2-53. Proper drainage is an essential part of road construction. Poor drainage results in mud, washouts, and heaves, all of which are expensive in terms of delays and repairs to both roads and vehicles.

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## Chapter 3 Curves Section I - Simple Horizontal Curves Curve Points

3-1. By studying TM 5-232, the surveyor learns to locate points using angles and distances. In construction surveying, the surveyor must often establish the line of a curve for road layout or some other construction.

3-2. The surveyor can establish curves of short radius, usually less than one tape length, by holding one end of the tape at the center of the circle and swinging the tape in an arc, marking as many points as desired.

3-3. As the radius and length of curve increases, the tape becomes impractical, and the surveyor must use other methods. Measured angles and straight line distances are usually picked to locate selected points, known as stations, on the circumference of the arc.

## Types Of Horizontal Curves

3-4. A curve may be simple, compound, reverse, or spiral (figure 3-1). Compound and reverse curves are treated as a combination of two or more simple curves, whereas the spiral curve is based on a varying radius.

## Simple

3-5. The simple curve is an arc of a circle. It is the most commonly used. The radius of the circle determines the "sharpness" or "flatness" of the curve. The larger the radius, the "flatter" the curve.

## Compound

3-6. Surveyors often have to use a compound curve because of the terrain. This curve normally consists of two simple curves curving in the same direction and joined together.

## Reverse

3-7. A reverse curve consists of two simple curves joined together but curving in opposite directions. For safety reasons, the surveyor should not use this curve unless absolutely necessary.

## Spiral

3-8. The spiral is a curve with varying radius used on railroads and some modern highways. It provides a transition from the tangent to a simple curve or between simple curves in a compound curve.

## Stationing

3-9. On route surveys, the surveyor numbers the stations forward from the beginning of the project. For example, 0+00 indicates the beginning of the project. The 15+52.96 would indicate a point 1,552,96 feet from the beginning. A full station is 100 feet or 30 meters, making 15+00 and 16+00 full stations. A plus station indicates a point between full stations. (15+52.96 is a plus station.) When using the metric system, the surveyor does not use the plus system of numbering stations. The station number simply becomes the distance from the beginning of the project.

## Elements Of A Simple Curve

3-10. Figure 3-2 shows the elements of a simple curve. They are described as follows, and their abbreviations are given in parentheses.

## Point Of Intersection (Pi)

3-11. The point of intersection marks the point where the back and forward tangents intersect. The surveyor indicates it one of the stations on the preliminary traverse.

## Intersecting Angle (I)

3-12. The intersecting angle is the deflection angle at the PI. The surveyor either computes its value from the preliminary traverse station angles or measures it in the field.

## Radius (R)

3-13. The radius is the radius of the circle of which the curve is an arc.

## Point Of Curvature (Pc)

3-14. The point of curvature is the point where the circular curve begins. The back tangent is tangent to the curve at this point.

## Point Of Tangency (Pt)

3-15. The point of tangency is the end of the curve. The forward tangent is tangent to the curve at this point.

## Length Of Curve (L)

3-16. The length of curve is the distance from the PC to the PT measured along the curve.

## Tangent Distance (T)

3-17. The tangent distance is the distance along the tangents from the PI to the PC or PT. These distances are equal on a simple curve.

## Central Angle ()

3-18. The central angle is the angle formed by two radii drawn from the center of the circle (O) to the PC
and PT. The central angle is equal in value to the I angle.

## Long Chord (Lc)

3-19. The long chord is the chord from the PC to the PT.

## External Distance (E)

3-20. The external distance is the distance from the PI to the midpoint of the curve. The external distance bisects the interior angle at the PI.

## Middle Ordinate (M)

3-21. The middle ordinate is the distance from the midpoint of the curve to the midpoint of the long chord.

The extension of the middle ordinate bisects the central angle.

## Degree Of Curve (D)

3-22. The degree of curve defines the "sharpness" or "flatness" of the curve (figure 3-3). There are two definitions commonly in use for degree of curve, the arc definition and the chord definition.

## Arc Definition

3-23. The arc definition states that the degree of curve (D) is the angle formed by two radii drawn from the center of the circle (point O, figure 3-3) to the ends of an arc 100 feet or 30.48 meters long. In this definition, the degree of curve and radius are inversely proportional using the following formula:

\begin{tabular}{l l} \hline Degree of curve & Length of Arc \\ \hline
360${}^{\text{e}}$ & Circumference \\ Circumference & $=2$$\pi$$\pi$$\pi$$\pi$ \\ \hline \end{tabular}

3-24. As the degree of curve increases, the radius decreases. It should be noted that for a given intersecting angle or central angle, when using the arc definition, all the elements of the curve are inversely proportioned to the degree of curve. This definition is primarily used by civilian engineers in highway construction.

3-25. *English system.* Substituting D = 1 and length of arc = 100 feet, we obtain

1 360  100 2R = 1 360:  100 6.283185308 R
Therefore,

R =  36,000 divided by 6.283185308  R =  5,729.58 ft
3-26. *Metric system*. In the metric system, using a 30.48-meter length of arc and substituting D = 1, we obtain

1 360  30.48 2R = 1 360:  30.48 6.283185308 R
Therefore,

* [10] R = 10,972.8 _divided by 6.283185308_

## Chord Definition

3-27. The chord definition states that the degree of curve is the angle formed by two radii drawn from the center of the circle (point O, figure 3-3, page 3-5) to the ends of a chord 100 feet or 30.48 meters long. The radius is computed by the following formula:

R = 50 ft Sin 12 D or 15.24 m Sin 12 D
3-28. The radius and the degree of curve are not inversely proportional even though, as in the arc definition, the larger the degree of curve the "sharper" the curve and the shorter the radius. The chord definition is used primarily on railroads in civilian practice and for both roads and railroads by the military.

3-29. *English system*. Substituting D = 1 and given Sin 12 1 = 0.0087265355.

R = 50 ft Sin 12 D or  50 0.0087265355  R =  5,729.65 ft
3-30. *Metric system*. Using a chord 30.48 meters long, the surveyor computes R by the formula

R =  15.24 m 0.0087265355
3-31. Substituting D = 1 and given Sin 12 1 = 0.0087265335, solve for R as follows:

R =  15.24 0.0087265355  R =  1,746.40 m

## Chords

3-32. On curves with long radii, it is impractical to stake the curve by locating the center of the circle and swinging the arc with a tape. The surveyor lays these curves out by staking the ends of a series of chords
(figure 3-4). Since the ends of the chords lie on the circumference of the curve, the surveyor defines the arc in the field. The length of the chords varies with the degree of curve. To reduce the discrepancy between the arc distance and chord distance, the surveyor uses the following chord lengths:


Degree of
Curve
Radius
Feet
Radius
Meters
Chord
Feet
Length
meters
from
1 - 3
5,730 - 1,910
1,745 - 585
100
30

3 - 8
 1,910 - 720
 585 - 220
50
15

8 - 16
 720 - 360
 220 - 110
25
7.5
over
16
 360 - 150
 110 - 45
10
3

3-33. The chord lengths above are the maximum distances in which the discrepancy between the arc length and chord length will fall within the allowable error for taping, which is 0.02 foot per 100 feet on most construction surveys. Depending upon the terrain and the needs of the project foremen, the surveyor may stake out the curve with shorter or longer chords than recommended.



## Deflection Angles

3-34. The deflection angles are the angles between a tangent and the ends of the chords from the PC. The surveyor uses them to locate the direction in which the chords are to be laid out. The total of the deflection angles is always equal to one half of the I angle. This total serves as a check on the computed deflection angles.

## Simple Curve Formulas

3-35. The following formulas are used in the computation of a simple curve. All of the formulas, except those noted, apply to both the arc and chord definitions.

\begin{tabular}{c c c} $R$ = & $\frac{5729.58\,ft}{D}$ & $\frac{1746.38\,m}{D}$ ($arc$$definition$) \\ $D$ = & $\frac{5729.58\,ft}{D}$ & $\frac{1746.38\,m}{R}$ ($arc$$definition$) \\ $R$ = & $\frac{50\,ft}{Sin\,\,4_{2}\,D}$ & $\frac{15.24\,m}{Sin\,\,4_{2}\,D}$ ($chord$$definition$) \\ \end{tabular}

 \(\begin{array}{c}\mbox{Sin }\nu_{2}\,D=\frac{50\,ft}{R}\mbox{ or }Sin \nu_{2}\,D=\frac{15.24\,m}{R}\mbox{ (}chord\mbox{ }definition)\\ \\ T=\,R\mbox{ (}Tan\,1\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!
3-36. L is the distance around the arc for the arc definition, or the distance along the chords for the chord definition.

$PC=PI=T$

$PT=PC+L$

$E=R$$\left(\frac{1}{\cos\,\nu_{2}\,I}=1\right)$or $E=T(Tan\,\nu_{4}\,I)$

$M=R$$(1=\,cos\,\nu_{2}\,I)$

$LC=2$$R$$(Sin\,\nu_{2}\,I)$
3-37. In the following formulas, C equals the chord length and d equals the deflection angle. All the formulas are exact for the arc definition and approximate for the chord definition.

$d=(2)(100\,\mathrm{f})$$\mathrm{ord}=(2)(30.48\,\mathrm{m})$
3-38. This formula gives an answer in degrees.

$d=0.3(c)(d)$in the English system $or$

(0.3 x D)(C)

.3048
3-39. In the metric system. The answer will be in minutes.

## Solution Of A Simple Curve

3-40. To solve a simple curve, the surveyor must know three elements. The first two are the PI station value and the I angle. The third is the degree of curve, which is given in the project specifications or computed using one of the elements limited by the terrain (see section II). The surveyor normally determines the PI and I angle on the preliminary traverse for the road. This may also be done by triangulation when the PI is inaccessible.

## Chord Definition

3-41. The six-place natural trigonometric functions from table A-1, pages A-2 through A-91, were used in the example. When a calculator is used to obtain the trigonometric functions, the results may vary slightly. Assume that the following is known: PI = 18+00, I = 45, and D = 15.


Chord Definition (Feet)

$$R=\frac{50\,ft}{Sin\,\nu_{2}\,D}\,or\,\frac{50}{0.130526}=383.07\,ft$$

$$T\,=\,R\,(Tan\,\nu_{2}\,I)\,=\,383.07\,x\,0.414214\,=\,158.67\,ft$$

$$L=\,\left(\frac{I}{D}\right)100\,ft\,or\,L=\frac{45}{15}\,x\,100=300.00\,ft$$

$PC\,=\,PI-T=1,800-158.67=1,641.33\,or\,\,station\,16+41.33$
Chord Definition (Feet)

\[R=\frac{50\,ft}{Sin\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\

## Chords

3-42. Since the degree of curve is 15 degrees, the chord length is 25 feet. The surveyor customarily places the first stake after the PC at a plus station divisible by the chord length. The surveyor stakes the centerline of the road at intervals of 10, 25, 50 or 100 feet between curves. Thus, the level party is not confused when profile levels are run on the centerline. The first stake after the PC for this curve will be at station 16+50. Therefore, the first chord length or subchord is 8.67 feet. Similarly, there will be a subchord at the end of the curve from station 19+25 to the PT. This subchord will be 16.33 feet. The surveyor designates the subchord at the beginning, C1, and at the end, C2 (figure 3-2, page 3-3).

## Deflection Angles

3-43. After the subchords have been determined, the surveyor computes the deflection angles using the formulas above. Technically, the formulas for the arc definitions are not exact for the chord definition. However, when a one-minute instrument is used to stake the curve, the surveyor may use them for either definition. The deflection angles are

$d\ =\ 0.3^{\prime}$$\ CD$

$d_{std}\ =\ 0.3\,x\,25\,x\,15^{\circ}\ =\ 112.5^{\prime}\ or\ 1^{\circ}\,52.5^{\prime}$

$d_{1}\ =\ 0.3\,x\,8.67\,x\ 15^{\circ}\ =\ 0^{\circ}\ 39.015^{\prime}$

$d_{2}\ =\ 0.3\,x\ 16.33\,x\ 15^{\circ}\ =\ 73.485^{\prime}\ or\ 1^{\circ}\,13.485^{\prime}$
3-44. The number of full chords is computed by subtracting the first plus station divisible by the chord length from the last plus station divisible by the chord length and dividing the difference by the standard (std) chord length. Thus, we have (19+25 - 16+50)  25 equals 11 full chords. Since there are 11 chords of 25 feet, the sum of the deflection angles for 25-foot chords is 11 x 1 52.5' = 20 37.5'.

3-45. The sum of d${}_{1}$, d${}_{2}$, and the deflections for the full chords is--

$\rm d_{1}=0^{\circ}$ 39.015'

$\rm d_{2}=1^{\circ}$ 13.485'

$\rm d_{std}=20^{\circ}$ 37.500'

Total 22${}^{\circ}$ 30.000'
3-46. The surveyor should note that the total of the deflection angles is equal to one half of the I angle. If the total deflection does not equal one half of I, a mistake has been made in the calculations. After the total deflection has been decided, the surveyor determines the angles for each station on the curve. In this step, they are rounded off to the smallest reading of the instrument to be used in the field. For this problem, the surveyor must assume that a one-minute instrument is to be used. The curve station deflection angles are listed on page 3-10.

STATION
CHORD LENGTH
DEFLECTION ANGLES

PC 16+41.33
+50
C18.67
d1 0 39.015' or 0 39'
dstd + 1 52.500'
+75
Cstd25
2 31.515' or 2 32'
+ 1 52.500'
17+00
25
4 24.015' or 4 24'
+ 1 52.500'
+25
25
6 16.515' or 6 17'
+ 1 52.500'
+50
25
8 9.015' or 8 09'
+ 1 52.500'
+75
25
10 1.515' or 10 02'
+ 1 52.500'
18+00
25
11 54.015' or 11 54'
+ 1 52.500'
+25
25
13 46.515' or 13 47'
+ 1 52.500'
+50
25
15 39.015' or 15 39'
+ 1 52.500'
+75
25
17 31.515' or 17 32'
+ 1 52.500'
19+00
25
19 24.015' or 19 24'
+ 1 52.500'
+25
25
21 26.015' or 21 27'
d2 + 1 13.485'
PT 19+41.33
C216.33
22 30.000' or 22 30'

## Special Cases

3-47. The curve that was just solved had an I angle and degree of curve whose values were whole degrees.

When the I angle and degree of curve consist of degrees and minutes, the procedure in solving the curve does not change, but the surveyor must take care in substituting these values into the formulas for length and deflection angles. For example, if I = 42 15' and D = 5 37', the surveyor must change the minutes in each angle to a decimal part of a degree, or D = 42.25000, I = 5.61667. To obtain the required accuracy, the surveyor should convert values to five decimal places.

3-48. An alternate method for computing the length is to convert the I angle and degree of curve to minutes; thus, 42 15' = 2,535 minutes and 5 37' = 337 minutes. Substituting into the length formula gives

L = 2,535 337  x 100 = 752.23 feet.
3-49. This method gives an exact result. If the surveyor converts the minutes to a decimal part of a degree to the nearest five places, the same result is obtained.

3-50. Since the total of the deflection angles should be one half of the I angle, a problem arises when the I
angle contains an odd number of minutes and the instrument used is a one-minute instrument. Since the surveyor normally stakes the PT prior to running the curve, the total deflection will be a check on the PT.

Therefore, the surveyor should compute to the nearest 0.5 degree. If the total deflection checks to the nearest minute in the field, it can be considered correct.

## Curve Tables

3-51. The surveyor can simplify the computation of simple curves by using tables. Table A-5, page A-110, lists long chords, middle ordinates, externals, and tangents for a 1-degree curve with a radius of 5,730 feet for various angles of intersection. Table A-6, page A-146, lists the tangent, external distance corrections (chord definition) for various angles of intersection and degrees of curve.

## Arc Definition

3-52. Since the degree of curve by arc definition is inversely proportional to the other functions of the curve, the values for a one-degree curve are divided by the degree of curve to obtain the element desired.

For example, table A-5 lists the tangent distance and external distance for an I angle of 75 degrees to be 4,396.7 feet and 1,492.5 feet, respectively. Dividing by 15 degrees, the degree of curve, the surveyor obtains a tangent distance of 293.11 feet and an external distance of 99.50 feet.

## Chord Definition

3-53. To convert these values to the chord definition, the surveyor uses the values in table A-5. From table A-6, a correction of 0.83 feet is obtained for the tangent distance and for the external distance, 0.29 feet.

3-54. The surveyor adds the corrections to the tangent distance and external distance obtained from table A-5. This gives a tangent distance of 293.94 feet and an external distance of 99.79 feet for the chord definition.

3-55. After the tangent and external distances are extracted from the tables, the surveyor computes the remainder of the curve.

## Comparison Of Arc And Chord Definitions

3-56. Misunderstandings occur between surveyors in the field concerning the arc and chord definitions. It must be remembered that one definition is no better than the other.

## Different Elements

3-57. Two different circles are involved in comparing two curves with the same degree of curve. The difference is that one is computed by the arc definition and the other by the chord definition. Since the two curves have different radii, the other elements are also different.

## 5,730-Foot Definition

3-58. Some engineers prefer to use a value of 5,730 feet for the radius of a 1-degree curve, and the arc definition formulas. When compared with the pure arc method using 5,729.58, the 5,730 method produces discrepancies of less than one part in 10,000 parts. This is much better than the accuracy of the measurements made in the field and is acceptable in all but the most extreme cases. Table A-5 is based on this definition.

## Curve Layout

3-59. The following is the procedure to lay out a curve using a one-minute instrument with a horizontal circle that reads to the right. The values are the same as those used to demonstrate the solution of a simple curve (above).

## Setting Pc And Pt

3-60. With the instrument at the PI, the instrumentman sights on the preceding PI and keeps the head tapeman on line while the tangent distance is measured. A stake is set on line and marked to show the PC
and its station value.

3-61. The instrumentman now points the instrument on the forward PI, and the tangent distance is measured to set and mark a stake for the PT.

## Laying Out Curve From Pc

3-62. The procedure for laying out a curve from the PC is described as follows. Note that the procedure varies depending on whether the road curves to the left or to the right.

## Road Curves To Right

3-63. The instrument is set up at the PC with the horizontal circle at 0 00' on the PI.


The angle to the PT is measured if the PT can be seen. This angle will equal one half of the I angle if the PC and PT are located properly.

Without touching the lower motion, the first deflection angle, d1 (0 39'), is set on the horizontal
circle. The instrumentman keeps the head tapeman on line while the first subchord distance, C1
(8.67 feet), is measured from the PC to set and mark station 16+50.

The instrumentman now sets the second deflection angle, d1 + dstd (2 32'), on the horizontal
circle. The tapemen measure the standard chord (25 feet) from the previously set station (16+50) while the instrument man keeps the head tapeman on line to set station 16+75.

The succeeding stations are staked out in the same manner. If the work is done correctly, the last
deflection angle will point on the PT, and the last distance will be the subchord length, C2 (16.33
feet), to the PT.

## Road Curves To Left

3-64. As in the procedures noted, the instrument occupies the PC and is set at 0 00' pointing on the PI.


The angle is measured to the PT, if possible, and subtracted from 360 degrees. The result will equal one half the I angle if the PC and PT are positioned properly.

The first deflection, d1 (0 39'), is subtracted from 360 degrees, and the remainder is set on the
horizontal circle. The first subchord, C1 (8.67 feet), is measured from the PC, and a stake is set
on line and marked for station 16+50.

The remaining stations are set by continuing to subtract their deflection angles from 360 degrees and setting the results on the horizontal circles. The chord distances are measured from the
previously set station.

The last station set before the PT should be C2 (16.33 feet from the PT), and its deflection should
equal the angle measured in (1) above plus the last deflection, d2 (1 14').

## Laying Out Curve From Intermediate Setup

3-65. When it is impossible to stake the entire curve from the PC, the surveyor must use an adaptation of the above procedure.


Stake out as many stations from the PC as possible.

Move the instrument forward to any station on the curve.

Pick another station already in place, and set the deflection angle for that station on the
horizontal circle. Sight that station with the instruments telescope in the reverse position.

Plunge the telescope, and set the remaining stations as if the instrument was set over the PC.

## Laying Out Curve From Pt

3-66. If a setup on the curve has been made and it is still impossible to set all the remaining stations due to some obstruction, the surveyor can "back in" the remainder of the curve from the PT. Although this procedure has been set up as a method to avoid obstructions, it is widely used for laying out curves. When using the "backing in method," the surveyor sets approximately one half the curve stations from the PC and the remainder from the PT. With this method, any error in the curve is in its center where it is less noticeable.

## Road Curves To Right

3-67. Occupy the PT, and sight the PI with one half of the I angle on the horizontal circle. The instrument is now oriented so that if the PC is sighted, the instrument will read 0 00'.

3-68. The remaining stations can be set by using their deflections and chord distances from the PC or in their reverse order from the PT.

## Road Curves To Left

3-69. Occupy the PT and sight the PI with 360 degrees minus one half of the I angle on the horizontal circle. The instrument should read 0 00' if the PC is sighted.

3-70. Set the remaining stations by using their deflections and chord distances as if computed from the PC
or by computing the deflections in reverse order from the PT.

## Chord Corrections

3-71. Frequently, the surveyor must lay out curves more precisely than is possible by using the chord lengths previously described.

3-72. To eliminate the discrepancy between chord and arc lengths, the chords must be corrected using the values taken from the nomography in table A-11, page A-166. This gives the corrections to be applied if the curve was computed by the arc definition.

3-73. Table A-10, page A-165, gives the corrections to be applied if the curve was computed by the chord definition. The surveyor should recall that the length of a curve computed by the chord definition was the length along the chords. Figure 3-5 illustrates the example given in table A-9, page A-160. The chord distance from station 18+00 to station 19+00 is 100 feet. The nominal length of the subchords is 50 feet.

## Intermediate Stake

3-74. If the surveyor desires to place a stake at station 18+50, a correction must be applied to the chords, since the distance from 18+00 through 18+50 to 19+00 is greater than the chord from 18+00 to 19+00. Therefore, a correction must be applied to the subchords to keep station 19+00 100 feet from 18+00. In figure 3-5, if the chord length is nominally 50 feet, then the correction is 0.19 feet. The chord distance from 18+00 to 18+50 and 18+50 to 19+00 would be 50.19.

## Section Ii - Obstacles To Curve Location Terrain Restrictions

3-75. To solve a simple curve, the surveyor must know three parts. Normally, these will be the PI, I angle, and degree of curve. Sometimes, however, the terrain features limit the size of various elements of the curve. If this happens, the surveyor must determine the degree of curve from the limiting factor.

## Inaccessible Pi

3-76. Under certain conditions, it may be impossible or impractical to occupy the PI. In this case, the surveyor locates the curve elements by using the following steps (figure 3-6).


Mark two intervisible points A and B, one on each of the tangents, so that line AB (a random line connecting the tangents) will clear the obstruction.

Measure angles a and b by setting up at both A and B.

Measure the distance AB.

Compute inaccessible distances AV and BV as follows:
I = a + b  K = 180  I  AV = AB Sin b Sin K   BV = AB Sin b Sin K   PI = Sta A + AV

Determine the tangent distance from the PI to the PC on the basis of the degree of curve or other given limiting factor.

Locate the PC at a distance T minus AV from the point A and the PT at distance T minus BV
from point B.

Proceed with the curve computation and layout.

## Inaccessible Pc

3-77. When the PC is inaccessible, as illustrated in figure 3-7, page 3-16, and both the PI and PT are set and readily accessible, the surveyor must establish the location of an offset station at the PC.


Place the instrument on the PT and back the curve in as far as possible.

Select one of the stations (for example, "P") on the curve, so that a line PQ, parallel to the tangent line AV, will clear the obstacle at the PC.

Compute and record the length of line PW so that point W is on the tangent line AV and line PW is perpendicular to the tangent. The length of line PW = R (1 - Cos dp), where dp is that portion
of the central angle subtended by AP and equal to two times the deflection angle of P.

Establish point W on the tangent line by setting the instrument at the PI and laying off angle V (V = 180 - I). This sights the instrument along the tangent AV. Swing a tape using the computed length of line PW and the line of sight to set point W.

Measure and record the length of line VW along the tangent.

Place the instrument at point P. Backsight point W and lay off a 90-degree angle to sight along
line PQ, parallel to AV.

Measure along this line of sight to a point Q beyond the obstacle. Set point Q, and record the distance PQ.

Place the instrument at point Q, backsight P, and lay off a 90-degree angle to sight along line
QS. Measure, along this line of sight, a distance QS equals PW, and set point S. Note that the station number of point S = PI - (line VW + line PQ).

Set an offset PC at point Y by measuring from point Q toward point P a distance equal to the
station of the PC minus station S. To set the PC after the obstacle has been removed, place the instrument at point Y, backsight point Q, lay off a 90-degree angle and a distance from Y to the PC equal to line PW and QS. Carefully set reference points for points Q, S, Y, and W to insure
points are available to set the PC after clearing and construction have begun.

## Inaccessible Pt

3-78. When the PT is inaccessible, as illustrated in figure 3-8, and both the PI and PC are readily accessible, the surveyor must establish an offset station at the PT using the method for inaccessible PC with the following exceptions.


Letter the curve so that point A is at the PT instead of the PC (see figure 3-8).

Lay the curve in as far as possible from the PC instead of the PT.

Angle dp is the angle at the center of the curve between point P and the PT, which is equal to two
times the difference between the deflection at P and one half of I. Follow the steps for inaccessible PC to set lines PQ and QS. Note that the station at point S equals the computed station value of PT plus YQ.

Use station S to number the stations of the alignment ahead.

## Obstacle On Curve

3-79. Some curves have obstacles large enough to interfere with the line of sight and taping. Normally, only a few stations are affected. The surveyor should not waste too much time on preliminary work. Figure 3-9, page 3-18, illustrates a method of bypassing an obstacle on a curve.


Set the instrument over the PC with the horizontal circle at 000', and sight on the PI.

Check I/2 from the PI to the PT, if possible.

Set as many stations on the curve as possible before the obstacle, point b.

Set the instrument over the PT with the plates at the value of I/2. Sight on the PI.

Back in as many stations as possible beyond the obstacle, point e.

After the obstacle is removed, the obstructed stations c and d can be set.


## Curve Through Fixed Point

3-80. Because of topographic features or other obstacles, the surveyor may find it necessary to determine the radius of a curve which will pass through or avoid a fixed point and connect two given tangents. This may be accomplished as follows (figure 3-10):


Given the PI and the I angle from the preliminary traverse, place the instrument on the PI and
measure angle d, so that angle d is the angle between the fixed point and the tangent line that lies on the same side of the curve as the fixed point.

Measure line y, the distance from the PI to the fixed point.

Compute angles c, b, and a in triangle COP.
c =  90  (d +  I/2)

To find angle b, first solve for angle e
Sin e = Sin c Cos I/2  Angle b =  180   angle e  a =  180  (b +  c)

Compute the radius of the desired curve using the formula
R = y Sin c Sin a

Compute the degree of curve to *five decimal places*, using the following formulas:
(_arc method_) $D=5$,729.58 $ft/R$

$D=1$,746.385 $meters/R$

(_chord method_) $Sin\ D=2$ (50 $feet/R$)

$Sin\ D=2$ (15.24 $meters/R$)

Compute the remaining elements of the curve and the deflection angles, and stake the curve.

## Limiting Factors

    3-81. In some cases, the surveyor may have to use elements other than the radius as the limiting factor in
    determining the size of the curve. These are usually the tangent T, external E, or middle ordinate M. When
    any limiting factor is given, it will usually be presented in the form of T equals some value x, T
                                                                                                   x or T
    x. In any case, the first step is to determine the radius using one of the following formulas:


Given: Tangent; then R = T/(Tan 12I)
        External; then R =
        E/[(1/Cos 12I) - 1]
        Middle Ordinate; then R =
        M/(1 - Cos 12I)

3-82. The surveyor next determines D. If the limiting factor is presented in the form T equals some value x,
the surveyor must compute D, hold to five decimal places, and compute the remainder of the curve. If the
limiting factor is presented as
                               , then D is rounded down to the nearest 12 degree. For example, if E
                                                                                                     50
feet, the surveyor would round down to the nearest 12 degree, recompute E, and compute the rest of the
curve data using the rounded value of D, The new value of E will be equal to or greater than 50 feet.

3-83. If the limiting factor is
                               , the D is rounded up to the nearest 12 degree. For example, if M
                                                                                                45 feet,
then D would be rounded up to the nearest 12 degree, M would be recomputed, and the rest of the curve
data computed using the rounded value of D. The new value of M will be equal to or less than 45 feet.

3-84. The surveyor may also use the values from table B-5 to compute the value of D. This is done by dividing the tabulated value of tangent, external, or middle ordinate for a 1-degree curve by the given value of the limiting factor. For example, given a limiting tangent T
45 feet and I = 20 20' , the T for a 1-
degree curve from table B-5 is 1,027.6 and D = 1,027.6/45.00 = 22.836. Rounded up to the nearest half degree, D = 23. Use this rounded value to recompute D, T and the rest of the curve data.

## Section Iii - Compound And Reverse Curves Compound Curves

3-85. A compound curve is two or more simple curves which have different centers, bend in the same direction, lie on the same side of their common tangent, and connect to form a continuous arc. The point where the two curves connect (namely, the point at which the PT of the first curve equals the PC of the second curve) is referred to as the point of compound curvature (PCC).

3-86. Since their tangent lengths vary, compound curves fit the topography much better than simple curves.

These curves easily adapt to mountainous terrain or areas cut by large, winding rivers. However, since compound curves are more hazardous than simple curves, they should never be used where a simple curve will do.

## Compound Curve Data

3-87. The computation of compound curves presents two basic problems. The first is where the compound curve is to be laid out between two successive PIs on the preliminary traverse. The second is where the curve is to be laid in between two successive tangents on the preliminary traverse. (See figure 3-11.)

## Compound Curve Between Successive Pis

3-88. The calculations and procedure for laying out a compound curve between successive PIs are outlined in the following steps. This procedure is illustrated in figure 3-11a.


Determine the PI of the first curve at point A from field data or previous computations.

Obtain I1, I2, and distance AB from the field data.

Determine the value of D1, the D for the first curve. This may be computed from a limiting
factor based on a scaled value from the road plan or furnished by the project engineer.

Compute R1, the radius of the first curve as shown above.

Compute T1, the tangent of the first curve.
T = R (Tan 12 I)

Compute T2, the tangent of the second curve.
T = AB  T

Compute R2, the radius of the second curve.
R = T Tan 12 I

Compute D2 for the second curve. Since the tangent for the second curve must be held exact, the
value of D2 must be carried to five decimal places.

Compare D1 and D2. They should not differ by more than 3 degrees. If they vary by more than 3
degrees, the surveyor should consider changing the configuration of the curve.

If the two Ds are acceptable, then compute the remaining data and deflection angles for the first curve.

Compute the PI of the second curve. Since the PCC is at the same station as the PT of the first
curve, then PI2 = PT1 + T2.

Compute the remaining data and deflection angles for the second curve, and lay in the curves.

## Compound Curve Between Successive Tangents

3-89. The following steps explain the laying out of a compound curve between successive tangents. This procedure is illustrated in figure 3-11b, page 3-21.


Determine the PI and I angle from the field data and/or previous computations.

Determine the value of I1 and distance AB. The surveyor may do this by field measurements or
by scaling the distance and angle from the plan and profile sheet.

Compute angle C.

**Figure Captions**

Compute I2.
I  =  180  (I +  C)

Compute line AC.
AC = AB Sin I Sin C

Compute line BC.
BC = AB Sin I Sin C

Compute the station of PI1.
PI  =  PI   AC

Determine D1 and compute R1 and T1 for the first curve as described above.

Compute T2 and R2 as described above.

Compute D2 according to the formulas above.

Compute the station at PC.
PC  =  PI - (AC + T)

Compute the remaining curve data and deflection angles for the first curve.

Compute PI2.
PI  = PT + T

Compute the remaining curve data and deflection angles for the second curve, and stake out the
curves.

## Staking Compound Curves

3-90. Care must be taken when staking a curve in the field. Two procedures for staking compound curves are described.

## Compound Curve Between Successive Pis

3-91. Stake the first curve as described above.

Verify the PCC and PT2 by placing the instrument on the PCC, sighting on PI2, and laying off
I2/2. The resulting line-of-sight should intercept PT2.

Stake the second curve in the same manner as the first.

## Compound Curve Between Successive Tangents

3-92. Place the instrument at the PI and sight along the back tangent.

Lay out a distance AC from the PI along the back tangent, and set PI1.

Continue along the back tangent from PI2 a distance T1, and set PC1.

Sight along the forward tangent with the instrument still at the PI.

Lay out a distance BC from the PI along the forward tangent, and set PI2.

Continue along the forward tangent from PI a distance T2, and set PT2.

Check the location of PI1 and PI2 by either measuring the distance between the two PIs and
comparing the measured distance to the computed length of line AB, or by placing the
instrument at PI1, sighting the PI, and laying off I1. The resulting line-of-sight should intercept
PI2.

Stake the curves as outlined above.

## Reverse Curves

3-93. A reverse curve is composed of two or more simple curves turning in opposite directions. Their points of intersection lie on opposite ends of a common tangent, and the PT of the first curve is coincident with the PC of the second. This point is called the point of reverse curvature (PRC).

3-94. Reverse curves are useful when laying out such things as pipelines, flumes, and levees. The surveyor may also use them on low-speed roads and railroads. They cannot be used on high-speed roads or railroads since they cannot be properly superelevated at the PRC. They are sometimes used on canals, but only with extreme caution, since they make the canal difficult to navigate and contribute to erosion.

## Reverse Curve Data

3-95. The computation of reverse curves presents three basic problems. The first is where the reverse curve is to be laid out between two successive PIs. (See figure 3-12, page 3-24) In this case, the surveyor performs the computations in exactly the same manner as a compound curve between successive PIs. The second is where the curve is to be laid out so it connects two parallel tangents (figure 3-13, page 3-25). The third problem is where the reverse curve is to be laid out so that it connects diverging tangents (figure 3-14, page 3-26).

## Connecting Parallel Tangents

3-96. Figure 3-13, page 3-25, illustrates a reverse curve connecting two parallel tangents. The PC and PT
are located as follows.


Measure p, the perpendicular distance between tangents.

Locate the PRC and measure m1 and m2. (If conditions permit, the PRC can be at the midpoint
between the two tangents. This will reduce computation, since both arcs will be identical.)

Determine R1.

Compute I1.
  Cos I = R  m R

Compute L1 from
L = R Sin I

R2, I2, and L2 are determined in the same way as R1, I1, and L1. If the PRC is to be the midpoint, the values for arc 2 will be the same as for arc 1.


Stake each of the arcs the same as a simple curve. If necessary, the surveyor can easily
determine other curve components. For example, the surveyor needs a reverse curve to connect
two parallel tangents. No obstructions exist so it can be made up of two equal arcs. The degree of curve for both must be 5. The surveyor measures the distance p and finds it to be 225.00 feet.
$m_{1}=m_{2}$$and$$L_{1}=L_{2}$

$R_{1}=R_{2}$$and$$l_{1}=l_{2}$

$R_{1}=\frac{50\,ft}{Sin\,l_{2}\,D}=\frac{50\,ft}{0.043619}=1_{,1}146.29\,ft$ $\begin{array}{c}\mbox{\it Cos}\;I_{1}=\frac{R_{1}\;-\;m_{1}}{R_{1}}=\frac{1, 033.79}{1,146.29}=0.901857\\ \\ \mbox{\it I}_{1}=25^{\circ}36^{\prime}\end{array}$

$\begin{array}{c}\mbox{\it L}_{1}=R_{1}\;Sin\;I_{1}=1,145.29\;x\;0.432086=495.30 \end{array}$

The PC and PT are located by measuring off L1 and L2.

## Connecting Diverging Tangents

3-97. The connection of two diverging tangents by a reverse curve is illustrated in figure 3-14. Due to possible obstruction or topographic consideration, one simple curve could not be used between the tangents. The PT has been moved back beyond the PI. However, the I angle still exists as in a simple curve.

The controlling dimensions in this curve are the distance Ts to locate the PT and the values of R1 and R2, which are computed from the specified degree of curve for each arc.


Measure I at the PI.

Measure Ts to locate the PT as the point where the curve is to join the forward tangent. In some
cases, the PT position will be specified, but Ts must still be measured for the computations.

Perform the following calculations:

Determine R1 and R2. If practical, have R1 equal R2.
$$\begin{array}{l}\mbox{\it Angle }s=180-(90+l\,)=90-l\\ \\ m=T_{s}\;(Tan\,l)\\ \\ L=T_{s}\,\frac{T_{s}}{Cos\,l}\\ \\ \mbox{\it angle }e\;=\;I_{1}\;(\mbox{\it by similar triangles})\\ \\ \mbox{\it angle }f\;=\;I_{1}\;(\mbox{\it by similar triangles})\end{array}$$
* therefore, $$\begin{array}{l}\mbox{\it}l_{2}=I+I_{1}\\ \\ n\;=\;(R_{2}\,-m)\,Sin\,e\\ \\ p=\;(R_{2}\,-m)\,Cos\,e\end{array}$$

Determine g by establishing the value of I1.
Cos I = R +  p R + R

Knowing Cos I1, determine Sin I1.

**Abstract**

We study the $\alpha$-function of the $\alpha$-

Measure TL from the PI to locate the PC.

Stake arc 1 to PRC from PC.

Set instrument at the PT and verify the PRC (invert the telescope, sight on PI, plunge, and turn
angle I2/2).

Stake arc 2 to the PRC from PT.
3-98. For example, in figure 3-14, a reverse curve is to connect two diverging tangents with both arcs having a 5-degree curve. The surveyor locates the PI and measures the I angle as 41 degrees. The PT
location is specified and the Ts is measured as 550 feet.

$R_{1}=R_{2}=\frac{50\,ft}{Sin\,\,\%\,D}=\frac{50\,ft}{0.043619}=1,$
Angle s = 90  I = 49

$$m=T_{s}\,Tan\,\,I=550\,\,x\,0.869287=478.11\,ft$$

\[L=\frac{T_{2}}{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,
3-99. The PC is located by measuring TL. The curve is staked using 5-degree curve computations.

## Section Iv - Transition Spirals Spiral Curves

3-100. In engineering construction, the surveyor often inserts a transition curve, also known as a spiral curve, between a circular curve and the tangent to that curve. The spiral is a curve of varying radius used to gradually increase the curvature of a road or railroad. Spiral curves are used primarily to reduce skidding and steering difficulties by gradual transition between straight-line and turning motion, and/or to provide a method for adequately superelevating curves.

3-101. The spiral curve is designed to provide for a gradual superelevation of the outer pavement edge of the road to counteract the centrifugal force of vehicles as they pass. The best spiral curve is one in which the superelevation increases uniformly with the length of the spiral from the TS or the point where the spiral curve leaves the tangent.

3-102. The curvature of a spiral must increase uniformly from its beginning to its end. At the beginning, where it leaves the tangent, its curvature is zero; at the end, where it joins the circular curve, it has the same degree of curvature as the circular curve it intercepts.

## Theory Of A.R.E.A. 10-Chord Spiral

3-103. The spiral of the American Railway Engineering Association, known as the A.R.E.A. spiral, retains nearly all the characteristics of the cubic spiral. In the cubic spiral, the lengths have been considered as measured along the spiral curve itself, but measurements in the field must be taken by chords. Recognizing this fact, in the A.R.E.A. spiral the length of spiral is measured by 10 equal chords, so that the theoretical curve is brought into harmony with field practice. This 10-chord spiral closely approximates the cubic spiral. Basically, the two curves coincide up to the point where = 15 degrees. The exact formulas for this A.R.E.A. 10-chord spiral, when does not exceed 45 degrees, are given below.

## Spiral Elements

3-104. Figures 3-15, page 3-30, and 3-16, page 3-31, show the notations applied to elements of a simple circular curve with spirals connecting it to the tangents.


TS = the point of change from tangent to spiral

SC = the point of change from spiral to circular curve

CS = the point of change from circular curve to spiral

ST = the point of change from spiral to tangent

SS = the point of change from one spiral to another (not shown in figure 3-15 or figure 3-16)
3-105. The symbols PC and PT, TS and ST, and SC and CS become transposed when the direction of stationing is changed.


a = the angle between the tangent at the TS and the chord from the TS to any point on the spiral

A = the angle between the tangent at the TS and the chord from the TS to the SC

b = the angle at any point on the spiral between the tangent at that point and the chord from the TS

B = the angle at the SC between the chord from the TS and the tangent at the SC

c = the chord from any point on the spiral to the TS

C = the chord from the TS to the SC

d = the degree of curve at any point on the spiral

D = the degree of curve of the circular arc

f = the angle between any chord of the spiral (calculated when necessary) and the tangent
through the TS

I = the angle of the deflection between initial and final tangents; the total central angle of the circular curve and spirals

k = the increase in degree of curve per station on the spiral

L = the length of the spiral in feet from the TS to any given point on the spiral

Ls = the length of the spiral in feet from the TS to the SC, measured in 10 equal chords

o = the ordinate of the offsetted PC; the distance between the tangent and a parallel tangent to the offsetted curve

r = the radius of the osculating circle at any given point of the spiral

R = the radius of the central circular curve

s = the length of the spiral in stations from the TS to any given point

S = the length of the spiral in stations from the TS to the SC

u = the distance on the tangent from the TS to the intersection with a tangent through any given point on the spiral

U = the distance on the tangent from the TS to the intersection with a tangent through the SC; the longer spiral tangent

v = the distance on the tangent through any given point from that point to the intersection with the tangent through the TS

V = the distance on the tangent through the SC from the SC to the intersection with the tangent through the TS; the shorter spiral tangent

x = the tangent distance from the TS to any point on the spiral

X = the tangent distance from the TS to the SC

y = the tangent offset of any point on the spiral

Y = the tangent offset of the SC

Z = the tangent distance from the TS to the offsetted PC (Z = X/2, approximately)

 = the central angle of the spiral from the TS to any given point

 = the central angle of the whole spiral

Ts = the tangent distance of the spiraled curve; distance from TS to PI, the point of intersection
of tangents

Es = the external distance of the offsetted curve

## Spiral Formulas

3-106. The following formulas are for the exact determination of the functions of the 10-chord spiral when the central angle, , does not exceed 45 degrees. These are suitable for the compilation of tables and for accurate fieldwork.

d = ks = kL 100  D = kS = kL  100   = ks 2 = d 2 = kL 20,000 = dL 200  ks 2 = DS 2 = kL 20,000 = DL 200  A = ( /3)  0.00297  seconds  B =   A
C = L (Cos 0.3  + 0.004 Exsec 34 )
(Exsec = 1 Tan 12 ()

X = C Cos A  Y = C Sin A  U = C Sin B Sin   V = C Sin A Sin  R = 50 ft Sin 12 D  (chord definition)  Z = X  (R Sin )  o = Y  (R Vers )  (Vers = 1  Cos )  T = (R + o) Tan (12 I) + Z  Es = (R + o)Exsec (12 I) + o
(Exsec (12 I) = Tan (12 I)(Tan (14 I)

## Empirical Formulas

3-107. For use in the field, the following formulas are sufficiently accurate for practical purposes when
does not exceed 15 degrees.

a =  /3 (degrees)  A = /3 (degrees)  a =  10 ks (minutes)  S =  10 kS (minutes)

## Spiral Lengths

3-108. Different factors must be taken into account when calculating spiral lengths for highway and railroad layout.

## Highways

3-109. Spirals applied to highway layout must be long enough to permit the effects of centrifugal force to be adequately compensated for by proper superelevation. The minimum transition spiral length for any degree of curvature and design speed is obtained from the relationship Ls = 1.6V3/R, in which Ls is the minimum spiral length in feet, V is the design speed in miles per hour, and R is the radius of curvature of the simple curve. This equation is not mathematically exact but an approximation based on years of observation and road tests.

3-110. Table 3-1 is compiled from the above equation for multiples of 50 feet. When spirals are inserted between the arcs of a compound curve, use Ls = 1.6V3/Ra. Ra represents the radius of a curve of a degree equal to the difference in degrees of curvature of the circular arcs.

## Railroads

3-111. Spirals applied to railroad layout must be long enough to permit an increase in superelevation not exceeding 1 14 inches per second for the maximum speed of train operation. The minimum length is determined from the equation Ls = 1.17 EV. E is the full theoretical superelevation of the curve in inches, V
is the speed in miles per hour, and Ls is the spiral length in feet.

3-112. This length of spiral provides the best riding conditions by maintaining the desired relationship between the amount of superelevation and the degree of curvature. The degree of curvature increases uniformly throughout the length of the spiral. The same equation is used to compute the length of a spiral between the arcs of a compound curve. In such a case, E is the difference between the superelevations of the two circular arcs.

D
30 mph
40 mph
50 mph
60 mph
70 mph
Ls
Ls
Ls
Ls
Ls
1-00
0
0
0
0
0
0
0
0
0
0
1-30
.01
150
.02
150
.02
150
.04
150
.05
150
2-00
.01
150
.02
150
.03
150
.05
150
.06
200
2-30
.01
150
.03
150
.04
150
.06
150
.08
250
3-00
.02
150
.03
150
.05
150
.07
200
.09
300
3-30
.02
150
.04
150
.06
150
.08
200
.10
350
4
.02
150
.04
150
.06
150
.09
250
.10
400
5
.03
150
.05
150
.08
150
.10
300


6
.03
150
.06
150
.10
200
.10
350


7
.04
150
.07
150
.10
250


8
.05
150
.08
150
.10
300


9
.05
150
.09
150
.10
300


10
.06
150
.10
200


11
.06
150
.10
200


12
.07
150
.10
200


13
.07
150
.10
250


14
.08
150
.10
250


15
.09
150


16
.09
150


17
.10
150


18
.10
150


19
.10
150


20
.10
150


21
.10
150


22
.10
150


23
.10
150


24
.10
200


25
.10
200

## Spiral Calculations

3-113. Spiral elements are readily computed from the formulas given above. To use these formulas, certain data must be known. These data are normally obtained from location plans or by field measurements.

3-114. The following computations are for a spiral when D, V, PI station, and I are known.

D =  4  I =  24 10  PI station =  42 + 61.70  V = 60 mph

## Determining Ls


Assuming that this is a highway spiral, use either the equation above or table 3-1, page 3-33.


From table 3-1, when D = 4 and V = 60 mph, the value for Ls is 250 feet.

## Determining

= DL  200  = 4 (250) 200 = 50

## Determining O

o =  Y  (R Vers )
3-115. From page 3-28,

R = 50 ft Sin 12 D   R = 50 ft . 0348994   R = 1,432.69 ft
Using = 5, we find (see table A-9, page A-160), Y = 0.029073 x Ls

$Y=0.029073$ x 250

$Y=7.27$ ft

$o=Y=$ (R $Vers$)

(Vers A = 1 = Cos A)

$0=7.27=$ (1,432.69 x 0.00381)

## Determining Z

**Abstract**

We study the $\alpha$-function of the \
3-116. From table A-9 we see that

X = .999243 x L  X =  999243 x 250  X =  249.81 ft  R =  1,432.69 ft  Sin 5 =  0.08716  2 = 249.81 - (1,432.69 $x$ 0.08716)

2 = 124.94 $ft$

## Determining Ts

T  = (R +  o) Tan (12 I) +  Z
3-117. From the previous steps, R = 1,432.69 feet, o = 1.81 feet, and Z = 124.94 feet.

Tan I 2  Tan 24 10 2  = Tan 12 05  0.21408  T = (1,432.69 +  1.81) (0.21408) +  124.94  T =  432.04 ft

## Determining Length Of The Circular Arc (La)

$L_{a}=\frac{1-2\Lambda}{D}$$x$$100$

$I=24^{\circ}10^{\prime}=24.16667^{\circ}$

$\Lambda=5^{\circ}$

$D=4^{\circ}$

$24.16667-10$

$x$$100=354.17$$fe$

$L_{a}=\frac{1-2\Lambda}{D}$$x$$100$

## Determining Chord Length

Chord length = L 10  Chord length = 250 10 = 25 ft

## Determining Station Values

3-118. With the data above, the curve points are calculated as follows:

\begin{tabular}{l c c} Station PI & $=42+61.70$ & \\ Station TS & $=\_4+32.04$ & $=\_5$ \\ Station TS & $=38+29.66$ & \\  & $+2+50.00$ & $=\_5$ \\ Station SC & $=40+79.66$ & \\  & $+3+54.17$ & $=\_5$ \\ Station CS & $=44+33.83$ & \\  & $+2+50.00$ & $=\_5$ \\ Station ST & $=46+83.83$ & \\ \end{tabular}

= 42 + 61.70
= -4 + 32.04
= 38 + 29.66
  +2 + 50.00
= 40 + 79.66
  +3 + 54.17
= 44 + 33.83
  +2 + 50.00
= 46 + 83.83

## Determining Deflection Angles

3-119. One of the principal characteristics of the spiral is that the deflection angles vary as the square of the distance along the curve.

   a A  L L
3-120. From this equation, the following relationships are obtained:

$$a_{1}=\frac{(1)^{2}A}{(10)^{2}},a_{2}=4a_{1},a_{3}=9a,=16a_{1},...,a_{9}=(10)^{2}$$
3-121. 81a1, and a10 = 100a1 = A. The deflection angles to the various points on the spiral from the TS or ST are a1, a2, a3 . . . a9 and a10. Using these relationships, the deflection angles for the spirals and the circular arc are computed for the example spiral curve. Page 3-31 states that

\(\begin{array}{c}\mbox{$\begin{array}{c}\mbox{\rm$\begin{array}{c}\mbox{\rm$ \begin{array}{c}\mbox{\rm$\begin{array}{c}\mbox{\rm$\begin{array}{c}\mbox{\rm$ \begin{array}{c}\mbox{\rm$\begin{array}{c}\mbox{\rm$\begin{array}{c}\mbox{\rm$ \begin{array}{c}\mbox{\rm$\begin{array}{c}

3-122. Page 3-32 states that, a = ks2.


Station
Deflection Angle

38
+ 29.66 (TS)
a0
= 0 00'

+ 54.66
a1 = 10ks2 = 10(1.6)(0.25)2
= 0 01'

+ 79.66
a2 = 4a1
= 0 04'
39
+ 04.66
a3 = 9a1
= 0 09'

+ 29.66
a4 = 16a1
= 0 16'
39
+ 54.66
a5 = 25a1
= 0 25'

+ 79.66
a6 = 36a1
= 0 36'
40
+ 04.66
a7 = 49a1
= 0 49'

+ 29.66
a8 = 64a1
= 1 04'

+ 54.66
a9 = 81a1
= 1 21'
40
+ 79.66 (SC)
a10 = 100a1 = A =/3
= 1 40'
41
+ 00.00
d1 = 0.3c1 D = 0.3' (20.34)(4)
= 0 24.4'
42

d2 = d1 + D/2
= 2 24.4'
43

d3 = d2 + D/2
= 4 24.4'
44

d4 = d3 + D/2
= 6 24.4'

+ 33.83 (CS)
d5 = d4 + 0.3c2D


= 6 24.4' + 0.3' (33.83)(4)


= I  2
2


= 24 10  10
2

= 7 05'

+ 33.83 CS
a  =  A =
3 = 5
3
= 1 40'

 +58.83
a9 = 81a1
= 1 21'

+ 83.83
a8 = 64a1
= 1 04'
45
+ 08.83
a7 = 49a1
= 0 49'

+ 33.83
a6 = 36a1
= 0 36'

+ 58.83
a5 = 25a1
= 0 25'

+ 83.83
a4 = 16a1
= 0 16'
46
+ 08.83
a3 = 9a1
= 0 09'

+ 33.83
a2 = 4a1
= 0 04'

+ 58.83
a1 = 10ks2 = 10(1.6)(0.25)2
= 0 01'

+ 83.83 (ST)
a0
= 0 00'

## Spiral Curve Layout

3-123. The following is the procedure to lay out a spiral curve, using a one-minute instrument with a horizontal circle that reads to the right. Figure 3-17 illustrates this procedure.

## Setting Ts And St

3-124. With the instrument at the PI, the instrumentman sights along the back tangent and keeps the head tapeman on line while the tangent distance (Ts) is measured. A stake is set on line and marked to show the TS and its station value.

3-125. The instrumentman now sights along the forward tangent to measure and set the ST.


## Laying Out First Spiral From Ts To Sc

3-126. Set up the instrument at the TS, pointing on the PI, with 0 00' on the horizontal circle.

Check the angle to the ST, if possible. The angle should equal one half of the I angle if the TS
and ST are located properly.

The first deflection (a1 / 0 01') is subtracted from 360 degrees, and the remainder is set on the
horizontal circle. Measure the standard spiral chord length (25 feet) from the TS, and set the first
spiral station (38 + 54.66) on line.

The remaining spiral stations are set by subtracting their deflection angles from 360 degrees and measuring 25 feet from the previously set station.

## Laying Out Circular Arc From Sc To Cs

3-127. Set up the instrument at the SC with a value of A minus A (5 00' - 1 40' = 3 20') on the horizontal circle. Sight the TS with the instrument telescope in the reverse position.


Plunge the telescope. Rotate the telescope until 0 00' is read on the horizontal circle. The instrument is now sighted along the tangent to the circular arc at the SC.

The first deflection (d1 /0 24') is subtracted from 360 degrees, and the remainder is set on the
horizontal circle. The first subchord (c1 / 20.34 feet) is measured from the SC, and a stake is set
on line and marked for station 41+ 00.

The remaining circular arc stations are set by subtracting their deflection angles from 360 degrees and measuring the corresponding chord distance from the previously set station.

## Laying Out Second Spiral From St To Cs

3-128. Set up the instrument at the ST, pointing on the PI, with 0 00' on the horizontal circle.

Check the angle to the CS. The angle should equal 1 40' if the CS is located properly.

Set the spiral stations using their deflection angles in reverse order and the standard spiral chord length (25 feet).
3-129. Correct any error encountered by adjusting the circular arc chords from the SC to the CS.

## Intermediate Setup

3-130. When the instrument must be moved to an intermediate point on the spiral, the deflection angles computed from the TS cannot be used for the remainder of the spiral. In this respect, a spiral differs from a circular curve.

## Calculating Deflection Angles

    3-131. Following are the procedures for calculating the deflection angles and staking the spiral.

               Example:
                           D = 4


Ls = 250 ft (for highways)

V =60 mph

I = 24 10'

Point 5 = intermediate point

Calculate the deflection angles for the first five points. These angles are: a1 = 0 01', a2 = 0 04',
a3 = 0 09', a4 = 0 16', and a5 = 0 25'.

The deflection angles for points 6, 7, 8, 9, and 10, with the instrument at point 5, are calculated
with the use of table 3-2. Table 3-2 is read as follows: with the instrument at any point, coefficients are obtained which, when multiplied by a1, give the deflection angles to the other
points of the spiral. Therefore, with the instrument at point 5, the coefficients for points 6, 7, 8,
9, and 10 are 16, 34, 54, 76, and 100, respectively.

Multiply these coefficients by a1 to obtain the deflection angles. These angles are a6 = 16a1 = 0
16', a7 = 34a1 = 0 34', a8 = 54a1 = 0 54', a9 = 76a1 = 1 16', and a10 = 100a1 = 1 40'.

Table 3-2 is also used to orient the instrument over point 5 with a backsight on the TS. The
angular value from point 5 to point zero (TS) equals the coefficient from table 3-2 times a1. This
angle equals 50a1 = 0 50'.

Deflection angle to chordpoint number
Transit at chord-point number
0
TS

1

2

3

4

5

6

7

8

9
10 sc
OTS
0
2
8
18
32
50
72
98
128
162
200
1 ........  1
0
5
14
27
44
65
90
119
152
189
2 ........  4
4
0
8
20
36
56
80
108
140
176
3 ........  9
10
7
0
11
26
45
68
95
126
161
4 ........  16
18
16
10
0
14
32
54
80
110
144
5 ........  25
28
27
22
13
0
17
38
63
92
125
6 ........  36
40
40
36
28
16
0
20
44
72
104
7 ........  49
54
55
52
45
34
19
0
23
50
81
8 ........  64
70
72
70
64
54
40
22
0
26
56
9 ........  81
88
91
90
85
76
63
46
25
0
29
10SC ........  100
108
112
112
108
100
88
72
52
28
0

## Staking

3-132. Stake the first five points according to the procedure shown above. Check point 5 by repetition to insure accuracy.

3-133. Set up the instrument over point 5. Set the horizontal circle at the angular value determined above.

With the telescope inverted, sight on the TS (point zero).

3-134. Plunge the telescope, and stake the remainder of the curve (points 6, 7, 8, 9, and 10) by subtracting the deflection angles from 360 degrees.

## Field Notes For Spirals

3-135. Figure 3-18, page 3-40, shows a typical page of data recorded for the layout of a spiral. The data were obtained from the calculations shown above.

## Section V - Vertical Curves Function And Types

3-136. When two grade lines intersect, there is a vertical change of direction. To insure safe and comfortable travel, the surveyor rounds off the intersection by inserting a vertical parabolic curve. The parabolic curve provides a gradual direction change from one grade to the next.

3-137. A vertical curve connecting a descending grade with an ascending grade, or with one descending less sharply, is called a sag or invert curve. An ascending grade followed by a descending grade, or one ascending less sharply, is joined by a summit or overt curve.

## Computations

3-138. In order to achieve a smooth change of direction when laying out vertical curves, the grade must be brought up through a series of elevations. The surveyor normally determines elevation for vertical curves for the beginning (point of vertical curvature or PVC), the end (point of vertical tangency or PVT), and all full stations. At times, the surveyor may desire additional points, but this will depend on construction requirements.

## Length Of Curve

3-139. The elevations are vertical offsets to the tangent (straightline design grade) elevations. Grades G1
and G2 are given as percentages of rise for 100 feet of horizontal distance. The surveyor identifies grades as plus or minus, depending on whether they are ascending or descending in the direction of the survey. The length of the vertical curve (L) is the horizontal distance (in 100-foot stations) from PVC to PVT. Usually, the curve extends 12 L stations on each side of the point of vertical intersection (PVI) and is most conveniently divided into full station increments.

3-140. A sag curve is illustrated in figure 3-20, page 3-44. The surveyor can derive the curve data as follows (with BV and CV being the grade lines to be connected).

3-141. Determine values of G1 and G2, the original grades. To arrive at the minimum curve length (L) in stations, divide the algebraic difference of G1 and G2 (AG) by the rate of change (r), which is normally included in the design criteria. When the rate of change (r) is not given, use the following formulas to compute L: (Summit Curve)

$L=125\,ft=\frac{(G_{2}-G_{1})}{4}$$or\,L=38.10\,m$
(Sag Curve)

$L=100\,ft\,\frac{(G_{2}-G_{1})}{4}$$or\,L=38.10\,m$
3-142. If L does not come out to a whole number of stations from this formula, it is usually extended to the nearest whole number. Note that this reduces the rate of change. Thus, L = 4.8 stations would be extended to 5 stations, and the value of r computed from r = G/L. These formulas are for road design only.

The surveyor must use different formulas for railroad and airfield design.

## Station Interval

3-143. Once the length of curve is determined, the surveyor selects an appropriate station interval (SI).

The first factor to be considered is the terrain. The rougher the terrain, the smaller the station interval. The second consideration is to select an interval which will place a station at the center of the curve with the same number of stations on both sides of the curve. For example, a 300-foot curve could not be staked at 100-foot intervals but could be staked at 10-, 25-, 30-, 50-, or 75-foot intervals. The surveyor often uses the same intervals as those recommended for horizontal curves, that is 10, 25, 50, and 100 feet.

3-144. Since the PVI is the only fixed station, the next step is to compute the station value of the PVC, PVT, and all stations on the curve.

PVC = PVI - L/2

PVT = PVI + L/2

3-145. Other stations are determined by starting at the PVI, adding the SI, and continuing until the PVT is
reached.

## Tangent Elevations

    3-146. Compute tangent elevations PVC, PVT, and all stations along the curve. Since the PVI is the fixed
    point on the tangents, the surveyor computes the station elevations as follows:

             Elev PVC = Elev PVI + (-1 x L/2 x G1)
             Elev PVT = Elev PVI + (L/2 x G2)

    3-147. The surveyor may find the elevation of the stations along the back tangent as follows:

             Elev of sta = Elev of PVC + (distance from the PVC x G1).


    3-148. The elevation of the stations along the forward tangent is found as follows:

             Elev of sta = Elev of PVI + (distance from the PVI x G2)


## Vertical Maximum

3-149. The parabola bisects a line joining the PVI and the midpoint of the chord drawn between the PVC and PVT. In figure 3-19, line VE = DE and is referred to as the vertical maximum (Vm). The value of Vm is computed as follows: (L= length in 100-foot stations. In a 600-foot curve, L = 6.)

$$Vm=\frac{L}{\beta}(G_{2}-G_{1})or$$

$$Vm=\nu_{2}\;(\left(\frac{Elev\;PVC+Elev\;PVT}{2}\right)-\;elev\;PVI)$$

3-150. In practice, the surveyor should compute the value of Vm using both formulas, since working both provides a check on the Vm, the elevation of the PVC, and the elevation of the PVT.

## Vertical Offset

3-151. The value of the vertical offset is the distance between the tangent line and the road grade. This value varies as the square of the distance from the PVC or PVT and is computed using the formula:

Vertical Offset = (Distance)${}^{2}$$\star$
3-152. A parabolic curve presents a mirror image. This means that the second half of the curve is identical to the first half, and the offsets are the same for both sides of the curve.

## Station Elevation

3-153. Next, the surveyor computes the elevation of the road grade at each of the stations along the curve.

The elevation of the curve at any station is equal to the tangent elevation at that station plus or minus the vertical offset for that station, The sign of the offset depends upon the sign of Vm (plus for a sag curve and minus for a summit curve).

## First And Second Differences

3-154. As a final step, the surveyor determines the values of the first and second differences. The first differences are the differences in elevation between successive stations along the curve, namely, the elevation of the second station minus the elevation of the first station, the elevation of the third station minus the elevation of the second, and so on. The second differences are the differences between the differences in elevation (the first differences), and they are computed in the same sequence as the first differences.

3-155. The surveyor must take great care to observe and record the algebraic sign of both the first and second differences. The second differences provide a check on the rate of change per station along the curve and a check on the computations. The second differences should all be equal. However, they may vary by one or two in the last decimal place due to rounding off in the computations. When this happens, they should form a pattern. If they vary too much and/or do not form a pattern, the surveyor has made an error in the computation.

3-156. Example: A vertical curve connects grade lines G1 and G2 (figure 3-19). The maximum allowable slope (r) is 2.5 percent. Grades G1 and G2 are found to be -10 and +5.

L = G r = 15 2.5 = 6 stations  V = G x L 8 = (15)(6) 8 = 11.25 feet
3-157. The vertical offsets for each station are computed as in figure 3-20. The first and second differences are determined as a check. Figure 3-21, page 3-44, illustrates the solution of a summit curve with offsets for 50-foot intervals.

## High And Low Points

3-158. The surveyor uses the high or low point of a vertical curve to determine the direction and amount of runoff, in the case of summit curves, and to locate the low point for drainage.

3-159. When the tangent grades are equal, the high or low point will be at the center of the curve. When the tangent grades are both plus, the low point is at the PVC and the high point at the PVT. When both tangent grades are minus, the high point is at the PVC and the low point at the PVT. When unequal plus and minus tangent grades are encountered, the high or low point will fall on the side of the curve that has the flatter gradient.

## Horizontal Distance

3-160. The surveyor determines the distance (x, expressed in stations) between the PVC or PVT and the high or low point by the following formula:

**Figure Captions**
3-161. G is the flatter of the two gradients and L is the number of curve stations.

## Vertical Distance

3-162. The surveyor computes the difference in elevation (y) between the PVC or PVT and the high or low point by the formula

y = ( G  G) 2L  (x) + Gx
3-163. Example: From the curve in figure 3-21, G1 = + 3.2%, G2 = - 1.6%, L = 4 (400). Since G2 is the flatter gradient, the high point will fall between the PVI and the PVT.

 = 1.6 4 1.6  (+3.2) = 1.3333 sta = 133.33 feet  x = G L G  G PVT   x =  sta of high point  (16 + 00)   133.33 =  14 + 66.67  y = ( G  G) 2L  (x) + Gx  Elev PT +  y =  elev high point  128.00 +  1.07 =  129.07

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## Chapter 4 Earthwork Section I - Planning Of Earthwork Operations Importance

4-1. In road, railroad, and airfield construction, the movement of large volumes of earth (earthwork) is one of the most important construction operations. It requires a great amount of engineering effort.

4-2. The planning, scheduling, and supervising of earthwork operations are of major importance in obtaining an efficiently operated construction project. To plan a schedule, the quantities of clearing, grubbing, and stripping, as well as the quantities and positions of cuts and fills, must be known. Then, the most efficient type and number of pieces of earthmoving equipment can be chosen, the proper number of personnel assigned, and the appropriate time allotted.

4-3. Earthwork computations involve the calculation of volumes or quantities, the determination of final grades, the balancing of cuts and fills, and the planning of the most economical haul of material. The surveyor uses field notes and established grade to plot the cross sections at regular stations and at any plus stations which may have been established at critical intermediate points. The line representing the existing ground surface and those lines representing the proposed cut or fill enclose cross-section areas. The surveyor uses these areas and the measured distances along the centerline to compute earthwork volumes.

## Cross Sections

4-4. The cross section used in earthwork computations is a vertical section. It is perpendicular to the centerline at full and plus stations and represents the boundaries of a proposed or existing cut or fill. Typical cross sections for a roadbed are illustrated in figure 4-1, page 4-2.

4-5. The determination of cross-section areas is simplified when the sections are plotted on cross-section paper. This is usually done to the same vertical and horizontal scale, standard practice being 1 inch equals 10 feet. However, if the vertical cut or fill is small in comparison with the width, the surveyor may use an exaggerated vertical scale to gain additional precision in plotting such sections.

4-6. The surveyor must take care, however, when computing areas of this type of plotted section that the proper area is obtained. For example, a 1 inch equals 10 foot scale, both vertical and horizontal, yields 100 square feet, but 1 inch equals 10 foot horizontal and 1 inch equals 2 foot vertical yields only 20 square feet. An exaggerated vertical scale is used in figure 4-2, page 4-3, to illustrate a five-level section.

4-7. The side slopes of a cross section are expressed by a ratio of horizontal distance to vertical distance.

A 1 12:1 side slope indicates a slope extending 1 12 feet horizontally per foot of vertical rise or fall. Slopes may be inclined more or less sharply than this, such as 3:1, 2:1, or 1:1. The surveyor usually determines the slope by the design specifications based on the stability of the soil in cut or fill. However, the need for economy in construction operations must often be considered. For example, cut slopes may be flattened more than is required by soil characteristics solely to produce enough material for a nearby fill. This practice is more economical than operating a borrow pit to obtain this material.

## Section Ii - Areas Area Computation

4-8. The surveyor can determine cross-section areas for construction earthwork volumes by one of the following methods: the counting squares method, the geometric method (geometry of trapezoids and triangles), the stripper method, or the double-meridian-distance method. The stripper and counting-thesquares methods are simple and give approximate results, while the other methods give results as accurate as the cross-section field data will permit. Standard practice requires that cut and fill areas of a cross section, where both occur simultaneously, be determined separately.

## Counting-Squares Method

4-9. To make a hasty approximation of a cross-section area plotted on cross-section paper, count the number of squares enclosed by the boundary lines of the section. Then multiply the total number of counted squares by the number of square feet represented by a single square.

4-10. For example, the cross section in figure 4-2 encloses approximately 350 1/10-inch squares or
3.51-inch squares. The scales of the cross section indicate that one 1/10-inch square represents 1 foot horizontally and 6 inches vertically, or one half of a square foot in area. Therefore, the approximate area of the cross section is 350 divided by 2 equals 175 square feet. Using the 1-inch square, which represents 10 feet horizontally and 5 feet vertically or 50 square feet in area, the cross-section area is approximately 3.5 x 50 = 175 square feet.

## Geometric Method

4-11. To compute the area of a cross section by the geometric method, sometimes called the trapezoidal method, subdivide the area into simple geometrical figures, calculate each area according to its geometry, and total the results. There is no set rule for performing the subdivisions. The computer selects those subdivisions which will produce the most direct and accurate results. Figure 4-3a illustrates the subdivision of a typical three-level section into five triangles. Figure 4-3b illustrates the subdivision of a five-level section into two triangles and two trapezoids. The following computations apply to the geometric method in figure 4-2, page 4-3. Basic formulas are as follows.

$$A=\frac{bh}{2}\ (area\ of\ a\ triangle)$$

##

$A=h$$\frac{b_{1}+b_{2}}{2}$ (_area of a trapezoid_)
4-12. A=area; b, b1, and b2 = the lengths of the bases; and h = the perpendicular distance, or height, between parallel bases for a trapezoid and from base to vertex for a triangle.

|                                               | square feet    |
|-----------------------------------------------|----------------|
| 2A of triangle AJK = 5.7 X 4.0                | = 22.8         |
| 2A of triangle ABJ = 5.2 (5.7 + 6.0)          | = 60.8         |
| 2A of trapezoid BCIJ = 9.3 (5.2 + 4.2)        | = 87.4         |
| 2A of trapezoid CDHI = 15.0 (4.2 + 4.7)       | = 133.5        |
| 2A of trapezoid DEGH = 4.8 (4.7 + 1.5)        | = 29.8         |
| 2A of triangle EFG = 1.5 x 4.5                | = 6.8          |
| Total (double area of AFHK)                   | = 341.1        |
|                                               |                |
| Area of the cross section = 341.1  2 = 170.5 |                |

4-13. Note that the computation is simplified by adding all the numerical products for triangles and trapezoids together and then dividing the total by 2. The dashed line, AJ, is added to subdivide quadrilateral ABJK into two triangles, AJK and ABJ.

## Stripper Method

4-14. To determine the area of a plotted cross section by strip measurements, subdivide the area into strips by vertical lines spaced at regular intervals. Measure the total length of these lines by cumulatively marking the length of each line along the edge of a stripper made of paper or plastic. Then, multiply the cumulative total of the average base lengths by the width of the strip. Regular intervals of 3, 5, or 10 feet, depending upon the roughness of the ground, give satisfactory results for strip widths. Due regard must be given to the horizontal and vertical scales of the cross section. The procedure is illustrated in figure 4-4.

4-15. The stripper shown is 5 squares wide by 60 squares long. Its zero index is placed at the intersection of the ground and side-slope line of the section.

4-16. The stripper is moved an interval of 5 squares to the right with zero reading at the bottom. It is then moved another 5 squares to the right with the previous top reading (2.5) now adjacent to the bottom line.

The stripper is again moved 5 squares to the right for another interval with the previous top reading (6.0) adjacent to the bottom line.

4-17. This process of moving 5 squares to the right and bringing the top reading to the bottom line is continued until the stripper reaches the right edge of the cross section with a final reading of 53.0. Multiply this last reading (53.0) by the strip width used (5) to get the number of squares in the section (265.0). To find the area of the cross section in square feet, multiply the number of squares by the area in square feet of one square.

## Double-Meridian-Distance Method

4-18. The double-meridian-distance (DMD) method gives a more precise value for a cross-section area than the stripper method. It does, however, involve more effort and time. It is essential that the elevations (latitudes) and the distance from the centerline (departures) of all points on the cross section be known.

4-19. The method is based on the theory that the area of a right triangle equals one half of the product of the two sides. Since latitudes and departures are at right angles to each other, the area bounded by the distance, the latitude, and the departure is a right angle. The surveyor can determine this area by taking one half of the product of the latitude and the departure. However, depending on its location, the triangle may add to or subtract from the total area of the irregular figure.

4-20. To avoid determining a plus or minus area for each triangle, a slight refinement is made. The departure is added twice. It is first added when determining the DMD of the course and second, when determining the next course  s DMD. Multiplying the DMD of each course by its latitude results in twice the area, but the sign of this product illustrates whether the area adds to or subtracts from the figure area.

4-21. A step-by-step procedure to work out a DMD area is given below and illustrated in figure 4-5.


Compute and record all the latitudes and departures.

Select the far left station (D) as the first point and D-E as the first course to avoid negative areas
in the DMD.

The DMD of the first course equals the departure of the course itself, 4.0.

The DMD of any other course (E-F) equals the DMD of the preceding course (D-E) plus the departure of the preceding course (D-E) and the departure of the course (E-F) itself or 4.0 + 4.0 + 30.0 = 38.0. For the next course (F-I), the same procedure is followed. Add together the DMD of the preceding course, the departure of the preceding course, and the departure of the course itself, or 38.0 + 30.0 + 30.0 = 98.0.

The DMD of the last course is numerically equal to its departure but with the opposite sign (+14.0).

Multiply each DMD value by its latitude. Positive products are entered under north double areas
and negative products under south double areas.

The sum of all north double areas minus the sum of all the south double areas, DISREGARDING THE SIGNS, equals twice the cross-section areas. Divide this double area by 2 to get the true cross-section area.

## Area By Planimeter

4-22. The surveyor uses a polar planimeter to measure the area of a plotted figure. There are two types of planimeters. One has a fixed scale, and one has an adjustable scale. Basically, the surveyor uses both in the same way, with the exception that the fixed scale cannot be adjusted to yield a 1:1 ratio when tracing areas.

## Operation

4-23. The planimeter (figure 4-6) touches the paper at four points: the anchor point (B), the tracing point
(A), the drum (C), and the support wheel (G). The adjustable tracing arm (E) is graduated to permit adjustment to the scale of the plotted figure. This adjustment provides a direct ratio between the area traced by the tracing point and the revolutions of the roller. The scale screws, F1, F2, and F3, are used to accomplish the proper adjustment of the tracing arm scale. Proper scale settings are provided with each instrument. If the scale setting provided yields an area that is too large, the scale reading must be increased and vice versa.

4-24. As the planimeter encircles the area to be measured, the drum (C) revolves and records the answer in tens and hundreds. A vernier (M) is mounted adjacent to the drum and enables a single unit (ones) reading. The disk (D) is attached to the drum by a worm gear, counting the number of drum revolutions and giving the thousands reading. The surveyor must first read the disk for thousands, then the drum for hundreds and tens, and finally, the vernier for single units (ones).

## Procedures

4-25. The following are rules for using a planimeter.

Always measure cut and fill areas separately.

Check the accuracy of the planimeter as a measuring device to guard against errors due to temperature changes and other noncompensating factors. A simple method of testing its consistency of operation is to trace an area of 1 square inch with the arm set for a 1:1 ratio. The disk, drum, and vernier combined should read 1.000 for this area.

Before measuring a specific area, determine the scale of the plot and set the adjustable arm of the
planimeter according to the chart in the planimeter case. Check the setting by carefully tracing a
known area, such as five large squares on the cross-section paper, and verifying the reading on the disk, drum, and vernier. If the reading is inconsistent with the known area, readjust the arm
settings until a satisfactory reading is obtained.

To measure an area, set the anchor point of the adjusted planimeter at a convenient position outside the plotted area; place the tracing point on a selected point on the perimeter of the cross
section; take an initial reading from the disk, drum, and vernier; continue tracing the perimeter clockwise, keeping the tracing point carefully on the line being followed; and when the tracing point closes on the initial point, again take a reading from the disk, drum, and vernier. The difference between the initial reading and the final reading gives a value proportional to the area being traced.

Make two independent measurements of the area to insure accurate results. Make the second
measurement with the tracing point placed at a point on the opposite side of the first measurement. This procedure gives two compensating readings. The mean of these readings is more accurate than either one individually.

To measure plotted areas larger than the capacity of the planimeter, divide the areas into sections and measure each separately.


## Section Iii - Earth And Rock Excavation Classes Of Excavated Material

4-26. Excavated material is usually classified as common excavation, loose rock, and solid rock. Although classifying excavation material is not a survey function, the surveyor must differentiate among the different types so excavation records will match the construction work. When performing surveys to determine quantities of excavated materials, the surveyor must record common excavation, loose-rock excavation, and solid-rock excavation data separately in the field notes.

4-27. Common excavation involves the moving of earth or of earth with detached boulders less than onehalf cubic yard in volume. Loose-rock excavation involves the moving of consolidated materials which have been loosened without blasting with picks, bars, or simple air and mechanical devices. Solid-rock excavation involves the moving of rock from solid beds or the breaking up of boulders measuring 1 cubic yard or more by means of explosives.

## Borrow Pits

4-28. When there is an imbalance in the volume of cuts and fills in construction projects, it is often necessary to borrow the required fill dirt from borrow pits outside the construction limits but near the fill site. Any time the haul distance between the last available dirt and the fill site becomes too far, it is cheaper to establish a borrow pit.

4-29. Under some circumstances, it is not necessary to survey borrow pits. However, it is often necessary to buy the fill dirt. The surveyor must determine how much earth was removed from the borrow pit. This can be done by establishing a grid over the area to be excavated. The grid can beat any convenient interval
(for example, 10-, 25-, 50-, or 100-foot squares).

4-30. Once the grid is staked, the surveyor can determine the elevation of each grid corner by leveling. The volume of earth that has been removed can be computed at any time by reestablishing the grid corners and determining their new elevation. The surveyor does this by subtracting the average elevation of the grid corners after excavation from the average elevation of the same grid corners before excavation and multiplying the difference by the number of square feet in the grid square.

4-31. When laying out the grid, the surveyor must lay out two baselines parallel to two adjacent sides of the grid for use in reestablishing the grid. The surveyor should place them far enough outside the area of excavation to avoid destruction but close enough to be convenient. (See figure 4-7.)

    4-32. The surveyor should treat waste areas or dumps where excess material is deposited in the same
    manner as borrow pits, with the exception that the volume to be measured is the volume deposited, not
    excavated.


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## Chapter 5 Bridge Surveying Section I - Location Surveys

5-1. Bridge surveying is necessary to locate a site, obtain information for design, and furnish lines and grades for construction. A reconnaissance survey is made at all possible sites. A preliminary survey is made at the best site to establish horizontal and vertical control and to obtain information for the bridge design and construction planning. A location survey is made to lay out the bridge according to the bridge plans. During the actual construction, the surveyor establishes any additional lines and grades required by the construction foreman.

5-2. The accuracy of measurements and the number and type of survey markers vary with the degree of precision demanded and the type of construction. Variations may range from hand-level and sketchboard work for a tactical bridge to precise measurements for a prefabricated steel bridge.

## Reconnaissance

5-3. Tentative bridge sites are selected by reconnaissance and the more promising ones are reconnoitered in detail. The selection of a bridge site is governed by both tactical and technical considerations. Tactical requirements fix the general area for the bridge site. Technical requirements fix the exact location and may sometimes eliminate sites that are tactically acceptable. For permanent construction, technical considerations govern the bridge location.

## Access Roads

5-4. Maps or prepared overlays show existing roads and the distances of railheads from the bridge site.

Descriptive symbols indicate the width, condition, and types of roads. The surveyor draws sketches of approach roads to be constructed on overlays and includes them in the reconnaissance report.

## Bridge Length

5-5. The surveyor determines the length of the bridge crossing to estimate the materials required for construction. Depending on the distance and equipment available, the surveyor measures this distance with a tape, an electronic measuring device, or by stadia method.

## Banks

5-6. The surveyor reports on the character and shape of the riverbanks. This includes the amount and type of vegetation; the slope, height, and composition of the banks; and pertinent dimensions of any natural dikes. The surveyor selects tentative abutment positions and measures the size and location of any usable abutments or piers for possible use in the proposed construction.

## Character Of The Flow

5-7. The surveyor determines stream velocity by timing a floating object over a measured course. Highwater levels are determined by noting drift and marks on vegetation or piers, questioning local inhabitants, and consulting tide tables and local flood records.

## Character Of The River Bottom

5-8. The surveyor observes the character of the river bottom for each site and reports information on the design of intermediate supports. If a floating bridge is to be constructed, the surveyor determines the character of the river bottom so the holding power of anchors can be estimated.

## Profile

5-9. The surveyor profiles the streambed or gap to facilitate the design of intermediate supports. The profile interval is measured by a tape or cable stretched horizontally across the stream or gap or by the instrument-stadia method. Vertical measurements for the profile are referenced to the horizontal tape, cable, or water surface. For floating bridges, profiles are required only for setting trestles near the shores.

## Local Materials

5-10. The surveyor estimates and records quantities of local materials such as standing timber, sand and gravel beds, and available cement, water, and lumber.

## Soundings

5-11. A survey is made to determine the relief of the bottom of the stream along the centerline and along lines on each side of the centerline. The surveyor must make soundings and determine the depth of each sounding in relation to the datum used for vertical control.

## Location

5-12. The location of each sounding is referenced to control stations onshore. The design engineer specifies the distance from the centerline and intervals between soundings. Unless otherwise specified, intervals between soundings are 25 feet for a fairly uniform streambed and 10 feet for an irregular streambed. For more accurate location of soundings, the surveyor should use the intersection method. This would include setting instruments on the ends of a baseline on shore and reading simultaneous angles.

## Procedures

5-13. Figure 5-1 shows one method of taking soundings. The instrument is set up over C and sighted on F.

A sounding boat travels on the range line, CF, from the far shore toward the near shore. The instrumentman signals the sounding crew until they are online at the proper distance as measured by tape or stadia. The sounding crew proceeds along the centerline, CF, taking readings at the specified intervals. In shallow water, direct rod readings can be taken for profile elevations by setting the instrument near the river s edge.

In deeper rivers, the depth of water is measured directly from the boat, using the most suitable measuring device.

5-14. The surveyor records the data obtained by the sounding and ground crews in order to provide a complete set of profile notes for the construction design. To establish profiles on each side of the centerline, stakes are set at a specified distance from the centerline at B, D, E, and G. Using the same procedure as for the centerline soundings, the surveyor sets up the instrument at B, then at D, and sights on E and G, respectively.

## Foundation Investigation

5-15. Data on foundation investigations serve as the basis for determining bearing capacities and substructure design. Subsurface investigations are made by borings, test pits, trenches, and field tests. The surveyor must often make measurements incident to these investigations. The surveyor s duties include referencing boreholes and test pits to nearby instrument stations and recording elevations of strata encountered at the various sites. These data are used in preparing a profile illustrating subsurface conditions.

## Section Ii - Bridge Site Layout Abutments

5-16. Construction plans show whether the abutments are pile-bent or crib-bent. The surveyor checks the layout after excavation and before any concrete is poured. The surveyor must also check abutment elevations and, in the case of concrete, establish lines for setting forms. Care must be taken to stake abutments according to the construction plans. The distance between abutments must be within steel fabrication limits, especially for prefabricated sections. The surveyor then ties abutment stakes to a horizontal control system.

5-17. The survey procedure for setting an abutment at right angles to the bridge centerline is illustrated in figure 5-2. The foundation, ABCD, is shown in the plan. AB is the face, and points J and K are established near the site on the centerline of the bridge. The staking is done as follows:


Set the instrument at point H (station 40+97.5). Sight on point J. Invert the instrument and use a tape to locate point F.

Turn 90-degree angles and use a tape to locate points C and D.

Move the instrument to point F (station 41+37.5), sight on H, and turn 90-degree angles to locate points A and B. Locate points E and G in line with points A and B, respectively, and use as horizontal control points.

## Wing Walls

5-18. The procedure for laying out wing walls is merely an extension of the layout of an abutment. The surveyor sets the instrument at B (figure 5-3), sights on G, and turns the wing angle. Points L and M are located at any convenient distance along this line.

5-19. The surveyor sets the instrument at A and locates points N and O. Since points A and B may be lost or damaged during construction, the surveyor locates two points (L and M; N and O) on the line of sight of the front of each wing wall. To relocate point A, the instrument is set at point O and sighted through point N. The surveyor may also locate point A by setting the instrument up on N, sighting on O, and inverting.

## Piers

5-20. After the centerline of the bridge is established, the surveyor locates the piers by taping. If taping is impractical, they can be located by triangulation. The surveyor sets stakes establishing the centerline (C and E) on each side of the river. The surveyor lays out CD and EF approximately at right angles to the centerline as shown in figure 5-4, page 5-6. For well-proportioned triangles, the length of the baselines should equal at least one-half CE.

5-21. To locate piers at A and B, the surveyor should follow these steps.


Establish and carefully reference baselines CD and EF.

Measure the length of each baseline commensurate with the required precision of line CE.

Measure all angles of the triangles CDE and EFC.

Compute the distance CE from the triangle CDE and check it against the same distance computed from the triangle EFC. The difference in computed length must be within the prescribed limits of error.

Compute angles BDC, ADC, BFE, and AFE. (Since A and B are located by the construction plans, it is possible to determine their distance from C and E.)

Draw a triangulation diagram, showing computed angles and distances and measured angles and distances.

Turn computed angles BDC, ADC, BFE, and AFE.

Set targets DA and DB on the far shore and FB and FA on the near shore, so that the intersecting
lines can be reestablished without turning angles. Carefully reference these points.

Use two instruments to position crib piers. They will occupy two points such as F and D simultaneously. The intersection of sights FA and DA locates the pier A.

## Piles

5-22. The surveyor positions piles, records pile-driving data, and marks piles for cutoff as specified by the construction plans.

5-23. Figure 5-5 shows points A and B established as a reference line 10 feet from the centerline of the bridge. A wire rope is stretched between these points with a piece of tape or a cable clip marking each pilebent position, such as C and D. The surveyor can locate the upstream pile, pile number 1, by measuring the offset (4 feet) from the line AB at C. A template, designed to space the piles properly (3 feet in the figure)
and nailed to pile number 1 after the pile is driven, is then floated into position. The surveyor positions the rest of the piles using the template.



5-24. If it is impractical to stretch a cable to the far shore, the surveyor sets up an instrument at some convenient distance from the centerline of the bridge and positions the template by sighting on a mark located the same distance from the centerline of the template. The surveyor determines the distance of the template from the shore, either by angle measuring or taping. During driving, the surveyor must keep a complete record of the following:


Location and number of piles.

Dimensions.

Kind of wood.

Total penetration.

Average drop of hammer.

Average penetration under last five blows.

Penetration under last blow.

Amount of cutoff.
5-25. Elevations are marked on the two end piles. Two 3- by 12-inch planks are nailed to guide the saw in cutting piles to the specified height.

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## Chapter 6 Site Layout Section I - Building Layout Objectives

6-1. The objectives of surveying for building construction are to lay out the proposed structure according to prepared plans and to mark the controlling points of the structure in the manner that is most useful to the construction forces. This marking consists of indicating the corners of the building and other horizontal and vertical positions by means of stakes, batter boards with string lines, drill holes, cut-and-fill notations, and similar conventional methods.

6-2. The actual layout of the building is usually preceded by some form of reconnaissance and location survey. The following procedures are typical of major building projects:


Performing reconnaissance (aerial, map, and ground).

Selecting site (paper and instrument).

Establishing control (horizontal and vertical).

Taking topography (plane table or transit stadia).

## Orientation

6-3. The building and its foundation are positioned according to the controlling dimensions and references appearing on prepared plans. The dimensions and references include the overall length and width of the structure, distances to road centerlines and to other structures, measurements within the structure itself, and miscellaneous determinations concerning the approaches and rights-of-way.

## Layout Of A Simple Building

6-4. The plans for construction of a building give the location and elevation of the work relative to existing utilities and survey control marks. The dimensions of the building are part of the necessary data for establishing line and formula grade. Figure 6-1, page 6-2, illustrates a typical building layout using the following steps.


Establish baseline AB and locate CD by measurement.

At point C, turn 90 degrees from B and locate corner stakes E and F by measurement.

Locate points H and G from point D in the same way.

Check diagonals (EH and FG) by the formula c = a + b (where c is the diagonal and a and
b, the two sides).

Install batter boards.

Establish line and grade.

## Batter Boards

6-5. The surveyor locates the corners of the building and determines the elevation of its foundation by carrying forward elevations from a benchmark, or other point of known elevation, to the foundation. To mark the general location, the surveyor sets stakes or slats. These will guide the initial excavation and rough grading. However, the stakes will be disturbed or destroyed during this work, and some more suitable marks must be placed to continue the construction. These suitable marks are called batter boards. The surveyor uses these temporary devices to mark the outline and grade of the structure and any special construction inside or outside.

## Placement

6-6. Batter boards of two 2- by 4-inch stakes driven into the ground and a crosspiece of 1- by 6-inch lumber nailed to each stake. The surveyor drives the stakes about 3 to 4 feet away from the building line so they will not be disturbed by the construction but will be far enough apart to straddle the line to be marked.

Note that in figure 6-2 only three stakes, one of them being a common post for two directions, are driven on outside corners. The length of the stakes is determined by the required grade line. They must be long enough to accept the 1- by 6-inch crosspiece to mark the grade. The surveyor cuts the 1- by 6-inch crosspiece long enough to join both stakes and nails it firmly to them after the grade has been established.

The top of the crosspiece becomes the mark from which the grade will be measured.

## Use Of Instrument

6-7. The surveyor sets all batter boards for one structure to the same grade or level line. An instrument is used to locate the building lines and mark them on the top edge of the crosspiece. A nail is driven at each of these marked points. A cord stretched over the top edge of two batter boards and held against the nails defines the building line and grade elevation.

## Use Of Cord

6-8. Sometimes, an instrument is not available for marking the building line on the batter boards. If the corner stakes have not been disturbed, the surveyor can transfer the building line to the batter boards by stretching a cord over the batter boards and using plumb bobs held over the corner stakes. The surveyor moves the cord on each batter board until it just touches both plumb bob strings, marks the position of the cords, and drives in the nails.

## Procedures

6-9. The surveyor sets and marks the batter boards as follows:


After the corner stakes are laid out, drive 2- by 4-inch stakes 3 to 4 feet outside of each corner.
These are selected to bring all crosspieces to the same elevation.

The surveyor marks these stakes at the grade of the top of the foundation or at some whole number of inches or feet above or below the top of the foundation. Use a level to mark the same grade or elevation on all stakes.

Nail 1- by 6-inch boards to the stakes to the top edge of the boards and flush with the grade
marks. Mark the distance in crayon on these boards.

Locate the prolongation of the building lines on the batter boards by using an instrument or a line and plumb bob.

Drive nails into the top edges of the batter boards to mark the building line.

## Interior Transfer Of Line And Grade

6-10. Occasionally, it is necessary to transfer lines and grades from outside to inside a building and to the upper stories for establishing wall faces, floor levels, and columns or for setting machinery precisely. The surveyor does this by traversing and leveling.

## Location

6-11. The surveyor locates instrument stations outside of the building to establish a line that, when extended, will intersect the building at a window or doorway. The instrument is set on the station farthest from the building and sighted on the point nearest the building. The surveyor transfers the line to the building by sighting the instrument on a plumb bob held in an upper-story window.

6-12. From this point, the line is extended in any direction inside the building by setting up on the point and using the outside stations as a backsight. The line is prolonged by double centering. Because of the short sights used, the surveyor may accurately set an angle that is to be turned to clear an obstruction and then measure by repetition.

## Direct Leveling

6-13. To transfer vertical control into a building, the surveyor uses direct leveling, if possible. For elevation transfer to an upper story, a steel tape is suspended with a weight attached to the lower or zero end. To insure accuracy, the weight should approximately equal the normal tension of the fully supported tape minus one half of the weight of the suspended portion of the tape. A level is set up on the first floor, and a reading is taken on the suspended tape.

6-14. Another reading is taken on the tape with a level set on the upper floor. This gives data from which the HI of the instrument on the upper floor are computed. A rod is now held on some point on the upper floor to be used as a benchmark and its elevation determined. The surveyor may also establish elevations on the second floor by using the rod upside down (often called an inverted rod) and marking the elevation on a wall.

## Section Ii - Utilities Layout Drainage

6-15. Utilities drainage refers to the sewer systems of the disposal point. The area to be drained for surface water and liquid waste. The design includes the installation and any area around and location of a drainage or storm sewer it that will drain into the installation. The system will depend upon the size and intensity of the rainfall in inches per hour is topography of the area to be drained, the based on records of past storms. The runoff intensity of rainfall expected, the runoff characteristics are determined by the type of characteristics of the area, and the location soil and ground cover.

## Design And Location

6-16. Using the factors mentioned and the best available topographic map of the area, the surveyor designs and locates the sewer lines on paper. Once the paper location is accomplished, the centerline of the ditch is staked and profile levels run. The profile and grade lines are plotted and cut stakes set.

6-17. After the trench is dug, batter boards are set for the alignment of pipes and placement of manholes or drop inlets. The surveyor usually places batter boards for sewer alignment at intervals of 10 to 25 feet and sets them on edge across the trench (figure 6-3). Then the surveyor determines the interval between batter boards, the station number, and the elevation of the sewer grade at each batter board.

6-18. The term sewer grade is interchangeable with such other terms as invert grade, pipe grade, flow line, and grade line elevation. They all mean the same thing, the elevation of the low point on the inside circumference of the pipe. All sewer lines are designed with this elevation as the controlling factor. The surveyor must set all grade marks on the batter boards between two successive manholes at the same distance above the invert grade.

## Battens

6-19. The surveyor nails battens (small pieces of wood) to the batter boards to indicate sewer alignment.

All battens are set vertically on the same side of the batter boards, with the same edges directly over the centerline of the sewer. As work progresses, the surveyor must check the alignment of these battens frequently. This is done by sighting past the edges marking the centerline. Any batten that has been moved or disturbed will be visible immediately.

## Sighting Cords

6-20. The surveyor uses a sighting cord stretched parallel to the centerline of the sewer at a uniform distance above the invert grade to transfer line and grade into the trench. After computing the invert elevation, the surveyor adds an even number of feet to establish the elevation of the cord at each batter board. This position is marked on the centerline edge of each batten by a nail. The sighting cord is fastened to the battens at these nails and this establishes the alignment of the sewer. The centerline is directly below the cord, and the sewer invert grade is at the selected distance below the cord.

## Grade Transfer

6-21. To transfer the grade, usually in feet or feet and inches, from the sighting cord to the pipe, the surveyor uses a rod or stick called a grade pole, with a mark at a distance from the foot piece equal to the distance between the sighting cord and the invert grade (figure 6-3, page 6-5). The foot piece is placed on the invert of the pipe, and the rod plumb is held. The pipe end is then raised or lowered until the mark on the grade pole is on a horizontal line with the cord. A plumb line is held lightly against the cord and the pipe shifted sideways until its crown is directly below the point of the plumb bob. The grade pole is again placed in position, held plumb, and its mark checked against the cord.



## Chapter 7 Traverse Section I - Selection Of Traverse Definition

7-1.

A traverse is a series of straight lines called traverse legs. The surveyor uses them to connect a series of selected points called traverse stations (TS). The surveyor makes distance and angle measurements and uses them to compute the relative positions of the traverse stations on some system of coordinates.

## Starting Control

7-2.

Since the purpose of a traverse is to locate points relative to each other on a common grid, the surveyor needs certain elements of starting data, such as the coordinates of a starting point and an azimuth to an azimuth mark. There are several ways in which the starting data can be obtained, and the surveyor should make an effort to use the best data available to begin a traverse. The different variations in starting control are grouped into several general categories.

## Known Control Available

7-3.

Survey control is available in the form of existing stations with the station data published in a trigonometric list, or higher headquarters may establish the station and provide the station data. The surveyor obtains the azimuth to an azimuth mark (starting direction) by referring to a trigonometric list or computing from known coordinates.

## Maps Available

7-4.

When survey control is not available in the area, the surveyor must assume the coordinate of the starting station. The assumed data approximates the correct coordinate as closely as possible to facilitate operations. When a map of the area is available, the approximate coordinate of the starting station is scaled from the map. (For survey purposes, starting data scaled from a map are considered to be assumed data.) The surveyor determines the starting direction by scaling it from the map.

## No Maps Available

7-5.

When neither survey control nor maps are available, the coordinate of the starting point is assumed. The surveyor determines the starting direction by the most accurate means available.

## Types Of Traverse

7-6.

Construction surveying makes use of two basic types of traverseopen traverse and closed traverse.

## Open Traverse

7-7.

An open traverse (figure 7-1, page 7-2) originates at a starting station, proceeds to its destination, and ends at a station whose relative position is not previously known.

The open traverse is the least desirable type of traverse because it provides no check on fieldwork or starting data. For this reason, the planning of a traverse always provides for closure of the traverse. Traverses are closed in all cases where time permits.

## Closed Traverse

7-8.
         A closed traverse starts at a point and ends at the same point or at a point whose
relative position is known. The surveyor adjusts the measurements by computations to
minimize the effect of accidental errors made in the measurements. Large errors are
corrected.

## Traverse Closed On Starting Point

7-9.

A traverse which starts at a given point, proceeds to its destination, and returns to the starting point without crossing itself in the process is referred to as a loop traverse (figure 7-2). The surveyor uses this type of traverse to provide control of a tract or parcel boundary, and data for the area computation within the boundary. This type of traverse is also used if there is little or no existing control in the area and only the relative position of the points is required.

7-10.

A loop traverse starts and ends on a station of assumed coordinates and azimuth without affecting the computations, area, or relative position of the stations. If, however, the coordinates must be tied to an existing grid system, the traverse starts from a known station and azimuth on that system. While the loop traverse provides some check upon the fieldwork and computations, it does not provide for a check of starting data or insure detection of all the systematic errors that may occur in the survey.

## Traverse Closed On Second Known Point

                     7-11.
                              A traverse closed on a second known point begins at a point of known
                     coordinates, moves through the required point(s), and terminates at a second point of
                     known coordinates. The surveyor prefers this type of traverse because it provides a check
                     on the fieldwork, computations, and starting data. It also provides a basis for comparison
                     to determine the overall accuracy of the work.


## Fieldwork

7-12.

In a traverse, three stations are considered to be of immediate significance.

Surveyors refer to these stations as the rear station, the occupied station, and the forward station. The rear station is the station from which the surveyors performing the traverse have just moved or a point to which the azimuth is known. The occupied station is the station at which the party is located and over which the instrument is set. The immediate destination of the party is the forward station or the next station in succession.

## Horizontal Angles

7-13.

Always measure horizontal angles at the occupied station by sighting the instrument at the rear station and measuring the clockwise angles to the forward station. To measure horizontal angles, make instrument pointings to the lowest visible point of the target which marks the rear and forward stations.

## Distance

7-14.

Measure the distance in a straight line between the occupied station and the forward station. Use horizontal taping procedures or electronic distance measuring equipment.

## Traverse Stations

7-15.

The surveyor selects sites for traverse stations as the traverse progresses. The surveyor locates the stations in such a way that at any one station both the rear and forward stations are visible.

## Selection Of Stations

7-16.

If the distance is measured with tape, the line between stations must be free of obstacles for the taping team. The surveyor should keep the number of stations in a traverse to a minimum to reduce the accumulation of instrumental errors and the amount of computing required. Short traverse legs require the establishment and use of a greater number of stations and may cause excessive errors in azimuth because small errors in centering the instrument, in station marking equipment, and in instrument pointings are magnified and absorbed in the azimuth closure as errors in angle measurement.

## Station Markers

7-17.

Traverse station markers are usually 2- by 2-inch wooden stakes, 6 inches or more in length. The surveyor drives these stakes, called hubs, flush with the ground. The center of the top of the hub is marked with a surveyor  s tack or with an X to designate the exact point of reference for angular and linear measurements.

7-18.

To assist in recovering the station, the surveyor drives a reference (witness)
stake into the ground so that it slopes toward the station. The surveyor must write the identification of the station on the reference stake with a lumber crayon or china marking pencil or on a tag attached to the stake. Signal cloth may also be tied to the reference stake to further assist in identifying or recovering the station.

## Station Signals

7-19.

A signal must be erected over survey stations to provide a sighting point for the instrument operator and to serve as a reference for tape alignment by the taping team. The most commonly used signal is the range pole.

7-20.

When measuring angles, the surveyor places the tapered point of the range pole on the station mark and uses a rod level to make the pole vertical for observations. The surveyor should check the verticality of the pole by verifying that the bubble remains centered at other points on the range pole. The range pole is maintained in a vertical position throughout the observation period either by use of a range pole tripod or by someone holding the pole. To prevent the measurement of angles to the wrong point, the surveyor places the range pole in a vertical position only when it is being used to mark a survey station.

## Organization Of Traverse Party

7-21.

The number of personnel available to perform survey operations depends on the unit s Table of Organization and Equipment (TOE). The organization of these people into a traverse party and the duties assigned to each member will depend on the unit  s Standing Operating Procedure (SOP). The organization and duties of traverse party members are based on the functional requirements of the traverse.

## Chief Of The Party

7-22.

The chief of the party selects and marks the locations for the traverse stations and supervises the work of the other members of the party. The chief of the party also assists in the reconnaissance and planning of the survey.

## Instrument Operator

7-23.

The instrument operator measures the horizontal angles at each traverse station.

## Recorder

7-24.
        The recorder keeps the field notes (see appendix B) for the party in a field
notebook, and records the angles measured by the instrument operator, the distances
measured by the tapeman, and all other data pertaining to the survey. The recorder is
usually the party member designated to check the taped distances by pacing between
traverse stations.

## Tapemen

7-25.

Two tapemen measure the distance from one traverse station to the next.

## Rodman

7-26.

The rodman assists the chief of the party in marking the traverse stations, removes the target from the rear station when signaled by the instrument operator, and moves the target forward to the next traverse station.

## Variations

7-27.

The number of party members may be reduced by combining the positions of party chief, instrument operator, and recorder. It is possible that one of the tapemen may double as a rodman, but it is best to have two tapemen and a separate rodman.

Note. It is possible to reduce the number of personnel in a traverse party, but there should be two tapemen and a separate rodman.

## Section Iii - Computations Azimuth Computation

7-28.

The azimuth of a line is defined as the horizontal angle, measured clockwise, from a base direction to the line in question. Depending upon the starting data and the desired results, the base direction used will be grid north. In extreme circumstances, the starting azimuth may even be a magnetic azimuth. In order for a traverse to be computed, the surveyor determines an azimuth for each leg of the traverse (figure 7-2, page 7-3).

Note. The surveyor must determine an azimuth for each leg of the traverse.

7-29.
The azimuth for each succeeding leg of the traverse is determined by adding the
value of the measured angle at the occupied station to the azimuth from the occupied
station to the rear station. The example which follows illustrates this procedure. It should be noted that on occupation of each successive station, the first step is to compute the back azimuth of the preceding traverse leg (the azimuth from the occupied station to the
rear station).


Example


Given:

Azimuth from station

A to azimuth mark (Az)
12000
Angle azimuth mark-A-B
31015
| Angle A-B-C                  | 27057     |
|------------------------------|------------|
| Angle B-C-A                  | 31328     |
| Angle C-A-azimuth            | 5 19       |
|                              |            |
| Require:                     |            |
| All leg azimuth              |            |
|                              |            |
| Solution                     |            |
|                              |            |
| At station A                 |            |
| Az from A to Az mark         | 12000     |
| (+) Angle Az mark-A-B        | 31015     |
|                              | 43000     |
| (-) Full circle              |            |
| 36000                       |            |
| Az line A-B                  | 7015      |
| (+) 180 to determine back Az | 18000     |
| Back Az line A-B             | 25015     |
| (+) Angle A-B-C              | 27057     |
|                              |            |
| 52112                       |            |
|                              |            |
| (-) Full circle              | 36000     |
| Az B-C                       | 16112     |
| (+) 180 to determine back Az | 18000     |
| Back Az line B-C             | 31412     |
| (+) Angle B-C-A              | 31328     |
|                              | 65440     |
| (-) Full circle              | 36000     |
| Az line C-A                  | 29440     |
| (-) 180 to determine back Az | 18000     |
| Back Az line C-A             | 11440     |
| (+) Angle C-A-Az mark        | 519       |
| AZ line A-Az mark            | 11959     |
| (note error)                 |            |

## Azimuth Adjustment

7-30.

The surveyor must determine the need for adjustment before beginning final coordinate computations. If the angular error of closure falls within computed allowable error, the surveyor may adjust the azimuths of the traverse.

## Allowable Angular Error (Ae)

7-31.
        The allowable angular error is determined by the formula AE = 1  n or 20  per
station, whichever is less, where N is the number of traverse stations. If azimuth error
does not fall within allowable error, the surveyor must reobserve the station angles of the
traverse in the field.


In the example given, N equals 3.
AE =  1  =  1.73  or 104   AE =  20  x 3 =  60

Therefore, 60 seconds is the allowable error.

## Azimuth Corrections

7-32.

Prior to determining a correction, the surveyor computes the actual error. The azimuth error is obtained by subtracting the computed closing azimuth from the known closing azimuth. This subtraction provides the angular error with the appropriate sign. By

reversing this sign, the azimuth correction with the appropriate sign is obtained. For example, the azimuth from point A to an azimuth mark is 120 00 . The closing azimuth of a traverse to the same azimuth mark is determined to be 119 59 . This falls within allowable limits, so the surveyor may compute the error and correction as follows: Azimuth error
= computed azimuth - known azimuth

= 119 59  - 120 00  = 00 01
Azimuth Correction
=  + 00 01


## Application Of Azimuth Corrections

7-33.
Since traverse adjustment is based on the assumption that errors present have
accumulated gradually and systematically throughout the traverse, the azimuth correction
is applied accordingly. The correction is distributed equally among the angles of the traverse with any remainder distributed to the larger angles. For example, assume that the
traverse for which the azimuth correction was determined consists of three traverse legs and four angles.
Station
Measured Angle
A
310 15
B
270 57
c
313 28
A (closing)
5 19
7-34.
The azimuth correction is divided by the total number of angles. (In this case, +
01   4 = 15  per angle.) Each of the four angles is increased by 15 seconds.

Station
Measured
Angle
Azimuth
Correction
Adjusted
Angle
A
310 15
+15
310 15  15
B
270 57
+15
270 57  15
c
313 28
+15
313 28  15
A
5 19
+15
5 19  15

## Action After Adjustment

7-35.

After the angles are adjusted, the surveyor computes adjusted azimuth of each leg of the traverse by using the starting azimuth and the adjusted angles at each traverse station. The surveyor should compute the adjusted azimuth throughout the entire traverse and check against the correct azimuth to the closing azimuth mark before beginning any further traverse computations.

## Azimuth-Bearing Angle Relationship

7-36.
        Since the functions (sine, cosine, tangent, and so on) of the azimuth and the
bearing are numerically the same, the surveyor may use either one to compute the
traverse. The choice of which is to be used will depend upon the computer and the
equipment available.

## Azimuth And Bearing

7-37.

If a calculator with angular functions is available, the use of the azimuth would obviously be easier, since it eliminates the need to compute the bearing. If such a calculator is not available and the functions must be determined from tables, it is necessary to compute the bearing angles since the tabulation of functions is normally published for angles of 0 degrees to 90 degrees. The bearing of a line is the acute angle (angle less than 90 degrees) formed by the line in question and the northsouth line through the occupied point. Figure 7-3, page 7-8, illustrates the relationship between the azimuth of a line and its bearing.

## Quadrants

7-38.

The manner in which bearing angles are computed from a given azimuth depends on the quadrant in which the azimuth lies. Figure 7-4 shows the four quadrants and their relationship to each other. When the azimuth is in the first quadrant, 0 degrees to 90 degrees, the bearing is equal to the azimuth. When the azimuth is in the second quadrant, 90 degrees to 180 degrees, the bearing is equal to 180 degrees minus the azimuth. When the azimuth is in the third quadrant, 180 degrees to 270 degrees, the bearing is equal to the azimuth minus 180 degrees. When the azimuth is in the fourth quadrant, 270 degrees to 360 degrees, the bearing is equal to 360 degrees minus the azimuth.
7-39.

Since the numerical values of the bearings repeat in each quadrant, the surveyor must label them and indicate into which quadrant they fall. This is done by indicating whether the bearing angle is measured from the north or south line and whether it is east or west of that line. For example, a line with an azimuth of 341 12  30  falls in the fourth or northwest quadrant and its bearing is N 18 47  30  W.

## Coordinate Computations

7-40.

If the coordinate of a point and the azimuth and distance from that point to a second point are known, the surveyor can compute the coordinate of the second point. In figure 7-5, the coordinate of station A is known and the coordinate of B is to be determined. The azimuth and distance from station A to B are determined by measuring the horizontal angle from the azimuth mark to station B and the distance from station A to B. The grid casting and northing lines through both stations are shown.

7-41.

Since the grid is a rectangular system and the casting and northing lines form right angles at the point of intersection, the computation of the difference in northing
(side dN) and difference in casting (side dE) employs the formulas for the computation of a right triangle. The distance from A to B is the hypotenuse of the triangle, and the bearing angle (azimuth) is the known angle. The following formulas are used to compute dN and dE:

dN =  Cos Azimuth x Distance  dE =  Sin Azimuth x Distance
7-42.

In figure 7-5, page 7-9, the traverse leg falls in the first (northeast) quadrant since the value of the casting increases as the line goes east, and the value of the northing increases as it goes north. Both the dE and dN are positive and are added to the casting and northing of station A to obtain the coordinate of station B.

7-43.

If the surveyor uses a calculator with trigonometric functions to compute the traverse, the azimuth is entered directly and the machine provides the correct sign of the function and the dN and dE. If the functions are taken from tables, the computer provides the sign of the function by inspection. All lines going north have positive dNs; south lines have negative. Lines going east have positive dEs; west lines have negative. Figure 7-6 illustrates the relationship of quadrant to sign.

## Determination Of Dn And De

7-44.
In figure 7-7 the azimuth from A-B is 70 15  15  and the distance is 568.78.
dN =  Cos 70 15  15  x 568.78
dN = +0.337848 x 568.78 = +192.16
dE =  Sin 70 15  15  x 568.78
dE = +0.941200 x 568.78 = +535.34
7-45.

The azimuth from B-C is 161 12  30  and the distance is 548.74 (note SE
quadrant).

dN =  Cos 161 12  30  x 548.74

dN = 0.946696 x 548.74 = 519.49

dE = Sin 161 12  30  x 548.74

dE = +0.322128 x 548.74 = +176.76

7-46.

The azimuth from C- A is 294 40  45 , and the distance is 783.74 (note NW
quadrant).

$dN=$ Cos 294${}^{\circ}$ 40${}^{\circ}$ 45${}^{\circ}$ x 783.74

$dN=$ 0.417537 x 783.74 = +327.24

$dE=$ Sin 294 ${}^{\circ}$ 40${}^{\circ}$ 45${}^{\circ}$ x 783.74

$dE=$ 0.908660 x 783.74 = 712.15

## Accuracy And Specifications

7-47.

The overall accuracy of a traverse depends on the equipment and methods used in the measurements, the accuracy achieved, and the accuracy of the starting and closing data. An accuracy ratio of 1:5,000 is normally sought in construction surveying. In obtaining horizontal distances, an accuracy of at least 0.02 foot per 100 feet must be obtained. When using a one-minute instrument, the surveyor turns the horizontal angles once in each position, namely, one direct and one indirect, with angular closure of 20
seconds per station or 1  number of stations. whichever is less.

## Linear Error

                     7-48.
                              To determine the acceptability of a traverse, the surveyor must compute the
                     linear error of closure and the allowable error or the accuracy ratio or both. The first step
                     in either case is to determine the linear error in dN and dE. In the case of a loop traverse,
                     the algebraic sum of the dNs should equal zero. Any discrepancy is the linear error in dN.
                     The same is true for dEs.

     Linear Error dN (eN) =
                                0.09
     Linear Error dE (eE) =
                                0.05

7-49.
        The surveyor computes the linear error of closure (eL) using the Pythagorean
theorum.

Linear Error (eL) = (eN) + (eE)  eL = (0.09) + (0.05)  eL = 0.0106 = 0.1029

## Allowable Error

7-50.

The surveyor then computes the allowable error (AE) using the appropriate accuracy ratio (1/5,000 or 1/3,000) and the total length of the traverse.

1 5,000  AE Length of Traverse  AE = 1 x Length of Traverse 5,000   AE = 1 x 1901.26 5,000 = 0.3802
7-51.

Compare this to the linear error of closure. If the AE is greater than the eL, the traverse is good and can be adjusted. If it is not good, it must be rerun.

## Ratio Of Accuracy

7-52.

The ratio of accuracy provides a method of determining the traverse accuracy and comparing it to established standards. The ratio of accuracy is the ratio of the eL to the total length of the traverse, after it is reduced to a common ratio and rounded down.

el

$$\frac{\mbox{\it Total length}}{\mbox{\it Total length}}=\frac{0.1029}{1,901.26}= \frac{0.1029\div 0.1029}{\mbox{\it 1,901.26}\div 0.1029}=\frac{1}{18,476.77}\mbox{\it or }\frac{1}{18,000}$$
7-53.

If the accuracy ratio does not fall within allowable limits, the traverse must be rerun. It is very possible that the distances as measured are correct and that the error can be attributed to large, compensating angular errors.

## Coordinate Adjustment

7-54.

The surveyor makes the adjustment of the traverse using the compass rule. The compass rule says that, for any leg of the traverse, the correction to be given to the dN or dE is to the total correction for dN or dE as the length of the leg is to the total length of the traverse. The total correction for dN or dE is numerically equal to the eN or eE, but with the opposite sign.

## Formulas

7-55.

In figure 7-7, page 7-11, the dN is -0.09 and the dE is -0.05 and the total corrections are +0.09 and +0.05, respectively. Note the following formulas:
dN Correction per station = Total dN Correction
Length of Traverse  x Distance to Station
dE Correction per station = Total dE Correction
Length of Traverse  x Distance to Station
7-56.

For the first leg in the traverse in figure 7-7, the corrections are computed as follows:

$dN$ Correction = $\frac{+0.09}{1,901.26}$$x$ 568.78 = +0.03

$dE$ Correction = $\frac{+0.05}{1,901.26}$$x$ 568.78 = +0.01

## Loop Traverse

7-57.

When adjusting a loop traverse, the surveyor applies the correction to the dNs and dEs prior to computing the coordinates. The total correction must equal the total error. Sometimes, due to round off, the total correction will not equal the total error. If this happens and the difference is one, reduce the correction to the shortest line or increase the longest line. When the error is greater than one, you may arbitrarily reduce/increase the corrections until the total correction equals the total error.

7-58.
The coordinate of the previous station  dN  correction equals the coordinate of
the next station. From figure 7-7 you compute as follows:


Sta A
7,486.79
5,497.53

+ 192.19
+ 535.35
Sta B
7,678.98
6,032.88

7-59.

When adjusting a traverse that starts and ends on two different stations, the surveyor computes the coordinates before the error is determined. In this case, the correction per leg is determined in the same manner as shown, but the correction is applied directly to the coordinates. The correction to be applied after the first leg is equal to the correction computed for the first leg. The correction to be applied after the second leg is equal to the correction for the first leg plus the correction computed for the second leg. The correction for the third leg equals the first correction plus the second correction plus the correction computed for the third leg and so on throughout the traverse. The last correction must be equal to the total correction required.

This page intentionally left blank.


0

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.000 000
4.85
0.000 000
4.85
1.000 000 .00
60'
01
.000 291
4.85
.000 291
4.83
3 437.746 674
1.000 000 .00
59
02
.000 582
4.85
.000 582
4.85
1 718.873 192
1.000 000 .00
58
03
.000 873
4.85
.000 873
4.85
1 145.915 295
1.000 000 .02
57
04
.001 104
4.83
.000 164
4.83
859.436 305
0.999 999 .00
56
05
.001 454
4.85
.001 454
4.85
687.548 889
.999 999 .02
55
06
.001 745
4.85
.001 745
4.85
572.957 213
.999 998 .00
54
07
.002 036
4.85
.002 036
4.85
491.106 003
.999 998 .02
53
08
.002 327
4.85
.002 327
4.85
429.717 571
.999 997 .00
52
09
.002 618
4.85
.002 618
4.85
381.970 991
.999 997 .02
51


10
0.002 909
4.85
0.002 909
4.85
343.773 708
0.999 996 .02
50
11
.003 200
4.85
.003 200
4.85
312.521 367
.999 995 .02
49
12
.003 491
4.85
.003 491
4.85
286.477 734
.999 994 .02
48
13
.003 782
4.83
.003 782
4.83
264.440 799
.999 993 .02
47
14
.004 072
4.85
.004 072
4.85
245.551 983
.999 992 .03
46
15
.004 363
4.85
.004 363
4.85
229.181 664
.999 990 .02
45
16
.004 654
4.85
.004 654
4.85
214.857 622
.999 989 .02
44
17
.004 945
4.85
.004 945
4.85
202.218 750
.999 988 .03
43
18
.005 236
4.85
.005 236
4.85
190.984 186
.999 986 .02
42
19
.005 627
4.85
.005 527
4.85
180.932 198
.999 985 .03
41


20
0.005 818
4.85
0.005 818
4.85
171.885 399
0.999 983 .03
40
21
.006 109
4.83
.006 109
4.85
163.700 191
.999 981 .02
39
22
.006 399
4.85
.006 400
4.85
156.259 084
.999 980 .03
38
23
.006 690
4.85
.006 691
4.83
149.465 021
.999 978 .02
37
24
.006 981
4.85
.005 981
4.85
143.237 122
.999 976 .03
36
25
.007 272
4.85
.007 272
4.85
137.507 447
.999 974 .05
35
26
.007 563
4.85
.007 563
4.85
132.218 503
.999 971 .03
34
27
.007 854
4.85
.007 854
4.85
127.321 336
.999 969 .03
33
28
.008 145
4.85
.006 145
4.85
122.773 955
.999 967 .05
32
29
.008 436
4.85
.008 436
4.85
118.540 180
.999 964 .03
31


30
0.008 727
4.83
0.008 727
4.85
114.588 650
0.999 962 .05
30
31
.009 017
4.85
.009 018
4.85
110.892 051
.999 959 .03
29
32
.009 308
4.85
.009 309
4.85
107.370 558
.999 957 .05
28
33
.009 599
4.85
.009 600
4.85
104.170 945
.999 954 .05
27
34
.009 890
4.85
.009 891
4.83
101.106 902
.999 951 .05
26
35
.010 181
4.85
.010 181
4.85
98.217 943
.999 948 .05
25
36
.010 472
4.85
.010 472
4.85
95.489 475
.999 945 .05
24
37
.010 763
4.85
.010 763
4.85
92.908 487
.999 942 .05
23
38
.011 054
4.83
.011 054
4.85
90.463 336
.999 939 .05
22
39
.011 344
4.85
.011 345
4.85
88.143 572
.999 936 .07
21


40
0.011 635
4.85
0.011 636
4.85
85.939 791
0.999 932 .05
20
41
.011 926
4.85
.011 927
4.85
83.843 507
.999 929 .07
19
42
.012 217
4.85
.012 218
4.85
81.847 041
.999 925 .05
18
43
.012 608
4.85
.012 509
4.85
79.943 430
.999 922 .07
17
44
.012 799
4.85
.012 800
4.85
78.126 342
.999 918 .07
16
45
.013 090
4.83
.013 091
4.85
76.390 009
.999 914 .07
15
46
.013 380
4.85
.013 382
4.85
74.729 165
.999 910 .05
14

Cos
d."
Cot
d."
Tan
d."
Sin d."

0

Sin
d."
Tan
d."
Cot
d."
Cos
d."
47
.013 671
4.85
.013 673
4.85
73.138 991
.999 907 .07
13
48
.013 962
4.85
.013 964
4.83
71.615 070
.999 903 .08
12
49
.014 253
4.85
.014 254
4.85
70.153 346
.999 898 .07
11


50
0.014 544
4.85
0.014 545
4.85
68.750 087
0.999 894 .07
10
51
.014 835
4.85
.014 836
4.85
67.401 854
.999 890 .07
09
52
.015 126
4.83
.015 127
4.85
66.105 473
.999 886 .08
08
53
.016 416
4.85
.015 418
4.85
64.858 008
.999 881 .08
07
54
.015 707
4.85
.015 709
4.65
63.656 741
.999 877 .08
06
55
.015 998
4.85
.016 000
4.85
62.499 164
.999 872 .08
05
56
.016 289
4.85
.016 291
4.85
61.382 905
.999 867 .07
04
57
.016 580
4.85
.016 582
4.85
60.305 820
.999 863 .08
03
58
.016 871
4.85
.016 873
4.85
59.265 872
.999 858 .08
02
59
.017 162
4.83
.017 164
4.85
66.261 174
.999 853 .08
01


60
0.017 452

0.017 455
57.289 962
0.999 848

00

Cos
d."
Cot
d."
Tan
d."
Sin d."

1

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.017 452
4.85
0.017 455
4.85
57.289 962
0.999 848
.08
60'
01
.017 743
4.85
.017 746
4.85
55.350 590
.999 843
.10
59
02
.018 034
4.85
.018 037
4 85
56.441 517
.999 837
.08
58
03
.018 325
4.85
.018 328
4.85
54.561 300
.999 832
.08
57
04
.018 616
4.85
.018 619
4.85
53.708 588
.999 827
.10
56
05
.018 907
4.85
.018 910
4.85
52.882 109
.999 821
.08
55
06
.019 197
4.85
.019 201
4.85
52.080 673
.999 816
.10
54
07
.019 488
4.85
.019 492
4.85
51.303 157
.999 810
.10
53
08
.019 779
4.85
.019 783
4.85
50.548 506
.999 804
.08
52
09
0020 070
4.85
.020 074
4.85
49.815 726
.999 799
.10
51


10
0.020 361
4.85
0.020 365
4.85
49.103 881
0.999 793
.10
50
11
.020 652
4.83
.020 656
4.85
48.412 084
.999 787
.10
49
12
.020 942
4.85
.020 947
4.85
47.739 501
.999 781
.10
48
13
.021 233
4.85
.021 238
4.85
47.085 343
.999 775
.12
47
14
.021 524
4.85
.021 529
4.85
46.448 862
.399 768
.10
46
15
.021 815
4.85
.021 820
4.85
45.829 351
.999 762
.10
45
16
.022 106
4.85
.022 111
4.85
45.226 141
.999 756
.12
44
17
.022 397
4.83
.022 402
4.85
44 638 596
.999 749
.10
43
18
.022 687
4.85
.022 693
4.85
44.066 113
.999 743
.12
42
19
.022 978
4.85
.022 984
4.85
43.508 122
.999 736
.12
41


20
0.023 269
4.85
0.023 275
4.85
42.964 077
0.939 729
.12
40
21
.023 560
4.85
.023 566
4.85
42 433 464
.939 722
.10
39
22
.023 851
4.83
.023 857
4.85
41.915 799
.999 716
.12
38
23
.024 141
4.85
.024 148
4.85
41.410 583
.999 709
.13
37
24
.024 432
4.85
.024 439
4.87
40.917 412
.999 701
.12
36
25
.024 723
4.85
.024 731
4.86
40.435 837
.999 694
.12
35
26
.025 014
4.85
.025 022
4.85
39.965 461
.999 687
.12
34
27
.025 305
4.83
.025 313
4.85
39.505 895
.999 680
.13
33
28
.025 595
4.85
.025 604
4.85
39.056 771
.999 672
.12
32
29
.025 886
4.85
.025 895
4.85
38.617 738
.999 665
.13
31
30
0.026 177
4.85
0.026 136
4.85
36.188 459
0.999 657
.12
30
31
.026 468
4.85
.026 477
4.85
37.768 613
.999 650
.13
29
32
.026 759
4.83
.026 768
4.85
37.357 892
.993 642
.13
28
33
.027 049
4.85
.027 059
4.85
36.956 001
.839 634
.13
27
34
.027 340
4.85
.027 350
4.85
36.562 659
.999 626
.13
26
35
.027 631
4.85
.027 641
4.87
36.177 596
.999 618
.13
25
36
.027 922
4.83
.027 933
4.85
35.800 553
.999 610
.13
24
37
.028 212
4.83
.028 224
4.85
35.431 282
.999 602
.13
23
38
.026 503
4.85
.028 515
4.85
35.069 546
.999 594
.15
22
39
.028 794
4.85
.028 806
4.85
34.715 115
.939 585
.13
21


40
0.029 085
4.83
0.029 097
4.85
34.367 771
0.999 577
.15
20
41
.029 375
4.85
.029 388
4.85
34.027 303
.999 568
.13
19
42
.029 666
4.85
.029 679
4.85
33.693 509
.999 560
.15
18
43
.029 957
4.85
.029 970
4.87
33.366 194
.999 551
.15
17
44
.030 248
4.85
.030 262
4.85
33.045 173
.999 542
.15
16
45
.030 539
4.83
.030 553
4.85
32.730 264
.999 534
.16
15
46
.030 829
4.85
.030 844
4.85
32.421 295
.999 525
.15
14
47
.031 120
4.85
.031 135
4.85
32.118 039
.999 516
.15
13
48
.031 411
4.85
.031 426
4.85
31.820 516
.999 507
.17
12

Cos
d."
Cot
d."
Tan
d."
Sin
d."
1

Sin
d."
Tan
d."
Cot
d."
Cos
d."
49
.031 702
4.83
.031 717
4,87
31.528 392
.999 497
.15
11


50
0.031 992
4.85
0.032 009
4.85
31.241 577
0.999 488
.15
10
51
.032 283
4.85
.032 300
4.85
30.959 928
.999 47$
.17
09
52
.032 574
4.63
.032 591
4.85
30.683 307
.999 469
.15
08
53
.032 864
4.85
.032 882
4.85
30.411 580
.999 460
.17
07
54
.033 155
4.85
.033 173
4.87
30.144 619
.999 450
.16
06
55
.033 446
4.85
.033 465
4.85
29.882 299
.999 441
.17
05
56
.033 737
4.83
.033 756
4,85
29.624 499
.999 431
.17
04
57
.034 027
4.85
.034 047
4.85
29.371 106
.999 421
.17
03
58
.034 318
4.85
.034 338
4.85
29.122 005
.999 411
.17
02
59
.034 609
4.83
.034 630
4.85
28.877 089
.999 401
.17
01


60
0.034 899

0.034 921
28.636 253
0.999 391
00

Cos
d."
Cot
d."
Tan
d."
Sin
d."


2

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.034 899
4.85
0.034 921
4.85
28.6363
0.999 391
.17
60'
01
.035 190
4.85
0.35 212
4.85
28.3994
.999 381
.18
59
02
.035 481
4.85
.035 503
4.87
28.1664
.999 370
.17
58
03
.035 772
4.83
.035 795
4.85
27.9372
.999 360
.17
57
04
.036 062
4.85
.036 088
4.85
27.7117
.999 350
.18
56
05
.036 353
4.85
.036 377
4.85
27.4899
.990 339
.18
55
06
.038 644
4.83
.036 668
4.87
27.2715
.999 328
.17
54
07
.036 934
4.85
.036 960
4.85
27.0566
.999 318
.18
53
08
.037 225
4.85
.037 251
4.85
26.8450
.999 307
.18
52
09
.037 515
4.83
.037 542
4.87
26.6367
.999 296
.18
51


10
0.037 806
4.85
0.037 834
4.85
26.4316
0.999 285
.18
50
11
.038 097
4.85
.038 125
4 85
26.2296
.999 274
.18
49
12
.038 388
4.83
.038 416
4.85
26.0307
.999 263
.18
48
13
.038 678
4.85
.038 707
4.87
25.8348
.999 252
.20
47
14
.038 969
4.85
.038 999
4.85
25.6418
.999 240
.18
46
15
.039 260
4.83
.039 290
4.85
25.4517
.999 229
.18
45
16
.039 550
4.85
.039 581
4.87
25.2644
.999 218
.20
44
17
.039 841
4.85
.039 873
4.85
25.0798
.999 206
.20
43
18
.040 132
4.83
.040 164
4.87
24.8978
.999 194
.18
42
19
.040 422
4.85
.040 456
4.85
24.7185
.999 183
.20
41


20
0.040 713
4.85
0.040 747
4.85
24.5418
0.999 171
.20
40
21
.041 004
4.83
.041 038
4.87
24.3675
.999 159
.20
39
22
.041 294
4.85
,041 330
4.85
24.1957
.999 147
.20
38
23
.041 585
4.85
.041 821
4.85
24.0263
.999 135
.20
37
24
.041 876
4.83
.041 912
4.87
23.8593
.999 123
.20
36
25
.042 166
4.85
.042 204
4.85
23.6945
.999 111
.22
35
26
.042 457
4.35
.042 495
4.87
23.5321
.999 098
.20
34
27
.042 748
4.83
.042 737
4.85
23.3718
.999 086
.22
33
28
.043 038
4.85
.043 078
4.87
23.2137
.999 073
.20
32
29
.043 329
4.83
.043 370
4.85
23.0577
.999 061
.22
31


30
0.043 619
4.85
0.043 661
4.85
22.9038
0.999 048
.22
30
31
.043 910
4.85
.043 952
4.87
22.7519
.999 035
.20
29
32
.044 201
4.83
.044 244
4.85
22.6020
.999 023
.22
28
33
.044 491
4.83
.044 535
4.87
22.4541
.990 010
.22
27
34
.044 782
4.85
.044 827
4.85
22.3081
.998 997
.22
26
35
.045 072
4.85
.045 118
4.87
22.1640
.998 984
.22
25
36
.045 363
4.85
.045 410
4.85
22.0217
.998 971
.23
24
37
.045 654
4.83
.045 701
4.87
21.8813
.998 957
.22
23
38
.045 944
4.85
.045 993
4.85
21.7426
.998 944
.22
22
39
.046 235
4.83
.046 284
4.87
21.6056
.998 931
.23
21


40
0.046 525
4.85
0.046 576
4.85
21.4704
0.998 917
.22
20
41
.046 816
4.83
.046 867
4.87
21.3369
.998 904
.23
19
42
.047 106
4.85
.047 159
4.85
21.2049
.998 890
.23
18
43
.047 397
4.85
.047 450
4.87
21.0747
.999 876
.23
17
44
.047 688
4.83
.047 742
4.85
20.9460
.993 862
.23
16
45
.047 978
4.83
.048 033
4.87
20.8188
.998 848
.23
15
46
.048 269
4.83
.048 325
4.87
20.6932
.993 834
.23
14
47
.048 559
4.85
.048 617
4.85
20.5691
.998 820
.23
13

Cos
d."
Cot
d."
Tan
d."
Sin
d."
2

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.048 850
4.83
.048 908
4.87
20.4465
.998 806
.23
12
49
049 140
4,85
.049 200
4.85
20.3253
.998 792
.23
11


50
0.049 431
4.83
0.049 491
4.87
20.2056
0.998 778
.25
10
51
.049 721
4.85
.049 783
4.87
20.0872
.998 763
.23
09
52
.050 012
4.83
.050 075
4.85
19.9702
.998 749
.25
08
53
.050 302
4.85
.050 366
4.87
19.8546
.998 734
.25
07
54
.050 593
4.83
.050 658
4.85
19.7403
.998 719
.23
06
55
.050 883
4.85
.050 949
4.87
19.6273
.996 705
.25
05
56
.051 174
4.83
.051 241
4.87
19.5156
.998 690
.25
04
57
.051 464
4.85
.051 533
4.85
19.4051
.998 675
.25
03
58
.051 755
4.83
.051 824
4.87
19.2959
.998 660
.25
02
59
.052 045
4.85
.052 116
4.87
19.1879
.998 645
.25
01


60
0.052 336

0.052 408
19.0811
0.998 630
00

Cos
d."
Cot
d."
Tan
d."
Sin
d."


3

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.052 336
4.83
0.052 408
4.85
19.0811
17.60
0.998 630
.27
60'
01
.052 626
4.85
.052 699
4.87
18.9755
17.40
.998 614
.25
59
02
.052 917
4.83
.052 991
4.87
18.8711
17.22
.998 599
.27
58
03
.053 207
4.85
.053 283
4.87
18.7678
17.03
.998 583
.25
57
04
.053 498
4.83
.053 575
4.85
18.6656
16.85
.998 568
.27
56
05
.053 788
4.85
.053 866
4.87
18.5645
16.66
.988 552
.25
55
06
.054 079
4.83
.054 153
4.87
18.4645
16.50
.988 537
.27
54
07
.054 369
4.85
.054 450
4.87
18.3655
16.30
.998 521
.27
53
08
.054 660
4.83
.064 742
4.85
18.2677
16.15
.998 505
.27
52
09
.054 950
4 .85
.055 033
4.87
18.1708
15.97
.998 489
.27
51


10
0.055 241
4.83
0.055 325
4.87
18.0750
15.80
0.998 473
.27
50
11
.005 501
4.85
.055 617
4.87
17.9802
15.65
.998 457
.27
49
12
.055 822
4.83
.055 909
4.85
17.8863
15.48
.998 441
.28
48
13
.056 112
4.83
.056 200
4.87
17.7934
15.32
.998 424
.27
47
14
.056 402
4.85
.056 492
4.87
17.7015
15.15
.998 408
.27
46
15
.056 693
4.83
.056 784
4.87
17.6106
15.02
.998 392
.28
45
16
.056 983
4.65
.057 076
4.87
17.5205
14.85
.998 375
.27
44
17
.057 274
4.83
.057 368
4.87
17.4314
14.70
.998 359
.28
43
18
.057 564
4.83
.057 660
4.86
17.3432
14 57
.998 342
.28
42
19
.057 854
4.85
.057 951
4.87
17.2558
14.42
.998 325
.28
41


20
0.058 145
4.83
0.058 243
4.87
17.1693
14.27
0.998 308
.28
40
21
.0583 435
4.85
.058 535
4.87
17.0837
14.12
.998 291
.28
39
22
.058 726
4.83
.058 827
4.87
16.9990
14.00
.998 274
.28
38
23
.059 016
4.83
.059 119
4.87
16.9150
13.85
.998 257
.28
37
24
,059 306
4.85
.059 411
4.87
16.8319
13.72
.998 240
.28
36
25
.059 597
4.83
.059 703
4.87
16.7496
13.58
.998 223
.30
35
26
.059 887
4.83
.059 995
4.87
16.6681
13.45
.998 205
.28
34
27
.060 177
4.85
.060 287
4.87
16.5874
13.32
.998 188
.30
33
28
.060 468
4.83
.060 579
4.87
16.5075
13.20
.998 170
.28
32
29
.060 758
4.85
.086 871
4.87
16.4283
13.07
.998 153
.30
31


30
0.061 049
4.83
0.061 163
4.87
16.3499
12.95
0.998 135
.30
30
31
.061 339
4.83
.061 455
4.87
16.2722
12.83
.998 117
.30
29
32
.061 629
4.85
.061 747
4.87
16.1952
12.70
.998 099
.30
28
33
.061 920
4.83
.062 039
4.87
16.1190
12.58
.998 081
.30
27
34
.062 210
4.83
.062 331
4.87
16.0435
12.47
.998 063
.30
26
35
.062 500
4.85
.062 623
4.87
15.9687
12.37
.998 045
.30
25
36
.062 791
4.83
.062 915
4.87
15.8946
12.23
.998 027
.32
24
37
.063 081
4.83
.063 207
4.87
15.8211
12.13
.998 008
.30
23
38
.063 371
4.83
.063 499
4.87
15.7463
12.02
.997 990
.30
22
39
.063 661
4.85
.063 791
4.87
15.6762
11.90
.997 972
.32
21


40
0.063 952
4.83
0.064 083
4.87
15.6048
11.80
0.997 953
.32
20
41
.064 242
4.83
.064 375
4.87
15.5340
11.70
.997 934
.30
19
42
.064 532
4.85
.064 667
4.87
15.4638
11.58
.997 916
.32
18
43
.064 823
4.83
.064 959
4.87
15.3943
11.48
.997 897
.32
17
44
.065 113
4.83
.065 251
4.87
15.3254
11.38
.997 878
.32
16
45
.065 403
4.83
.065 543
4.88
15.2571
11.30
.997 859
.32
15
46
.065 693
4.85
.065 836
4.87
15.1893
11.18
.997 840
.32
14

Cos
d."
Cot
d."
Tan
d."
Sin
d."
3

Sin
d."
Tan
d."
Cot
d."
Cos
d."
47
.065 984
4.83
.066 128
4.87
15.1222
11.08
.997 821
.33
13
48
.066 274
4.83
.066 420
4.87
15.0557
10.98
.997 901
.32
12
49
.066 564
4.33
.066 712
4.87
14.9898
10.90
.997 782
.32
11


50
0.066 854
4.85
0.067 004
4.87
14.9244
10.80
0.997 763
.33
10
51
.067 145
4.83
.067 296
4.88
14.8596
10.70
.997 743
.32
09
52
.067 435
4.83
.067 589
4.87
14.7954
10,62
.997 724
.33
08
53
.067 725
4.83
.067 681
4.87
14.7317
10.53
.997 704
.33
07
54
.068 015
4.83
.068 173
4.87
14.6685
10.43
.997 684
.33
06
55
.068 306
4.83
.068 465
4.83
14.6059
10.35
.997 665
.32
05
56
.068 596
4.83
.068 758
4.87
14.5438
10.25
.997 645
.33
04
57
.086 886
4.83
.069 050
4.87
14.4823
10.18
.997 625
.33
03
58
.069 176
4.83
.069 342
4.88
14.4212
10.08
.997 604
.35
02
59
.069 466
4.83
.069 635
4.87
14.3607
10.00
.997 584
.33
01


60
0.069 756

0.069 927
14.3007
0.997 564
00

Cos
d."
Cot
d."
Tan
d."
Sin
d."

4

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.069 756
4.85
0.069 927
4.87
14.3007
9.93
0.997 564
.33
60'
01
.070 047
4.83
.070 219
4.87
.2411
9.83
.997 544
.35
59
02
.070 337
4.83
.070 511
4.88
.1821
9.77
.897 523
.33
58
03
.070 627
4.83
.070 804
4.87
.1235
9.67
.997 503
.35
57
04
.070 917
4.83
.071 096
4.88
.0655
9.60
.897 482
.33
56
05
.071 207
4.83
.071 389
4.87
14.0079
9.53
.997 462
.35
55
06
.071 497
4.85
.071 681
4.87
13.9507
9.45
.997 441
.35
54
07
.071 788
4.83
.071 973
4.88
.8940
9.37
.997 420
.35
53
08
.072 078
4.83
.072 266
4.87
.8378
9.28
.997 399
.35
52
09
.072 368
4.83
.072 558
4.88
.7821
9.23
.997 378
.35
51


10
0.072 658
4.83
0.072 351
4.87
13.7267
9.13
0.997 357
.35
50
11
.072 948
4.83
.073 143
4.87
.6719
9.08
.997 336
.37
49
12
.073 238
4.83
.073 435
4.88
.6174
9.00
.997 314
.35
48
13
.073 528
4.83
.073 728
4.87
.5634
8.93
.997 293
.35
47
14
.073 818
4.83
.074 020
4.88
.5098
8.87
.997 272
.37
46
15
.074 108
4.85
.074 313
4.87
.4566
8.78
.997 250
.35
45
16
.074 399
4.83
.074 605
4.88
.4039
8.73
.997 229
.37
44
17
.074 689
4.83
.074 898
4.87
.3515
8.65
.997 207
.37
43
18
.074 979
4.83
.076 190
4.88
.2996
8.60
.997 185
.37
42
19
.075 269
4.83
.075 483
4.87
.2480
8.52
.997 163
.37
41


20
0.075 559
4.83
0.075 775
488
13.1369
8.47
0.997 141
.37
40
21
.075 849
4.83
.076 068
4.88
.1461
8.38
.997 119
.37
39
22
.076 139
4.83
.076 361
4.87
.0958
8.33
.997 097
.37
38
23
.076 429
4.83
.076 653
4.88
13.0458
8.27
.997 075
.37
37
24
.076 719
4.83
.076 946
4.87
12.9962
8.22
.997 053
.38
36
25
.077 009
4.83
.077 238
4.88
.9469
8.13
.997 030
.37
35
26
.077 299
4.83
.077 531
4.88
.8981
8.03
.997 008
.38
34
27
.077 589
4.83
.077 824
4.87
.8496
8.03
.996 985
.37
33
28
.077 879
4.83
.078 116
4.86
.8014
7.97
.996 963
.38
32
29
.078 169
4.83
.078 409
4.86
.7536
7.90
.996 940
.38
31


30
0.078 459
4.83
0.078 702
4.87
12.7062
7.85
0.996 917
.38
30
31
.078 749
4.83
.078 994
4.88
.6591
7.78
.996 994
.37
29
32
.079 039
4.83
.079 287
4.88
.6124
7.73
.996 872
.40
28
33
.079 329
4.83
.079 660
4.88
.5660
7.68
.996 848
.38
27
34
.079 619
4.83
.079 873
4.87
.5199
7.62
.996 825
.38
26
35
.079 909
4.83
.080 165
4.88
.4742
7.57
.996 802
.33
25
36
.080 199
4.83
.080 458
4.88
.4288
7.50
.996 779
.38
24
37
.080 489
4.83
.080 751
4.88
.3838
7.47
.996 756
.40
23
38
.080 779
4.83
.031 044
4.87
.3390
7.40
.996 732
.38
22
39
.081 069
4.83
.081 336
4.88
.2946
7.35
.996 709
.40
21


40
0.081 359
4.83
0.081 629
4.88
12.2505
7.30
0.996 685
.40
20
41
.081 649
4.83
.081 922
4.88
.2067
7.25
.996 661
.40
19
42
.081 939
4.82
.082 215
4.88
.1632
7.18
.996 637
.38
18
43
.082 228
4.83
.082 508
4.88
.1201
7.15
.996 614
.40
17
44
.082 518
4.83
.082 801
4.88
.0772
7.10
.996 590
.40
16
45
.082 808
4.83
.083 094
4.87
12.0346
7.05
.996 566
.42
15
46
.083 098
4.83
.083 386
4.88
11.9923
6.98
.996 541
.40
14

Cos
d."
Cot
d."
Tan
d."
Sin
d."
4

Sin
d."
Tan
d."
Cot
d."
Cos
d."
47
.083 388
4.83
.083 679
4.88
.9504
6.95
.996 517
.40
13
48
.083 678
4.83
.083 972
4.88
.9087
6.90
.996 493
.42
12
49
.083 968
4.83
.084 265
4.88
.8673
6.85
.996 468
.40
11


50
0.068 258
4.82
0.084 558
4.88
11.8262
6.82
0996 444
.42
10
51
.084 547
4.83
.084 851
4.88
.7853
6.75
.996 419
.40
09
52
.084 837
4.83
.085 144
4.83
.7448
6.72
.996 395
.42
08
53
.085 127
4.83
.085 437
4.83
.7045
6.67
.996 370
.42
07
54
.085 417
4.83
.085 730
4.88
.6848
6.62
.996 345
.42
06
55
.085 707
4.83
.086 023
4.88
.6248
6.58
.996 320
.42
05
56
.085 997
4.82
.086 316
4.88
.5853
6.53
.996 295
.42
04
57
.086 286
4.83
.086 609
4.88
.5461
6.48
.996 270
.42
03
58
.086 576
4.83
.086 902
4.90
.5072
6.45
.996 245
.42
02
59
.086 866
4.83
.087 196
4.88
.4685
6.40
.996 220
.42
01


60
0.087 156

0.087 489
11.4301
0.996 195
00

Cos
d."
Cot
d."
Tan
d."
Sin
d."

5

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.087 156
4.83
0.087 489
4.88
11.4301
6.37
0.996 195
.43
60'
01
.087 446
4.82
.087 782
4.88
.3919
6.32
.996 169
.42
59
02
.087 735
4.83
.088 075
4.88
.3540
6.28
.996 144
.43
58
03
.088 025
4.83
.088 368
4.88
.3163
6.23
.996 118
.42
57
04
.088 315
4.83
.088 661
4.88
.2789
6.20
.996 093
.43
56
05
.088 605
4.82
.088 954
4.90
.2417
6.15
.996 067
.43
55
06
.088 894
4.83
.089 248
4.88
.2048
6.12
.996 041
.43
54
07
.089 184
4.83
.089 541
4.88
.1681
6.08
.996 015
.43
53
08
.089 474
4.82
.089 834
4.88
.1316
6.03
.996 989
.43
52
09
.089 763
4.83
.090 127
4.90
.0954
6.00
.995 963
.43
51


10
0.090 053
4.83
0.090 421
4.88
11 0594
5.95
0.995 937
.43
50
11
.090 343
4.83
0.090 714
4.89
11.0237
5.92
.995 911
.45
49
12
.090 633
4.82
.091 007
4.88
10.9882
5.88
.995 884
.43
48
13
.090 922
4.83
.091 300
4.90
.9529
5.85
.995 858
.43
47
14
.091 212
4.83
.091 594
4.88
.9178
5.82
.935 832
.45
46
15
.091 502
4.82
.091 887
4.88
.8829
5.77
.995 805
.45
45
16
.091 791
4.83
.092 180
4.90
.8483
5.73
.995 778
.43
44
17
.092 081
4.83
.092 474
4.88
.8139
5.70
.995 752
.45
43
18
.092 371
4.82
.092 767
4.90
.7797
5.67
.995 725
.45
42
19
.092 660
4.83
.093 061
4.88
.7457
5.63
.995 698
.45
41


20
0.092 950
4.82
0.093 354
4.88
10.7119
5.60
0.995 671
.45
40
21
.093 239
4.83
.093 647
4.90
.6783
5.55
.995 644
.45
39
22
.093 529
4.83
.093 941
4.88
.6460
5.53
.995 617
.47
38
23
.093 819
4.82
.094 234
4.90
.6118
5.48
.995 589
.45
37
24
.094 108
4.83
.094 528
4.88
.5789
5.45
.995 562
.45
36
25
.094 398
4.82
.094 821
4.90
.5462
5.43
.995 535
.47
35
26
.094 687
4.83
.095 116
4.88
.5136
5.35
.995 507
.47
34
27
.094 977
4.83
.095 408
4.90
.4813
5.37
.995 479
.45
33
28
.095 267
4.82
.095 702
4.88
.4491
5.32
.995 452
.47
32
29
.095 556
4.83
.095 995
4.90
.4172
5.30
.995 424
.47
31


30
0.095 846
4.82
0.096 289
4.90
10.3854
5.27
0.995 396
.47
30
31
.096 135
4.83
.096 583
4.88
.3538
5.23
.995 368
.47
29
32
.096 425
4.82
.096 876
4.90
.3224
5.18
.995 340
.47
28
33
.096 714
4.83
.097 170
4.90
.2913
5.18
.995 312
.47
27
34
.097 004
4.82
.097 464
4.88
.2602
5.13
.995 284
.47
26
35
.097 293
4.83
.097 757
4.90
.2294
5.10
.995 256
.48
25
36
.097 583
4.82
.098 051
4.90
.1988
5.08
.995 227
.47
24
37
.097 872
4.83
.098 345
4.88
.1683
5.03
.995 199
.48
23
36
.098 162
4.82
.098 638
4.90
.1381
5.02
.995 170
.47
22
39
.098 451
4.83
.093 932
4.90
.1080
5.00
.995 142
.48
21


40
0.098 741
4.82
0.099 226
4.88
10.0780
4.95
0.995 113
.48
20
41
.099 030
4.83
.099 519
4.90
.0483
4.93
.995 084
.47
19
42
.099 320
4.82
.099 813
4.90
10.0187
4.90
.995 056
.48
18
43
.099 609
4.83
.100 107
4.90
9.8893
4.87
.995 027
.48
17
44
.099 899
4.82
.100 401
4.90
.9601
4.85
.994 998
.48
16
45
.100 188
4.82
.100 695
4.90
.9310
4.82
.994 969
.50
15
46
.100 477
4.83
.100 989
4.88
.9021
4.78
.994 939
.48
14

Sin
d."
Tan
d."
Cot
d."
Cos
d."

5

Sin
d."
Tan
d."
Cot
d."
Cos
d."
47
.100 767
4.82
.101 282
4.90
.8734
4.77
.994 910
.48
13
48
.101 056
4.83
.101 576
4.90
.9448
4.73
.994 881
.50
12
49
.101 346
4.82
.101 870
4.90
.8164
4.70
.994 881
.48
11


50
0.101 635
4.82
0.102 164
4.90
9.7882
4.68
0.994 822
.50
10
51
.101 924
4.83
.102 458
4.90
.7601
4.65
.994 792
.50
09
52
.102 214
4.82
.102 752
4.90
.7322
4.63
.994 762
.48
08
53
.102 503
4.83
.103 046
4.90
.7044
4.60
.994 733
.50
07
54
.102 793
4.82
.103 340
4.90
.6768
4.58
.994 703
.50
06
55
.103 082
4.82
.103 634
4.90
.6493
4.55
.994 673
.50
05
56
.103 371
4.83
.103 928
4.90
.6220
4.52
.994 643
.50
04
57
.103 661
4.82
.104 222
4.90
.5949
4.50
.994 613
.50
03
58
.103 950
4.82
.104 516
4.90
.5679
4.47
.994 583
.52
02
59
.104 239
4.32
.104 810
4.90
.5411
4.45
.994 552
.50
01


60
0.104 528

0.105 104
9.5144
0.994 522
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

6

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.104 528
4.83
0.105 104
4.90
9.514 36
44.25
0.944 522
.52
60'
01
.104 818
4.82
.105 398
4.90
.487 81
44.00
.994 491
.50
59
02
.105 107
4.82
.105 692
4.92
.461 41
43.77
,994 461
.52
58
03
.105 396
4 83
.105 987
4.90
.435 15
43.52
.994 430
.50
57
04
.105 686
4.82
.106 281
4.90
.409 04
43.28
.994 400
.52
56
05
.105 975
4.82
.106 575
4.90
.383 07
43.05
.994 369
.52
55
06
.106 264
4.82
.106 869
4.90
.357 24
42.82
.994 338
.52
54
07
.106 553
4.83
.107 163
4.92
.331 55
42.60
.994 307
.52
53
08
.106 843
4.82
.107 458
4.90
.305 99
42.35
.994 276
.52
52
09
.107 132
4.82
.107 752
4.90
.280 58
42.13
.994 245
.52
51


10
0.107 421
4.82
0.108 046
4.90
9.255 30
41.90
0.994 214
.53
50
11
.107 710
4.82
.108 340
4.92
.230 16
41.67
.994 182
.52
49
12
.107 999
4.83
.108 635
4.90
.205 16
41.47
.994 151
.52
48
13
.108 289
4 82
.108 929
4.90
.180 28
41.23
.994 120
.52
47
14
.108 578
4.82
.109 223
4.92
.155 54
41.02
.994 088
.53
46
15
.108 867
4.82
.109 518
4.90
.130 93
40.78
.994 056
.52
45
16
.109 156
4 82
.109 812
4.92
.106 46
40.58
.994 025
.53
44
17
.109 445
4.82
.110 107
4.90
.082 11
40.37
.993 993
.53
43
18
.109 734
4.82
.110 401
4.90
.057 89
40.17
.993 961
.53
42
19
.110 023
4.83
.110 695
4.92
.033 79
39.93
.993 929
.53
41


20
0.110 313
4.82
0.110 990
4.90
9.009 83
39.75
0.993 897
.53
40
21
.110 602
4.82
.111 264
4.92
8.965 98
39.52
.993 865
.53
39
22
.110 891
4.82
.111 579
4.90
.862 27
39.33
.993 833
.55
38
23
.111 180
4.82
.111 873
4.92
.938 67
39.12
.993 800
.53
37
24
.111 469
4.82
.112 168
4.92
.915 20
38.92
.993 768
.55
36
25
.111 758
4.82
.112 463
4.90
.891 85
38.72
.993 735
.53
35
26
.112 047
4.82
.112 757
4.92
.868 62
38.52
.993 703
.55
34
27
.112 336
4.82
.113 052
4.90
.846 55
38.32
.993 670
.53
33
28
.112 625
4.82
.113 346
4.92
.882 52
38.13
.993 638
.55
32
29
.112 914
4.82
.113 641
4.92
.799 64
37.92
.993 605
.55
31


30
0.113 203
4.82
0.113 936
4.90
8.776 89
37.73
0.993 572
.55
30
31
.113 492
4.82
.114 230
4.92
.754 25
37.55
.993 539
.55
29
32
.113 781
4.82
.114 525
4.92
.731 72
37.35
.993 506
.55
28
33
.114 070
4.82
.114 820
4.90
.709 31
37.17
.993 473
.57
27
34
.114 359
4.82
.115 114
4.92
.687 01
36.98
.993 439
.55
26
35
.114 648
4.82
.115 409
4.92
.664 82
36.78
.993 406
.55
25
36
.114 937
4.82
.115 704
4.92
.642 75
36.62
.993 373
.57
24
37
.115 226
4.82
.115 999
4.92
.620 78
36.42
.993 339
.55
23
38
.115 515
4.82
.116 294
4.90
.598 93
36.25
.993 306
.57
22
39
.115 804
4.82
.116 588
4.92
.577 18
36.05
.993 272
.57
21


40
0.116 093
4.82
0.116 883
4.92
8.555 55
35.88
0.993 238
.55
20
41
.116 382
4.82
.117 178
4.92
.534 02
35.72
.993 205
.57
19
42
.116 671
4.82
.117 473
4.92
.512 59
35.52
.993 171
.57
18
43
.116 960
4.82
.117 768
4.92
.491 28
35.35
.993 137
.57
17
44
.117 249
4.80
.118 063
4.92
.470 07
35.18
.993 103
.58
16
45
.117 537
4.82
.118 358
4 92
.448 96
35.02
.993 068
.57
15
46
.117 826
4.82
.118 653
4 92
.427 95
34.83
.993 034
.57
14
47
.118 115
4.82
.118 948
4.92
.407 05
34.67
.993 000
.57
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
6

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.116 404
4.82
.119 243
4.92
.386 25
34.50
.992 966
.58
12
49
.118 693
4.82
.119 538
4.92
.365 55
34.32
.992 931
.58
11


50
0.118 982
4.80
0.119 833
4.92
8.344 96
34.17
0.992 896
57
10
51
.119 270
4.82
.120 128
4.92
.324 46
34.00
.992 862
.58
09
52
.119 559
4.82
.120 423
4.92
.304 06
33.83
.992 827
.58
08
53
.119 843
4.82
.120 718
4.92
.283 76
33.68
.992 792
.58
07
54
.120 137
4.82
.121 013
4.92
.263 55
33.50
.992 757
.58
06
55
.120 426
4.83
.121 308
4.93
.243 45
33.35
.992 722
.58
05
56
.120 714
4.82
.121 604
4.92
.223 44
33.22
.992 687
.58
04
57
.121 033
4.82
.121 899
4.92
.205 52
33.03
.992 652
.58
03
58
.121 292
4.82
.122 194
4.92
.183 70
32.87
.992 617
.58
02
59
.121 581
4.80
.122 489
4.93
.163 98
32.72
.992 582
.60
01


60
0.121 869

0.122 785
8.144 35
0.992 546
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."


7

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.121 869
4.82
0.122 785
4.92
8.144 35
32 57
0.992 546
.58
60'
01
.122 158
4.82
.123 080
4.92
.124 81
32.42
.992 511
.60
59
02
.122 447
4.80
.123 375
4.92
.105 36
32.27
.992 475
.60
58
03
.122 735
4.82
.123 670
4.93
.086 00
32.10
.992 439
.58
57
04
.123 024
4.82
.123 966
4.92
.066 74
31.97
.992 404
.60
56
05
.123 313
4.80
.124 261
4.93
.047 56
31.80
.992 368
.60
55
06
.123 601
4.82
.124 557
4.92
.028 48
31.67
.992 333
.60
54
07
.123 890
4.82
.124 852
4.92
.009 48
31.50
.992 296
.60
53
08
.124 179
4.80
.125 147
4.93
7.99 58
31.37
.992 260
.60
52
09
.124 467
4.82
.125 443
4.92
.971 76
31.23
.992 224
.62
51


10
0.124 756
4.82
0.125 738
4.93
7.953 02
31.07
0.992 187
.60
50
11
.125 045
4.80
.126 034
4.92
.934 38
30.93
.992 151
.60
49
12
.125 333
4.82
.126 329
4.93
.915 82
30.90
.992 115
.62
48
13
.126 622
4.80
.126 625
4.92
.897 34
30.65
.992 078
.60
47
14
.126 910
4.82
.126 920
4.93
.878 95
30.52
.992 042
.62
46
15
.126 199
4.32
.127 216
4.93
.360 64
30.37
.992 005
.62
45
16
.126 488
4.80
.127 512
4.92
.842 42
30.23
.991 968
.62
44
17
.176 776
4.82
.127 807
4.93
.824 28
30.10
.991 931
.62
43
18
.127 065
4.80
.128 103
4.93
.806 22
29.95
.991 894
.62
42
19
.127 353
4.82
.128 399
4.92
.788 25
29.83
.991 957
.62
41


20
0.127 642
4.30
.128 694
4.93
7.770 35
29.68
0.991 820
.62
40
21
.127 930
4.82
.128 990
4.93
.752 54
29.57
.991 783
.62
39
22
.128 219
4.80
.129 286
4.93
.734 80
29.42
.991 746
.62
38
23
.128 507
4.82
.129 582
4.92
.717 15
29.30
.991 709
.63
37
24
.128 796
4.80
.129 877
4.93
.699 57
29.15
.991 671
.62
36
25
.129 084
4.82
.130 173
4.93
.682 08
29.03
.991 634
.63
35
26
.129 373
4.80
.130 469
4.93
.664 66
28.90
.991 596
.63
34
27
.129 661
4.80
.130 765
4.93
.647 32
28.78
.991 558
.62
33
28
.129 949
4.82
.131 061
4.93
.630 05
28.63
.991 521
.63
32
29
.130 238
4.80
.131 357
4.92
.612 87
28.53
.991 483
.63
31


30
0.130 528
4.82
0.131 652
4.93
7.595 75
28.38
0.991 445
.63
30
31
.130 815
4.80
.131 948
4.93
.578 72
28.27
.991 407
.86
29
32
.131 103
4.80
.132 244
4.93
.561 76
28.15
.998 369
.63
28
33
.131 391
4.82
.132 540
4.83
.544 87
28.02
.991 331
.65
27
34
.131 680
4.80
.132 836
4.93
.528 06
27.00
.991 292
.63
26
35
.131 968
4.80
.133 132
4.93
.511 32
27.78
.991 254
.63
25
36
.132 256
4.82
.133 428
4.95
.494 65
27.65
.991 216
.65
24
37
.132 545
4.80
.133 725
4.93
.478 06
27.53
.991 177
.65
23
38
.132 833
4.80
.134 021
4.93
.461 54
27.42
.991 138
.63
22
39
.133 121
4.82
.134 317
4.93
.445 09
27.30
.991 100
.65
21


40
0.133 410
4.80
0.134 613
4.93
7.428 71
27.18
0.991 061
.65
20
41
.133 698
4.80
.134 909
4.93
.412 40
27.07
.991 022
.65
19
42
.133 986
4.80
.135 205
4.95
.396 16
26.95
.990 083
.65
18
43
.134 274
4.82
.135 502
4.93
.379 99
26.83
.990 994
.65
17
44
.134 563
4.80
.135 793
4.93
.363 89
26.72
.990 905
.65
16
45
.134 851
4.80
.136 094
4.93
.347 86
26 60
.990 866
.65
15
46
.135 139
4.80
.136 390
4.95
.331 90
26.50
.990 827
.67
14

Sin
d."
Tan
d."
Cot
d."
Cos
d."
7

Sin
d."
Tan
d."
Cot
d."
Cos
d."
47
.135 427
4.82
.136 687
4.93
.316 00
26.37
.990 787
.65
13
48
.135 716
4.80
.136 983
4.93
.330 18
26.27
.990 748
.67
12
49
.136 004
4.80
.137 279
4.95
.284 42
26.15
.990 708
.65
11


50
0.136 292
4.80
0.137 576
4.93
7.268 73
26.05
0.990 669
.67
10
51
.136 580
4.80
.137 872
4.95
.253 10
25.93
.990 629
.67
09
52
,136 868
4.80
.138 169
4.93
.237 54
25.83
.990 589
.67
08
53
,137 156
4.82
.136 465
4.93
.222 04
25.72
.990 549
.67
07
54
,137 445
4.80
.136 761
4.95
.206 61
25.60
.990 509
.67
06
55
.137 733
4,80
.139 058
4.93
.191 25
25.52
.990 469
.67
05
56
,138 021
4,80
.139 354
4.95
.175 94
25.53
.990 429
.67
04
57
.138 309
4.80
.139 651
4.95
.160 71
25.30
.990 389
.67
03
58
.138 597
4,80
.139 948
4.93
.145 53
25.18
.990 349
.67
02
59
,133 883
4,80
.140 244
4.95
.130 42
25.08
.995 309
.68
01


60
0.139 173

0.140 541
7.115 37
0.099 268
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

8

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.139 173
4.80
0.140 541
4.93
7.113 37
24.98
0.990 268
.67
60'
01
.139 461
4.80
.140 837
4.95
.100 38
24.87
.990 228
.68
59
02
.139 749
4.80
.141 134
4.95
.085 46
24.78
.990 187
.68
58
03
.140 037
4.80
.141 431
4.95
.070 59
24.67
.990 146
.66
57
04
.140 325
4.80
.141 728
4.93
.055 79
24.57
.990 105
.67
56
05
.140 613
4.80
.142 024
4.95
.041 05
24.47
.990 065
.68
55
06
.140 901
4.80
.142 321
4.95
.026 37
24.38
.990 024
.68
54
07
.141 189
4.88
.142 618
4.95
.011 74
24.27
.989 983
.68
53
08
.141 477
4.80
.142 915
4.95
6.997 18
24.17
.989 942
.70
52
09
.141 765
4.80
.143 212
4.93
.982 68
24.08
.989 900
.68
51


10
0.142 053
4.80
0.143 508
4.95
6.968 23
23.97
0.989 859
.68
50
11
.142 341
4.80
.143 805
4.95
.953 85
23.88
.989 818
.70
49
12
.142 629
4.80
.144 102
4.95
.939 52
23 78
.989 776
.68
48
13
.142 917
4.80
.144 399
4.95
.925 25
23.68
.989 735
.70
47
14
.143 205
4.80
.144 696
4.95
.911 04
23.60
.989 693
.70
46
15
.143 493
4.78
.144 993
4.95
.896 88
23.50
.989 651
.68
45
16
.143 780
4.80
.145 290
4.95
.882 78
23.40
.989 610
.70
44
17
.144 068
4.80
.145 587
4.95
.868 74
23.32
.989 568
.70
43
18
.144 356
4.80
.145 884
4.95
.854 75
23.22
.989 526
.70
42
19
.144 644
4.80
.146 181
4 95
.840 32
23.13
.989 484
.70
41


20
0.144 932
4.80
0.146 478
4.97
6.826 94
23.03
0.989 442
.72
40
21
.145 220
4.78
.146 776
4.95
.813 12
22.93
.989 399
.70
39
22
.145 507
4.80
.147 073
4.95
.799 36
22.87
.989 357
.70
38
23
.145 795
4.80
.147 370
4.95
.785 64
22.75
.989 315
.72
37
24
.146 083
4.80
.147 667
4.95
.771 99
22 68
.989 272
.70
36
25
.145 371
4.80
.147 964
4.97
.758 38
22.58
.989 230
.72
35
26
.146 659
4.78
.148 262
4.95
.744 83
22.50
.989 187
.72
34
27
.146 946
4.80
.148 559
4.95
.731 33
22.40
.989 144
.70
33
28
.147 234
4.80
.148 856
4.97
.717 89
22.32
.989 102
.72
32
29
.147 522
4.78
.149 154
4.95
.704 50
22.23
.989 059
.72
31


30
0.147 809
4.80
0.149 451
4.95
6.691 16
22.15
.989 016
.72
30
31
.148 097
4.80
0.149 748
4.97
.677 87
22.07
.988 973
.72
29
32
.148 385
4.78
.150 046
4.95
.664 63
21.98
.988 930
.73
28
33
.148 672
4.80
.150 343
4.97
.651 44
21.88
.988 886
.72
27
34
.146 960
4.80
.150 641
4.95
.638 31
21 80
.988 843
.72
26
35
.149 248
4.78
.150 938
4.97
.625 23
21.73
.988 800
.73
25
36
.149 535
4.80
.151 236
4.95
.612 19
21.63
.988 756
.72
24
37
.149 823
4.80
.151 533
4.97
.599 21
21.57
.988 713
.73
23
38
.150 111
4.78
.151 831
4.97
.586 27
21.47
.988 669
.72
22
39
.150 398
4.80
.152 129
4.95
.573 39
21.40
.988 626
.73
21


40
0.150 686
4.78
0.152 426
4.97
6.560 55
21.30
.988 582
.73
20
41
.150 973
4.80
.152 724
4.97
.547 77
21.23
.988 538
.73
19
42
.151 261
4.78
.153 022
4.95
.535 03
21.15
.988 494
.73
18
43
.151 548
4 80
.153 319
4.97
.522 34
21.07
.988 450
.73
17
44
.151 836
4.78
.153 617
4.97
5.09 70
21.00
.988 406
.73
16
45
.152 123
4.80
.153 915
4.97
.497 10
20.90
.988 362
.75
15
46
.152 411
4.78
.154 213
4.95
.464 66
208.3
.988 317
.73
14

Sin
d."
Tan
d."
Cot
d."
Cos
d."


8

Sin
d."
Tan
d."
Cot
d."
Cos
d."
47
.152 698
4 80
.154 510
4.97
.472 06
207.5
.988 273
.75
13
48
.152 986
4.78
.154 808
4.97
.459 61
20.68
.988 223
.73
12
49
.153 273
4.80
.156 106
4.97
.447 20
20.60
.998 184
.75
11


50
0.153 561
4.78
0.155 404
4.97
6.434 84
20.52
0.988 139
.75
10
51
.153 848
4.80
.155 702
4.97
.422 53
20.45
.938 094
.73
09
52
.154 136
4.78
.156 000
4.97
.410 26
20.37
.988 050
.75
08
53
.154 423
4.78
.156 298
4.97
.398 04
20.28
.988 005
.75
07
54
.154 710
4.80
.156 596
4.97
.385 87
20.22
.987 960
.75
06
55
.154 998
4.78
.156 894
4.97
.373 74
20.15
.987 916
.75
05
56
.155 285
4.78
.157 192
4.97
.361 65
20.07
.987 870
.77
04
57
.155 572
4.80
.157 490
4.97
.349 61
20.00
.987 824
.75
03
58
.155 860
4.76
.157 788
4.97
.337 61
18.92
.987 779
.75
02
59
.156 147
4.76
.158 086
4.97
.325 66
19.85
.987 734
.77
01


60
0.156 434

0.158 384
6.313 75
0.987 688
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."


9

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.156 434
4.80
0.158 384
4.98
6.313 75
19.77
0.987 688
.75
60'
01
.156 722
4.78
.158 683
4.97
.301 89
19.70
.987 643
.77
59
02
.157 009
4.78
.158 981
4.97
.290 67
19.63
.987 597
.77
58
03
.157 296
4.80
.159 279
4.97
.278 29
19.57
.987 551
.75
57
04
.157 584
4.78
.159 577
4.98
.266 55
19.48
.987 506
.77
56
05
.157 871
4.78
.159 876
4.97
.254 86
19.42
.987 460
.77
55
06
.158 158
4.78
.160 174
4.97
.243 21
19.35
.987 414
.77
54
07
.158 445
4.78
.160 472
4.98
.231 60
19.28
.987 368
.77
53
08
.158 732
4.80
.160 771
4.97
.220 03
19.20
.987 322
.78
52
09
.159 020
4.78
.161 069
4.98
.208 51
19.13
.987 275
.77
51


10
0.159 307
4.78
0.161 368
4.97
6.197 03
19.07
0.987 229
.77
50
11
.159 594
4.78
.161 666
4.98
.185 59
19.00
.987 183
.78
49
12
.159 881
4.78
.161 95
4.97
.174 19
18.93
.987 136
.77
48
13
.160 168
4.78
.162 263
4.98
.162 83
18.87
.987 090
.78
47
14
.160 455
4.80
.162 562
4.97
.151 51
18.80
.987 043
.78
46
15
.160 743
4.78
.162 860
4.98
.140 23
18.73
.986 996
.77
45
16
.161 030
4.78
.163 159
4.98
.128 99
18.87
.986 950
.78
44
17
.161 317
4.78
.163 458
4.97
.117 79
18.58
.986 903
.78
43
18
.161 604
4.78
.163 756
4.98
.106 64
18.53
.986 856
.78
42
19
.161 891
4.78
.164 055
4.98
.095 52
18.47
.986 809
.78
41


20
0.162 176
4.78
0.164 354
4.97
6.084 44
18.40
0986 762
.80
40
21
.162 465
4.78
.164 652
4.98
.073 40
18.33
.986 714
.78
39
22
.162 752
4.78
.164 951
4.98
.062 40
18.28
.986 667
.78
38
23
.163 039
4.78
.165 250
4.98
.051 43
18.20
.986 620
.80
37
24
.163 326
4.78
.165 549
4.98
.040 51
18.15
.986 572
.78
36
25
.163 613
4.78
.165 648
4.98
.029 62
18.07
.986 525
.80
35
26
.163 900
4.78
.166 147
4.98
.018 78
18.02
.986 477
.80
34
27
.164 187
4.78
.166 446
4.98
.007 97
17.95
.986 429
.80
33
28
.164 474
4.78
.166 745
4.98
5.997 20
17.90
.986 381
.78
32
29
.164 761
4.78
.167 044
4.98
.986 46
17.83
.986 334
.80
31


30
0.165 048
4.77
0.167 343
4.98
5.975 76
17.77
0.986 296
.80
30
31
.165 334
4.78
.167 642
4.98
.965 10
17.70
.986 238
.82
29
32
.165 621
4.78
.167 941
4.98
.954 48
17.63
.986 189
.80
28
33
.165 908
4.78
.168 240
4.98
.943 90
17.58
.986 141
.80
27
34
.166 195
4.78
.168 539
4.98
.933 35
17.53
.986 093
.80
26
35
.166 482
4.78
.168 838
4.98
.922 83
17.45
.986 045
.82
25
36
.166 769
4.78
.168 137
5.00
.912 36
17.42
.986 996
.82
24
37
.167 056
4.77
.169 437
4.98
.901 91
17.33
.985 947
.80
23
38
.167 342
4.78
.169 736
4.98
.891 51
17.28
.985 899
.82
22
39
.167 629
4.78
.170 035
4.98
.881 14
17.23
.985 850
.82
21


40
0.167 916
4.78
0.170 334
5.00
5.870 80
17.15
0.985 801
.82
20
41
.168 203
4.77
.170 634
4.98
.860 51
17.12
.985 752
.82
19
42
.168 489
4.78
.170 933
5.00
.850 24
17.05
.985 703
.82
18
43
.168 776
4.78
.171 233
4.98
.840 01
16.98
.985 654
.82
17
44
.169 063
4.78
.171 532
4.98
.829 82
16.93
.985 605
.82
16
45
.169 350
4.77
.171 831
5.00
.819 66
16.88
.965 556
.82
15
46
.169 636
4.78
.172 131
4.98
.809 53
16.82
.985 507
.83
14

Sin
d."
Tan
d."
Cot
d."
Cos
d."


9

Sin
d."
Tan
d."
Cot
d."
Cos
d."
47
.169 923
4.77
.172 430
5.00
.799 44
16.77
.985 457
.82
13
48
.170 209
4.78
.172 730
5 00
.789 38
16.70
.985 408
.83
12
49
.170 496
4.78
.173 030
4.98
.779 36
16.65
.985 358
.82
11


50
0.170 783
4.77
.173 329
5 00
5.769 37
16.60
0.985 309
.83
10
51
.171 069
4.78
.173 629
5.00
.759 41
16.53
.985 259
.83
09
52
.171 356
4.78
.173 929
4.98
.749 49
16.48
.985 209
.83
08
53
.171 643
4.77
.174 228
5.00
.739 60
16.43
.988 159
.33
07
54
.171 929
4.78
.174 528
5.00
.729 74
16.37
.965 109
.83
06
55
.172 216
4.77
.174 828
4.98
.719 92
16.32
.985 059
.83
05
56
.172 502
4.78
.175 127
5.00
.710 13
16.27
.985 009
.83
04
57
.172 789
4.77
.175 427
5.00
.700 37
16.22
.984 959
.83
03
58
.173 075
4.78
.175 727
5.00
.690 64
16.17
.984 909
.85
02
59
.173 362
4.77
.176 027
5.00
.680 94
16.10
.984 858
.83
01


60
0.173 648

0.176 327
5.671 28
0.534 803
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

10

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.173 648
4.78
0.176 327
5.00
5.671 28
16.07
0.984 808
.85
60'
01
.173 935
4.77
.176 627
5.00
.661 651
16.00
.984 757
.83
59
02
.174 221
4.78
.176 927
5.00
.652 05
15.95
.984 707
.85
58
03
.174 508
4.77
.177 227
5.00
.642 48
15.88
.984 656
.85
57
04
.174 794
4.77
.177 527
5.00
.632 95
15.85
.984 605
.85
56
05
.175 080
4.78
.177 827
5.00
.623 44
15.78
.984 554
.85
55
06
.175 367
4.77
.178 127
5.00
.613 97
15.75
.984 503
.85
54
07
.176 653
4.77
.178 427
5.00
.604 52
15.68
.984 452
.85
53
08
.175 939
4.78
.178 727
5.02
.595 11
15.63
.984 350
.87
52
09
.176 226
4.77
.179 028
5.00
.585 73
15.58
.984 350
.87
51


10
0.176 512
4.77
0.179 328
5.00
5.676 38
15.53
0.984 298
.85
50
11
.176 798
4.78
.179 828
5.00
.567 06
15.48
.984 247
.85
49
12
.177 085
4.77
.179 928
5.02
.557 77
15.43
.984 196
.87
48
13
.177 371
4.77
.180 229
5.00
.548 61
15.40
.984 144
.87
47
14
.177 657
4.78
.180 529
5.00
.539 27
15.33
.984 092
.85
46
15
.177 944
4.77
.180 829
5.02
.530 07
15.28
.984 041
.87
45
16
.178 230
4.77
.181 130
5.00
.520 90
15.23
.963 989
.87
44
17
.178 516
4.77
.181 430
5.02
.511 76
15.20
.983 937
.87
43
18
.178 802
4.77
.181 731
5.00
.502 64
15.13
.983 885
.87
42
19
.179 088
4.78
.182 031
5.02
.493 56
15.08
.983 833
.87
41


20
0.179 375
4.77
0.182 332
5.00
5.484 51
15.05
0.983 781
.87
40
21
.179 661
4.77
.182 632
5.02
.475 48
15.00
.983 729
.88
39
22
.179 947
4.77
.182 933
5.02
.466 48
14.95
.983 676
.87
38
23
.180 233
4.77
.183 234
5.00
.457 51
14.90
.983 624
.88
37
24
.180 519
4.77
.183 534
5.02
.448 57
14.85
.983 571
.87
36
25
.180 805
4.77
.183 835
5.02
.439 55
14.82
.983 519
.88
35
26
.181 091
4.77
.184 136
5.02
.430 77
14.75
.983 466
.87
34
27
.181 377
4.77
.184 437
5.00
.421 92
14.72
.983 414
.88
33
28
.181 663
4.75
.184 737
5.02
.413 09
14.67
.983 361
.88
32
29
.181 950
4.77
.185 038
5.02
.404 29
14.62
.983 308
.88
31


30
0.182 236
4.77
0.185 339
5.02
5.395 52
14.58
0.983 255
.88
30
31
.182 522
4.77
.185 640
5.02
.386 77
14.53
.983 202
.88
29
32
.182 808
4.77
.185 941
5.02
.378 05
14.48
.983 149
.88
28
33
.183 094
4.75
.186 242
5.02
.369 36
14.43
.983 096
.90
27
34
.183 379
4.77
.186 543
5.02
.360 70
14.40
.983 042
.88
26
35
.183 665
4.77
.186 844
5.02
.352 06
14.35
.982 989
.90
25
36
.183 951
4.77
.187 145
5.02
.343 45
14.30
.982 935
.88
24
37
.187 237
4.77
.187 446
5.02
.334 87
14.27
.982 882
.90
23
38
.184 523
4.77
.187 747
5.02
.326 31
14.22
.982 828
.90
22
39
.184 809
4.77
.188 048
5.02
.317 78
14.17
.982 774
.88
21


40
0.185 095
4.77
0.188 349
5.03
5.309 28
14.13
0.982 721
.90
20
41
.185 381
4.77
.188 651
5.02
.300 80
14.08
.982 667
.90
19
42
.185 667
4.75
.188 952
5.02
.292 35
14.03
.982 613
.90
18
43
.185 952
4.77
.189 253
5.03
.283 93
14.00
.982 559
.90
17
44
.186 238
4.77
.189 555
5.02
.275 53
13.97
.982 505
.92
16
45
.186 524
4.77
.189 856
5.02
.267 15
13.92
.982 450
.90
15
46
.186 810
4.77
.190 157
5.03
.258 80
13.87
.982 396
.90
14

Sin
d."
Tan
d."
Cot
d."
Cos
d."


10

Sin
d."
Tan
d."
Cot
d."
Cos
d."
47
.187 096
4.75
.190 459
5.02
.250 48
13 83
.982 342
.92
13
48
.187 351
4.77
.190 760
5.03
.242 13
13.78
.982 287
.90
12
49
.187 667
4.77
.191 062
5.02
.233 91
13.75
.982 233
.92
11


50
0.187 953
4.75
0.191 363
5.03
5.225 66
13.70
0.982 178
.92
10
51
.188 238
4.77
.191 665
5.02
.217 44
13.65
.982 123
.90
09
52
.188 524
4.77
.191 966
5.03
.209 25
13.63
.982 069
.92
08
53
.188 810
4.75
.192 268
5.03
.201 07
13.57
.932 014
.92
07
54
.189 095
4.77
.192 570
5.02
.192 93
13.55
.981 959
.92
06
55
.189 331
4.77
.192 871
5.03
.184 80
13.48
.981 904
.92
05
56
.189 667
4.75
.193 173
5.03
.176 71
13.47
.981 849
.93
04
57
.189 952
4.77
.193 475
5.03
.168 83
13.42
.981 793
.92
03
58
.190 238
4.75
.193 777
5.02
.160 58
13.37
.981 738
.92
02
59
.190 523
4. 77
.194 078
5.03
.152 56
13.35
.981 683
.93
01


60
0.190 809

0.194 380
5.144 55
0.981 627
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

11

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.190 809
4.77
0.194 380
5.03
5.144 55
13.28
0.981 627
.92
60'
01
.191 095
4.75
.194 682
5.03
.136 58
13.27
.981 572
.93
59
02
.191 380
4,77
.194 984
5.03
128 62
13.22
.981 518
.93
58
03
.191 666
4,75
.195 286
5.03
.120 69
13.17
.981 460
.92
57
04
.191 951
4,77
.195 588
5.03
.112 79
13.15
.981 405
.93
56
05
.192 237
4.75
.195 890
5.03
.104 90
13.10
.981 349
.93
55
06
.192 522
4.75
.196 192
5.03
.097 04
13.05
.981 293
.93
54
07
.192 807
4.77
.196 494
5.03
.089 21
13 03
.981 237
.95
53
08
.193 093
4.75
.196 796
5.03
.081 39
12.98
.981 180
.93
52
09
.193 379
4.77
.197 099
5.03
.073 60
12.93
.981 124
.93
51


10
0.193 664
4.75
0.197 401
5.03
5.065 84
12.92
0.981 068
.93
50
11
.193 949
4.75
.197 703
5.03
.058 09
12.87
.981 012
.95
49
12
.194 234
4.77
.198 005
5.05
.050 37
12.83
.980 955
.93
48
13
.194 520
4.75
.198 308
5.03
.042 67
12.80
.980 899
.95
47
14
.194 805
4.75
.198 610
5.03
.034 99
12.75
.980 842
.95
46
15
.195 090
4.77
.198 912
5.05
.027 34
12.72
.980 785
.95
45
16
.195 376
4.75
.199 215
5.03
.019 71
12.68
.980 728
.93
44
17
.195 661
4.75
.199 517
5.05
.012 10
12.65
.980 672
.95
43
18
.195 946
4.75
.199 820
5.03
.004 51
12.60
.980 615
.96
42
19
.196 231
4.77
.200 122
5.05
4.996 95
12.58
.980 558
.97
41


20
0.196 517
4.75
0.200 425
5.03
4.989 40
12.53
0.980 500
.95
40
21
.196 802
4.75
.200 727
5.05
.981 88
12 50
.980 443
.95
39
22
.197 087
4.75
.201 030
5.05
.974 38
12.47
.980 386
.95
38
23
.197 372
4.75
.201 333
5.03
.966 90
12.42
.980 329
.97
37
24
.197 657
4.75
.201 635
5.05
.959 45
12.40
.980 271
.95
36
25
.197 942
4.77
.201 938
5.05
.952 01
12.35
.980 214
.97
35
26
.198 228
4.75
.202 241
5.05
.944 60
12.32
.930 156
.97
34
27
.196 513
4.75
.202 544
5.05
.937 21
12.28
.980 098
.95
33
28
.196 798
4.75
.202 847
5.03
.929 84
12.25
.980 041
.97
32
29
.199 083
4.75
.203 149
5.05
.922 49
12.22
.979 983
.97
31


30
0.199 368
4.75
0.203 452
5.05
4.915 16
12.18
.979 925
.97
30
31
.199 653
4.75
.203 755
5.05
.907 85
12.15
.979 867
.97
29
32
.199 938
4.75
.204 058
5 05
.900 56
12.10
.979 809
.98
28
33
.200 223
4.75
.204 361
5.05
.893 30
12.08
.979 750
.97
27
34
.200 508
4.75
.204 664
5.05
.886 05
12.05
.979 692
.97
26
35
.200 793
4.75
.204 967
5.07
.878 82
12.00
.979 634
.98
25
36
.201 078
4.75
.205 271
5.05
.871 62
11.97
.979 575
.97
24
37
.201 363
4.75
.205 574
5.05
.864 44
11.95
.979 517
.98
23
38
.201 648
4.75
.205 877
5.05
.857 27
11.90
.979 458
.98
22
39
.201 933
4.75
.206 180
5.05
.850 13
11.88
.979 399
.97
21


40
0.202 218
4.73
0.206 483
5.07
4.843 00
11.83
0.979 341
.98
20
41
.202 502
4.75
.206 787
5.05
.835 90
11.80
.979 282
.98
19
42
.202 787
4.75
.207 090
5.05
.828 82
11.78
.979 223
.98
18
43
.203 072
4.75
.207 393
5.07
.821 75
11.73
.979 164
.98
17
44
.203 357
4.75
.207 697
5.05
.814 71
11.70
.979 105
1.00
16
45
.203 642
4 75
.208 000
5 07
.807 69
11.68
.979 045
.98
15
46
.203 927
4.73
.208 304
5.05
.800 68
11.63
.978 986
.98
14

Sin
d."
Tan
d."
Cot
d."
Cos
d."


11

Sin
d."
Tan
d."
Cot
d."
Cos
d."
47
.204 211
4.75
.208 607
5.07
.793 70
11.62
.978 927
1.00
13
48
.204 496
4.75
.208 911
5.05
.786 73
11.58
.976 867
.88
12
49
.204 781
4.73
.209 214
5.07
.779 78
11.53
.978 808
1.00
11


50
0.205 065
4.75
0.209 518
5.07
4.772 86
11.52
0.978 748
.98
10
51
.205 350
4.75
.209 822
5.07
.765 95
11.48
.978 689
1.00
09
52
.205 635
4.75
.210 126
5.05
.759 06
11.45
.978 629
1.00
08
53
.205 920
4.73
.210 429
5.07
.752 19
11.42
.978 569
1.00
07
54
.206 204
4.75
.210 733
5.0
.745 34
11.38
.978 509
1.00
06
55
.206 489
4.73
.211 037
5.07
.738 51
11.35
.978 449
1.00
05
56
.206 773
4.75
.211 341
5.07
.731 70
11.33
.978 389
1.00
04
57
.207 058
4.75
.211 645
5.07
.724 90
11.28
.978 329
1.02
03
58
.207 343
4.73
.211 949
5.07
.718 13
11.27
.978 268
1.00
02
59
.207 627
4.75
.212 263
5.07
.711 37
11.23
.978 208
1.00
01


60
0.207 912

0.212 557
4.704 63
0.978 148
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

12

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.207 912
4.73
0.212 557
5.07
4.704 63
11.20
0.978 143
1.02
60'
01
.208 196
4.75
.212 861
5.07
.697 91
11.17
.978 087
1.02
59
02
.208 481
4.73
.213 165
5.07
.691 21
11.15
.978 026
1.00
58
03
.208 765
4.75
.213 469
5.07
.684 52
11.10
.977 966
1 02
57
04
.209 050
4.73
.213 773
5.07
.677 86
11.08
.977 905
1.00
56
05
.209 334
4.75
.214 077
5.07
.671 21
11.06
.977 844
1.02
55
06
.209 619
4.73
.214 381
5.08
.664 58
11.02
.977 783
1.02
54
07
.209 903
4.73
.214 686
5.07
.657 97
10.98
.977 722
1.02
53
08
.210 187
4.75
.214 990
5.07
.651 33
10.97
.977 661
1.02
52
09
.210 472
4.73
.215 294
5.08
.644 80
10.92
.977 600
1.02
51


10
0.210 756
4.73
0.215 599
5.07
4.638 25
10.90
0.977 539
1 03
50
11
.211 040
4.75
.215 903
5.03
.631 71
10.88
.977 477
1.02
49
12
.211 325
4.73
.216 208
5.07
.625 18
10.83
.977 416
1.03
48
13
.211 609
4.73
.216 512
5.08
.618 68
10.82
.977 354
1.02
47
14
.211 893
4.75
.216 817
5.07
.612 19
10.78
.977 293
1.03
46
15
.212 178
4.73
.217 121
5.08
.605 72
10.75
.977 231
1.03
45
16
.212 462
4.73
.217 426
5.08
.599 27
10.73
.977 169
1.02
44
17
.212 746
4.73
.217 731
5.07
.592 83
10.70
.977 108
1.03
43
18
.213 030
4.75
.218 035
5.08
.586 41
10.67
.977 046
1.03
42
19
.213 315
4.73
.218 340
5.08
.580 01
10.63
.976 984
1.05
41


20
0.213 599
4.73
0.218 645
5.08
4.573 63
10.62
0.976 921
1.03
40
21
.213 883
4.73
.218 950
5.07
.567 26
10.58
.976 859
1.03
39
22
.214 167
4.73
.219 254
5.08
.560 91
10.55
.976 797
1.03
38
23
.214 451
4.73
.219 559
5.08
.554 58
10.53
.978 635
1.05
37
24
.214 735
4.73
.219 864
5.08
.548 26
10.50
.976 672
1.03
36
25
.215 019
4.73
.220 169
5.08
.541 96
10.47
.976 610
1.05
35
26
.215 303
4.75
.220 474
5.08
.535 68
10.46
.976 547
1.03
34
27
.215 588
4.73
.220 779
5.08
.529 41
10.42
.976 485
1.05
33
28
.215 872
4.73
.221 084
5.08
.523 16
10.38
.976 422
1.05
32
29
.216 156
4.73
.221 389
5.10
.516 93
10.37
.976 359
1.05
31


30
0.216 440
4.73
0.221 695
5.08
4.510 71
10.33
0.976 296
1.05
30
31
.216 724
4.73
.222 000
5.08
.504 51
10.32
976 233
1.05
29
32
.217 008
4.73
.222 305
5.08
.498 32
10.28
.976 170
1.05
28
33
.217 292
4.72
.222 610
5.10
.492 15
10.25
.976 107
1.05
27
34
.217 575
4.73
.222 916
5.08
.486 00
10.23
.976 044
1.07
26
35
.217 859
4.73
.223 221
5.08
.479 86
10.20
.975 980
1.05
25
36
.218 143
4.73
.223 526
5.10
.473 74
10.17
.975 917
1.07
24
37
.218 427
4.73
.223 832
5.08
.467 64
10.15
.975 853
1.05
23
38
.218 711
4.73
.224 137
5.10
.461 55
10.12
.975 790
1.07
22
39
.218 995
4.73
.224 443
5.08
.455 48
10.10
.975 726
1.07
21


40
0.219 279
4.72
0.224 748
5.10
4.449 42
10.07
0.975 662
1.07
20
41
.219 562
4.73
.225 054
5.10
.443 38
10.05
.975 598
1.05
19
42
.219 845
4.73
.225 360
5.08
.437 35
10.02
.975 535
1.07
18
43
.220 130
4.73
.225 665
5.10
.431 34
10.00
.975 471
1.08
17
44
.220 414
4.72
.226 971
5.10
.425 34
9.97
.975 406
1.07
16
45
.220 697
4.73
.226 277
5.10
.419 36
9.93
.975 342
1.07
15
46
.220 981
4.73
.226 583
5.10
.413 40
9.92
.975 278
1.07
14
47
.221 265
4.72
.226 889
5 08
.407 45
9.88
.975 214
1.08
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
12

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.221 548
4.73
.227 194
5.10
.401 52
9.87
.975 149
1.07
12
49
.221 832
4.73
.227 500
5 10
.395 60
9.85
.975 085
1.08
11


50
0.222 116
4.72
0.227 806
5.10
4.389 69
9.80
0.975 020
1.07
10
51
.222 399
4.73
.228 112
5.10
.383 81
9.80
.974 956
1.08
09
52
.222 683
4.73
.377 418
5.10
.377 93
9.77
.974 891
1.08
08
53
.222 967
4.72
.228 724
5.12
.372 07
9.73
.974 826
1.08
07
54
.223 250
4.73
.229 031
5.10
.366 23
9.72
.974 761
1.08
06
55
.223 534
4.72
.229 337
5.10
.360 40
9.68
.974 696
1.08
05
56
.223 817
4.73
.229 643
5.10
.354 59
9.67
.974 631
1.08
04
57
.224 101
4.72
.229 949
5.10
.348 79
9.65
.974 566
1.08
03
58
.224 384
4.73
.230 255
5.12
.343 00
9.62
.974 501
1.10
02
59
.224 668
4.72
.230 562
5.10
.337 23
9.53
.974 435
1.08
01


60
0.224 951

0.230 868
4.331 48
0.974 370
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.224 951
4.72
0.230 868
5.12
4.331 48
9.58
0.974 370
1 08
60'
01
.225 234
4.73
.231 175
5.10
.325 73
9.53
.974 305
1.10
59
02
.225 518
4.72
.231 481
5.12
.320 01
9.52
.974 239
1.10
58
03
.225 801
4.73
.231 788
5.10
.314 30
9.50
.974 173
1 06
57
04
.226 085
4.72
.232 094
5.12
.308 60
9.48
.974 108
1.10
56
05
.226 368
4.72
.232 401
5.10
.302 91
9.45
.974 042
1.10
55
06
.226 651
4.73
.232 707
5.12
.297 24
9.42
.973 976
1.10
54
07
.226 935
4.72
.233 014
5.12
.291 59
9.40
.973 910
1.10
53
08
.227 218
4.72
.233 321
5.10
.285 95
9.38
.973 844
1.10
52
09
.227 501
4.72
.233 627
5,12
.280 32
9.35
.973 778
1.10
51


10
0.227 784
4.73
0.233 934
5.12
4.274 71
9.33
0.973 712
1.12
50
11
.228 068
4.72
.234 241
5.12
.269 11
9.32
.973 645
1.10
49
12
.228 351
4.72
.234 548
5.12
.263 52
9.28
.973 579
1.12
48
13
.228 634
4.72
.234 855
5.12
.257 95
9.27
.973 512
1.10
47
14
.228 917
4.72
.235 162
5.12
.252 39
9.73
.973 446
1.12
46
15
.229 200
4.73
.235 469
5.12
.246 85
9.22
.973 379
1.10
45
16
.229 484
4.72
.235 776
5.12
.241 32
9.20
.973 313
1.12
44
17
.229 767
4.72
.236 083
5.12
.235 80
9.17
.973 246
1.12
43
18
.230 050
4.72
.236 390
5.12
.230 30
9.15
.973 179
1.12
42
19
.230 333
4.72
.236 697
5.12
.224 81
9 13
.973 112
1.12
41


20
0.230 616
4.72
0.237 004
5.13
4.219 33
9.10
0.973 045
1.12
40
21
.230 899
4.72
.237 312
5.12
.213 87
9.08
.972 978
1.12
39
22
.231 182
4.72
.237 619
5.12
.208 42
9.07
.972 911
1.13
38
23
.231 465
4.72
.237 926
5.13
.202 98
9.03
.972 843
1.12
37
24
.231 748
4.72
.238 234
5.12
.197 56
9.02
.972 776
1.13
36
25
.232 031
4.72
.238 541
5.12
.192 15
9.00
.972 708
1.12
35
26
.232 314
4.72
.238 848
5.13
.186 75
8.97
.972 641
1.13
34
27
.232 597
4.72
.239 156
5.13
.181 37
8.96
.972 573
1.12
33
28
.232 880
4.72
.239 464
5.12
.176 00
8.93
.972 506
1.13
32
29
.233 163
4.70
.239 771
5.13
.170 64
8.90
.972 438
1.13
31


30
0.233 445
4.72
0.240 079
5.12
4.165 30
8.88
0.972 370
1.13
30
31
.233 728
4.72
.240 386
5.13
.159 97
8.87
.972 302
1.13
29
32
.234 011
4.72
.240 694
5.13
.154 65
8.85
.972 234
1.13
28
33
.234 294
4.72
.241 002
5.13
.149 34
8.82
.972 166
1.13
27
34
.234 577
4.70
.241 310
5.13
.144 05
8.80
.972 098
1.15
26
35
.234 859
4.72
.241 618
5.12
.138 77
8.78
.972 029
1.13
25
36
.235 142
4.72
.241 925
5.13
.133 50
8.75
.971 961
1.13
24
37
.235 425
4.72
.242 233
5.13
.128 25
8.73
.971 893
1.15
23
38
.235 708
4.70
.242 541
5.13
.123 01
8.72
.971 824
1.15
22
39
.235 990
4.72
.242 849
5.13
.117 78
8.70
.971 755
1.13
21


40
0.236 273
4.72
0.243 157
5.15
4.112 56
8.67
0.971 687
1.15
20
41
.236 556
4.70
.243 466
5.13
.107 36
8.67
.971 618
1.15
19
42
.236 838
4.72
.243 774
5 13
.102 16
8.62
.971 549
1.15
18
43
.237 121
4.70
.244 082
5 13
.096 99
8.62
.971 480
1.15
17
44
.237 403
4.72
.244 390
5 13
.091 82
8.60
.971 411
1.15
16
45
.237 686
4.70
.244 698
5 15
.086 66
8.57
.971 342
1.15
15
46
,237 968
4.72
.245 007
5 13
.081 52
8.55
.971 273
1.15
14

Sin
d."
Tan
d."
Cot
d."
Cos
d."


13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
47
.238 251
4.70
.245 315
5 15
.076 39
8.53
.971 204
1.17
13
48
.238 533
4.72
.245 624
5,13
.071 27
8.52
.971 134
1.15
12
49
.238 816
4.70
.245 932
5.15
.066 16
8.48
.971 065
1.17
11


50
0.239 098
4.72
0.246 241
5 13
4.061 07
8.47
0.970 995
1.15
10
51
.239 381
4.70
.246 549
5.15
.055 99
8.45
.970 926
1.17
09
52
.239 663
4.72
.246 858
5.13
.050 92
8.43
.970 859
1.17
08
53
.239 946
4.70
.247 166
5.15
.045 86
8.42
.970 786
1.17
07
54
.240 228
4.70
.247 475
5.15
.040 81
8.38
.970 716
1.15
06
55
.240 510
4.72
.247 768
5.13
.035 78
8.37
.970 647
1.17
05
56
.240 793
4.70
.248 092
5.15
.030 76
8.37
.970 577
1.18
04
57
.241 075
4.70
.248 401
5.15
.025 74
8.33
.970 506
1.17
03
58
.241 357
4.72
.248 710
5.15
.020 74
8.30
.970 436
1.17
02
59
.241 640
4.70
.249 019
5.15
.015 76
8.30
.970 366
1.17
01


60
0.241 922

0.249 328
4.010 78
0.970 296
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

14

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.241 922
4.70
0.249 328
5.15
4.010 78
8.27
0.970 296
1.18
60'
01
.242 204
4.70
.249 637
5.15
.005 82
8.27
.970 225
1.17
59
02
.242 486
4.72
.249 946
5.15
.000 86
8.23
.970 155
1.18
58
03
.242 769
4.70
.250 255
5.15
3.995 92
8.22
.970 084
1.17
57
04
.243 051
4.70
.250 564
5.15
.990 99
8.20
.970 014
1.18
56
05
.243 333
4.70
.250 873
5.17
.986 07
8.17
.969 943
1.18
55
06
.243 615
4.70
.251 183
5.15
.981 17
8.17
.969 872
1.18
54
07
.243 897
4.70
.251 492
5.15
.976 27
8.13
.969 801
1.18
53
08
.244 179
4.70
.251 801
5.17
.971 39
8.13
.969 730
1.18
52
09
.244 461
4.70
.252 111
5.15
.966 51
8.10
.969 659
1.18
51


10
0.244 743
4.70
0.252 420
5.15
3.961 65
8.08
0.969 588
1.18
50
11
.245 025
4.70
.252 729
5.17
.956 80
8.07
.969 517
1.20
49
12
.245 307
4.70
.253 039
5.15
.951 96
8.05
.969 445
1.18
48
13
.245 589
4.70
.253 348
5.17
.947 13
8.02
.969 374
1.20
47
14
.245 871
4.70
.253 658
5.17
.942 32
8.02
.969 302
1.18
46
15
.246 153
4.70
.253 968
5.15
.937 51
8.00
.969 231
1.20
45
16
.246 435
4.70
.254 277
5.17
.932 71
7.97
.969 159
1.18
44
17
.246 717
4.70
.254 587
5.17
.927 93
7.95
.969 088
1.20
43
18
.246 999
4.70
.254 897
5.17
.923 16
7.95
.969 016
1.20
42
19
.247 281
4.70
.255 207
5.15
.918 39
7.92
.968 944
1 20
41


20
0.247 563
4.70
0.255 516
5.17
3.913 64
7.90
0.968 872
1.20
40
21
.247 845
4.68
.255 826
5.17
.908 90
7.88
.968 800
1.20
39
22
.248 126
4.70
.256 136
5.17
.904 17
7.87
.968 728
1.22
38
23
.248 408
4.70
.256 446
5.17
.899 45
7.85
.968 655
1.20
37
24
.248 690
4.70
.256 756
5.17
.894 74
7.83
.968 583
1.20
36
25
.248 972
4.68
.257 066
5.18
.890 04
7.80
.968 511
1.22
35
26
.249 253
4.70
.257 377
5.17
.885 36
7.80
.968 438
1.20
34
27
.249 535
4.70
.257 687
5.17
.880 68
7.78
.968 366
1.22
33
28
.249 817
4.68
.257 997
5.17
.876 01
7.75
.968 293
1.22
32
29
.250 098
4.70
.258 307
5.18
.871 36
7.75
.968 220
1.20
31


30
0.250 380
4.70
0.258 618
5.17
3.866 71
7.72
0.968 148
1.22
30
31
.250 662
4.68
.258 928
5.17
.862 08
7.72
.968 075
1.22
29
32
.250 943
4.70
.259 238
5.18
.857 45
7.68
.968 002
1.22
28
33
.251 225
4.68
.259 549
5.17
.852 84
7.67
.967 929
1.22
27
34
.251 506
4.70
.259 859
5.18
.848 24
7.67
.967 856
1.23
26
35
.251 788
4.68
.260 170
5.17
.843 64
7.63
.967 782
1.22
25
36
.252 069
4.70
.260 480
5.18
.839 06
7.62
.967 709
1.22
24
37
.252 351
4.68
.260 791
5 18
.834 49
7.62
.967 636
1.23
23
38
.252 632
4.70
.261 102
5.16
.829 92
7.58
.967 562
1.22
22
39
.252 914
4.68
.261 413
5.17
.825 37
7.57
.967 469
1.23
21


40
0.253 195
4.70
0.261 723
5.18
3.820 83
7.55
0.967 415
1.22
20
41
.253 477
4.68
.262 034
5.18
.816 30
7.55
.967 342
1.23
19
42
.253 758
4.68
.262 345
5.18
.811 77
7.52
.967 268
1.23
18
43
.254 039
4.70
.262 656
5.18
.807 26
7.50
.967 194
1.23
17
44
.254 321
4.68
.262 967
5.18
.802 76
7.48
.967 120
1.23
16
45
.254 602
4.68
.263 278
5.18
.798 27
7.48
.967 046
1.23
15
46
.254 883
4.70
.263 589
5.18
.793 78
7.45
.966 972
1.23
14
47
.255 165
4.68
.263 900
5.18
.789 31
7.43
.966 898
1.25
13

Sin
d."
Tan
.d"
Cot
d."
Cos
d."
14

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.255 446
4.68
.264 211
5.20
.784 85
7.42
.966 823
1.23
12
49
.255 727
4.68
.264 523
5.18
.780 40
7.42
.966 749
123
11


50
0.256 008
4.68
0.264 834
5.18
3.775 95
7.38
0.966 675
1.25
10
51
.256 289
4.70
.265 145
5.20
.771 52
7.38
.966 600
1.23
09
52
.256 571
4.68
.265 457
5.18
.767 09
7.35
.966 526
1.25
08
53
.256 852
4.68
.265 768
5.18
.762 68
7.33
.966 451
1.25
07
54
.257 133
4.68
.266 079
5.20
.758 28
7.33
.966 376
1.25
06
55
.257 414
4.68
.266 391
5.18
.753 88
7.30
.966 301
1.25
05
56
.257 695
4.68
.266 702
5.20
.749 50
7.30
.966 226
1.25
04
57
.257 976
4.68
.267 014
5.20
.745 12
7.28
.966 151
1.25
03
58
.258 257
4 68
.267 326
5.18
.740 75
7.25
966 076
1.25
02
59
.258 538
4.68
.267 637
5.20
.736 40
7.25
.966 001
1.25
01


60
0.258 819

0.267 949
3.732 05
0.965 926
00

Sin
d."
Tan
.d"
Cot
d."
Cos
d."

15

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.258 819
4.66
0.267 949
5.20
3.732 05
7.23
0.965 926
1.27
60'
01
.259 100
4.68
.268 261
5.20
.727 71
7.22
.965 850
1.25
59
02
.259 381
4.68
.268 573
5.20
.723 38
7.18
.965 775
1.25
58
03
.259 662
4.68
.268 885
5.20
.719 07
7.18
.965 700
1.27
57
04
.259 943
4.68
.269 197
5.20
.714 76
7.17
.965 624
1.27
56
05
.260 224
4.68
.269 509
5.20
.710 46
7.17
.965 548
1.25
55
06
.260 505
4.67
.269 821
5.20
.706 16
7.13
.965 473
1.27
54
07
.260 785
4.68
.270 133
5.20
.701 88
7.12
.965 397
1.27
53
08
.261 066
4.68
.270 445
5.20
.697 61
7.10
.965 321
1.27
52
09
.261 347
4.68
.270 757
5.20
.693 35
7.10
.965 245
1.27
51


10
0.261 628
4.67
0.271 069
5.22
3.689 09
7.07
0.965 169
1.27
50
11
.261 908
4.68
.271 382
5.20
.684 85
7.07
.965 093
1.28
49
12
.262 189
4.68
.271 694
5.20
.680 61
7.05
.965 016
1.27
48
13
.262 470
4.68
.272 006
5.22
.676 38
7.02
.964 940
1.27
47
14
.262 751
4.67
.272 319
5.20
.672 17
7.02
.964 864
1.28
46
15
.263 031
4.68
.272 631
5.22
.667 96
7.00
.964 787
1.27
45
16
.263 312
4.67
.272 944
5.20
.663 76
6.98
.964 711
1.28
44
17
.263 592
4.68
.273 256
5.22
.659 57
6.98
.964 634
1.28
43
18
.263 873
4.68
.273 569
5.22
.665 38
6.95
.964 567
1.27
42
19
.264 154
4.67
.273 882
5.20
.661 21
6.93
.964 481
1.28
41


20
0.264 434
4.68
0.274 194
5.22
3.647 05
6.93
0.964 404
1.28
40
21
.264 715
4.67
.274 507
5.22
.642 89
6.92
.964 327
1.28
39
22
.264 995
4.68
.274 820
5.22
.638 74
6.88
.964 250
1.28
38
23
.265 276
4.67
.275 133
5.22
.634 61
6.88
.964 173
1.30
37
24
.265 556
4.68
.276 446
5.22
.630 48
6.87
.964 095
1.28
36
25
.265 837
4.67
.275 759
5.22
.626 36
6.87
.964 018
1.28
35
26
.266 117
4.67
.276 072
5.22
.622 24
6.83
.963 941
1.30
34
27
.266 397
4.68
.276 385
5.22
.618 14
6.82
.963 863
1.28
33
28
.266 678
4.67
.276 698
5.22
.614 05
6.82
.963 786
1.30
32
29
.266 958
4.67
.277 011
5.23
.609 96
6.80
.963 708
1.30
31


30
0.267 238
4.68
0.277 325
5.22
3.605 88
6.78
0.963 630
1.28
30
31
.267 519
4.67
.277 638
5.22
.601 81
6.77
.963 553
1.30
29
32
.267 799
4.67
.277 951
5.23
.597 75
6.75
.963 475
1.30
28
33
.268 079
4.67
.278 265
5.22
.593 70
6.73
.963 397
1.30
27
34
.268 359
4.68
.278 578
5.22
.589 66
6.73
.963 319
1.30
26
35
.268 640
4.67
.278 891
5.23
.585 62
6.70
.963 241
1.30
25
36
.266 920
4.67
.279 205
5.23
.581 60
6.70
.963 163
1.32
24
37
.269 200
4.67
.279 519
5.22
.577 58
6.68
.963 084
1.30
23
38
.269 480
4.67
.279 832
5.23
.573 57
6.67
.963 006
1.30
22
39
.262 760
4.67
.280 146
5.23
.569 57
6.67
.962 928
1.32
21


40
0.270 040
4.67
0.280 460
5.32
3.565 57
6.63
0.962 849
1.32
20
41
.270 320
4.67
.280 773
5.23
.561 59
6.63
.962 770
1.30
19
42
.270 600
4.67
.281 087
5.23
.557 61
6.62
.962 692
1.32
18
43
.270 880
4.67
.281 401
5.23
.553 64
6.60
.962 613
1.32
17
44
.271 160
4.67
.281 715
5.23
.549 68
6.58
.962 534
1.32
16
45
.271 440
4.67
.282 029
5.23
.545 73
6.57
.962 456
1.32
15
46
.271 720
4.67
.282 343
5.23
.541 79
6.57
.962 376
1.32
14
47
.272 000
4.67
.282 657
5.23
.537 85
6.53
.962 297
1.32
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
15

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.272 280
4.67
.282 971
5.25
.533 93
6 53
.962 218
1.32
12
49
.272 560
4.67
.283 286
5.23
.530 01
6.53
.962 139
1.33
11


50
0.272 840
4.67
0.283 600
5.23
3.526 09
6.50
0.962 059
1.32
10
51
.273 120
4.67
.283 914
5.25
.522 19
6 50
.961 980
1.32
09
52
.273 400
4.65
.284 229
5.23
.518 29
6.47
.961 301
1.33
08
53
.273 679
4.67
.284 543
5.23
.514 41
6.47
.961 821
1.33
07
54
.273 959
4.67
.234 857
5.25
.510 53
6.45
.961 741
1.32
06
55
.274 239
4.67
.285 172
5.25
.506 66
6.45
.961 662
1.33
05
56
.274 519
4.65
.265 487
5.23
.502 79
6.42
.961 582
1.33
04
57
.274 798
4.67
.285 801
5.25
.498 94
6.42
.961 502
1.33
03
58
.275 078
4.67
.286 116
5.25
.495 09
6.40
.961 422
1.33
02
59
.276 358
4 65
.286 431
5.23
.491 25
6.40
.961 342
1.33
01


60
0.275 637

0.286 745
3.487 41
0.961 262
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

16

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.275 637
4 67
0.286 745
5.25
3.487 41
6.37
0.961 262
1.35
60'
01
.275 917
4.67
.287 060
5 25
.483 59
6.37
.961 181
1.33
59
02
.276 197
4.65
.237 375
5 25
.479 77
6.35
.961 101
1.33
58
03
.276 476
4.67
.287 690
5 25
.475 96
6.33
.961 021
1.35
57
04
.276 756
4.65
.288 005
5 25
.472 16
6.32
.960 940
1.33
56
05
.277 036
4.67
.288 320
5.25
.468 37
6.32
.960 860
1.35
55
06
.277 315
4.65
.288 635
5 25
.464 58
6.30
.960 779
1.35
54
07
.277 594
4.67
.288 950
5.27
.460 80
6.28
.960 698
1.33
53
08
.277 874
4.65
.289 266
5.25
.457 03
6.27
.960 618
1.35
52
09
.278 153
4.65
.289 581
5.25
.453 27
6.27
.960 537
1.35
51


10
0.278 432
4.67
0.289 896
5.25
3.440 51
6.25
0.960 456
1.35
50
11
.278 712
4.65
.290 211
5.27
.445 76
6.23
.960 375
1.35
49
12
.278 991
4.65
.290 527
5.25
.442 02
6.22
.980 294
1.37
48
13
.279 270
4.67
.290 842
5.27
.438 29
6.22
.960 212
1.35
47
14
.279 550
4.65
.291 158
5.25
.434 56
6.20
.960 131
1.35
46
15
.279 829
4.65
.291 473
5.27
.430 84
6.18
.960 050
1.37
45
16
.280 108
4.67
.291 789
5.27
.427 13
6.17
.959 968
1.35
44
17
.280 388
4.65
.292 105
5.25
.423 43
6.17
.959 887
1.37
43
18
.280 667
4.65
.292 420
5.27
.419 73
6.15
.959 805
1.35
42
19
.280 946
4.65
.292 736
5.27
.416 04
6.13
.959 724
1.37
41


20
0.281 225
4.65
0.293 052
5.27
3.412 36
6.12
0.959 642
1.37
40
21
.281 504
4.65
.293 368
5.27
.408 69
6.12
.959 560
1.37
39
22
.281 783
4 65
.293 684
5.27
.405 02
6.10
.959 478
1.37
38
23
.282 062
4.65
.294 000
5.27
.401 36
6.08
.959 396
1.37
37
24
.282 341
4.65
.294 316
5.27
.397 71
6.08
.959 314
1.37
36
25
.282 620
4 67
.294 632
5.27
.394 06
6.07
.959 232
1.37
35
26
.282 900
4.65
.294 948
5.28
.390 42
6.05
.959 150
1.38
34
27
.283 179
4.63
.295 265
5.27
.386 79
6.03
.959 067
1.37
33
28
.283 457
4.65
.295 581
5.27
.383 17
6.03
.958 985
1.38
32
29
.283 736
4.65
.295 897
5.27
.379 55
6.02
.958 902
1.37
31


30
0.284 015
4 65
0.296 213
5.28
3.375 94
6.00
0.958 820
1.38
30
31
.284 294
4.65
.296 530
5.27
.372 34
5.98
.958 737
1.38
29
32
.284 573
4.65
.296 846
5.28
.368 75
5.98
.958 654
1.37
28
33
.284 852
4.65
.297 163
5.28
.365 16
5.97
.958 572
1.38
27
34
.284 131
4.65
.297 480
5.27
.361 58
5.97
.958 489
1.38
26
35
.285 410
4.63
.297 796
5.28
.358 00
5.95
.958 406
1.38
25
36
.285 688
4.65
.298 113
5.28
.354 43
5.93
.958 323
1.40
24
37
.285 967
4.65
.298 430
5.28
.350 87
5.93
.958 239
1.38
23
38
.286 246
4.65
.298 747
5.27
.347 32
5.92
.958 156
1.38
22
39
.286 525
4.63
.299 063
5.28
.343 77
5.90
.958 073
1.38
21


40
0.286 803
4.65
0.299 380
5.28
3.340 23
5.88
0.957 990
1.40
20
41
.287 082
4.65
.299 697
5.28
.336 70
5.88
.957 906
1.40
19
42
.287 361
4.63
.300 014
5.28
.333 17
5.87
.957 822
1.38
18
43
.287 639
4.65
.300 331
5.30
.329 65
5.85
.957 739
1.40
17
44
.287 918
4.63
.300 649
5.28
.326 14
5.83
.957 655
1 40
16
45
.288 196
4.65
.300 966
5.28
.322 64
5.83
.957 571
1.40
15
46
.288 475
4.63
.301 283
5.28
.319 14
5.82
.957 487
1.38
14
47
.288 753
4.65
.301 600
5.30
.315 65
5.82
.957 404
1.42
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
16

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.289 032
4.63
.301 918
5.28
.312 16
5.80
.957 319
1.40
12
49
.289 310
4.65
.302 235
5.30
.308 68
5.78
.957 235
1.40
11


50
0.289 589
4.63
0.302 553
5.28
3.305 21
5.78
0.957 151
1.40
10
51
.283 867
4.63
.302 870
5.30
.301 74
5.75
.957 067
1.40
09
52
.290 145
4.65
.303 188
5.30
.298 29
5.77
.956 983
1.42
08
53
.290 424
4.63
.303 506
5.28
.294 83
5.73
.956 898
1.40
07
54
.290 702
4.65
.303 823
5.30
.291 39
5.73
.956 814
1.42
06
55
.290 981
4.63
.304 141
5.30
.287 95
5.72
.956 729
1.42
05
56
.291 259
4.63
.304 459
5.30
.284 52
5.72
.956 644
1.40
04
57
.291 537
4.63
.304 777
5.30
.281 09
5.70
.956 560
1.42
03
58
.291 815
4.65
.305 095
5.30
.277 67
5.68
.956 475
1.42
02
59
.292 094
4.63
.305 413
5.30
.274 26
5.68
.956 390
1.42
01


60
0.292 372

0.305 731
3.270 85
0.956 305
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

17


d."
Tan
d."
Cot
d."
Cos
d."
00'
0.292 372
4.63
0.305 731
5.30
3.270 35
5.67
0.956 305
1.42
60'
01
.292 650
4.63
.306 049
5.30
.267 45
5.65
.956 220
1.43
59
02
.292 928
4.63
.306 367
5.30
.264 06
5.65
.956 134
1.42
58
03
.293 206
4.63
.306 685
5.30
.260 67
5.63
.956 049
1 42
57
04
.293 484
4.63
.307 003
5.32
.257 29
5.62
.955 964
1.42
56
05
.293 762
4.63
.307 322
5.30
.253 92
5.62
.955 879
1.43
55
06
.294 040
4.63
.307 640
5.32
.250 55
5.60
.955 793
1.43
54
07
.294 318
4.63
.307 959
5.30
.247 19
5.60
.955 707
1.42
53
08
.294 596
4.63
.308 277
5.32
.243 83
5.57
.955 622
1.43
52
09
.294 874
4.63
.308 596
5.30
.240 49
5.58
.955 536
1.43
51


10
0.295 152
4.63
0.308 914
5.32
3.237 14
5.55
0.955 450
1.43
50
11
.295 430
4.63
.309 233
5.32
.233 81
5.55
.955 364
1.43
49
12
.295 708
4.63
.309 552
5.30
.230 48
5.55
.955 278
1.43
48
13
.296 986
4.63
.309 870
5.32
.227 15
5.52
.955 192
1.43
47
14
.296 264
4.63
.310 189
5 32
.223 84
5.52
.955 106
1.43
46
15
.296 542
4.62
.310 503
5.32
.220 53
5.52
.955 020
1.43
45
16
.296 819
4.63
.310 827
5.32
.217 22
5.50
.954 934
1.45
44
17
.297 097
4.63
.311 146
5.32
.213 92
5.48
.954 847
1.43
43
18
.297 375
4.63
.311 465
5.32
.210 63
5.48
.984 761
1.45
42
19
.297 653
4.62
.311 784
5.33
.207 34
5.47
.954 674
1.43
41


20
0.297 930
4.63
0.312 104
5.32
3.204 06
5.45
0.954 588
1.45
40
21
.298 208
4.63
.312 423
5.32
.200 79
5.45
.954 501
1.45
39
22
.298 486
4.62
.312 742
5.33
.197 52
5.43
.954 414
1.45
38
23
.298 763
4.63
.313 062
5.32
.194 26
5.43
.954 327
1.45
37
24
.299 041
4.62
.313 381
5.32
.191 00
5.42
.954 240
1.45
36
25
.299 318
4.63
.313 700
5.33
.187 75
5.40
.954 153
1.45
35
26
.299 596
4.62
.314 020
5.33
.184 51
5.40
.954 066
1.45
34
27
.299 873
4.63
.314 340
5.32
.181 27
5.38
.953 979
1.45
33
28
.300 151
4.62
.314 659
5.33
.178 04
5.38
.953 892
1.47
32
29
.300 428
4.63
.314 979
5.33
.174 81
5.37
.953 804
1.45
31


30
0.300 706
4.62
0.315 299
5.33
3.171 59
5.35
0.953 717
1.47
30
31
.300 983
4.63
.315 619
5.33
.168 38
5.35
.953 629
1.45
29
32
.301 261
4.62
.315 939
5.32
.165 17
5.33
.953 542
1.47
28
33
.301 536
4.62
.316 258
5.33
.161 97
5.33
.953 454
1.47
27
34
.301 815
4.63
.316 578
5.35
.158 77
5.32
.953 366
1.45
26
35
.302 093
4.62
.316 899
5.33
.155 68
5.30
.953 279
1.47
25
36
.302 370
4.62
.317 219
5.33
.152 40
5.30
.953 191
1.47
24
37
.302 647
4.62
.317 539
5.33
.149 22
5.28
.953 103
1.47
23
36
.302 924
4.63
.317 859
5.33
.146 05
5.28
.953 016
1.48
22
39
.303 202
4.62
.318 179
5.35
.142 88
5.27
.952 926
1.47
21


40
0.303 479
4.62
0.318 500
5.33
3.139 72
5.27
0.952 838
1.47
20
41
.303 756
4.62
.318 820
5.35
.136 56
5.25
.952 750
1.48
19
42
.304 033
4.62
.319 141
5.33
.133 41
5.23
.952 661
1.47
18
43
.304 310
4.62
.319 461
5.35
.130 27
5.23
.952 573
1.48
17
44
.304 587
4.62
.319 782
5.35
.127 13
5.22
.952 484
1.47
16
45
.304 864
4.62
.320 103
5.33
.124 00
5.22
.92 396
1.48
15
46
.305 141
4.62
.320 423
5 35
.120 87
5.20
.952 307
1.48
14
47
.305 418
4.62
.320 744
5.35
.177 75
5.18
.952 218
1.48
13
48
.305 695
4.62
.321 065
5.35
.114 64
5.18
.952 129
1.48
12
17


d."
Tan
d."
Cot
d."
Cos
d."
49
.305 972
4.62
.321 386
5.35
.111 53
5.18
.952 040
1.48
11


50
0.306 249
4.62
0.321 707
5.35
3.108 42
5.17
0.951 951
1.48
10
51
.305 526
4.62
.322 028
5.35
.105 32
5.15
.951 862
1.48
09
52
.306 803
4.62
.322 349
5.35
.102 23
5.15
.951 773
1.48
08
53
.307 080
4.62
.322 670
5.35
.099 14
5.13
.951 684
1.50
07
54
.307 357
4.60
.322 991
5.35
.096 06
5.13
.951 594
1.48
06
55
.307 633
4.62
.323 312
5.37
.092 98
5.12
.951 505
1.50
05
56
.307 910
4.62
.323 634
5.35
.089 91
5.10
.951 415
1.48
04
57
.308 187
4.62
.323 955
5.37
.086 85
5.10
.951 326
1.50
03
58
.308 464
4.60
.324 277
5.35
.083 79
5.10
.951 236
1.50
02
59
.308 740
4.62
.324 598
5.37
.080 73
5.08
.951 146
1.48
01


60
0.309 017

0.324 920
3.077 68
0.951 057
00

18

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.309 017
4.62
0.324 920
5.35
3.077 68
5.07
0.951 057
1.50
60'
01
.309 294
4.60
.325 241
5.37
.074 64
5.07
.950 967
1.50
59
02
.309 570
4.62
.325 563
5.37
.071 60
5.05
.950 877
1.52
58
03
.309 847
4.60
.325 885
5.37
.068 57
5.05
.950 786
1.50
57
04
.310 123
4.62
.326 207
5.35
.065 54
5.03
.950 696
1.50
56
05
.310 400
4.60
.326 528
5.37
.062 52
5.03
.950 606
1.50
55
06
.310 676
4.62
.326 850
5.37
.059 50
5.02
.950 516
1.52
54
07
.310 953
4.60
.327 172
5.37
.056 49
5.00
.950 425
1.50
53
08
.311 229
4.62
.327 494
5.38
.053 49
5.00
.950 335
1.52
52
09
.311 506
4.60
.327 817
5.37
.050 49
5.00
.950 244
1.50
51


10
0.311 782
4.62
0.328 139
5.37
3.047 49
4.98
0.950 154
1.52
50
11
.312 059
4.60
.328 461
5.37
.044 50
4.97
.950 063
1.52
49
12
.312 335
4.60
.328 783
5.38
.041 52
4.97
.949 972
1.52
48
13
.312 611
4.62
.329 106
5.37
.038 54
4.97
.949 881
1.52
47
14
.312 888
4.60
.329 428
5.38
.035 56
4.93
.949 790
1.52
46
15
.313 164
4.60
.329 751
5.37
.032 60
4.95
.949 699
1.52
45
16
.313 440
4.60
.330 073
5.38
.029 63
4.93
.949 608
1.52
44
17
.313 716
4.60
.330 396
5.37
.026 67
4.92
.949 517
1.53
43
18
.313 992
4.62
.330 718
5.38
.023 72
4.92
.949 425
1.52
42
19
.314 269
4.60
.331 041
5.38
.020 77
4.90
.940 334
1.52
41


20
0.314 545
4.60
0.331 364
5.38
3.017 83
4.90
0.949 243
153
40
21
.314 821
4.60
.331 687
5.38
.014 89
4.88
.949 151
1.53
39
22
.315 097
4.60
.332 010
5.38
.01196
4.88
.949 059
1.52
38
23
.315 373
4.60
.332 333
5.38
.009 03
4.87
.948 568
1.53
37
24
.315 649
4.60
.332 656
5.38
.006 11
4.87
.948 876
1.53
36
25
.315 925
4.60
.332 979
5.39
.003 19
4.85
.948 784
1.53
35
26
.316 201
4.60
.333 302
5.38
.000 28
4.83
.948 692
1.53
34
27
.316 477
4.60
.333 625
5.40
2.997 38
4.85
.948 600
1.53
33
28
.316 753
4.60
.333 949
5.38
.994 47
4.82
.948 508
1.53
32
29
.317 029
4.60
.334 272
5.38
.991 58
4.83
.948 416
1.53
31


30
0.317 305
4.58
0.334 595
5.40
2.983 68
4.80
0.948 324
1.55
30
31
.317 580
4.60
.334 919
5.38
.985 80
4.80
.948 231
1.53
29
32
.317 856
4.60
.335 242
5.40
.982 92
4.80
.948 139
1.55
28
33
.318 132
4.60
.335 556
5.40
.980 04
4.78
.948 046
1.53
27
34
.318 408
4.60
.335 890
5.38
.977 17
4.78
.947 954
1.55
26
35
.318 684
4.58
.336 213
5.40
.974 30
4.77
.947 861
1.55
25
36
.318 959
4.60
.336 537
5.40
.971 44
4.77
.947 768
1.53
24
37
.319 235
4.60
.336 861
5.40
.968 58
4.75
.947 676
1.55
23
38
.319 511
4.58
.337 185
5.40
.96573
4.75
.947 583
1.55
22
39
.319 786
4.60
.337 509
5.40
.962 88
4.73
.947 490
1.55
21


40
0.320 062
4.58
0.337 833
5.40
2.960 04
4.72
0.947 397
1.55
20
41
.320 337
4.60
.338 157
5.60
.95721
4.73
.947 304
1.57
19
42
.320 613
4.60
.338 481
5.42
.954 37
4.70
.947 210
1.55
18
43
.320 889
4.58
.338 806
5.40
.951 55
4.72
.947 117
1 55
17
44
.321 164
4.58
.339 130
5.40
.948 72
4.68
.947 024
1.57
16
45
.321 439
4.60
.339 454
5 42
.945 91
4.70
.946 930
1 55
15
46
.321 715
4.58
.339 779
5.42
.943 09
4.68
.946 837
1.57
14
47
.321 990
4.60
.340 103
5.42
.940 28
4.67
.946 743
1.57
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
18

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.322 266
4.58
.340 428
5.40
.937 48
4.67
.946 649
1.57
12
49
.322 541
4.58
.340 752
5.42
.934 68
4.65
.946 555
1.55
11


50
0.322 816
4.60
0.341 077
5.42
2.931 89
4.65
0.946 462
1.57
10
51
.323 092
4.58
.341 402
542
.929 10
4.63
.946 368
1.57
09
52
.323 367
4.58
.341 727
5.42
.926 32
4.63
.946 274
1.57
08
53
.323 642
4.58
.342 052
5.42
.923 54
4.63
.946 180
1.58
07
54
.323 917
4.60
.342 377
5.42
.920 76
4.62
.946 085
1.57
06
55
.324 193
4.58
.342 702
5.42
.917 99
4.60
.945 991
1.57
05
56
.324 468
4.58
.343 027
5.42
.915 23
4.62
.945 897
1.58
04
57
.324 743
4.58
.343 352
5.42
.912 46
4.58
.945 302
1.57
03
58
.325 018
4.58
.343 677
5.42
.909 71
4.58
.945 708
1.58
02
59
.325 293
4.58
.344 002
5.43
.906 96
4.58
.945 613
1.57
01


60
0.325 568

0.344 328
2.904 21
0.945 519
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

19

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.325 568
4.58
0.344 328
5.42
2.904 21
4.57
0.945 519
1.58
60'
01
.325 843
4.58
.344 653
5.42
.901 47
4.57
.945 424
1.58
59
02
.326 118
4.58
.344 978
5.43
.898 73
4.55
.946 329
1.58
58
03
.326 393
4.58
.345 304
5.43
.896 00
4.55
.945 234
1.58
57
04
.326 668
4.58
.345 630
5.42
.893 27
4.53
.945 189
1.58
56
05
.326 943
4.58
.345 955
5.43
.890 55
4.53
.945 044
1.58
55
06
.327 218
4.58
.346 281
5.43
.887 83
4.53
.944 949
1.58
54
07
.327 493
4.58
.346 607
5.43
.885 11
4.52
.944 854
1.60
53
08
.327 768
4.57
.346 933
5.43
.882 40
4.50
.944 758
1.58
52
09
.329 042
4.58
.347 259
5.43
.889 70
4.50
.944 663
1.58
51


10
0.328 317
4.58
0.347 585
5.43
2.877 00
4.50
0.944 568
1.60
50
11
.328 502
4.58
.347 911
5.43
.874 30
4.48
.944 472
1.60
49
12
.328 867
4.57
.348 237
5.43
.871 61
4.48
.944 376
1.58
48
13
.329 141
4.58
.348 563
5.43
.868 92
4.47
.944 281
1.60
47
14
.329 416
4.58
.348 889
5.45
.866 24
4.47
.944 185
1.60
46
15
.329 691
4.57
.349 216
5.43
.863 56
4.45
.944 089
1.60
45
16
.329 965
4.58
.349 542
5.43
.860 89
4.45
.943 993
1.60
44
17
.330 240
4.57
.349 868
5.45
.858 22
4.45
.943 897
1.60
43
18
.330 514
4.58
.350 195
5.45
.855 55
4.43
.943 801
1.60
42
19
.330 789
4.57
.350 522
5.43
.852 89
4.43
.943 705
1.60
41


20
0.331 063
4.58
0.350 848
5.45
2.850 23
4.42
0.943 609
1.62
40
21
.331 338
4.57
.351 175
5.45
.847 58
4.40
.943 512
1.60
39
22
.331 612
4.58
.351 502
5.45
.844 94
4.42
.943 416
1.62
38
23
.331 887
4.57
.351 829
5.45
.842 29
4.40
.943 319
1.60
37
24
.332 161
4.57
.352 156
5.45
.839 65
4.38
.943 223
1.62
36
25
.332 435
4.58
.352 483
5.45
.839 02
4.38
.943 126
1 62
35
26
.332 710
4.57
.352 810
5.45
.834 39
4.38
.943 029
1.62
34
27
.332 984
4.57
.353 137
5.45
.831 76
4.37
.942 932
1.60
33
28
.333 258
4.58
.353 464
5.45
.829 14
4.35
.942 836
1.62
32
29
.333 533
4.57
.353 791
5.47
.826 53
4.37
.942 739
1.63
31


30
0.333 807
4.57
0.354 119
5.45
2.823 31
4.35
0.942 641
1.62
30
31
.334 081
4.57
.354 446
5.45
.821 30
4.33
.942 544
1.62
29
32
.334 355
4.57
.354 773
5.45
.818 70
4.33
.942 447
1.62
28
33
.334 629
4.57
.355 101
5.47
.816 10
4.33
.942 350
1.63
27
34
.334 903
4.58
.355 429
5.45
.813 50
4.32
.942 252
1.62
26
35
.335 178
4.57
.355 766
5.47
.810 91
4.30
.942 155
1.63
25
36
335 452
4.57
.356 084
5.47
.808 33
4.32
.942 057
1.62
24
37
.335 726
4.57
.356 412
5,47
.805 74
4.30
.941 960
1.63
23
38
.336 000
4.57
.356 740
5.47
.803 16
4.28
.941 862
1.63
22
39
.336 274
4.55
.357 068
5.47
.800 59
4.28
.941 764
1.63
21


40
0.336 547
4.57
0.357 396
5.47
2.798 02
4.28
0.941 666
1 62
20
41
.336 821
4.57
.387 724
5.47
.795 45
4.27
.941 569
1.63
19
42
.337 095
4.57
.358 052
5.47
.792 89
4.27
.941 471
1.65
18
43
.337 369
4.57
.358 380
5.47
.790 33
4.25
.911 372
1.63
17
44
.337 643
4.57
.358 708
5.48
.787 78
4.25
.941 274
1.63
16
45
.337 917
4.55
.359 037
5.47
.785 23
4.23
.941 176
1.63
15
46
.338 190
4.57
.359 365
5.48
.782 69
4.25
.941 078
1.65
14
47
.338 464
4.57
.359 694
5.47
.780 14
4.22
.940 979
1.63
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
19

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.338 738
4.57
.360 022
5.48
.777 61
4.23
.940 881
1.65
12
49
.339 012
4.55
.360 351
5.47
.775 07
4.22
.940 782
1.63
11


50
0.339 285
4.57
0.360 679
5.48
2.772 54
4.20
0.940 684
1.65
10
51
.339 559
4.55
.361 008
6.48
.770 02
4.20
.940 585
1.65
09
52
.339 832
4.57
.361 337
5.48
.767 50
4.20
.940 486
1.65
08
53
.340 106
4.57
.361 666
5.48
.764 98
4.18
.940 387
1.65
07
54
.340 380
4.55
.361 995
5.48
.762 47
4 18
.940 288
1.65
06
55
.340 653
4.57
.362 324
5.48
.759 96
4 17
.940 189
1.65
05
56
.340 927
4.55
.362 653
5.48
.757 46
4.17
.940 090
1.65
04
57
.341 200
4.55
.362 982
5.50
.754 96
4.17
.939 991
1.67
03
58
.341 473
4.57
.363 312
5.48
.752 46
4 15
.939 891
1.65
02
59
.341 747
4.55
.363 641
5.48
.749 97
4.15
.939 792
1.65
01


60
0.342 020

0.363 970
2.747 48
0.939 693
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

20

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.342 020
4.55
0.363 970
5.50
2.747 477
41.40
0.939 693
1.67
60'
01
.342 293
4.57
.364 300
5.48
.744 993
41.35
.939 593
1.67
59
02
.342 567
4.55
.364 629
5.50
.742 512
41.28
.939 493
1.65
58
03
.342 840
4.55
.364 959
5.48
.740 035
41.22
.939 394
1.67
57
04
.343 113
4.57
.365 288
5.50
.737 562
41.15
.939 294
1.67
56
05
.343 367
4.55
.365 618
5.50
.735 093
41.08
.939 194
1.67
55
06
.343 660
4.55
.365 948
5.50
.732 628
41.02
.939 094
1.67
54
07
.343 933
4.55
.366 278
5.50
.730 167
40.95
.938 994
1.67
53
08
.344 206
4.55
.366 608
5.50
.727 710
40.88
.938 894
1.67
52
09
.344 479
4.55
.366 938
5.50
.725 257
40.82
.938 794
1.67
51


10
0.344 752
4.55
0.367 268
5.50
2.722 808
40.77
0.938 694
1.68
50
11
.345 025
4.55
.367 598
5.50
.720 362
40.70
.938 593
1.67
49
12
.345 298
4.55
.367 928
5.52
.717 920
40.62
.938 493
1.67
48
13
.345 571
4.55
.368 259
5.50
.715 483
40.57
.938 393
1.68
47
14
.345 844
4.55
.368 589
5.50
.713 049
40.50
.938 292
1.68
46
15
.346 117
4.55
.368 919
5.52
.710 619
40.45
.938 191
1.67
45
16
.346 390
4.55
.369 250
5.52
.708 192
40.37
.938 091
1.68
44
17
.346 663
4.55
.369 581
5.52
.705 770
40.32
.937 990
1.68
43
18
.346 936
4.53
.369 911
5.52
.703 351
40.25
.937 889
1.68
42
19
.347 208
4.55
.370 242
5.52
.700 936
40.18
.937 783
1.68
41


20
0.347 481
4.55
0.370 573
5.52
2.698 525
40.12
0.937 687
1.68
40
21
.347 754
4.55
.370 904
5.52
.696 118
40.05
.937 586
1.68
39
22
.348 027
4.53
.371 235
5.52
.693 715
40.00
.937 485
1.70
38
23
.348 299
4.55
.371 566
5.52
.691 315
39.93
.937 383
1.68
37
24
.348 572
4.55
.371 897
5.52
.688 919
39.87
.937 282
1.68
36
25
.348 845
4.53
.372 228
5.52
.686 527
39.82
.937 181
1.70
35
26
.349 117
4.55
.372 559
5.52
.684 138
39.73
.937 079
1.70
34
27
.349 390
4.53
.372 890
5.53
.681 754
39.70
.936 977
1.68
33
28
.349 662
4.55
.373 222
5.32
.679 372
39.62
.936 876
1.70
32
29
.349 935
4.53
.373 553
5.53
.676 995
39.57
.936 774
1.70
31


30
0.350 207
4.55
0.373 885
5.52
2.674 621
39.48
0.936 672
1.70
30
31
.350 480
4.53
.374 216
5.53
.672 252
39.45
.936 570
1.70
29
32
.350 752
4.55
.374 548
5.53
.669 688
39.37
.936 468
1.70
28
33
.351 025
4.53
.374 880
5.52
.667 523
39.32
.936 366
1.70
27
34
.351 297
4.53
.375 211
5.53
.665 164
39.25
.936 264
1.70
26
35
.351 569
4.55
.375 543
5.53
.662 809
39.20
.936 162
1.70
25
36
.351 842
4.53
.375 875
5.53
.660 467
39.13
.936 060
1.72
24
37
.352 114
4.53
.376 207
5.53
.660 109
39.07
.935 957
1.70
23
38
.352 386
4.53
.376 539
5.55
.655 765
39.02
.935 855
1.72
22
39
.352 658
4.53
.376 872
5.53
.653 424
38.95
.935 752
1.70
21


40
0.352 931
4.53
0.377 204
5.53
2.651 087
38.90
0.935 650
1.72
20
41
.353 203
4.53
.377 536
5.55
.648 753
38.83
.935 547
1.72
19
42
.353 475
4.53
.377 869
5.53
.646 423
38.77
.935 444
1.72
18
43
.353 747
4.53
.378 201
5.55
.644 097
38.72
.935 341
1.72
17
44
.354 019
4.53
.378 534
5.53
.641 774
38.65
.935 238
1.72
16
45
.354 291
4.53
.378 866
5.55
.639 455
38.60
.935 135
1.72
15
46
.354 563
4.53
.379 199
5.55
.637 139
38.53
.935 032
1.72
14
47
.354 835
4.53
.379 532
5.53
.634 827
38.47
.934 929
1.72
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
20

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.355 107
4.53
.379 864
5.55
.632 519
38.42
.934 826
1.73
12
49
.355 379
4.53
.380 197
5.55
.630 214
38.37
.934 722
1 72
11


50
0.355 651
4.53
0.380 530
5.55
2.627 912
38.30
0.934 619
1.73
10
51
.355 923
4.52
.380 863
5.55
.625 614
38.28
.934 515
1.72
09
52
.356 194
4.53
.381 196
5.55
.623 320
38.18
.934 412
1.73
08
53
.356 466
4.53
.381 530
5.55
.621 029
38.13
.934 308
1.73
07
54
.356 738
4.53
.381 863
5.55
.618 741
38.07
.934 204
1.72
06
55
.357 010
4.52
.382 196
5.57
.616 457
38.00
.934 101
1.73
05
56
.357 281
4.53
.382 530
5.55
.614 177
37.95
.933 997
1.73
04
57
.357 553
4.53
.382 863
5.55
.611 900
37.90
.933 893
1.73
03
58
.357 825
4.52
.383 197
5.55
.609 626
37.83
.933 789
1.73
02
59
.358 096
4.53
.383 530
5.57
.607 356
37.78
.933 685
1.75
01


60
0.358 368

0.383 864
2.605 089
0.933 580
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

21

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.358 368
4.53
0.383 864
5.57
2.605 089
37.72
0.933 658
1.73
60'
01
.358 640
4.52
.384 198
5.57
.602 826
37.67
.933 476
1.73
59
02
.358 911
4.53
.384 532
5.57
.600 566
37.62
.933 372
1.75
58
03
.359 183
4.52
.384 866
5.57
.598 309
37.55
.933 267
1.73
57
04
.359 454
4.52
.385 200
5.57
.596 056
37.48
.933 168
1.75
56
05
.359 725
4.50
.385 534
5.57
.593 807
37.43
.933 058
1.73
55
06
.359 997
4.52
.385 868
5.57
.591 561
37.38
.932 954
1.75
54
07
.360 268
4.53
.386 202
5.57
.589 318
37.33
.932 849
1.75
53
08
.360 540
4.52
.386 536
5.58
.587 078
37.27
.932 744
1.75
52
09
.360 811
4.52
.386 871
5.57
.584 842
37.32
.932 639
1.75
51


10
0.361 082
4.52
0.387 205
5.58
2.582 609
37.15
932 534
1.75
50
11
.361 353
4.53
.387 540
5.57
.580 380
37.10
.932 429
1.75
49
12
.361 625
4.52
.387 874
5.58
.578 154
37.05
932 324
1.75
48
13
.361 896
4.52
.388 209
5.58
.575 931
36.98
932 219
1.77
47
14
.362 167
4.52
.388 544
5.58
.573 712
36.93
932 113
1 75
46
15
.362 438
4.52
.388 879
5.58
.571 496
36.88
932 008
1.77
45
16
.362 709
4.52
.389 214
5.58
.569 283
36.82
931 902
1.75
44
17
.362 982
4.52
.389 549
5.58
.567 074
36.78
931 797
1.77
43
18
.363 251
4.52
.389 884
5.58
.564 867
36.70
931 691
1.75
42
19
.363 522
4.52
.390 219
5.58
.562 665
36.67
931 586
1.77
41


20
0.363 793
4.52
0.390 554
5.58
2.560 465
36.60
0.931 480
1.77
40
21
.364 064
4.52
.390 889
5.60
.558 269
36.55
.931 374
1.77
39
22
.364 335
4.52
.391 225
5.58
.556 076
36.50
.931 268
177
38
23
.364 606
4.52
.391 560
5.60
.553 866
36.45
.931 162
1.77
37
24
.364 877
4.52
.391 896
5.58
.551 699
36.38
.931 056
1.77
36
25
.365 148
4.50
.392 231
5.30
.549 516
36.33
.930 950
1.78
35
26
.365 418
4.52
.392 567
5.60
.547 336
36.28
.930 843
1.77
34
27
.365 689
4.52
.392 903
5.60
.545 459
36.23
.930 737
1.77
33
28
.365 960
4.52
.393 239
5.58
.542 985
36.17
.930 631
1.78
32
29
.366 231
4.50
.393 574
5.60
.540 815
36.12
.930 524
1.77
31


30
0.366 501
4.52
0.393 910
5.62
2.538 648
36.07
0.930 418
1.78
30
31
.386 772
4.50
.394 247
5.60
.536 484
36.02
.930 311
1.78
29
32
.367 042
4.52
.394 583
5.60
.534 323
35.97
.930 204
1.78
28
33
.367 313
4.52
.394 919
5.60
.532 165
35.90
.930 097
1.78
27
34
.367 584
4.50
.395 255
5.62
.530 011
35.85
.929 990
1.77
26
35
.367 854
4.52
.395 592
5.60
.527 860
35.80
.929 884
1.80
25
36
.368 125
4.50
.395 928
5.62
.523 712
35.70
.929 776
1.78
24
37
.368 395
4.50
.396 265
5.60
.523 567
35.70
.929 669
1.78
23
38
.368 665
4.52
.396 601
5.62
.521 425
35.65
.929 562
1.78
22
39
.368 936
4.50
.396 938
5.62
.519 286
35.58
.929 455
1.78
21


40
0.369 206
4.50
0.397 275
5.60
2.517 151
34.55
.929 348
1.80
20
41
.369 476
4.52
.397 611
5.62
.515 018
35.48
.929 240
1.78
19
42
.369 747
4.50
.397 948
5.62
.512 889
35.43
.929 133
1.80
18
43
.370 017
4.50
.398 285
5.62
.510 763
35.38
.929 025
1.80
17
44
.370 287
4.50
.398 622
5.63
.508 640
35.23
.928 917
1.78
16
45
.370 557
4.52
.398 960
5.62
.506 520
35.28
.928 810
1.80
15
46
.370 828
4.50
.399 297
5.62
.504 403
35.33
.928 702
1.80
14
47
.371 098
4.50
.399 634
5.62
.502 289
35 18
.928 594
1.80
13

Cos
d."
Cot
d."
Tan
d."
Sin
d."
21

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.371 368
4.50
.399 971
5.63
.500 178
35.12
.928 486
1.80
12
49
.371 638
4.50
.400 309
5.62
.498 071
35.08
.928 378
1.80
11


50
0.371 908
4.50
0.400 646
5.63
2.495 966
35.02
0.928 270
1.82
10
51
.372 178
4.50
.400 984
5.63
.493 865
34.98
.928 161
1.80
09
52
.372 448
4.50
.401 322
5.63
.491 766
34.92
.928 053
1.80
08
53
.372 718
4.50
.401 660
5.62
.489 671
34.88
.927 945
1.82
07
54
.372 988
4.50
.401 997
5.63
.487 578
34.82
.927 836
1.80
06
55
.373 258
4.50
.402 335
5 63
.485 489
34.78
.927 728
1.82
05
56
.373 528
4.48
.402 673
5 63
.483 402
34.72
.927 619
1.82
04
57
.373 797
4.50
.403 011
5.65
.481 319
34.67
.927 510
1.80
03
58
.374 067
4.50
.403 350
5.63
.479 239
34.63
.927 402
1.82
02
59
.374 337
4.50
.403 688
5.63
.477 161
34.57
.927 293
1.82
01


60
0.374 607

0.404 026
2.475 087
0.927 184
00

Cos
d."
Cot
d."
Tan
d."
Sin
d."

22

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.374 607
4.48
0.404 026
5.65
2.475 087
34.53
0.927 184
1.82
60'
01
.374 876
4.50
.404 365
5.63
.473 015
34.47
.927 075
1.82
59
02
.375 146
4.50
.404 703
5.65
.470 947
34.42
.926 966
1.82
58
03
.375 416
4.48
.405 042
5.63
.468 882
34.38
.926 857
1.83
57
04
.375 685
4.50
.405 380
5.65
.466 819
34.32
.920 747
1.82
56
05
.375 955
4.48
.405 719
5.65
.464 760
34.28
.926 638
1.82
55
06
.376 224
4.50
.406 058
5.65
.462 703
34.23
.926 529
1.83
54
07
.376 494
4.46
.406 397
5.65
.460 649
34.17
.926 419
1.82
53
08
.376 763
4.50
.406 736
5.65
.458 599
34.13
.926 310
1.83
52
09
.377 033
4.48
.407 075
5.65
.456 551
34.08
.926 200
1.83
51


10
0 377 302
4.48
0.407 414
5.65
2.454 506
34.03
0.926 090
1.83
50
11
.377 571
4.50
.407 753
5.65
.452 464
33.98
.925 980
1.82
49
12
.377 841
4.48
.408 092
5.67
.450 425
33.93
.925 871
1.83
48
13
.378 110
4.48
.408 432
5.65
.448 389
33.88
.925 761
1.83
47
14
.378 379
4.50
.408 771
5.67
.446 356
33.83
.925 651
1.83
46
15
.378 649
4.48
.409 111
5.65
.444 326
33.80
.925 541
1.85
45
16
.378 918
4.48
.409 450
5.67
.442 298
33.73
.925 430
1.83
44
17
.379 187
4.48
.409 790
5.67
.440 274
33.70
.925 320
1.83
43
18
.379 456
4.48
.410 130
5.67
.438 252
33.65
.925 210
1.85
42
19
.379 725
4.48
.410 470
5.67
.436 233
33.60
.925 099
1.83
41


20
0.379 994
4.48
0.410 810
5.67
2.434 217
33.55
0.924 989
1.85
40
21
.380 263
4.48
.411 150
5.67
4.32 204
33.50
.924 878
1.83
39
22
.380 532
4.48
.411 490
5.67
.430 194
33.47
.924 768
1.85
38
23
.380 801
4.48
.411 830
5.67
.428 186
33.40
.924 657
1.85
37
24
.381 070
4.48
.412 170
5.68
.426 182
33.37
.924 546
1.85
36
25
.381 339
4.48
.412 511
6.67
.424 180
33.32
.924 435
1.85
35
26
.381 608
4.48
.412 851
5.68
.422 181
33.27
.924 324
1.85
34
27
.381 877
4.48
.413 192
5.67
.420 185
33.22
.924 213
1.85
33
28
.382 146
4.48
.413 532
5.68
.418 192
33.18
.924 102
1.85
32
29
.382 415
4.47
.413 873
5.68
.416 201
33.12
.923 991
1.85
31


30
0.382 683
4.48
0.414 214
5.67
2.414 214
33.08
.923 880
1.87
30
31
.382 952
4.48
.414 554
5.68
.412 229
33.03
.923 768
1.85
29
32
.383 221
4.48
.414 895
5.68
.410 247
33.00
.923 657
1.87
28
33
.383 490
4.47
.415 236
5.68
.408 267
32.93
.923 545
1.85
27
34
.383 758
4.48
.415 557
5.70
.406 291
32.90
.923 434
1.87
26
35
.384 027
4.47
.415 919
5.68
.404 317
32.85
.923 322
1.87
25
36
.384 295
4.48
.416 260
5.68
.402 346
32.82
.923 210
1.87
24
37
.384 564
4.47
.416 601
5.70
.400 377
32.75
.923 098
1.87
23
38
.384 832
4.48
.416 943
5.68
.398 412
32.72
.922 986
1.85
22
39
.385 101
4.47
.417 284
5.70
.396 449
32.67
.922 875
1.88
21


40
0.385 369
4.48
0.417 626
5.68
2.394 489
32.62
0.922 762
1.87
20
41
.385 638
4.47
.417 967
5.70
.392 532
32.58
.922 650
1.87
19
42
.385 906
4.47
.418 309
5.70
.390 577
32.53
.922 538
1.87
18
43
.386 174
4.48
.418 651
5.70
.388 625
32.48
.922 426
1.88
17
44
.386 443
4.47
.418 993
5.70
.386 676
32.45
.922 313
1.87
16
45
.386 711
4.47
.419 335
5.70
.384 726
32.38
.922 201
1.88
15
46
.386 979
4.47
.419 677
5.70
.382 786
32.37
.922 088
1.87
14

Cos
d."
Cot
d."
Tan
d."
Sin
d."


22

Sin
d."
Tan
d."
Cot
d."
Cos
d."
47
.387 247
4.48
.420 019
5.70
.380 844
32.30
.921 976
1.88
13
48
.387 516
4.47
.420 361
5.72
.378 906
32.27
.921 863
1.88
12
49
.387 784
4.47
.420 704
5.70
.376 970
32.22
.921 750
1.87
11


50
0.388 052
4.47
0.421 046
5.72
2.375 037
32.17
0.921 638
1.88
10
51
.388 320
4.47
.421 389
5.70
.373 107
32.13
.921 525
1.88
09
52
.388 583
4.47
.421 731
5.72
.371 179
32.08
.921 412
1.88
08
53
.388 856
4.47
.422 074
5.72
.369 254
32.03
.921 299
1.90
07
54
.389 124
4,47
.422 417
5.70
.367 332
32.00
.921 185
1.88
06
55
.389 392
4.47
.422 759
5.72
.365 412
31.95
.921 072
1.88
05
56
.389 660
4.47
.423 102
5.72
.363 495
31.92
.920 959
1.90
04
57
.389 928
4.47
.423 445
5.72
.361 580
31.87
.920 845
1.88
03
58
.390 196
4.45
.423 788
5.73
.359 668
31.82
.920 732
1.90
02
59
.390 463
4.47
.424 132
5.72
.357 759
31.78
.920 618
1.88
01


60
0.390 731

0.424 475
2.355 852
0.920 505
00

Cos
d."
Cot
d."
Tan
d."
Sin
d."

23

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.390 731
4.47
0.424 475
5.72
2.355 852
31 73
0.920 505
1.90
60'
01
.390 999
4.47
.424 818
5.73
.353 495
31.68
.920 391
1.90
59
02
.391 267
4.45
.425 162
5.72
.352 047
31 65
.920 277
1.88
58
03
.391 534
4.47
.425 505
5.73
.350 148
31 60
.920 164
1.90
57
04
.391 802
4.47
.425 849
5.72
.348 252
31 57
.920 050
1.90
56
05
.392 070
4.45
.426 192
5.73
.346 192
31.52
.919 936
1.92
55
06
.392 337
4.47
.426 536
5.73
.344 467
31.47
.919 821
1.90
54
07
.392 605
4.45
.426 880
5.73
.342 579
31 43
.919 707
1.90
53
08
.392 872
4.47
.427 224
5.73
.340 693
31.40
.919 593
1.90
52
09
.393 140
4.45
.427 568
5.73
.338 809
31.33
.913 479
1.92
51


10
0.393 407
4.47
0.427 912
5.73
2.336 929
31.32
0 919 364
1.90
50
11
.393 675
4.45
.428 256
5.75
.335 050
31.25
918 250
1.92
49
12
.393 942
4.45
.428 601
5.73
.333 175
3122
919 135
1.90
48
13
.394 209
4.47
.428 945
5.73
.331 302
31.18
919 021
1.92
47
14
.394 477
4.45
.428 289
5.75
.329 431
31.13
918 906
1.92
46
15
.394 744
4.45
.428 634
5.75
327 563
31.08
.918 791
1.92
45
16
.395 011
4.45
.429 979
5.73
.325 698
31.05
918 676
1.92
44
17
.395 278
4.47
.430 323
5.75
.323 835
31.02
918 561
1.92
43
18
.395 546
4.45
.430 668
5.75
.321 974
30.97
918 446
1.92
42
19
.395 813
445
.431 013
5.75
320 116
30 92
.918 331
1.92
41


20
0.396 080
4.45
0.431 358
5.75
2.318 261
30.88
0.918 216
1.92
40
21
.396 347
4.45
.431 703
5.75
.316 408
30.85
.918 101
1.92
39
22
.396 614
4.45
.432 048
5.75
.314 557
30.80
.917 986
1.93
38
23
.395 881
4.45
.432 393
5.77
.312 709
30.75
.917 870
1.92
37
24
.397 148
4.45
.432 739
5.75
.310 864
30.72
.917 755
1.93
36
25
.397 415
4.45
.433 084
5.77
.309 021
30.68
.917 639
1.93
35
26
.397 682
4.45
.433 430
5.75
.307 180
30.63
.917 523
1.92
34
27
.397 949
4.43
.433 775
5.77
.305 342
30.60
.917 408
1.93
33
28
.398 215
4.45
.434 121
5.77
.303 506
30.55
.917 292
1.93
32
29
.398 482
4.45
.434 467
5.75
.301 673
30.50
.917 176
1.93
31


30
0.398 749
4.45
0.434 812
5.77
2.299 843
30.48
0.917 060
1.93
30
31
399 016
4.45
.436 158
5.77
.298 014
30.43
.916 944
1.93
29
32
399 283
4.43
.435 504
5.77
.296 188
30.38
.916 828
1.93
28
33
393 549
4.45
.435 850
5.78
.294 365
30.05
.916 712
1.95
27
34
399 816
4.43
.436 197
5,77
.292 544
30.30
.916 595
1.93
26
35
400 082
4.45
.436 543
5.77
.290 726
30.27
.916 479
1.93
25
36
.400 349
4.45
.436 889
5.78
.288 910
30.23
.916 363
1.95
24
37
400 618
4.43
.437 236
5.77
.287 096
30.18
.916 246
1.93
23
38
.400 882
4.45
.437 582
5.78
.285 285
30.15
.916 130
1.95
22
39
.401 149
4.43
.437 929
5.78
.283 476
30.12
.916 013
1.95
21


40
0.401 415
4.43
0.438 276
5.77
2.291 669
30.07
0.915896
1.95
20
41
.401 681
4.45
.438 622
5.78
.279 865
30.02
.915 779
1.93
19
42
.401 948
4.43
.438 969
5.78
.278 064
30.00
.915 663
1.95
18
43
.402 214
4.43
.439 316
5.78
.276 264
29.95
.915 546
1.95
17
44
.402 480
4.45
.439 663
5.80
.274 467
29.90
.915 429
1.97
16
45
.402 747
4.43
.440 011
5.78
.272 673
29.87
.915 311
1.95
15
46
.403 013
4.43
.440 353
5.78
.270 881
29.83
.916 194
1.95
14
47
.403 279
4.43
.440 705
5.80
.269 091
29.78
.915 077
1.95
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
23

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.403 545
4.43
.441 053
5.78
.267 304
29.77
.914 960
1.97
12
49
.403 811
4.45
.441 400
5.80
.266 518
29.70
.914 842
1.95
11


50
0.404 078
4.43
.441 748
5.78
2.263 736
29.68
0.914 725
1.97
10
51
.404 344
4.43
.442 095
5.80
.261 955
29.63
.914 607
1.95
09
52
.404 610
4.43
.442 443
5.80
.260 177
29.58
.914 490
1.97
08
53
.404 876
4.43
.442 791
5.80
.258 402
29.57
.914 372
1.97
07
54
.405 142
4.43
.443 139
5.80
.256 628
29.52
.914 254
1.97
06
55
.405 408
4.42
.443 487
5.80
.254 857
29.47
.914 136
1.97
05
56
.405 673
4.43
.443 835
5.80
.263 089
29.45
.914 018
1.97
04
57
.405 939
4.43
.444 183
5.80
.251 322
29.40
.913 900
1.97
03
58
.406 205
4.43
.444 532
5.80
.249 558
29.37
.913 782
1.97
02
59
.406 471
4.43
.444 880
5.82
.247 796
29.32
.913 664
1.98
01


60
0.406 737

0.445 229
2.246 037
0.913 545
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

24

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.406 737
4.42
 0.445 229
5.80
2.246 037
29.28
0.913 545
1.97
60'
01
.407 002
4.43
.446 577
5.82
.244 280
29.25
.913 427
1.97
59
02
.407 268
4.43
.445 926
5.82
.242 525
29.22
.913 309
1.98
58
03
.407 534
4.42
.446 275
5.82
.240 772
29.17
.913 190
1.97
57
04
.407 799
4.43
.446 624
5.82
.239 022
29.13
.913 072
1.99
56
05
.408 065
4.42
.446 973
5.82
.237 274
29.10
.912 953
1.98
55
06
.408 330
4.43
.447 322
5.82
.235 528
29.05
.912 834
1.98
54
07
.408 596
4.42
.447 671
5.82
.233 785
29.03
.912 715
1.98
53
08
.406 861
4.43
.448 020
5.82
.232 043
28.93
.912 596
1.98
52
09
.409 127
4.42
.448 369
5.83
.230 304
28.93
.912 477
1.98
51


10
0.409 392
4.43
0.448 719
5.82
2.228 568
28.92
0.912 358
1.98
50
11
.409 658
4.42
.449 068
5.83
.226 833
28.87
.912 239
1.98
49
12
.409 923
4.42
.449 418
5.83
.225 101
28.83
.912 120
1.98
48
13
.410 188
4.43
.449 768
5.82
.223 371
28.80
.912 001
2.00
47
14
.410 454
4.42
.450 117
5.83
.221 643
28.75
.911 881
1.98
46
15
.410 719
4.42
.450 467
5.83
.219 918
28.73
.911 762
1.98
45
16
.410 984
4.42
.450 817
5.83
.218 194
28.68
.911 643
2.00
44
17
.411 249
4.42
.451 167
5.83
.216 473
28.65
.911 523
2.00
43
18
.411 514
4.42
.451 517
5.85
.214 754
28.60
.911 403
1.98
42
19
.411 779
4.43
.451 868
5.83
.213 038
28.58
.911 284
2.00
41


20
0.412 045
4.42
0.452 218
5.83
2.211 323
28.53
0.911 164
2.00
40
21
.412 310
4.42
.452 568
5.85
.209 611
28.50
.911 044
2.00
39
22
.412 575
4.42
.462 919
5.83
.207 901
28.47
.910 924
2.00
38
23
.412 840
4.40
.453 269
5.85
.206 193
28.42
.910 804
2.00
37
24
.413 104
4.42
.453 620
5.85
.204 488
28.40
.910 684
2.02
36
25
.413 369
4.42
 .453 971
5.85
.202 784
28.35
.910 563
2.00
35
26
.413 634
4.42
.454 322
5.85
.201 093
28.32
.910 443
2.00
34
27
.413 899
4.42
.454 673
5.85
.199 384
28.28
.910 323
2.02
33
28
.414 164
4.42
.455 024
5.85
.197 687
28.25
.910 202
2.00
32
29
.414 429
4.40
.455 375
5.85
.195 992
28.20
.910 082
2.02
31


30
0.414 693
4.42
0.455 726
5.87
2.194 300
28.16
0.909 961
2.00
30
31
.414 958
4.42
.456 078
5.85
.192 609
28.13
.909 841
2.02
29
32
.415 223
4.40
.456 429
5.87
.190 921
28.10
.900 720
2.02
28
33
.415 487
4.42
.456 781
5.85
.189 235
28.07
.909 599
2.02
27
34
.415 752
4.40
.457 132
5.87
.187 551
28.03
.909 478
2.02
26
35
.416 016
4.42
 457 484
5.87
.185 869
28.00
.909 357
2.02
25
36
.416 281
4.40
 .457 836
5.87
.184 189
27.95
.909 236
2.02
24
37
.416 545
4.42
 .458 188
5.87
.182 512
27.93
.909 115
2.02
23
38
.416 810
4.40
.458 540
5.87
.180 836
27.88
.908 994
2.03
22
39
.417 074
4.40
.458 892
5.87
.179 163
27.85
.908 872
2.02
21


40
0.417 338
4.42
0.459 244
5.87
2.177 492
27.82
0.908 751
2.02
20
41
.417 603
4.40
.459 596
5.88
.175 823
27.78
.908 630
2.03
19
42
.417 867
4.40
.459 949
5.87
.174 156
27.75
.908 508
2.02
18
43
.418 131
4.42
.460 301
5.88
.172 491
27.72
.908 387
2.03
17
44
.418 396
4.40
.460 654
5.87
.170 828
27.67
.908 265
2.03
16
45
.418660
4.40
.461 006
5.88
.169 168
27.65
.908 143
2.03
15
46
.418 924
4.40
.461 359
5.88
.167 509
27.60
.908 021
2.03
14
47
.419 188
4.40
.461 712
5.88
.165 853
27.98
.907 899
2.03
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
24

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.419 452
4.40
.462 065
5.88
.164 198
27.53
.907 777
2.03
12
49
.419 716
4.40
.462 418
5.88
.162 546
27.50
.907 655
2.03
11


50
0.419 980
4.40
0.462 771
5.88
2.160 896
27.47
.907 533
2.03
10
51
.420 244
4.40
.463 124
5.90
.159 248
27.43
.907 411
2.03
09
52
.420 508
4.40
.463 478
5.88
.157 602
27.40
.907 289
2.05
08
53
.420 772
4.40
.463 831
5.90
.155 958
27.37
.907 166
2.03
07
54
.421 036
4.40
.464 185
5.88
.154 316
27.33
.907 044
2.03
06
55
.421 300
4.38
.464 538
5.90
.152 676
27.30
.906 922
2.05
05
56
.421 563
4.40
.464 892
5.90
.151 038
27.27
.906 799
2.05
04
57
.421 827
4.40
.465 246
5.90
.149 402
27.43
.906 676
2.03
03
58
.422 091
4.40
.465 600
5.90
.147 768
27.18
.906 554
2.05
02
59
.422 355
4.38
.465 954
5.90
.146 402
27.17
.906 431
2.05
01


60
0.422 618

0.466 308
2.144 507
0.906 308
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

25

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.422 618
4.40
0.466 308
5.90
2.144 507
27.13
0.906 308
2.05
60'
01
.422 388
4.38
.466 662
5.90
.142 879
27.08
.906 185
2.05
59
02
.423 145
4.40
.467 016
5.92
.141 254
27.07
.906 062
2.05
58
03
.423 409
4.40
.467 371
5.90
.139 630
27.02
.905 939
2.07
57
04
.423 673
4.38
.467 725
5.92
.138 009
27.00
.905 815
2.05
56
05
.423 936
4.38
.468 080
5.90
.136 369
26.97
.905 692
2.05
55
06
.424 199
4.40
.468 434
5.92
.134 771
26.92
.905 569
2.07
54
07
.424 463
4.38
.468 789
5.92
.133 156
26.90
.905 445
2.05
53
08
.424 726
4.40
.469 144
5.92
.131 542
26.85
.905 322
2.07
52
09
.424 990
4.38
.469 499
5.92
.129 931
26.83
.905 198
2.05
51


10
0.425 253
4.38
0.469 854
5.92
2.128321
26.78
0.905 075
2.07
50
11
.425 516
4.38
.470 209
5.92
.126 714
26.77
.904 951
2.07
49
12
.425 779
4.38
.470 564
5.93
.125 108
26.72
.904 827
2.07
48
13
.426 042
4.40
.470 920
5.92
.123 505
26.70
.904 703
2.07
47
14
.426 306
4.38
.471 275
5.93
.121 903
26.67
.904 579
2.07
46
15
.426 569
4.38
.471 631
5.92
.120 303
26.62
.904 455
2.07
46
16
.426 932
4.38
.471 986
5.93
.118 706
26.60
.904 331
2.07
44
17
.427 095
4.33
.472 342
5.93
.117 110
26.57
.904 207
2.07
43
18
.427 358
4.38
.472 698
5.93
.115 516
26.52
.904 083
2.08
42
19
.427 621
4.38
.473 054
5.93
.113 925
26.50
.903 958
2.07
41


20
0.427 884
4.38
0.473 410
5.93
2.112 335
26.47
0.903 834
2.08
40
21
.428 147
4.38
.473 766
5.93
.110 747
26.43
.903 709
2.07
39
22
.428 410
4.37
.474 122
5.93
.109 161
26.40
.903 585
2.08
38
23
.428 672
4.38
.474 478
5.95
.107 577
26.37
.903 460
2.08
37
24
.423 935
4.38
.474 835
5.93
.105 996
26.33
.903 335
2.08
36
25
.429 198
4.38
.475 191
5.95
.104 415
26.30
.903 210
2.07
35
26
.429 461
4.37
.475 548
5.95
.102 837
26.27
.903 086
2.08
34
27
.429 723
4.38
.476 905
5.95
.101 261
26.25
.902 961
2.08
33
28
.429 986
4.38
.476 262
5.95
.099 686
26.20
.902 836
2.10
32
29
.430 249
4.37
.476 619
5.95
.098 114
26.17
.902 710
2.08
31


30
0.430 511
4.38
0.476 976
5.95
2.096 544
26.15
0.902 585
2.08
30
31
.430 774
4.37
.477 333
5.95
.094 975
26.12
.902 460
2.08
29
32
.431 036
4.38
.477 690
5.95
.093 408
26.07
.902 335
2.10
28
33
.431 299
4.37
.478 047
5.97
.091 844
26.05
.902 209
2.08
27
34
.431 561
4.37
.478 405
5.95
.090 281
26.02
.902 084
2.10
26
35
.431 823
4.38
.478 762
5.97
.088 720
25.98
.901 958
2.08
25
36
.432 086
4.37
.479 120
5.95
.087 161
25.95
.901 833
2.10
24
37
.432 348
4.37
.479 477
5.97
.085 604
25.92
.901 707
2.10
23
36
.432 610
4.38
.479 836
5.97
.084 049
25.90
.901 581
2.10
22
39
.432 873
4.37
.480 193
5.97
.082 495
25.85
.901 455
2.10
21


40
0.433 135
4.37
.480 551
5.97
2.080 944
25.83
.901 329
2.10
20
41
.433 397
4.37
.480 909
5.97
.079 394
25.78
.901 203
2.10
19
42
.433 659
4.37
.481 267
5.98
.077 847
25.77
.901 077
2.10
18
43
.433 921
4.37
.481 626
5.97
.076 301
25.73
.900 951
2.10
17
44
.434 183
4.37
.481 984
5.98
.074 757
25.70
.900 825
2.12
16
45
.434 445
4.37
.482 343
5.97
.073 215
25.68
.900 698
2.10
15
46
.434 707
4.37
.482 701
5.98
.071 674
25.63
.900 572
2.12
14
47
.434 969
4.37
.483 060
5.98
.070 136
25.62
.900 445
2.10
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
25

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.435 231
4.37
.483 419
5.98
.068 599
25.57
.900 319
2.12
12
49
.435 493
4.37
.483 778
5.98
.067 065
25.55
.900 192
2.12
11


50
0.435 755
4.37
0.484 137
5.98
2.065 532
25.52
0.900 065
2.10
10
51
.436 017
4.35
.484 496
5.98
.064 001
25.48
.899 939
2.12
09
52
.436 278
4.37
.484 855
5.98
.062 472
25.47
.899 812
2.12
08
53
.436 540
4.37
.485 214
6.00
.060 944
25.42
.899 685
2.12
07
54
.436 802
4.35
.485 574
5.98
.059 419
25.40
.899 558
2.12
06
55
.437 063
4.37
.485 933
6.00
.057 895
25.37
.899 431
2.12
05
56
.437 326
4.37
.486 293
6.00
.056 373
25.33
.899 304
2.13
04
57
.437 587
4.35
.486 653
6.00
.054 863
25.30
.899 176
2.12
03
58
.437 848
4.37
.487 013
6.00
.053 335
25.28
.899 049
2.12
02
59
.438 110
4.35
.487 373
6.00
.051 818
26.23
.899 922
2.13
01


60
0.438 371

0.487 733
2.050 304
0.898 794
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

26

Sin
d."
Tan
d."
Cot
a"
Cos
d."
00'
0.438 371
4.37
0.487 733
6.00
2.050 304
25.22
0898 794
2.13
60'
01
438 633
4.35
.488 093
6.00
.048 791
25.18
898 666
2.12
59
02
438 894
4.35
.488 453
6.00
.047 280
25.15
898 339
2.13
58
03
439 155
4.37
488 813
602
.045 771
25.13
.898 411
2.13
57
04
439 417
4.35
.489 174
600
.044 263
25.08
898 283
2.12
56
05
439 678
4.35
.489 534
6.02
.042 758
25.07
898 156
2.13
55
06
.439 939
4.35
.439 895
6.02
.041 254
25.03
898 028
2.13
54
07
440 200
4.37
.490 256
6.02
.039 752
25.00
.897 900
2.15
53
08
440 462
435
.490 617
6.02
.038 252
24.98
.897 771
2.13
52
09
.440 723
4.35
490 978
6.02
.036 753
24.95
897 643
2.13
51


10
0.440 984
4.35
0.491 339
6.02
2.035 256
24.90
.897 515
2.13
50
11
.441 245
4.35
.491 700
6.02
.033 762
24.90
.897 387
2.15
49
12
.441 506
4.35
.492 061
6.02
.032 268
24.85
.897 258
2.13
48
13
.441 767
4.35
.492 422
6.03
.030 777
24.83
.897 130
2.15
47
14
.442 028
4.35
.492 784
6.02
.029 287
24.80
.897 001
2.13
46
15
.442 289
4.35
.493 145
6.03
.027 799
24.77
.896 373
2.15
45
16
.442 550
4.33
.493 507
6.03
.026 313
24.73
.896 744
2.15
44
17
.442 810
4.35
.493 869
6.03
.024 829
24.72
.896 615
2.15
43
18
.443 071
4.35
.494 231
6.03
.023 346
24.68
.896486
2.13
42
19
.443 332
4.35
.494 593
6.03
.021 865
24.65
.896 358
2.15
41


20
0.443 593
4.33
0.494 955
6.03
2.020 386
24.62
0.896 229
2.17
40
21
.443 853
4.35
.495 317
6.03
.018 909
24.60
.896 099
2.15
39
22
.444 114
4.35
.495 679
6.05
.017 433
24.57
.895 970
2.15
38
23
.444 375
4.33
.496 042
6.03
.015 959
24.53
.895 841
2.15
37
24
.444 635
4.35
.495 404
6.05
.014 487
24.52
.895 712
2.17
36
25
.444 896
4.33
.496 767
6.05
.013 016
24.47
.895 582
2.15
35
26
.445 156
4.35
.497 130
6.03
.011 548
24.45
.895 453
2.17
34
27
.446 417
4.33
.497 492
6.05
.010 081
24.43
.895 323
2.15
33
28
.445 677
4.33
.497 855
6.05
.008 61S
24.38
.895 194
2.17
32
29
.445 937
4.35
.498 218
6.07
.007 152
24.37
.895 064
2.17
31


30
0.446 198
4.33
0.498 582
6.05
2.005 690
24.35
0.894 934
2.15
30
31
.446 458
4.33
.498 945
6.05
.004 229
24.30
.894 805
2.17
29
32
.446 718
4.35
.499 308
6.07
.002 771
24.28
.894 675
2.17
28
33
.446 979
4.33
.499 672
6.05
2.001 314
24.25
.894 545
2.17
27
34
.447 239
4.33
.500 035
6.07
1.999 859
24.22
.894 415
2.18
26
35
.447 499
4.33
.500 399
6.07
.998 406
24.20
.894 284
2.17
25
36
.447 759
4.33
.500 763
6.07
.996 954
24.17
.894 154
2.17
24
37
.448 019
4.33
.501 127
6.07
.995 504
24.15
.894 024
2.17
23
38
.448 279
4.33
.501 491
6.07
.994 055
24.10
.894 894
2.18
22
39
.448 539
4.33
.501 855
6.07
.992 609
24.08
.893 763
2.17
21


40
0.448 799
4.33
0 502 219
6.07
1.991 164
24.07
0.893 633
2.18
20
41
.449 059
4.33
.502 583
6.08
.989 720
24.02
.893 502
2.18
19
42
.449 319
4.33
.502 948
6.07
.968 279
24 00
.893 371
2.17
18
43
.449 579
4.33
.503 312
6.08
.986 839
23.98
.893 241
2.18
17
44
.449 839
4.32
.503 677
6.07
.985 400
23.93
.893 110
2.19
16
45
.450 098
4.33
.504 041
6.08
.983 964
23.92
.892 979
2.18
15
46
.450 358
4.33
.504 406
6.08
.982 529
23.90
.892 846
2.18
14
47
.450 618
4.33
.504 771
6.08
.981 095
23.85
.892 717
2.18
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
26

Sin
d."
Tan
d."
Cot
a"
Cos
d."
48
.450 878
4.32
.505 136
6.10
.979 664
23.83
.892 586
2.18
12
49
.451 137
4.33
.505 502
6.08
.978 233
23.80
.892 455
2.20
11


50
0.451 397
4.32
0.505 867
6.08
1.976 305
23.78
0892 323
2.18
10
51
.451 656
4 33
.506 232
6.10
.975 373
23.75
.892 192
2.16
09
52
.451 916
4.32
.506 598
6.08
.973 953
23.72
.892 061
2.20
08
53
.452 175
4.33
.506 963
6.10
.972 530
23.70
.891 929
2.18
07
54
.452 435
4.32
.507 329
6.10
.971 108
23.68
.891 798
2.20
06
55
.452 694
4.32
.507 695
6.10
.969 687
23.63
.891 666
2.20
05
56
.452 953
4.33
.508 061
6.10
.968 269
23.62
.891 534
2.20
04
57
.453 213
4.32
.508 427
6.10
.966 852
23.60
.891 402
2.20
03
58
.453 472
4.32
.508 793
6.10
.965 436
23.55
.891 270
2.18
02
59
.453 731
4.32
.509 159
6.10
.964 023
23.53
.891 139
2.20
01


60
0.453 930

0.509 525
1.962 611
0.891 007
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."


27

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.453 990
4.35
0.509 525
6.12
1.962 611
23.52
0.891 007
2.22
60'
01
.454 250
4.32
.509 892
6.10
.961 200
23.48
.890 874
2.20
59
02
.454 509
4.32
.510 258
6.12
.959 791
23.45
.810 742
2.20
58
03
.454 768
4.32
.510 625
6.12
.958 384
23.43
.890 610
2.20
57
04
.455 027
4.32
.510 992
6.12
.956 978
23.40
.890 478
2.22
56
05
.455 286
4.32
.511 359
6.12
.955 574
23.38
.890 345
2.20
55
06
.455 545
4.32
.511 726
6.12
.954 171
23.35
.890 213
2.22
54
07
.456 804
4.32
.512 093
6.12
.952 770
23.32
.890 080
2.20
53
08
.456 063
4.32
.512 460
6.13
.951 371
23.30
.869 948
2.22
52
09
.456 322
4.30
.512 828
6.12
.949 973
23.27
.889 815
2.22
51


10
9.456 580
4.32
0.513 195
6.13
1.948 577
23.23
9.889 682
2.22
50
11
.456 839
4.32
.513 563
6.12
.947 183
23.22
.889 549
2.22
49
12
.457 098
4.32
.513 930
6.13
.945 790
23.20
.889 416
2.22
48
13
.457 357
4.30
.514 298
6.13
.944 398
23.17
.889 283
2.22
47
14
.457 615
4.32
.514 666
6.13
.943 008
23.13
.889 150
2.22
46
15
.457 874
4.32
.515 034
6.13
.941 620
23.12
.869 017
2.22
45
16
.458 133
4.30
.515 402
6.13
.940 233
23.08
.888 884
2.22
44
17
.458 391
4.32
.515 770
6.13
.938 848
23.05
.888 751
2.23
43
18
.458 650
4.30
.516 138
6.15
.937 465
23.05
.888 617
2.22
42
19
.458 908
4.30
.516 507
6.13
.936 082
23.00
.888 484
2.23
41


20
0.459 166
4.32
0.516 875
6.15
1.934 702
22.98
0.888 360
2.22
40
21
.459 525
4.30
.517 244
6.15
.933 323
22.95
.888 217
2.23
39
22
.459 683
4.32
.517 613
6.15
.931 946
22.93
.888 083
2.23
38
23
.459 942
4.30
.517 982
6.15
.930 570
22.90
.887 949
2.23
37
24
.460 200
4.30
.518 351
6 15
.929 196
22.88
.887 815
2.23
36
25
.460 200
4.30
.518 351
6 15
.
.927 823
22.85
.987 681
2.22
35
26
.460 716
4.30
.519 089
6.15
.926 452
22.83
.887 548
2.25
34
27
.460 974
4.30
.519 458
6 17
.925 082
22.80
.887 413
2.23
33
28
.461 232
4.32
.519 828
6 15
.923 714
22.78
.887 279
2.23
32
29
.461 491
4.30
.520 197
6.17
.922 347
22.75
.887 145
2.23
31


30
0.461 749
4.30
0.520 567
6.17
1 920 982
22.72
0.887 011
2.25
30
31
.462 007
4.30
.520 937
6.17
.919 619
22.70
.886 876
2.23
29
32
.462 265
4.30
.521 307
6.17
.918 257
22.68
.886 742
2.23
28
33
.462 523
4.28
.521 677
6.17
.916 896
22.65
.886 608
2.25
27
34
.462 760
4 30
.522 047
6.17
.915 537
22.62
.886 473
2.25
26
35
.463 038
4.30
.522 417
6.17
.914 180
22.60
.886 338
2.23
25
36
.463 296
4.30
.522 787
6.18
.912 824
22.58
.886 204
2.25
24
37
.463 554
4.30
.523 158
6.17
.911 469
22.55
.886 069
2.25
23
38
.463 812
4.28
.523 528
6.18
.910 116
22.52
.885 934
2.25
22
39
.464 069
4.30
.523 899
6.16
.908 765
22.50
.885 799
2.25
21


40
0.464 327
4.28
0.524 270
6.18
1.907 415
22.48
0.885 664
2.25
20
41
.464 584
4.30
.524 641
6.18
.906 066
22.45
.885 529
2.25
19
42
.464 842
4.30
.525 012
6.18
.904 719
22.42
.885 394
2.27
18
43
.465 100
4.28
.525 383
6.18
.903 374
22.40
.885 258
2.25
17
44
.465 357
4.30
.525 754
6.18
.902 030
22.39
.885 123
2.25
16
45
.465 615
4.28
.526 125
6.20
.900 687
22.35
.884 988
2.27
15
46
.465 872
4.28
.526 497
6.18
.899 346
22.32
.884 852
2.25
14
47
.466 129
4.30
.426 868
6.20
.898 007
22.30
.884 717
2.27
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
27

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.466 387
4.28
.527 240
6.20
.896 669
22.28
.884 581
2.27
12
49
.466 644
4.26
.527 612
6.20
.895 332
22.25
.884 445
2.27
11


50
0.466 901
4 28
0.527 984
6.20
1.893 997
22.23
0.884 309
2.25
10
51
.467 158
4.30
.528 356
6.20
.892 663
22.20
.884 174
2.27
09
52
.467 416
4.28
.528 728
6.20
.891 331
22.17
.884 038
2.27
08
53
.467 673
4.28
.529 100
6.22
.890 001
22.17
.883 902
2.27
07
54
.467 930
4.28
.529 473
6.20
.888 671
22.12
.883 766
2.28
06
55
.468 187
4.28
.529 845
6.22
.887 344
22.12
.883 629
2.27
05
56
.468 444
4.28
.530 218
6.22
.886 017
22.08
.883 493
2.27
04
57
.468 701
4.28
.530 591
6.20
.884 692
22.05
.883 357
2.27
03
58
.468 958
4.28
.530 963
6.22
.883 369
22.03
.883 221
2.28
02
59
.469 215
4.26
.531 336
6.22
.882 047
22.02
.863 084
2.27
01


60
0.469 472

0.531 709
1.880 726
0.882 948
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

28

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.469 472
4.27
0.531 709
6.23
1.880 726
21.98
0 882 948
2.28
60'
01
.469 728
4.28
.532 083
6.22
.879 407
21.95
.862 811
2.28
59
02
.469 985
4.28
.532 456
6.22
.878 090
21.93
.862 674
2.27
58
03
.470 242
4.28
.532 829
6.23
.876 774
21.92
.882 538
2.28
57
04
.470 499
4.27
.533 203
6.23
.875 459
21.90
.882 401
2.28
56
05
.470 755
4.28
.533 577
6.22
.874 145
21.85
.882 264
2.28
55
06
.471 012
4.27
.533 950
6.23
.872 834
21.85
.882 127
2.28
54
07
.471 268
4.28
.534 324
6.23
.871 523
21.82
.881 990
2.28
53
08
.471 525
4.28
.534 698
6.23
.870 214
21.80
.881 853
2.30
52
09
.471 782
4.27
.535 072
6.23
.866 906
21.77
.881 715
2.28
51


10
0.472 038
4.27
0.535 446
6.25
1.867 600
21.75
0.881 578
2.28
50
11
.472 294
4 28
.535 821
6.23
.866 295
21.72
.881 441
2.30
49
12
.472 551
4.27
.536 195
6.26
.864 992
21.70
.881 303
2.28
48
13
.472 807
4.27
.536 570
6.25
.863 690
21.67
.881 166
2.30
47
14
.473 063
4.28
.536 946
6.23
.862 390
21.65
.881 028
2.28
46
15
.473 320
4.27
.537 319
6.25
.861 091
21.63
.880 691
2.30
45
16
.473 576
4.27
.537 694
6.25
.859 793
21.62
.880 753
2.30
44
17
.473 832
4.27
.538 069
6.27
.858 496
21.57
.880 615
2.30
43
18
.474 088
4.27
.538 445
6.25
.857 202
21.57
.880 477
2.30
42
19
.474 344
4.27
.538 820
6.25
.855 908
21.53
.880 339
2.30
41


20
0.474 600
4 27
0.539 195
6.27
1.854 616
21.52
0.880 201
2.30
40
21
.474 856
4.27
.539 571
6.25
.853 325
21.48
.880 063
2.30
39
22
.475 112
4.27
.539 946
6.27
.852 036
21.47
.879 925
2.30
38
23
.475 368
4.27
.540 322
6.27
.850 748
21.45
.879 787
2.30
37
24
.475 624
4.27
.540 698
6.27
.849 461
21.42
.879 649
2.32
36
25
.475 880
4.27
.541 074
6.27
.848 176
21.40
.879 510
2.30
35
26
.476 136
4.27
.541 450
6.27
.846 892
21.37
.879 372
2.32
34
27
.476 392
4.25
541 626
6.28
.845 610
21.35
.879 233
2.30
33
28
.476 647
4.27
.542 203
6.27
.844 329
21.33
.879 095
2.32
32
29
.476 903
4.27
.542 579
6.28
.843 049
21.30
.878 956
2.32
31


30
0.477 159
4.25
0.542 956
6.27
1.841 771
21.28
0.878 817
2.32
30
31
.477 414
4.27
.543 332
6.28
.840 494
21.27
.878 678
2.32
29
32
.477 670
4 25
.543 709
6.28
.839 216
21.23
.878 539
2.32
28
33
.477 925
4.27
.544 086
6.28
.837 944
21.22
.878 400
2.32
27
34
.478181
4.25
.544 463
6.28
.836 671
21.18
.878 261
2.32
26
35
.478 436
4.27
.544 840
6.30
.835400
21.17
.878 122
2 32
25
36
.478 692
4.25
.545 218
6.28
.834 130
21.15
.877 983
2.32
24
37
.478 947
4.27
.545 595
6.30
.832 861
21.12
.877 844
2.33
23
38
.479 203
4.26
.545 973
6.28
.831 594
21.12
.877 704
2.32
22
39
.479 458
4.25
.546 350
6.30
.830 327
21.07
.877 565
2.33
21


40
0.479 713
4.25
0.546 728
6.30
1.829 063
21.07
0.877 425
2.32
20
41
.479 968
4.25
.547 106
6.30
.827 799
21.03
.877 286
2.33
19
42
.480 223
4.27
.547 484
6.30
.826 537
21.00
.877 146
2.33
18
43
.480 479
4.25
.547 862
6.30
.825 277
21.00
.877 006
2.32
17
44
.480 734
4.25
.548 240
6.32
.824 017
20.97
.876 867
2.33
16
45
.480 989
4.25
.548 619
6.30
.822 759
20.93
.876 727
2.33
15
46
.481 244
4.25
.548 997
6.32
.821 503
20.93
.876 587
2.33
14
47
.481 499
4.25
.549 376
6.32
.820 247
20.90
.876 447
2.33
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
28

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.481 754
4.25
.549 755
6.32
.818 993
20.87
.876 307
2.33
12
49
.482 009
4.23
.550 134
6.32
.817 741
20.87
.876 167
2.35
11


50
0.482 263
4.25
0.550 513
6.32
1.816 489
20.83
0.876 026
2.33
10
51
.482 518
4.25
.550 892
6.32
.815 239
20.82
.875 886
2.33
09
52
.482 773
4.25
.551 271
6.32
.813 990
20.78
.875 746
2.35
08
53
.483 028
4.23
.551 650
6.33
.812 743
20.77
.875 605
2.33
07
54
.483 282
4.25
.552 030
6.32
.811 497
20.75
.875 465
2.35
06
55
.483 537
4.25
.552 409
6.33
.810 252
20.72
.875 324
2.35
05
56
.483 792
4.23
.562 789
6.33
.809 009
20.72
.875 183
2.35
04
57
.484 046
4.25
.553 169
6.33
.807 766
20.67
.875 042
2.33
03
58
.484 301
4.23
.553 549
6.33
.806 526
20.67
.874 902
2.35
02
59
,434 555
4.25
.553 929
6.33
.805 285
20.63
.874 761
2.35
01


60
0.464 810

0.554 309
1.804 048
0.874 620
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

29

Sin
d. "
Tan
d."
Cot
d."
Cos
d."
00'
0.484 810
4.23
0.554 309
6.33
1.804 048
20.62
.874 620
2.35
60'
01
.485 064
4.23
.554 689
6.35
.802 811
20.60
.874 479
2.35
59
02
.485 318
4.25
.555 070
6.33
.801 575
20.57
.874 338
2.37
58
03
.485 573
4.23
.555 450
6.35
.800 341
20.55
.874 196
2.35
57
04
.485 827
4.23
.555 831
6.35
.799 108
20.53
.874 055
2.35
56
05
.486 081
4.23
.556 212
6.35
.797 876
20.52
.873 914
2.37
55
06
.486 335
4.25
.556 593
6.35
.796 645
20.48
.874 772
2.35
54
07
.486 590
4.23
.5S6 974
6.35
.795 416
20.47
.873 631
2.37
53
08
.486 844
4.23
.557 355
6.35
.794 188
20.43
.873 489
2.37
52
09
.487 098
4.23
.557 736
6.37
.792 962
20.43
.873 347
2.36
51


10
0.487 352
4.23
0.558 118
6.35
1.791 736
20.40
0.873 206
2.37
50
11
.487 606
4.23
.558 499
6.37
.790 512
20.38
.873 064
2.37
49
12
.487 860
4.23
.558 881
6.37
.789 289
20.35
.872 922
2.37
48
13
.488 114
4.22
.559 263
6.37
.788 068
20.35
.872 780
2.37
47
14
.488 367
4.23
.559 645
6.37
.786 847
20.32
.872 638
2.37
46
15
.488 621
4.23
.560 027
6.37
.785 628
20.28
.872 496
2.37
45
16
.488 875
4.23
.560 409
6.37
.784 411
20.28
.872 354
2.37
44
17
.489 129
4.22
.560 791
6.38
.783 194
20.25
.872 212
2.38
43
18
.489 382
4.23
.561 174
6.37
.781 979
20.23
.872 069
2.37
42
19
.489 636
4.23
.561 556
6.38
.780 765
20.22
.871 927
2.38
41


20
0.489 890
4.22
0.561 939
6.38
1.779 552
20.18
0.871 784
2.37
40
21
.490 143
4.23
.562 322
6.38
.778 341
20.17
.871 642
2.38
39
22
.490 397
4.22
.562 705
6.38
.777 131
20.15
.871 499
2.37
38
23
.490 650
4.23
.563 088
6.38
.775 922
20.13
.871 357
2.38
37
24
.490 904
4.22
.563 471
6.38
.774 714
20.10
.871 214
2.38
36
25
.491 157
4.23
.563 854
6.40
.773 508
20 10
.871 071
2.38
35
26
.491 411
4.22
.564 238
6.38
.772 302
20.07
.870 928
2.38
34
27
.491 664
4.22
.564 621
6.40
.771 098
20.03
.870 785
2.38
33
28
.491 917
4.22
.565 005
6.40
.769 896
20.03
.870 642
2.38
32
29
.492 170
4.23
.565 389
6.40
.768 694
20.00
.870 499
2.38
31


30
0.492 424
4.22
0.565 773
6.40
1.767 494
19.98
0.870 356
2.40
30
31
.492 677
4.22
.566157
6.40
.766 295
19.97
.870 212
2.38
29
32
.492 930
4.22
.566 541
6.40
.765 097
19.93
.870 069
2.38
28
33
.493 183
4.22
.566 925
6.42
.763 901
19.93
.869 926
2.40
27
34
.493 436
4.22
.567 310
6.40
.762 705
19.90
.869 782
2.38
26
35
.493 689
4.22
.567 694
6.42
.761 511
19.88
.869 639
2.40
25
36
.493 942
4.22
.568 079
6.42
.760 318
19.85
.869 495
2.40
24
37
.494 195
4.22
.568 464
6.42
.759 127
19.85
.869 351
2.40
23
38
.494 448
4.20
.568 849
6.42
.757 936
19.82
.869 207
2.38
22
39
.494 700
4.22
.569 234
6.42
.756 747
19.80
.869 064
2.40
21


40
0.494 953
4.22
0.569 619
6.42
1.755 559
19.78
0.868 920
2.40
20
41
.495 206
4.22
.570 004
6.43
.754 372
19.75
.868 776
2.40
19
42
.495 459
4.20
.570 390
6.43
.753 187
19.75
.868 632
2.42
18
43
.495 711
4.22
.570 776
6.42
.752 002
19.72
.868 487
2.40
17
44
.495 964
4.22
.571 161
6.43
.750 819
19.70
.868 343
2.40
16
45
.496 217
4.20
.571 647
6.43
.749 637
19.65
.868 199
2.42
15
46
.496 469
4.22
.571 933
6.43
.748 456
19.65
.868 054
2.40
14
47
.496 722
4.20
.572 319
6.43
.747 277
19.65
.867 910
2.42
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
29

Sin
d. "
Tan
d."
Cot
d."
Cos
d."
48
.496 974
4.20
.572 705
6.45
.746 098
19.62
.867 765
2.40
12
49
.497 226
4.22
.573 092
6.43
.744 921
19.60
.867 621
2.42
11


50
0.497 479
4.20
0.573 478
6.45
1.743 745
19.57
0.867 476
2.42
10
51
.497 731
4.20
.573 865
6.45
.742 571
19.57
.867 331
2.40
09
52
.497 983
4.22
.574 252
6.43
.741 397
19.53
.867 187
2.42
08
53
.498 236
4.20
.574 638
6.47
.740 225
19.53
.867 042
2.42
07
54
.498 488
4.20
.575 026
6.45
.739 053
19.50
.866 897
2.42
06
55
.498 740
4 20
.575 413
6.45
.737 883
19.48
.866 752
2.42
05
56
.498 992
4.20
.575 800
6.45
.736 714
19.45
.866 607
2.43
04
57
.499 244
4.20
.576 187
6.47
.735 547
19.45
.866 461
2.42
03
58
.499 496
4.20
.576 575
6.45
.734 380
19.42
.866 316
2.42
02
59
.499 748
4.20
.576 962
6.47
.733 215
19.40
.866 171
2.43
01


60
0.500 000

0.577 350
1.732 051
0.866 025
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

30

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.500 000
4.20
0.577 350
6.47
1.732 051
19.38
0.866 025
2.42
60'
01
.500 252
4.20
.577 738
6.47
.730 888
19.37
.865 880
2.43
59
02
.500 504
4.20
.578 126
6.47
.729 726
19.35
.865 734
2.42
58
03
.503 756
4.18
.578 514
6.48
.728 565
19.32
.865 589
2.43
57
04
.501 007
4.20
.578 903
6.47
.727 406
19.30
.865 443
2.42
56
05
.501 259
4.20
.579 291
6.48
.726 248
19.28
.865 297
2.43
55
06
.501 511
4.18
.579 680
6.47
.725 091
19.27
.865 151
2.42
54
07
.501 762
4.30
.580 068
6.48
.723 935
19.25
.865 006
2.45
53
08
.502 014
4.20
.580 457
6.48
.722 780
19.23
.864 860
2.45
52
09
.502 266
4.18
.580 846
6.43
.721 626
1.20
.864 713
2.43
51


10
0.502 517
4.20
0.581 235
6.50
1.720 474
19.20
0.864 597
2.43
50
11
.502 769
4.18
.581 625
6.48
.719 322
19.17
.864 421
2.43
49
12
.503 020
4.18
.562 014
6.48
.718 172
19.16
.864 275
2.45
48
13
.503 271
4.20
.582 403
6.50
.717 023
19.13
.864 128
2.43
47
14
.503 523
4.18
.582 793
6.50
.715 875
19.12
.863 982
2.43
46
15
.503 774
4.18
.533 183
6.50
.714 728
19.08
.863 836
2.45
45
16
.504 025
4.18
.583 573
6.50
.713 583
19.08
.863 689
2.45
44
17
.504 276
4.20
.583 963
6.50
.712 438
19.05
.863 542
2.43
43
18
.504 528
4.18
.584 353
6.50
.711 295
19.03
.863 396
2.45
42
19
.504 779
4.18
.584 743
6.52
.710 153
19.02
.863 249
2.45
41


20
0.505 030
4.18
0.585 134
6.50
1.709 012
19.00
0863 102
245
40
21
.505 281
4.18
.585 524
6.52
.707 872
18.98
862 955
245
39
22
.505 532
4.18
.585 915
6.52
.706 733
18.97
.862 808
245
38
23
.505 783
4.18
.586 306
6.52
.705 595
18.93
.862 661
245
37
24
.506 034
4.18
.586 697
6.52
.704 459
18.93
.862 514
2.47
36
25
.506 285
4.17
.587 088
6.52
.703 323
18.90
862 366
2.45
35
26
.506 535
4.18
.587 479
6.52
.702 189
18.88
862 219
2.45
34
27
.506 786
4.18
.587 870
6.53
.701 056
18.87
862 072
247
33
28
.507 037
4.18
.588 262
652
.699 924
18.85
.861 924
245
32
29
.507 288
4.17
.588 653
6.53
.698 793
18.83
.861 777
247
31


30
0.507 538
4.18
0.589 045
6.53
1.697 663
18.82
0.861 629
2.47
30
31
.507 789
4.18
.589 437
6.53
.696 534
18.78
.861 481
2.45
29
32
.508 040
4.17
.589 829
6.53
.695 407
18.78
.861 334
247
28
33
.508 290
4.18
.590 221
6.53
.694 280
18.75
.861 186
2.47
27
34
.508 541
4.17
.590 613
6.55
.693 155
18.73
.861 038
2.47
26
35
.508 791
4.17
.591 006
6.53
.692 031
18.72
.860 890
2.47
25
36
.509 041
4.18
.591 398
6.55
.690 908
18.70
.860 742
2.47
24
37
.509 292
4.17
391 791
6.55
.689 786
18.68
.860 594
2.47
23
38
.509 542
4.17
.592 184
6.55
.688 665
18.67
.860 446
248
22
39
.509 792
4.13
.592 577
6.55
.687 545
1865
.860 297
2.47
21


40
0510 043
4.17
0.592 970
6.55
1.686 426
18.63
0.860 149
2.47
20
41
.510 293
4.17
.593 363
6.57
.685 308
18.60
.860 001
2.48
19
42
.510 543
4.17
.593 757
6.55
.684 192
18.58
.859 852
2.47
18
43
510 793
4.17
.594 160
6.57
.683 077
18.58
.859 704
2.48
17
44
511 043
4.17
.594 644
6.55
.681 962
18.55
.859 555
2.48
16
45
.511 293
4.17
.594 937
6.57
.680 849
18.53
.859 406
2.47
15
46
511 543
4.17
.595 331
6.57
.679 737
18.52
.859 258
2.48
14
47
.511 793
4.17
.595 725
6.58
.678 626
18.50
.859 109
2.48
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
30

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.512 043
4.17
.596 120
6.57
.677 516
1848
.868 960
2.48
12
49
.512 293
4.17
.596 514
6.57
.676 407
1847
.858 811
2.48
11


50
0.512 543
4.15
0.596 908
6.58
1.675 299
18.45
0.858 662
2.48
10
51
.512 792
4.17
.597 303
6.58
.674 192
18.43
0.858 513
2.48
09
52
.513 042
4.17
.597 698
6.58
.673 086
18.40
.858 364
2.50
08
53
.513 292
4.15
.598 093
6.58
.671 982
18.40
.858 214
2.48
07
54
.513 541
4.17
.598 488
6.58
.670 878
18.37
.858 065
2.50
06
55
.513 791
4.15
.598 883
6.58
.669 776
18.37
.857 915
2.48
05
56
.514 040
4.17
.599 278
6.60
.668 674
18.32
.857 766
2.50
04
57
.514 290
4.15
.599 674
6.58
.667 574
18.32
.857 616
2.48
03
58
.514 539
4.17
.600 069
6.60
.666 475
18.30
.857 467
2.50
02
59
.514 789
4.15
.600 465
6.60
.665 377
18.30
.857 317
2.50
01


60
0.515 038

0.600 861
1.664 279
0.857 167
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

31

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.515 038
4.15
0.600 861
6.60
1.664 279
18.27
0.857 167
2.50
60'
01
.515 287
4.17
.601 257
6.60
.663 183
18.25
.857 017
2.48
59
02
.515 537
4.15
.601 653
6.60
.662 088
18.23
.856 868
2.50
58
03
.515 786
4.15
.602 049
6.60
.660 994
18.20
.856 718
2.52
57
04
.516 035
4.15
.602 445
6.62
.659 902
18.20
.856 567
2.50
56
05
.516 284
4.15
.602 842
6.62
.658 810
18.18
.856 417
2.50
55
06
.516 533
4.15
.603 239
6.60
.657 719
18.17
.856 267
2 50
54
07
.516 782
4.15
.603 635
6.62
.656 629
18.13
.856 117
2.52
53
08
.517 031
4.15
.604 032
6.62
.655 541
18.13
.855 966
2.50
52
09
.517 280
4.15
.604 429
6.63
.654 453
18.12
.855 816
2.52
51


10
0.517 529
4.15
0.604 827
6.62
1.653 366
18.08
0.855 665
2.50
50
11
.517 778
4.15
.605 224
6.63
.652 281
18.08
.855 515
2.52
49
12
.518 027
4 15
.605 622
6.62
.651 196
18.05
.855 364
2.50
48
13
.518 276
4.15
.606 019
6.63
.650 113
18.05
.855 214
2.52
47
14
.518 525
4.13
.606 417
6.63
.649 030
18.02
.855 063
2 52
46
15
.518 773
4.15
.606 815
6.63
.647 949
18.00
.854 912
2.52
45
16
.519 022
4.15
.607 213
6.63
.646 869
18.00
.854 761
2.52
44
17
.519 271
4.13
.607 611
6.65
.645 789
17.97
.854 610
2.52
43
18
.519 519
4.15
.608 010
6.63
.644 711
17.35
.854 459
2.52
42
19
.519 768
4.13
.608 408
6.65
.643 634
17.93
.864 308
2.53
41


20
0.520 016
4.15
0.608 807
6.63
1.642 558
17.93
0.854 156
2.52
40
21
.520 265
4.13
.609 205
6.65
.641 482
17.90
.854 005
2.52
39
22
.520 513
4.13
.609 604
6.65
.640 408
17.88
.853 854
2.53
38
23
.520 761
4.15
.610 003
6.67
.639 335
17.87
.853 702
2.52
37
24
.521 010
4.13
.610 403
6.65
.638 263
17.85
.853 551
2.53
36
25
.521 258
4.13
.610 802
6.65
.637 192
17.83
.853 339
2.52
35
26
.521 506
4.13
.611 201
6.67
.636 122
17.82
.853 248
2.53
34
27
.521 754
4.13
.611 601
6.67
.635 053
17.80
.853 096
2.53
33
28
.522 002
4.15
.612 001
6.67
.633 985
17.78
.852 944
2.53
32
29
.522 251
4.13
.612 401
6.67
.632 918
17.77
.852 792
2.53
31


30
0.522 499
4.13
0.612 801
6.67
1.631 852
17.75
0.852 640
2.53
30
31
.522 747
4.13
.613 201
6.67
.630 787
17.73
.852 488
2.53
29
32
.522 995
4.12
.613 601
6.68
.629 723
17.72
.862 336
2.53
28
33
.523 242
4.13
.614 002
6.67
.628 660
17.70
.852 134
2.53
27
34
.523 490
4.13
.614 402
6.68
.627 598
17.68
.852 032
2.55
26
35
.523 738
4.13
.614 803
6.68
.626 537
17.67
.851 879
2.53
25
36
.523 986
4.13
.615 204
6.68
.625 477
17.65
.851 727
2.55
24
37
.524 234
4.12
.615 605
6.68
.624 418
17.63
.851 574
2.53
23
38
.524 481
4.13
.616 006
6.70
.623 360
17.62
.851 422
2.55
22
39
.524 729
4.13
.616 408
6.68
.622 303
17.60
.851 269
2.53
21


40
0.524 977
4.12
0.616 809
6.70
1.621 247
17.58
0.851 117
2.55
20
41
.525 224
4.13
.617 211
6.70
.620 192
17.57
.850 964
2.55
19
42
.525 472
4.12
.617 613
6.70
.619 138
17.55
.850 811
2.55
18
43
.525 719
4.13
.618 015
6.70
.618 035
17.53
.850 658
2.55
17
44
.525 967
4.12
.618 417
6 70
.617 033
17.52
.850 505
2.55
16
45
.526 214
4.12
.618 819
6.70
.615 982
17.50
.850 352
2.55
15
46
.526 461
4.13
.619 221
6.72
.614 932
17.48
.850 199
2.55
14
47
.526 709
4.12
.619 624
6.70
.613 883
17.47
.850 046
2.55
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
31

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.526 956
4.12
.620 026
6.72
.612 835
17.45
.849 893
2.57
12
49
.527 203
4.12
.620 429
6.72
.611 788
17.43
.849 739
2.55
11


50
0.527 450
4.12
0.620 832
6.72
1.610 742
17.42
0.849 586
2.55
10
51
.527 697
4.12
.621 235
6.72
.609 697
17.40
.849 433
2.57
09
52
.527 944
4.12
.621 638
6.73
.608 653
17.40
.849 279
2.57
08
53
.528 191
4.12
.622 042
6.72
.607 609
1737
.849 125
2.55
07
54
.528 438
4.12
.622 445
6.73
.606 567
17.35
.848 972
2.57
06
55
.528 685
4.12
.622 849
6.73
.605 526
17.33
.848 818
2.57
05
56
.528 932
4.12
.623 253
6.73
.604 486
1733
.848 664
2.57
04
57
.529 179
4.12
.623 657
6.73
.603 446
1730
.848 510
2.57
03
58
.529 426
4.12
.624 061
6.73
.602 408
17.28
.848 356
2.57
02
59
.529 673
4.10
.624 465
6.73
.601 371
1727
.848 202
2.57
01


60
0.529 919

0.624 869
1.600 335
0.848 048
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

32

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.529 919
4.12
0.624 869
6.75
1.600 335
17.27
0.848 048
2.57
60'
01
.530 166
4.12
.625 274
6 75
.599 299
17.23
.847 894
2.57
59
02
.530 413
4.10
.625679
6 73
.598 265
17.23
.847 740
2.58
58
03
.530 659
4.12
.626 083
6.75
.597 231
17.20
.847 585
2.57
57
04
.530 906
4.10
.626 488
6.77
.596 199
17.20
.847 431
2.58
56
05
.531 152
4.12
.626 894
6.75
.595 167
17.17
.847 276
2.57
55
06
.531 399
4.10
.627 299
675
.594 137
17.17
.847 122
2.58
54
07
.531 645
4.10
.627 704
6.77
593 107
17.15
.846 967
2.57
53
08
.531 891
4.12
.628 110
6.77
.592 078
17.12
.846 813
2.58
52
09
.532 138
4.10
.628 516
6.75
.591 091
17.12
.846 658
2.58
51


10
0.532 384
4.10
0.628 921
6.77
1.590 024
17.10
0.846 503
2.58
50
11
.532 630
4.10
.629 327
6.78
.588 998
1708
.846 348
2.58
49
12
.532 876
4.10
.629 734
6.77
.587 973
17.07
.846 193
2.58
48
13
.533 122
4.10
.630 140
6.77
.586 949
17.05
.846 038
2.58
47
14
.533 368
4.12
.630 546
678
.585 926
17.03
.846 883
2.58
46
15
.533 615
4.10
630 953
6.78
.584 904
17.02
.845 728
2.68
45
16
.533 861
4.08
.631 360
6.78
583 883
17.00
.845 573
2.60
44
17
.534 106
4.10
.631 767
6.78
.582 863
16.98
.845 417
2.58
43
18
.534 352
4.10
632 174
6.78
.581 844
16.98
.845 262
2.60
42
19
.534 598
4.10
632 581
6.78
.580 826
16.95
.845 106
258
41


20
0.534 844
4.10
0.632 988
6.80
1.579 808
16.93
0.844 951
2.60
40
21
.535 090
4.08
.633 396
6.80
.578 792
16.93
.844 795
2.58
39
22
.535 335
4.10
.633 804
6.78
.577 776
16.92
.844 640
2.60
38
23
.535 581
4.10
.634 211
6.80
.576 761
16.88
.844 484
2.60
37
24
.535 827
4.08
.634 619
6.80
.575 748
16.88
.844 328
2.60
36
25
.536 072
4.10
.635 027
6.82
.574 735
16.87
.844 172
2.60
35
26
.535 318
4.08
.635 436
6.80
.573 723
16.83
.844 016
2.60
34
27
.536 563
4.10
.635 844
6.82
.572 713
16.83
.843 860
2.60
33
28
.536 809
4.08
.636 253
6.80
.571 703
16.82
.843 704
2.60
32
29
.537 054
4.10
.636 661
6.82
.570 694
16.80
.843 548
2.62
31


30
0.537 300
4.08
0.637 070
6.82
1.569 686
16.80
0.843 391
2.60
30
31
.537 545
4.08
.637 479
6.82
.568 678
16.77
.843 235
2.60
29
32
.537 790
4.08
.637 888
6.83
.567 672
16.75
.843 079
2.62
28
33
.538 035
4.10
.638 298
6.82
.566 667
16.75
.842 922
2.60
27
34
.538 281
4.08
.638 707
6.83
.565 662
16.72
.842 766
2.62
26
35
.538 526
4.08
.639 117
6.83
.564 659
16.72
.842 609
2.62
25
36
.538 771
4.08
.639 527
6.83
.563 656
16.68
.842 452
2.60
24
37
.539 016
4.08
.639 937
6.83
.562 655
16.68
.842 296
2.62
23
38
.539 261
4.08
.640 347
6.83
.561 654
16.67
.842 139
2.62
22
39
.539 506
4.08
.640 757
6.83
.560 654
16.65
.841 982
2.62
21


40
0.539 751
4.08
0.641 167
6.85
1.559 655
16.63
0.841 825
2.62
20
41
.539 996
4.07
.641 578
6.85
.558 657
16.62
.841 668
2.62
19
42
.540 240
4.08
.641 989
6.83
.557 660
16.60
.841 511
2.62
18
43
.540 485
4.08
.642 399
6.85
.556 664
16.58
.841 354
2.63
17
44
.540 730
4.07
.642 810
6.87
.555 669
16.58
.841 196
2.62
16
45
.540 974
4.08
.643 222
6.85
.554 674
16.55
.841 039
2.62
15
46
.541 219
4.08
.643 633
6.85
.553 681
16 55
.840 882
2.63
14
47
.541 464
4.07
.644 044
6.87
.552 688
16.53
.840 724
2.62
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
32

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.541 708
4.08
.644 456
6.87
.551 696
16.52
.840 567
2.63
12
49
.541 953
4.07
.644 868
6.87
.550 705
16.50
.840 409
2.63
11


50
0.542 197
4.08
0.645 280
6.87
1.549 715
16.48
0.840 251
2.62
10
51
.542 442
4.07
.645 692
6.87
.548726
16.47
.840 094
2.63
09
52
.542 686
4.07
.646 104
6.87
.547 738
16.45
.839 936
2.63
08
53
.542 930
4.07
.646 516
6.88
.546 751
16.43
.839 778
2.63
07
54
.543 174
4.08
.646 929
6.88
.545 765
16.43
.839 620
2.63
06
55
.543 419
4.07
.647 342
6.88
.544 779
16.40
.839 462
2.63
05
56
.543 663
4.07
.647 755
6.88
.543 795
16.40
.839 304
2.63
04
57
.543 907
4.07
.648 168
6.88
.542 811
16.38
.839 146
2.65
03
58
.544 161
4.07
.648 581
6.88
.541 828
16.37
.838 987
2.63
02
59
.544 395
4.07
.648 994
6.90
.540 846
16.35
.838 829
2.63
01


60
0.544 639

0.649 403
1.539 865
0.838 671
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

33

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.544 639
4.07
0.649 408
6.88
1.539 865
16.33
0.836 671
2.65
60'
01
.544 883
4.07
.649 821
6.90
.538 885
16.33
.838 512
2.63
59
02
.545 127
4.07
.650 235
6.90
.537 905
16.30
.838 354
2.65
58
03
.545 371
4.07
.650 649
6.90
.535 927
16.30
.838 195
2.65
57
04
.545 615
4.05
.651 063
6.90
.535 949
16.27
.838 036
2.63
56
05
.545 858
4.07
.651 477
6.92
.534 973
16.27
.837 878
2.65
55
06
.546 102
4.07
.651 892
6.90
.533 997
16.25
.837 719
2.65
54
07
.546 346
4.05
.652 306
6.92
.533 022
16.23
.837 560
2.65
53
08
.546 589
4.07
.652 721
6.92
.632 048
16.22
.837 401
2.65
52
09
.546 833
4.05
.653 136
6.92
.531 075
16.22
.837 242
2.65
51


10
0.547 076
4.07
0.653 551
6.92
1.530 102
16.16
0.837 083
2.66
50
11
.547 320
4.05
.653 966
6.93
.529 131
16.18
.836 924
2.67
49
12
.547 563
4.07
.654 382
6.92
.528 160
16.17
.836 764
2.65
48
13
.547 807
4.05
.654 797
6.93
.527 190
16.13
.836 605
2.65
47
14
.548 050
4.05
.655 213
6.93
.526 222
16.15
.836 446
2.67
46
15
.548 293
4.05
.655 629
6.93
.525 253
16.12
.836 286
2.66
45
16
.548 536
4.07
.656 045
6.93
.524 286
16.10
.836 127
2.67
44
17
.548 780
4.05
.656 461
6.93
.523 320
16.08
.835 967
2.67
43
18
.549 023
4.05
.656 877
6.95
.522 355
16.08
.835 807
2.65
42
19
.549 266
4.05
.657 294
6.93
.521 390
16.07
.835 648
2.67
41


20
0.549 509
4.05
0.657 710
6.95
1.520 426
16.05
0.835 468
2.67
40
21
.549 752
4.05
.658 127
6.95
.519 463
16.03
.835 328
2.67
39
22
.549 995
4.05
.658 544
6.95
.518 501
16.02
.835 168
2.67
38
23
.550 238
4.05
.658 961
6.97
.517 540
16.00
.835 008
2.67
37
24
.550 481
4.05
.659 379
6.95
.516 530
16.00
.834 848
2.67
36
25
.550 724
4.03
.659 796
6.97
.515 620
15.98
.834 688
2.68
35
26
.550 966
4.05
.660 214
6.95
.514 661
15.95
.834 527
2.67
34
27
.551 209
4.05
.660 631
6.97
.513 704
15.95
.834 367
2.67
33
28
.551 452
4.03
.661 049
6.97
.512 747
15.95
.834 207
2.66
32
29
.551 694
4.05
.661 467
6.98
.511 790
15.92
.834 046
2.67
31


30
0.551 937
4.05
0.661 886
6.97
1510 835
15.90
0.833 886
2.68
30
31
.552 180
4.03
.662 304
6.98
509 881
15.90
.833 725
2.67
29
32
.552 422
4.03
.662 723
6.97
508 927
15.88
.833 565
2.68
28
33
.552 664
4.05
.663 141
6.98
.507 974
15.87
.833 404
2.68
27
34
.552 907
4.03
.663 560
6.98
.507 022
15.85
.833 243
2.68
26
35
.553 149
4.05
.663 979
6.98
.506 071
15.83
.833 082
2.68
25
36
.553 392
4.03
.664 398
7.00
.505 121
15.82
.832 921
2.68
24
37
.553 634
4.03
.664 813
6.98
.504 172
15.82
.832 760
2.68
23
38
.553 876
4.03
.665 237
7.00
.503 223
15.80
.832 599
2.68
22
39
.554 118
4.03
.665 657
7.00
.502 275
15.78
.832 438
2.68
21


40
0.554 360
4.03
0.666 077
7.00
1.501 328
15.77
0.832 277
2.70
20
41
.554 602
4.03
.666 497
700
.500 382
15.75
.832 115
2.68
19
42
554 844
4.03
.666 917
7.00
.499 437
15.75
.831 954
2.68
18
43
.555 086
4.03
.667 337
7.02
.499 492
15.72
.831 793
2.70
17
44
.555 328
403
.667 758
7.02
.497 549
15.72
.831 631
2.68
16
45
.555 570
4.03
.668 179
7.00
.496 606
15.70
.831 470
2.70
15
46
.555 812
4.03
.668 599
7.02
.495 664
15.68
.831 308
2.70
14
47
.556 054
4.03
.669 020
7.03
.494 723
15.68
.831 146
2.70
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
33

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.556 296
4.02
.669 442
7.02
.493 782
15.65
.830 984
2.68
12
49
.556 537
4.03
.669 863
7.02
.492 843
15.65
.830 823
270
11


50
0.556 779
4.03
0.670 284
7.03
1.491 904
15.63
0.830 661
2.70
10
51
.557 021
4.02
.670 706
7.03
.490 966
15.62
.830 499
2.70
09
52
.567 262
4.03
.671 128
7.03
.490 029
15.62
.830 337
2.72
08
53
.557 504
4.02
.671 550
7.03
.489 092
15.58
.830 174
2.70
07
54
.557 745
4.03
.671 972
7.03
.488 157
15.58
.830 012
2.70
06
55
.557 987
4.02
.672 394
7.05
.487 222
15.57
.829 850
2.70
05
56
.558 228
4.02
.672 817
7.05
.486 288
15.55
.829 688
2.72
04
57
.553 469
4.02
.673 240
7.03
.485 355
15.53
.829 525
2.70
03
58
.558 710
4.03
.673 662
7.05
.484 423
15.52
.829 363
2.72
02
59
.558 952
4.02
.674 085
7.07
.483 492
15.52
.829 200
2.70
01


60
0.559 193

0.674 509
1.482 561
0.829 038
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

34

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.559 193
4.02
0.674 509
7.05
1.482 561
15.50
0.829 038
2.72
60'
01
.559 434
4.02
.674 932
7.05
.481 631
15.48
.828 875
2.72
59
02
.559 675
4.02
.675 355
7.07
.480 702
15.47
.828 712
2.72
58
03
.559 916
4.02
.675 779
7.07
.479774
15.47
.828 549
2.72
57
04
.560 157
4.02
.676 203
7.07
.478 846
15.43
.828 386
2.72
56
05
.560 398
4.02
.676 627
7.07
.477 926
15.43
.828 223
2.72
55
06
.560 639
4.02
.677 051
7.07
.476 994
15.42
.828 060
2.72
54
07
.560 880
4.02
.677 475
7.08
.476 069
15.42
.827 897
2.72
53
08
.561 121
4.00
.677 900
7.07
.475 144
15.38
.827 734
2.72
52
09
.561 361
4.02
.678 324
7.08
.474 221
15.38
.827 571
2.73
51


10
0.561 602
4.02
0.678 749
7.08
1.473 298
15.37
0.827 407
2 72
50
11
.561 843
4.00
.676 174
7.08
.472 376
15.35
.827 244
2.72
49
12
.562 083
4.02
.679 599
7.10
.471 455
15.33
.827 081
2.73
48
13
.562 324
4.00
.680 025
7.08
.470 535
15.33
.826 917
2.73
47
14
.562 564
4.02
.680 450
7.10
.469 615
15.30
.826 753
2.72
46
15
.562 805
4.00
.680 876
7.10
.468 697
15.30
.826 590
2.73
45
16
.563 045
4.02
.681 302
7.10
.467 779
15.28
.826 426
2.73
44
17
.563 286
4.00
.681 728
7.10
.466 862
15.28
.826 262
2.73
43
18
.563 526
4.00
.682 154
7.10
.465 945
15.25
.826 098
2.73
42
19
.563 766
4 02
.682 580
7.12
.465 030
15.25
.825 934
2.73
41


20
0.564 007
4.00
0.683 007
7.10
1.464 115
15.23
0.825 770
2.73
40
21
.564 247
4.30
.683 433
7.12
.463 201
15.23
.825 606
2.73
39
22
.564 487
4.00
.683 860
7.12
.462 287
15.20
.825 442
2.73
38
23
.564 727
4.00
.684 287
7.12
.461 375
15.20
.825 278
2.75
37
24
.564 967
4.00
.684 714
7.13
.460 463
15.18
.825 113
2.73
36
25
.565 207
4.00
.685 142
7.12
.459 552
15.17
.824 949
2.73
35
26
.565 447
4.00
.685 569
7.13
.458 642
15.15
.824 785
2.75
34
27
.565 687
4.00
.685 997
7.13
.457 733
15.15
.824 620
2.73
33
28
.565 927
3.98
.686 425
7.13
.456 824
15.13
.824 456
2.75
32
29
.566 166
4.00
.686 853
7.13
.455 916
15.12
.824 291
2.75
31


30
0.566 406
4.00
0.687 281
7.13
1.455 009
15.10
0.824 126
2.75
30
31
.566 646
4.00
.687 709
7.15
.454 103
15.10
.823 961
2.73
29
32
.566 886
3 98
.688 138
7.15
.453 197
15.08
.823 797
2.75
28
33
.567 125
4.00
.688 567
7.13
.452 292
15.07
.823 632
2.75
27
34
.567 365
3.98
.688 995
7.17
.451 388
15.05
.823 467
2.75
26
35
.567 604
4.00
.689 425
7.15
.450 485
15.03
.823 302
2.77
25
36
.567 844
3.98
.689 854
7.15
.449 583
15.03
.823 136
2.75
24
37
.568 083
4.00
.690 283
7.17
.448 681
15.02
.822 971
2.75
23
38
.568 323
3.98
.690 713
7.17
.447 780
15.00
.822 306
2.75
22
39
.568 562
3.98
.691 143
7.15
.446 880
15.30
.822 641
2.77
21


40
0.568 801
3.98
0.691 572
7.18
1.445 980
14.98
0.822 475
2.75
20
41
.569 040
4.00
.692 003
7.17
.445 081
14.97
.882 310
2.77
19
42
.569 280
3.98
.692 433
7.17
.444 183
14 95
.882 144
2.77
18
43
.569 519
3.98
.692 863
7.18
.443 286
14.93
.821 978
2.75
17
44
.569 758
3.98
.693 294
7 18
.442 390
14.93
.821 813
2.77
16
45
.569 997
3.98
.693 725
7.18
.441 494
14.92
.821 647
2.77
15
46
.570 236
3.98
.694 156
7.18
.440 599
14.90
.821 481
2.77
14
47
.570 475
3.98
.694 587
7.18
.439 705
14.90
.821 315
2.77
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
34

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.570 714
3.97
.695 018
7.20
.438 811
14.87
.821 149
2.77
12
49
.570 952
3.98
.695 450
7.18
.437 919
14.87
.820 983
277
11


50
0.571 191
3.98
0.695 881
7.20
1.437 027
14.85
0.820 817
2.77
10
51
.571 430
3.98
.696 313
7.20
.436 136
14.85
.820 651
2.77
09
52
.571 669
3.97
.696 745
7.20
.435 245
14.83
.820 485
2.78
08
53
.571 907
3.98
.697 177
7.22
.434 355
14.82
.820 318
2.77
07
54
.572 146
3.97
.697 610
7.20
.433 466
14.80
.820 152
2.78
06
55
.572 384
3.98
.698 042
7.22
.432 578
14.78
.819 985
2.77
05
56
.572 623
3.97
.698 475
7.22
.431 691
14.78
.819 819
2.75
04
57
.572 861
3.98
.698 908
7.22
.430 804
14.77
.819 652
2.77
03
58
.573 100
3.97
.699 341
7.22
.429 918
14 75
.819 486
2.78
02
59
.573 338
3.97
.699 774
7.23
.429 033
14.75
.819 319
2.78
01


60
0.573 576

0.700 208
1.426 148
0.819 152
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

35

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.573 576
3.98
0.700 208
7.22
1.428 148
14.73
0.819 152
2.78
60'
01
573 815
3.97
.700 641
7.23
.427 264
14.72
.818 985
2.78
59
02
.574 053
3.97
.701 075
7.23
.426 381
14.70
.818 818
2.78
58
03
.574 291
3.97
.701 509
7.23
.425 499
14.70
.818 651
2.78
57
04
.574 829
3.97
.701 943
7.23
.424 617
14.68
.818 484
2.78
56
05
.574 767
3.97
.702 377
7.25
.423 736
14.67
.818 317
2.78
55
06
.575 005
3.97
.702 812
7.23
.422 856
14.65
.818 150
2.80
54
07
.575 243
3.97
.703 246
7.25
.421 977
14.65
.817 982
2.78
53
08
.575 481
3.97
.703 681
7.25
.421 098
14.63
.817 815
2.78
52
09
.575 719
3.97
.704 116
7.25
.420 220
14.62
.817 648
2.80
51


10
0.576 957
3.97
0704 551
7.27
1.419 343
14.62
0.817 480
2.78
50
11
.575 195
3.95
.704 987
7.25
.418 466
14.60
.817 313
2.80
49
12
.576 432
3.97
.705 422
7.27
.417 590
14.58
.817 145
2.80
48
13
.576 670
3.97
.705 858
7.27
.416 715
14.57
.816 977
2.80
47
14
.576 908
3.95
7Q 294
7.27
.415 841
14.57
.816 809
2.78
46
15
.577 145
3.97
.706 730
7.27
.414 967
14.55
.816 642
2.80
45
16
.577 383
3.95
707 166
7.28
.414 094
14.53
.816 474
2.80
44
17
.577 620
3.97
.707 603
7.27
.413 222
14.52
.816 306
2.80
43
18
.577 858
3.95
.708 039
7.28
.412 351
14.52
.816 138
2.82
42
19
.573 095
3.95
.706 476
7.28
.411 480
14.50
.815 969
2.80
41


20
0.578 332
3.97
0.708 913
7.28
1.410 610
14.50
0.815 801
2.80
40
21
.578 570
3.96
.709 350
7.30
.409 740
14.47
.815 633
2.80
39
22
.578 807
3.95
.709 738
7.28
.408 872
14.47
.815 465
2.82
38
23
.579 044
3.95
.710 225
7.30
.408 004
14.45
.815 296
2.80
37
24
.579 281
3.95
.710 663
7.30
.407 137
14.45
.815 128
2.82
36
25
.579 518
3.95
.711 101
7.30
.406 270
14.43
.814 959
2.80
35
26
.579 766
3.95
.711 539
7.30
.405 404
14.42
.814 791
2.82
34
27
.579 992
3.95
.711 977
7.32
.404 539
14.40
.814 622
2.82
33
28
.580 229
3.95
.712 416
7.30
.403 675
14.40
.814 453
2.82
32
29
.580 466
3.95
.712 854
7.32
.402 811
14.38
.814 284
2.80
31


30
0.580 703
3.95
0.713 293
7.32
1.401 948
14.37
0.814 116
2.82
30
31
.580 940
3.93
.713 732
7.32
.401 086
14.37
.813 947
282
29
32
.581 176
3.95
.714 171
7.33
.400 224
14.35
.813 778
283
28
33
.581 413
3.95
.714 611
7.32
.399 364
14.35
.813 608
282
27
34
.581 650
3.93
.715 050
7.33
.398 503
14.32
.813 439
2 82
26
35
.581 886
3.95
.715 490
7.33
.397 644
14.32
.813 270
2 82
25
36
.582 123
3.93
.715 930
7.33
.396 785
14.30
.813 101
2 83
24
37
.582 359
3.95
.715 370
7.33
.395 927
14.28
.812 931
2 82
23
38
.582 596
3.93
.715 810
7.33
.395 070
14.28
.812 762
2.83
22
39
.582 832
3.95
.717 250
7.35
.394 213
14.27
.812 592
2 82
21


40
0.583 069
3.93
0.717 691
7.35
1.393 357
14.25
0.812 423
2.83
20
41
.583 305
3.93
.718 132
7.35
.392 502
14.25
.812 253
2.82
19
42
.583 541
3.93
.718 573
7.35
.391 647
14.23
.812 084
2.83
18
43
.583 777
3.95
.719 014
7.35
.390 793
14.22
.811 014
2.83
17
44
.584 014
3.93
.719 455
7.37
.389 940
14.20
.811 744
2.83
16
45
.584 250
3.93
.719 897
7.37
.389 088
14.20
.811 574
2.83
15
46
.584 486
3.93
.720 339
7.37
.388 236
14.18
.811 404
2.83
14
47
.584 722
3.93
.720 781
7.37
.387 385
14.18
.811 234
2.83
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
35

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.584 958
3.92
721 223
7.37
.386 534
14.17
.811 064
2.83
12
49
.585 194
3.92
.721 665
7.38
.385 684
14.15
.810 894
2.85
11


50
0.585 429
3.93
0.722 168
7.37
1.384 835
14.13
0.810 723
2.83
10
51
.585 665
3.93
.722 550
7.38
.383 987
14.13
.810 553
2.83
09
52
.585 901
3.93
.722 993
7.38
.383 139
14.12
.810 383
2.85
08
53
.586 137
3.92
.723 436
7.38
.382 292
14.10
.810 212
2.83
07
54
.586 372
3.93
.723 879
7.40
.381 446
14.10
.810 042
2.85
06
55
.586 608
3.93
.724 323
7.38
.380 600
14.08
.809 871
2.85
05
56
.586 844
3.92
.724 766
7.40
.379 755
14.07
.809 700
2.83
04
57
.587 079
3.92
.725 210
7.40
.378 911
14.07
.809 530
2.85
03
58
.587 314
3.93
.725 654
7.40
.378 067
14.05
.809 359
2.85
02
59
.587 550
3.92
.726 098
7.42
.377 224
14.03
.809 188
2.85
01


60
0.587 785

0.726 543
1.376 382
0.809 017
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

36

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.587 785
3.93
0.726 543
7.40
1.376 382
14.03
0.809 017
2.85
60'
01
.588 021
3.92
.726 987
7.42
.375 540
14.02
.808 846
2.85
59
02
.588 256
3.92
.727 432
7.42
.374 699
14.00
.808 675
2.85
58
03
.588 491
3.92
.727 877
7.42
.373 859
14.00
.808 504
2.85
57
04
.588 726
3.92
.728 322
7.42
.373 019
13.97
.808 333
2.87
56
05
.588 961
3.92
.728 767
7.43
.372 181
13.98
.808 161
2.85
55
06
.589 189
3.92
.729 213
7.42
.371 342
13.95
.807 990
2.87
54
07
.589 431
3.92
.729 658
7.43
.370 505
13.95
.807 818
2.85
53
08
.589 666
3.92
.730 104
7.43
.369 668
13.93
.807 647
2.87
52
09
.589 901
3.92
.730 550
7.43
.368 832
13.93
.807 475
2.85
51


10
0.590 136
3.92
0.730 996
7.45
1.367 996
13.92
0.807 304
2.87
50
11
.590 371
3.92
.731 443
7.43
.367 161
13.90
.807 132
2.87
49
12
.590 606
3.90
.731 889
7.45
.366 327
13.90
.806960
2.87
48
13
.590 840
3.92
.732 443
7.45
.365 493
13.88
.806 788
2.85
47
14
.591 075
3.92
.732 783
7.45
.364 660
13.87
.806 617
2.87
46
15
.591 310
3.90
.733 230
7.47
.363 828
13.87
.806 445
2.87
45
16
.591 544
3.92
.733 678
7.45
.362 996
13.85
.806 273
2.89
44
17
.591 779
3.90
.734 125
7.47
.362 165
13.83
.806 100
2.87
43
18
.592 013
3.92
.734 573
7.47
.361 335
13.83
.805 928
2.87
42
19
.592 248
3.90
.735 021
7.47
.360 505
13.82
.805 756
2.87
41


20
0.592 482
3.90
0.735 469
7.47
1.359 676
13.80
0.806 584
2.88
40
21
.592 716
3.92
.735 917
7.48
.358 848
13.80
.805 411
2.87
39
22
.592 951
3.90
.736 366
7.48
.358 020
13.78
.805 239
2 88
38
23
.593 185
3.90
.736 815
7.48
.357 193
13.77
.805 066
2.87
37
24
.593 419
3.90
.737 264
7.48
.356 367
13.77
.804 894
2.88
36
25
.593 653
3.90
.737 713
7.48
.355 541
13.75
.804 721
2.88
35
26
.593 887
3.90
.738 162
7.48
.354 718
13.73
.804 548
2.87
34
27
.594 121
3.90
.738 611
7.50
.353 892
13.73
.804 376
2.88
33
28
.594 355
3.90
.739 061
7.50
.353 068
13.72
.804 203
2.88
32
29
.594 669
3.90
.739 511
7.50
.352 245
13.72
.804 030
2.88
31


30
0.594 823
3.90
.739 961
7.50
1.351 422
13.68
0.803 657
2.88
30
31
.595 057
3.88
.740 411
7.52
.350 601
13.70
.803 684
2.88
29
32
.595 290
3.90
.740 862
7.50
.349 779
13.67
.803 511
2.90
28
33
.595 524
3.90
.741 312
7.52
.348 959
13.67
.803 337
2.88
27
34
.595 568
3.88
.741 763
7.52
.348 139
13.65
.803 164
2.88
26
35
.595 991
3.90
.742 214
7.53
.347 320
13.65
.802 991
2.80
25
36
.596 225
3.88
.742 666
7.52
.346 501
13.63
.802 817
2.88
24
37
.596 458
3.80
.743 117
7.53
.345 683
13.62
.802 644
2.80
23
38
.596 692
3.88
.743 569
7.52
.344 866
13.62
.802 470
2.88
22
39
.596 925
3.90
.744 020
753
.344 049
13.60
.802 297
2.90
21


40
0.597 159
3.88
0.744 472
7.55
1.343 233
13.58
0.802 123
2.90
20
41
.597 392
3.88
.744 925
7.53
.342 418
13.58
.801 949
2.88
19
42
.597 625
3.88
.745 377
7.55
.341 603
13.57
.801 776
2.90
18
43
.597 858
3.88
.745 830
7.53
.340 789
13.57
.801 602
2.90
17
44
.598 091
3.90
.746 282
7.55
.339 975
13.55
.801 428
2.90
16
45
.598 325
3.88
.746 735
7.57
.339 162
13.53
.801 254
2.90
15
46
.598 558
3.88
.747 189
7.55
.338 350
13.52
.801 080
2.90
14
47
.598 791
3.88
.747 642
7.57
.337 539
13.52
.800 906
2.92
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
36

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.599 024
3.87
.748 096
7.55
.336 728
13.52
.800 731
2.90
12
49
.599 256
3.88
.748 549
7.57
.335 917
13.48
.800 557
2.90
11


50
0.599 499
3.88
0.749 003
7.58
1.335 108
13.50
0.800 383
2.92
10
51
.599 722
3.88
.749 458
7.57
.334 298
13.47
.800 208
2.90
09
52
.599 955
3.88
.749 912
7.57
.333 490
13.47
.800 034
2.92
08
53
.600 188
3.87
.750 366
7.58
.332 682
13.45
.799 859
2.90
07
54
.600 653
3.87
.751 276
7.58
.331 068
13.43
.799 510
2.92
06
55
.600 420
3.88
.750 821
7.58
.311 875
13.45
.799 685
2.92
05
56
.600 885
3.88
.751 731
7.60
.330 262
13.42
.799 335
2.92
04
57
.601 118
3.87
.752 187
7.58
.329 457
13.42
.799 160
2.92
03
58
.601 350
3.88
.752 642
7.60
.328 652
13.40
.798 985
2.90
02
59
.601 583
3.87
.753 098
7.60
.327 848
13.38
.799 811
2.92
01


60
0.601 815

0.753 554
1.327 045
0.798 636
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

37

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.601 815
3.87
0.753 554
7.60
1.327 045
13.38
0.798 636
2.93
60'
01
.602 047
3.88
.754 010
7.62
.326 242
13.37
.798 460
2.92
59
02
.602 280
3.87
754 467
7.60
.325 440
13.37
.798 285
2.92
58
03
.602 512
3.37
.754 923
7.62
.324 638
13.35
.798 110
2.92
57
04
.602 744
3.87
.755 380
7.62
.323 837
13.33
.797 935
2.93
56
05
.602 976
3.87
.755 837
7.62
.323 037
13.33
.797 759
2.92
55
06
.603 208
3.87
.756 294
7.62
.322 237
13.32
.797 584
2.93
54
07
.603 440
3.87
.756 751
7.63
.321 438
13.32
.797 408
2.92
53
08
.603 672
3.87
.757 209
7.63
.320 639
13.30
.797 233
2.93
52
09
.603 904
3.87
.757 667
7.63
.319 841
13.28
.797 057
2.92
51


10
0.604 136
3.85
0.758 125
7.63
1.319 044
13.28
0.796 882
2.93
50
11
.604 367
3.87
.758 583
7.63
.318 247
13.27
.796 706
2.93
49
12
.604 599
3.87
.759 041
7.65
.317 451
13.25
.796 530
2.93
48
13
.604 831
3.85
.759 500
7.65
.316 656
13.25
.796 354
2.93
47
14
.605 062
3.87
.759 959
7.65
.315 861
13.23
796 178
2.93
46
15
.605 294
3.87
.760 418
7.65
.315 067
13.23
796 002
2.93
45
16
.605 526
3.85
.760 877
7.65
.314 273
13.22
.795 826
2.93
44
17
.605 757
3.85
.761 336
7.67
.313 480
13.20
.795 650
2.95
43
18
.605 988
3.87
.761 796
7.67
.312 688
13.20
.795 473
2.93
42
19
.606 220
3.85
.762 256
7.67
.311 896
13.18
.795297
2.93
41


20
0.606 451
3.85
0.762 716
7.67
1.311 105
13.18
0.795 121
2.95
40
21
.606 682
3.87
.763 176
7.67
.310 314
13.17
.794 944
2.93
39
22
.606 914
3.85
.763 636
7.68
.309524
13.15
.794 768
2.95
38
23
.607 145
3.85
.764 097
7.68
.308 735
13.15
.794 591
2.93
37
24
.607 376
3.85
.764 558
7.68
.307 946
13.15
.794 415
2.95
36
25
.607 607
3.85
.765 019
7.68
.307 157
13.12
.794 238
2.95
35
26
.607 838
3.85
.765 480
7 68
.306 370
13.12
.794 061
2.95
34
27
.608 069
3.85
.765 941
7.70
.305 583
13.12
.793 884
2.95
33
28
.608 300
3.85
.766 403
7.70
.304 796
13.08
.793 707
2.95
32
29
.608 531
3.83
.766 865
7 70
.304 011
13.10
.793 530
2.95
31


30
0.608 761
3.85
0.767 327
7.70
1.303 225
13.07
0.793 353
2.95
30
31
.608 992
3.85
.767 7898
7.72
.302 441
13.07
.793 176
2.95
29
32
.609 223
3.85
.768 252
7.70
.301 657
13.07
.792 999
2.95
28
33
.603 454
3.83
.768 714
7.72
.300 873
13.05
.792 822
2.97
27
34
.609 634
3.85
.769 177
7.72
.300 090
13.03
.792 644
2.95
26
35
.609 915
3.83
.769 640
7.73
.299 308
13.03
.792 467
2.95
25
36
.610 145
3.85
.770 104
7.72
.298 526
13.02
.792 290
2.97
24
37
.610 376
3.83
.770 567
7.73
.297 745
13.00
.792 112
2.95
23
38
.610 606
3.83
.771 031
7.73
.296 965
13.00
.791 935
2.97
22
39
.610 836
3.85
.771 495
7.73
.296 185
12.98
.791 757
2.97
21


40
0.611 067
3.83
0.771 959
7.73
1.295 406
12.98
0.791 579
2.97
20
41
.611 297
3.83
.772 423
7.75
.294 627
12.97
.791 401
2.95
19
42
.611 527
3.83
.772 888
7.75
.293 349
12.97
.791 224
2.97
18
43
.611 757
3.83
.773 353
7.75
.293 071
12.95
.791 046
2.97
17
44
.611 987
3.83
.773 818
7.75
.292 294
12.93
.790 868
2.97
16
45
.612 217
3.83
.774 283
7.75
.291 518
12.93
.790 690
2.97
15
46
.612 447
3.83
.774 748
7.77
.290 742
1292
.790 511
2.97
14
47
.612 677
3.83
.775 214
7.77
.289 967
12.92
.790 333
2.97
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
37

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.612 907
3.83
.775 680
7.77
.289 192
12.90
.790 155
2.97
12
49
.613 137
3.83
.776 146
7.77
.288 418
12.88
.789 977
2.98
11


50
0.613 367
3.82
0.776 612
7.77
1.287 645
12.88
0.789 798
2.97
10
51
.613 598
3.83
.777 078
7.78
.286 872
12.88
.789 620
2.98
09
52
.613 826
3.83
.777 545
7.78
.286 099
12.85
.789 441
2.98
08
53
.614 056
3.82
.778 012
7.78
.285 328
12.85
.789 263
2.98
07
54
.614 285
3.83
.778 479
7.78
.284 557
12.85
.789 084
2.98
06
55
.614 515
3.82
.778 946
7.80
.283 786
12.83
.788 905
2.97
05
56
.614 744
3.83
.779 414
7.78
.283 016
12.82
.788 727
2.98
04
57
.614 974
3.82
.779 881
7.80
.282 247
12.82
.788 548
2.98
03
58
.615 203
3.82
.780 349
7.80
.281 478
12.82
.788 369
2.98
02
59
.615 432
3.82
.780 817
7.82
.280 709
12.78
.788 190
2.98
01


60
0.615 661

0.781 286
1.279 942
0.788 011
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

38

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.615 661
3.83
0781 286
7.80
1.279 942
12.78
0.788 011
2.98
60'
01
.615 891
3.82
.781 754
7.82
.279 174
12.77
.787 832
3.00
59
02
.616 120
3.82
.782 223
7.82
.278 408
12.77
.787 652
2.98
58
03
.616 349
3.82
.782 692
7.82
.277 642
12.77
.787 473
2.98
57
04
.615 675
3.82
.783 161
7.83
.276 876
12.73
.787 294
3.00
56
05
.616 807
3.82
.783 631
7.82
.276 112
12.75
.787 114
2.98
55
06
.617 036
3.82
.784 100
7.83
.275 347
12.72
.786 935
2.98
54
07
.617 265
3.82
.784 570
7.83
.274 584
12.73
.785 756
3.00
53
08
.617 494
3.80
.785 040
7.83
.273 820
12.70
.786 576
3.00
52
09
.617 722
3.82
.785 510
7.85
.273 058
12.70
.786 296
2.98
51


10
0.617 951
3.82
0.785 981
7.83
1.272 296
12.70
0.786 217
3.00
50
11
.618 180
3.80
.786 451
7.85
.271 534
12.68
.786 037
3.00
49
12
.618 408
3.82
.786 922
7.87
.270 773
12 67
.785 857
3.00
48
13
.618 637
3.80
.787 394
7.85
.270 013
12.67
.785 677
3.00
47
14
.618 865
3.82
.787 865
7.85
.269 253
12.65
.785 497
3.00
46
15
.619 094
3.80
.788 336
7.87
.268 494
12.65
.785 317
3.00
45
16
.619 322
3.82
.788 808
7.87
.267 735
12.63
.785 137
3.00
44
17
.619 551
3.80
.789 280
7.87
.266 977
12.62
.784 957
3.02
43
18
.619 779
3.80
.789 752
7.88
.266 220
12.62
.784 776
3.00
42
19
.620 007
3.80
.790 225
7.87
.265 463
12.62
.784 596
3.00
41


20
0.620 235
3.82
0.790 697
7.88
1.264 706
12.60
0.784 416
3.02
40
21
.620 464
3.80
.791 170
7.88
.263 950
12.58
.784 235
3.00
39
22
.620 692
3.80
.791 643
7.90
.263 195
12.58
.784 055
3.02
38
23
.620 920
3.80
.792 117
7.88
.262 440
12.57
.783 874
3.02
37
24
.621 148
3.80
.792 590
7.90
.261 686
12.57
.783 693
3.00
36
25
.621 376
3.80
.793 064
7.90
.260 932
12.55
.783 513
3.02
35
26
.621 604
3.78
.793 538
7 90
.260 179
12.53
.783 332
3.02
34
27
.621 831
3.80
.794 012
7.90
.259 427
12.53
.783 151
3.02
33
28
.622 059
3.80
.794 486
7.82
.258 675
12.53
.782 970
3.02
32
29
.622 267
3.80
.794 961
7.82
.257 923
12.52
.782 789
3.02
31


30
0.622 515
3.78
0.795 436
7.92
1.267 172
12.50
0.782 608
3.02
30
31
.622 742
3.860
.795 911
7.92
.256 422
12.50
.782 427
3.02
29
32
.622 970
3.78
.796 386
7.93
.255 672
12.48
.782 246
3.02
28
33
.623 197
3.80
.796 862
7.92
.254 923
12.48
.782 065
3.03
27
34
.623 425
3.78
.797 337
7.93
.254 174
12.47
.781 883
3.02
26
35
.623 652
3.80
.797 813
7.95
.253 426
12.47
.781 702
3.03
25
36
.623 880
3.78
.798 290
7.93
.252 678
12.45
.781 520
3.02
24
37
.624 107
3.78
.798 766
7.93
.251 931
12.43
.781 339
3.03
23
38
.624 334
3.78
.799 242
7.95
.251 185
12.43
.781 157
3.02
22
39
.624 561
3.80
.799 719
7.95
.250 439
12.43
.780 976
3.03
21


40
0.624 789
3.78
0.800 196
7.97
1.249 693
12.42
0.780 794
3.03
20
41
.625 016
3.78
.800 674
7.95
.248 948
12.40
.780 612
3.03
19
42
.625 243
3.78
.801 151
7.97
.248 204
12.40
.780 430
3.03
18
43
.625 470
3.78
.801 629
7.97
.247 460
12.38
.780 248
3.02
17
44
.625 697
3.77
.802 107
7.97
.246 717
12.38
.780 067
3.05
16
45
.625 923
3.78
.802 585
7.97
.245 974
12.37
.779 884
3.03
15
46
.626 150
3.78
.803 063
7.98
.245 232
12.37
.779 702
3.03
14
47
.626 377
3.78
.803 542
7.98
.244 490
12.35
.779 520
3.03
13

Cos
d."
Cot
d."
Tan
d."
Sin
d."
38

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.626 604
3.77
.804 021
7.98
.243 749
12.33
.779 338
3.03
12
49
.626 830
3.78
.804 500
7.98
.243 009
12.35
.779 156
305
11


50
.627 057
3.78
0.804 979
7.98
1.242 268
12.32
0.778 973
3.03
10
51
.627 284
3.77
.805 458
8.00
.241 529
12.32
.778 791
3.05
09
52
.627 510
3.78
.805 938
8.00
.240 790
12.30
.778 608
3.03
08
53
.627 737
3.77
.806 418
8.00
.240 052
12.30
.778 426
3.05
07
54
.627 963
3.77
.806 898
8.02
.239 314
12.30
.778 243
3.05
06
55
.628 189
3.78
.807 379
8.00
.238 576
12.28
.778 060
3.03
05
56
.628 416
3.77
.807 859
8.02
.237 839
12.27
.777 878
3.05
04
57
.628 642
3.77
.808 340
8.02
.237 103
12.27
.777 695
3.05
03
58
.628 868
3.77
.808 821
8.03
.236 367
12.25
.777 512
3.05
02
59
.629 094
3.77
.809 303
8.02
.235 632
12.25
.777 329
3.05
01


60
0629 320

0.809 784
1.234 897
0.777 146
00

Cos
d."
Cot
d."
Tan
d."
Sin
d."

39

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.629 320
3.77
0.809 784
8.03
1.234 897
12.23
0.777 146
3.05
60'
01
.629 546
3.77
.810 266
8.03
.234 163
12.23
.776 963
3.05
59
02
.629 772
3.77
.810 748
8.03
.233 429
12.22
.776 780
3.07
58
03
.629 998
3.77
.811 230
8.03
.232 696
12.22
.776 596
3.05
57
04
.630 224
3.77
.811 712
8.05
.231 963
12.20
.776 413
3.05
56
05
.630 450
3.77
.812 195
8.05
.231 231
12.18
.776 230
3.07
55
06
.630 676
3.77
.812 678
8.05
.230 500
12.18
.776 046
3.05
54
07
.630 902
3.75
.813 161
8.05
.229 769
12.18
.775 863
3.07
53
08
.631 127
3.77
.813 644
8.07
.229 038
12 17
.775 679
3.05
52
09
.631 353
3.75
.814 128
8.07
.228 308
12.15
.775 496
3.07
51


10
0.631 578
3.77
0.814 612
8.07
1.227 579
12.15
0.775 312
3.07
50
11
.631 804
3.75
.815 096
8.07
.226 850
12.15
.775 128
3.07
49
12
.632 029
3.77
.815 560
8.08
.226 121
12.13
.774 944
3.05
48
13
.632 255
3.75
.816 065
8.07
.225 393
12.12
.774 761
3.07
47
14
.632 480
3.75
.816 549
8.08
.224 666
12.12
.774 577
3.07
46
15
.632 705
3.77
.817 034
8.08
.223 939
12.12
.774 393
3.07
45
16
.632 931
3.75
.817 619
8.10
.223 212
12.08
.774 209
3.08
44
17
.633 156
3.75
.816 005
8.10
.222 487
12.10
.774 024
3.07
43
18
.633 381
3.75
.816 491
8.08
.221 761
12.08
.773 840
3.07
42
19
.633 606
3.75
.818 976
8.12
.221 036
12.07
.773 656
3.07
41


20
0.633 831
3.75
0.819 463
8.10
1.220 312
12.07
0.773 472
3.08
40
21
.634 056
3.75
.819 949
8.10
.219 588
12.05
.773 287
3.07
39
22
.634 281
3.75
.820 435
8.12
.218 865
12.05
.773 103
3.08
38
23
.634 506
3.75
.820 922
8.12
.218 142
12.03
.772 918
3.07
37
24
.634 731
3.73
.821 409
8.13
.217 420
12.03
.772 734
3.08
36
25
.634 955
3.75
.821 897
8.12
.216 698
12.02
.772 549
3.08
35
26
.635 180
3.75
.822 384
8.13
.215 977
12.02
.772 364
3.08
34
27
.635 405
3.73
.822 872
8.13
.215 256
12.00
.772 179
3.07
33
28
.635 629
3.75
.823 360
8.13
.214 536
12.00
.771 995
3.08
32
29
.635 854
3.73
.823 848
8.13
.213 816
11.98
.771 810
3.08
31


30
0.636 078
3.75
0.824 336
8.15
1.213 097
11.98
0.771 625
3.08
30
31
.636 303
3.73
.824 825
8 15
.212 378
11.97
.771 440
3.10
29
32
.633 527
3.73
.825 314
8.15
.211 660
11.97
.771 254
3.08
28
33
.636 751
3.75
.825 803
8.15
.210 942
11.95
.771 069
3.08
27
34
.636 976
3.73
.826 292
8.17
.210 225
11.93
.770 884
3.08
26
35
.637 200
3.73
.826 762
8 17
.209 509
11.95
.770 699
3.10
25
36
.637 424
3.73
.827 272
8.17
.208 792
11.92
.770 513
3.08
24
37
.637 648
3.73
.827 782
8.17
.208 077
11.92
.770 328
3.10
23
38
.637 872
3.73
.828 252
8.18
.207 362
11.92
.770 142
3.08
22
39
.638 096
3.73
.828 743
8.18
.206 647
11.90
.769 957
3.10
21


40
0.638 320
3.73
0.829 234
8.18
1.205 933
11.90
0.769 771
3.10
20
41
.638 544
3.73
.829 725
8.18
.205 219
11.88
.769 585
3.08
19
42
.638 768
3.73
.830 216
8.18
.204 506
11.88
.769 400
3.10
18
43
.638 992
.372
.830 707
8.20
.203 793
11.87
.769 214
3.10
17
44
.639 215
3.73
.831 199
8.20
.203 081
11.87
.769 028
3.10
16
45
.639 439
3.73
.831 691
8.20
.202 369
11.85
.768 842
3.10
15
46
.639 663
3.72
.832 183
8.22
.201 658
1185
.768 656
3.10
14
47
.639 886
3.73
.832 676
8.22
.200 947
1183
.768 470
3.10
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
39

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.640 110
3.72
.833 169
8.22
.200 237
1182
.768 284
3.12
12
49
.640 333
3.73
.833 662
8.22
.199 528
11.83
.768 097
3.10
11


50
0.640 557
3.72
0.834 155
8.22
1.198 818
11.80
0.767 911
3.10
10
51
.640 780
3.72
.834 648
8.23
.198 110
11.80
.767 725
3.12
09
52
.641 003
3.72
.835 142
8.23
.197 402
11.80
.767 538
3.10
08
53
.641 226
3.73
.835 636
8.23
.196 694
11.78
.767 352
3.12
07
54
.641 450
3.72
.836 130
8.23
.195 987
11.78
.767 165
3.10
06
55
.641 673
3.72
.836 624
8.25
.195 280
11.77
.766 979
3 12
05
56
.641 896
3 72
.837 119
8.25
.194 574
11.77
.766 792
3.12
04
57
.642 119
3.72
.837 614
8.25
.193 866
11 75
.766 605
3.12
03
58
.642 342
3.72
.838 109
8.25
.193 163
11.75
.766 418
3.12
02
59
.642 565
3.72
.838 604
8.27
.192 458
11.73
.766 231
3.12
01


60
0.642 768

0.839 100
1.191 754
0.766 044
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

40

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.642 788
3.70
0.839 100
8.25
1.191 754
11.73
0.766 044
3.12
60'
01
.643 010
3.72
.839 595
8.28
.191 050
11.72
.765 857
3.12
59
02
.643 233
3.72
.840 092
8.27
.190 347
11.72
.765 670
3.12
58
03
.643 456
3.72
.840 588
8.27
.189 644
11.72
.765 483
3.12
57
04
.643 679
3.70
.841 084
8.28
.188 941
11.68
.765 296
3.12
56
05
.643 901
3.72
.841 581
8.28
.186 240
11.70
.765 109
3.13
55
06
.644 124
3.70
.842 078
8.28
.187 538
11.68
.764 921
3.12
54
07
.644 346
3.72
.842 575
8.30
.186 837
11.67
.764 734
3.12
53
08
.644 569
3.70
.843 073
8.30
.186 137
11.67
.764 547
3.13
52
09
.644 791
3.70
.843 571
8.30
.185 437
11.65
.764 359
3.13
51


10
0.645 013
3.70
0.844 069
8.30
.184 738
11.65
0.764 171
3.12
50
11
.646 235
3.72
.844 567
8.32
.184 039
11.65
.763 984
3.13
49
12
.645 458
3.70
.845 066
8.30
.183 340
11.63
.763 796
3.13
48
13
.645 680
3.70
.845 680
8.32
.182 642
11.62
.763 608
3.13
47
14
.645 902
3.70
.846 063
8.32
.181 945
11.62
.763 420
3.13
46
15
.646 124
3.70
.846 562
8.33
.181 248
11.62
.763 232
3.13
45
16
.646 346
3.70
.847 062
8.33
.180 551
11.60
.763 044
3.13
44
17
.646 568
3.70
.847 562
8.33
.179 855
11.58
.762 856
3.13
43
18
.646 790
3.70
.848 062
8.33
.179 160
11 60
.762 668
3.13
42
19
.647 012
3.68
.848 562
8.33
.173 464
11.57
.762 480
3.13
41


20
0.647 233
3.70
0.849 C62
8.35
1.177 770
11.57
0.762 292
3.13
40
21
.647 455
3.70
.849 563
8.35
.177 076
11.57
.762 104
3.15
39
22
.647 677
3.68
.850 064
8.35
.176 382
11.55
.761 915
3.13
38
23
.647 898
3.70
.850 565
8.37
.175 689
11.55
.761 727
3.15
37
24
.648 120
3.68
.851 067
8.35
.174 996
11.53
.761 538
3.13
36
25
.648 341
3.70
.851 568
8.37
.174 304
11.53
.761 350
3.15
35
26
.648 563
3.68
.852 070
8.38
.173 612
11.52
.761 161
3.15
34
27
.648 784
3.70
.852 573
8.37
.172 921
11.52
.760 972
3.13
33
28
.649 006
3.68
.853 075
8.38
.172 230
11.52
.760 784
3.15
32
29
.649 227
3.68
.853 578
8.38
.171 539
11.48
.760 595
3.15
31


30
0.649 448
3.68
0.854 081
8.38
1.170 850
11.50
0.760 406
3.15
30
31
.649 669
3.68
.854 584
8.38
.170 160
11.48
.760 217
3.15
29
32
.649 890
3.68
.855 087
8.40
.169 471
11.47
.760 028
3.15
28
33
.650 111
3.68
.855 591
8.40
.168 783
11.47
.759 839
3.15
27
34
.650 332
3.68
.856 095
8.40
.168 095
11.47
.759 650
3.15
26
35
.650 553
3.68
.856 599
8.42
.167 407
11.45
.759 461
3.17
25
36
.650 774
3.68
.857 104
8.40
.166 720
11.45
.759 271
3.15
24
37
.650 995
3.68
.857 608
8.42
.166 033
11.43
.759 082
3.15
23
38
.651 216
3.68
.858 113
8.43
.165 347
11.42
.758 893
3.17
22
39
.651 437
3.67
.858 619
8.42
.164 662
11.43
.758 703
3.15
21


40
0.651 657
3.68
0.859 124
8.43
1.163 976
11.40
0.758 514
3.17
20
41
.651 878
3.67
.859 630
8.43
.163 292
11.42
.758 324
3.17
19
42
.652 098
3.63
.860 136
8.43
.162 607
11.40
.758 134
3.15
18
43
.652 319
3.67
.860 642
8.43
.161 923
11.38
.757 945
3.17
17
44
.652 539
3.68
.861 148
8.45
.161 240
11.38
.757 766
3.17
16
45
.652 760
3.67
.861 655
8.45
.160 557
11.37
.757 555
3.17
15
46
.652 980
3.67
.862 162
8.45
.159 875
11.37
.767 375
3.17
14
47
.653 200
3.63
.862 669
8.47
.159 193
11.37
.757 185
3.17
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
40

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.653 421
3.67
.863 177
8.47
.158 511
11.35
.756 995
3.17
12
49
.653 641
3.67
.863 685
8.47
.157 830
11.35
.756 805
3.17
11


50
0.653 861
3.67
0.864 193
8.47
1.157 149
11.33
0.756 615
3.17
10
51
.654 081
3.67
.864 701
8.47
.156 469
11.32
.766 425
3.18
09
52
.654 301
3.67
.865 209
8 48
.155 790
11.33
.756 234
3.17
08
53
.654 521
3.67
.865 718
8.48
.155 110
11.28
.756 044
3.18
07
54
.654 741
3.67
.866 227
8.48
.154 432
11.32
.755 853
3.17
06
55
.654 361
3.65
.866 736
8.50
.153 753
11.30
.755 663
3.18
05
56
.655 180
3.67
.867 246
8.50
.153 075
11.28
.755 472
3.17
04
57
.655 400
3.67
.867 756
8.50
.152 398
11.28
.755 282
3.18
03
58
.655 620
3.65
.868 266
8.50
.151 721
11.28
.755 091
3.18
02
59
.655 839
3.67
.868 776
8.52
.151 044
11.27
.754 900
3.17
01


60
0.656 059

0.869 287
1.150 368
0.754 710
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

41

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.656 059
3.67
0.869 287
8.52
1.150 368
11.25
0.754 710
3.18
60'
01
.656 279
3.65
.869 798
8.52
.149 693
11.25
.754 519
3.18
59
02
.656 498
3.65
.870 309
8.52
.149 018
11.25
.754 328
3.18
58
03
.656 717
3.67
.870 820
8.53
.148 343
11.23
.754 137
3.18
57
04
.656 937
3.65
.871 332
8.52
.147 669
11.23
.753 946
3.18
56
05
.657 156
3.65
.871 843
8.55
.146 995
11.22
.753 755
3.20
55
06
.657 375
3.65
.872 356
8.53
.146 322
11.22
.753 663
3.18
54
07
.657 594
3.67
.872 868
8.55
.145 649
11.22
.753 372
3.18
53
08
.657 814
3.65
.873 381
8.55
.144 976
11.20
.753 181
3.20
52
09
.658 033
3.65
.873 894
8.55
.144 304
11.18
.752 989
3.18
51


10
0.658 252
3.65
0.874 407
8.55
1.143 633
11.20
0.752 798
3.20
50
11
.658 471
3.63
.874 920
8.57
.142 961
11.17
.752 606
3.18
49
12
.658 689
3.65
.875 434
8.57
.142 291
11.17
.752 415
3.20
48
13
.658 908
3.65
.875 948
8.57
.141 621
11.17
.752 223
3.18
47
14
.659 127
3.65
.876 462
8.57
.140 951
11.17
.752 032
3.20
46
15
.659 346
3.63
.876 976
8.56
.140 281
11.13
.751 840
3.20
45
16
.659 564
3.65
.877 491
8.53
.139 613
11.15
.751 648
3.20
44
17
.659 733
3.65
.878 006
8.53
.138 944
11.13
.751 456
3.20
43
18
.660 002
3.63
.878 521
8.60
.138 276
11.12
.751 264
3.20
42
19
.660 220
3.65
.879 037
8.60
.137 609
11.13
.751 072
3.20
41


20
0.660 439
3.63
0.879 553
8.60
1.138 941
11.10
0.750 880
3.20
40
21
.660 657
3.63
.880 069
8.60
.136 275
11.10
.750 688
3.20
39
22
.660 875
3.65
.880 585
8.62
.135 609
11.10
.750 496
3.22
38
23
.661 094
3.63
.881 102
8.62
.134 943
11.10
.750 303
3.20
37
24
.661 312
3.63
.881 619
8.62
.134 277
11.08
.750 111
3.20
36
25
.661 530
3.63
.882 136
8.62
.133 612
11.07
.749 919
3.22
35
26
.661 748
3.63
.882 653
8.63
.132 948
11.07
.749 726
3.20
34
27
.661 966
3.63
.883 171
8.63
.132 284
11.07
.749 534
3.22
33
28
.662 184
3.63
.883 689
8.63
.131 620
11.05
.749 341
3.22
32
29
.662 402
3.63
.884 207
8.63
.130 957
11.05
.749 148
3.20
31


30
0662 620
3.63
0.884 725
8.65
1.130 294
11.03
0.748 956
3.22
30
31
.662 838
3.63
.865 244
8.65
.129 632
11.03
.748 763
3.22
29
32
.663 056
3.62
.885 763
8.65
.128 970
11.02
.748 570
3.22
28
33
.663 273
3.63
.886 282
8.67
.128 309
11.02
.748 377
3.22
27
34
.663 491
3.63
.886 802
8.65
.127 648
11.02
.748 184
3.22
26
35
.663 709
3.62
.887 321
8.68
.126 987
11.00
.747 991
3.22
25
36
.663 926
3.63
.887 342
8.67
.126 327
11.00
.747 798
3.22
24
37
.664 144
3.62
.888 362
8.67
.125 667
10.98
.747 605
3.22
23
38
.664 361
3.63
.888 882
8.68
.125 008
10.98
.747 412
3.23
22
39
.664 579
3.62
.889 403
8.68
.124 349
10.97
.747 218
3.22
21


40
0.664 796
3.62
0.889 924
8.70
1.123 691
10.97
0.747 026
3.22
20
41
.665 013
3.62
.890 446
8.68
.123 033
10.97
.746 832
3.23
19
42
.665 230
3.63
.890 967
8.70
.122 375
10.95
.746 638
3.22
18
43
.665 448
3 62
.891 489
8.72
.121 718
10.93
.746 446
3.23
17
44
.665 665
3.62
.892 012
8.70
.121 062
10.95
.746 251
3.23
16
45
.665 882
3.62
.892 534
8.72
.120 405
10.92
.746 057
3.22
15
46
.666 099
3.62
.893 057
8.72
.119 750
10.93
.745 864
3.23
14
47
.666 316
3.60
.893 580
8.72
.119 094
10.92
.745 670
3.23
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
41

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.666 532
3.62
.894 103
8.73
.118 439
10.90
.746 476
3.23
12
49
.666 749
3.62
.894 627
8.73
.117 785
10.92
.745 282
3.23
11


50
0 666 966
3.62
0.895 151
8.73
1.117 130
10.88
0.745 088
3.23
10
51
.667 183
3.60
.895 675
8.73
.116 477
10.90
.744 894
3.23
09
52
.667 399
3.62
.896 199
8.75
.115 823
10.87
.744 700
3.23
08
53
.667 616
3.62
.896 724
8.75
.115 171
10.88
.744 506
3.23
07
54
.667 833
3.60
.897 249
8.75
.114 518
10.87
.744 312
3.25
06
55
.668 049
3.60
.897 774
8.75
.113 866
10.85
.744 117
3.23
05
56
.668 265
3.62
.898 299
8.77
.113 215
10.87
.743 923
3.23
04
57
.668 482
3.60
.898 825
8.77
.112 563
10.83
.743 728
3.23
03
58
.668 698
3.60
.899 351
8.77
.111 913
10.85
.743 534
3.25
02
59
.668 914
3.62
.899 877
8.78
.111 262
10.82
.743 339
3.23
01


60
0.669 131

0900 404
1.110 613
0.743 145
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

42

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.669 131
3.60
0.900 404
8.78
1.110 613
10.83
0.743 145
3.25
60'
01
.669 347
3.60
.900 931
8.78
.109 963
10.82
.742 950
3.25
59
02
.669 563
3.60
.901 458
8.78
.109 314
10.82
.742 755
3.23
58
03
.669 779
3.60
.901 985
8.80
.108 665
10.80
.742 561
3.25
57
04
.669 995
3.60
.902 513
8.80
.108 017
10.80
.742 366
3.25
56
05
.670 211
3.60
.903 041
8.80
.107 369
10.78
.742 171
3.25
55
06
.670 427
3.58
.903 569
8.82
.106 722
10.78
.741 976
3.25
54
07
.670 642
3.60
.904 098
8.82
.106 075
10.78
.741 781
3.25
53
08
.670 858
3.60
.904 627
8.82
.105 428
10.77
.741 586
3.25
52
09
.671 074
3.58
.905 156
8.82
.104 782
10.75
.741 391
3.27
51


10
.671 289
3.60
0.905 685
8.83
1.104 137
10.77
0.741 195
3.25
50
11
.671 505
3.60
.906 215
8.83
.103 491
10.75
.741 000
3.25
49
12
.671 721
3.58
.906 745
8.83
.102 846
10.73
.740 805
3.27
48
13
.671 936
3.58
.907 275
8.83
.102 202
10.73
.740 609
3.25
47
14
.672 151
3.60
.907 805
8.85
.101 558
10.73
.740 414
3.27
46
15
.672 367
3.58
.908 336
8.85
.100 914
10.72
.740 218
3.25
45
16
.672 582
3.58
.908 867
8.85
.100 271
10.72
.740 023
3.27
44
17
.672 797
3.60
.909 398
8.87
.099 628
10.70
.739 827
3.27
43
18
.673 013
3.58
.909 930
8.87
.098 986
10.70
.739 631
3.27
42
19
.673 228
3.58
.910 462
8.87
.098 344
10.70
.739 435
3.27
41


20
0.673 443
3.58
0.910 994
8.87
1.097 702
10.68
0.739 239
3.27
40
21
.673 658
3.58
.911 526
8.88
.097 061
10.68
.739 043
3.25
39
22
.673 873
3 58
.912 059
8.88
.096 420
10.67
.738 848
3.28
38
23
.674 088
3.57
.912 592
8.88
.095 780
10.67
.738 651
3.27
37
24
.674 302
3.58
.913 125
8.90
.095 140
10.67
.738 455
3.27
36
25
.674 517
3.58
.913 659
8.90
.094 500
10.65
.738 259
3.27
35
26
.674 732
3.58
.914 193
8.90
.093 861
10.65
.738 063
3.27
34
27
.674 947
3.57
.914 727
8.90
.093 222
10.63
.737 867
3.28
33
28
.675 161
3.58
.915 261
8.92
.092 584
10.63
.737 670
3.27
32
29
.675 376
3.57
.915 796
8.92
.091 946
10.62
.737 474
3.28
31


30
0.675 590
3.58
0.916 331
8.92
1.091 309
10.63
0.737 277
3.27
30
31
.675 805
3.57
.916 866
8.93
.090 671
10.60
.737 081
3.28
29
32
.676 019
3.57
.917 402
8.93
.090 035
10.62
.736 884
3.28
28
33
.676 233
3.58
.917 938
8.93
.089 398
10.60
.736 687
3.27
27
34
.676 448
3.57
.918 474
8.93
.088 762
10.58
.736 491
3.28
26
35
.676 662
3.57
.919 010
8.95
.088 127
10.58
.736 294
3.28
25
36
.676 876
3.57
.919 547
8.95
.087 492
10.58
.736 097
3.28
24
37
.677 090
3.57
.920 084
8.95
.086 857
10.57
.735 900
3.28
23
38
.677 304
3.57
.920 621
8.97
.086 223
10.57
.735 703
3.28
22
39
.677 518
3.57
.921 159
8.97
.085 589
10.57
.735 506
3.28
21


40
0.677 732
3.57
0921 697
8.97
1.084 9S5
10.55
0.735 309
3.28
20
41
.677 946
3.57
.922 235
8.97
.084 322
10.53
.735 112
3.28
19
42
.678 160
3.55
.922 773
8.98
.083 690
10.55
.734 915
3.30
18
43
.678 373
3.57
.923 312
8.98
.083 057
10.53
.734 717
3.28
17
44
.678 587
3.57
.923 851
8.98
.882 425
10.52
.734 520
3.28
16
45
678 801
3.55
.924 390
9.00
.081 794
10.52
.734 323
3.30
15
46
.679 014
3.57
.924 930
9.00
.081 163
10.52
.734 125
3.30
14
47
.679 228
3.55
.925 470
9.00
.080 532
10.50
.733 927
3.28
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
42

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.679 441
3.57
.926 010
9.02
.079 902
10.50
.733 720
3.30
12
49
.679 655
3.55
.926 561
9.00
.079 272
10.50
.733 530
3.30
11


50
0.679 868
3.55
0.927 091
9.02
1.078 642
10.48
0.733 334
3.28
10
51
.680 081
3.57
.927 632
9.03
.078 013
10.48
.733 137
3.30
09
52
.680 295
3.55
.928 174
9.02
.077 384
10.47
.732 939
3.30
08
53
.680 508
3.55
.928 715
9.03
.076 766
10.47
.732 741
3.30
07
54
.680 721
3.55
.929 257
9.05
.076 128
10.45
.732 543
3.30
06
55
.680 934
3.55
.929 800
9.03
.075 501
10.47
.732 345
3.30
05
56
.681 147
3.55
.930 342
9.05
.074 873
10.43
.732 147
3.30
04
57
.681 360
3.55
.930 885
9.05
.074 247
10.45
.731 949
3.32
03
58
.681 573
3.55
.931 428
9.06
.073 620
10.43
.731 750
3.30
02
59
.681 786
3.53
.931 971
9.07
.072 994
10.42
.731 552
3.30
01


60
0.681 998

0.932 515
1.072 369
0.731 354
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

43

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.681 998
3.55
0.932 515
9.07
1.072 369
10.42
0.731 354
3.32
60'
01
.682 211
3.55
.933 059
9.07
.071 744
10.42
.731 155
3.30
59
02
.682 424
3.53
.933 603
9.08
.071 119
10.42
.730 957
3.32
58
03
.682 636
3.55
.934 148
9.08
.070 494
10.40
.730 758
3.30
57
04
.682 849
3.53
.934 693
9.08
.069 870
10.37
.730 560
3.32
56
05
.683 061
3.55
.935 238
9.08
.069 247
10.40
.730 361
3.32
55
06
.683 274
3.53
.935 783
9.10
.068 623
10.38
.730 162
3.32
54
07
.683 486
3.53
.936 329
9.10
.068 000
10.37
.729 963
3.30
53
08
.683 698
3.55
.936 875
9.12
.067 378
10.37
.729 765
3.32
52
09
.683 911
3.53
.937 422
9.10
.066 756
10.37
.729 566
3.32
51


10
0.664 123
3.53
0.937 968
9.12
1.066 134
10.35
0.729 367
3.32
50
11
.664 335
3.53
.933 515
9.13
.065 513
10.35
.729 168
3.32
49
12
.684 547
3.53
.939 063
9.12
.064 892
10.35
.728 969
3.33
48
13
.684 759
3.53
.939 610
9.13
.064 271
10.33
.728 769
3.32
47
14
.684 971
3.53
.940 158
9.13
.063 651
10.33
.728 570
3.32
46
15
.685 183
3.53
.940 706
9.15
.063 031
10.32
.728 371
3.32
45
16
.685 395
3.53
.941 255
913
.062 412
10.32
.728 172
3.33
44
17
.685 607
3.52
.941 803
9.15
.061 793
10.32
.727 972
3.32
43
18
.685 818
3.53
.942 352
9.17
.061 174
10.30
.727 773
3.33
42
19
.686 030
3.53
.942 902
9.15
.060 556
10.30
.727 573
3.32
41


20
0.686 242
3.52
0.943 451
9.17
1.059 938
10.28
0.727 374
3.33
40
21
.686 453
3.53
.944 001
9.18
.059 321
10.30
.727 174
3.33
39
22
.686 665
3.52
.944 552
9.17
.058 703
10.27
.726 974
3.32
38
23
.686 876
3.53
.945 102
9.18
.058 087
10.28
.726 775
3.33
37
24
.687 088
3.52
.945 663
9.18
.057 470
10.27
.726 375
3.33
36
25
.687 299
3.52
.946 204
9.20
.056 854
10.25
.726 375
3.33
35
26
.687 510
3.52
.946 756
9.18
.056 239
10.25
.726 175
3.33
34
27
.687 721
3.52
.947 307
9.20
.055 624
10.25
.725 975
3.33
33
28
.687 932
3.53
.947 859
9.22
.055 009
10.25
.725 775
3.33
32
29
.688 144
3.52
.948 412
9.22
.054 394
10.23
.725 575
3.35
31


30
0.688 355
3.52
0.948 965
9.22
1.053 780
10.23
0.725 374
3.33
30
31
.686 566
3.50
.949 518
9.22
.053 166
10.22
.725 174
3.33
29
32
.688 776
3.52
.950 071
9.22
.052 553
10.22
.724 974
3.35
28
33
.688 987
3.52
.950 624
9.23
.051 940
10.20
.724 773
3.33
27
34
.689 198
3.52
.961 173
9.25
.051 328
10.22
.724 573
3.35
26
35
.689 409
3.55
.951 733
9.23
.050 715
10.20
.724 372
3.33
25
36
.689 620
3.50
.952 287
9.25
.050 103
10.18
.724 172
3.35
24
37
.689 830
3.52
.952 842
9.25
.049 492
10.18
.723 971
3.33
23
38
.690 041
3.50
.953 397
9.27
.048 881
10.18
.723 771
3.35
22
39
.690 251
3.52
.953 953
9.25
.048 270
10.17
.723 S70
3.35
21


40
0.690 462
3.50
0.954 508
9.27
1.047 660
10.17
0.723 369
3.35
20
41
.690 672
3.50
.955 064
9.26
.047 050
10.17
.723 168
3.35
19
42
.690 882
3.52
.965 621
9.27
.046 440
10.15
.722 967
3.35
18
43
.691 093
3.50
.956 177
9.28
.045 831
10.15
.722 766
3.35
17
44
.691 303
3.50
.966 734
9.30
.045 222
10.13
.722 565
3.35
16
45
.691 513
3.50
.957 292
9.28
.044 614
10.13
.722 354
3.35
15
46
.691 723
3.50
.957 849
9.30
.044 006
10.13
.722 163
3.35
14
47
.691 933
3.50
.968 407
9.32
.043 398
10.13
.721 962
3.37
13

Sin
d."
Tan
d."
Cot
d."
Cos
d."
43

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.692 143
3.50
.968 966
9.30
.042 790
10.12
.721 760
3.35
12
49
.692 353
3.50
.969 524
9.32
.042 183
10.10
.721 559
3.37
11


50
0 692 563
3.50
0.960 083
9.32
1.041 577
10.12
0.721357
3.35
10
51
.692 773
3.50
.960 642
9.33
.040 970
10.10
.721 156
3.37
09
52
.692 983
3.48
.961 202
9.32
.040 364
10.08
.720 954
3.35
08
53
.693 192
3.50
.961 761
9.35
.039 759
10.08
.720 753
3.37
07
54
.693 402
3.48
.962 322
9.33
.039 154
10.08
.720 551
3.37
06
55
.693 611
3.50
.962 882
9.35
.038 549
10.08
.720 349
3.35
05
56
.693 821
3.48
.963 443
9.35
.037 944
10.07
.720 148
3.37
04
57
.694 030
3.50
.964 004
9.35
.037 340
10.05
.719 946
3.37
03
58
.694 240
3.48
.964 565
9.37
.036 737
10.07
.719 744
3.37
02
59
.684 449
3.48
.965 127
9.37
.036 133
10.05
.719  542
3.37
01


60
0.694 658

0.965 689
1.035 530
0.719 340
00

Sin
d."
Tan
d."
Cot
d."
Cos
d."

44

Sin
d."
Tan
d."
Cot
d."
Cos
d."
00'
0.694 658
3.50
0.965 689
9.37
1.035 530
10.03
0.719 340
3.37
60'
01
.694 868
3.48
.966 251
9.38
.034 928
10.05
.719 138
3.37
59
02
.695 077
3.48
.966 814
9.38
.034 325
10.02
.718 936
3.38
58
03
.695 286
3.48
.967 377
9.38
.033 724
10.03
.718 733
3.37
57
04
.695 495
3.48
.967 940
9.40
.033 122
10.02
.718 531
3.37
56
05
.695 704
3.48
.968 504
9.38
.032 521
10.02
.718 329
3.38
55
06
.695 913
3.48
.969 067
9.42
.031 920
10.02
.718 126
3.37
54
07
.696 122
3.47
.969 632
9.40
.031 319
10.00
.717 924
3.38
53
08
.696 330
3.48
.970 196
9.42
.030 719
9.98
.717 721
3.37
52
09
.696 539
3.48
.970 761
9.42
.030 120
10.00
.717 519
3.38
51


10
0.696 748
3.48
0.971 326
9.43
1.029 520
9.98
0.717 316
3.38
50
11
.696 957
3.47
.971 892
9.43
.028 921
9.97
.717 113
3.37
49
12
.697 165
3.48
.972 458
9.43
.028 323
9.98
.716 911
3.38
48
13
.697 374
3.47
.973 024
9.43
.027 724
9.97
.716 708
3.38
47
14
.697 582
3.47
.973 590
9.45
.027 126
9.95
.716 505
3.38
46
15
.697 790
3.48
.974 167
9.45
.026 529
9.97
.716 302
3.38
45
16
.697 999
3.47
.974 724
9.45
.025 931
9.93
.716 099
3.38
44
17
.698 207
3.47
.975 291
9.47
.025 335
9.95
.715 896
3.38
43
18
.698 415
3.47
.975 859
9.47
.024 738
9.93
.715 693
3.38
42
19
.698 623
3.48
.976 427
9.48
.024 142
9.93
.715 430
3.40
41


20
0.698 832
3.47
0.976 996
9.47
1.023 546
9.92
0.715 286
3.38
40
21
.699 040
3.47
.977 564
9.48
.022 951
9.92
.715 083
3.38
39
22
.699 248
3.45
.978 133
9.50
.022 356
9.92
.714 880
3.40
38
23
.699 455
3.47
.978 703
9.48
.021 761
9.92
.714 676
3.38
37
24
.699 663
3.47
.979 272
9.50
.021 166
9.90
.714 473
3.40
36
25
.699 871
3.47
.979 842
9.52
.020 572
9.88
.714 269
3.38
35
26
.700 079
3.47
.980 413
9.50
.019 979
9.90
.714 066
3.40
34
27
.700 287
3.45
.980 983
9.52
.019 385
9.88
.713 862
3.40
33
28
.700 494
3.47
.981 554
9.53
.018 792
9.87
.713 658
3.40
32
29
.700 702
3.45
.982 126
9.52
.018 200
9.88
.713 454
3 40
31


30
0.700 909
3.47
0.982 697
9.53
1.017 607
9.87
0.713 250
3.38
30
31
.701 117
3.45
.983 269
9.55
.017 015
9.85
.713 047
3.40
29
32
.701 324
3.45
.983 842
9.53
.016 424
9.85
.712 843
3.40
28
33
.701 531
3.47
.984 414
9.55
.015 833
9.85
.712 639
3.42
27
34
.701 739
3.45
.984 987
9.55
.015 242
9.85
.712 434
3.40
26
35
.701 946
3.45
.985 560
9.57
.014 651
9.83
.712 230
3.40
25
36
.702 153
3.45
.986 134
9.57
.014 061
9.83
.712 026
3.40
24
37
.702 360
3.45
.986 708
9.57
.013 471
9.82
.711 822
3.42
23
38
.702 567
3.45
.987 282
9.58
.012 882
9.82
.711 617
3.40
22
39
.702 774
3.45
.987 857
9.58
.012 293
9.82
.711 413
3.40
21


40
0.702 981
3.45
0.989 432
9.58
1.011 704
9.82
0.711 209
3.42
20
41
.703 188
3.45
.988 007
9.58
.011 115
9.80
.711 004
3.42
19
42
.703 395
3.43
.989 582
9.60
.010 527
9.80
.710 799
3.40
18
43
.703 601
3.45
.990 158
9.62
.009 939
9.78
.710 595
3.42
17
44
.703 808
3.45
.990 735
9.60
.009 352
9.78
.710 390
3.42
16
45
.704 015
3.43
.991 311
9.62
.003 765
9.78
.710 185
3.40
15
46
.704 221
3.45
.991 388
9.62
.008 178
9.77
.709 981
3.42
14
47
.704 428
3.43
.992 465
9.63
.007 592
9.77
.709 776
3.42
13

Cos
d."
Cot
d."
Tan
d."
Sin
d."
44

Sin
d."
Tan
d."
Cot
d."
Cos
d."
48
.704 634
3.45
.993 043
9.63
.007 006
9.77
.709 571
3.42
12
49
.704 841
3.43
.993 621
9.63
.006 420
9.75
.709 366
3.42
11


50
0.705 047
3.43
0.994 199
9.65
1.005 835
9.75
0.709 161
3.42
10
51
.705 253
3.43
.994 778
9.65
.005 250
9.75
.708 956
3.43
09
52
.705 459
3.43
.995 357
9.65
.004 665
9.73
.708 750
3.43
08
53
.705 665
3.45
.995 936
9.65
.004 081
9.73
.708 545
3.42
07
54
.705 872
3.43
.996 515
9.67
.003 497
9.73
.708 340
3.43
06
55
.706 078
3.43
.997 095
9.68
.002 913
9.72
.708 134
3.42
05
56
.706 284
3.42
.997 676
9.67
.002 330
9.72
.707 929
3.42
04
57
.706 489
3.43
.998 256
968
.001 747
9.72
.707 724
3.43
03
58
.706 695
3.43
.998 837
9.68
.001 164
9.70
.707 518
3.43
02
59
.706 901
3.43
.999 418
9.70
.000 582
9.70
.707 312
3.42
01


60
0.707 107

1.000 000
1.000 000
0.707 107
00

Cos
d."
Cot
d."
Tan
d."
Sin
d."


## Appendix A

A-1. Stadia work involves observing

The angle by which the line of sight departs from a horizontal line. This reading is the argument for entering the table.

The rod interval intercepted by the stadia wires, which are usually adjusted so that the distance
to the rod is exactly 100 times the reading on the rod when the telescope is level.
A-2. The table gives horizontal distances and differences of elevation for unit readings on the rod and for angle of elevation from 0 to 30.

A-3. *Example.* Rod reading is 3.25 feet and angle of inclination is 5 35'.
Horizontal Distance = 99.05 x 3.25 = 321.91 ft Difference of Elevation = 9.68 x 3.26 = 31.46 ft

## Stadia Reduction Formulas

A-4. The following formulas are used in computing stadia reductions.
Horizontal Distance = {Rod Interval x 100) Cos2a Vertical Distance = (Rod Interval x 100) 12 Sin2a

           a = Angle of inclination


|         | 0     | 1    | 2    | 3    |
|---------|--------|-------|-------|-------|
| Minutes |        |       |       |       |
|         | Hor.   |       |       |       |
| dist.   |        |       |       |       |
| Diff.   |        |       |       |       |
| elev.   |        |       |       |       |
| Hor.    |        |       |       |       |
| dist.   |        |       |       |       |
| Diff.   |        |       |       |       |
| elev.   |        |       |       |       |
| Hor.    |        |       |       |       |
| dist.   |        |       |       |       |
| Diff.   |        |       |       |       |
| elev.   |        |       |       |       |
| Hor.    |        |       |       |       |
| dist.   |        |       |       |       |
| Diff.   |        |       |       |       |
| elev.   |        |       |       |       |
| 0       | 100.00 | 0.00  | 99.97 | 1.74  |
| 2       | 100.00 | 0.06  | 99.97 | 1.80  |
| 4       | 100.00 | 0.12  | 99.97 | 1.86  |
| 6       | 100.00 | 0.17  | 99.96 | 1.92  |
| 8       | 100.00 | 0.23  | 99.96 | 1.98  |
| 10      | 100.00 | 0.29  | 99.96 | 2.04  |
| 12      | 100.00 | 0.35  | 99.96 | 2.09  |
| 14      | 100.00 | 0.41  | 99.95 | 2.15  |
| 16      | 100.00 | 0.47  | 99.95 | 2.21  |
| 18      | 100.00 | 0.52  | 99.95 | 2.27  |
| 20      | 100.00 | 0.58  | 99.95 | 2.33  |
| 22      | 100.00 | 0.64  | 99.94 | 2.38  |
| 24      | 100.00 | 0.70  | 99.94 | 2.44  |
| 26      | 99.99  | 0.76  | 99.94 | 2.50  |
| 28      | 99.99  | 0.81  | 99.93 | 2.56  |
| 30      | 99.99  | 0.87  | 99.93 | 2.62  |
| 32      | 99.99  | 0.93  | 99.93 | 2.67  |
| 34      | 99,99  | 0.99  | 99.93 | 2.73  |
| 36      | 99.99  | 1.05  | 99.92 | 2.79  |
| 38      | 99.99  | 1.11  | 99.92 | 2.85  |
| 40      | 99.99  | 1.16  | 99.92 | 2.91  |
| 42      | 99.99  | 1.22  | 99.91 | 2.97  |
| 44      | 99.98  | 1.28  | 99.91 | 3.02  |
| 46      | 99.98  | 1.34  | 99.90 | 3.08  |
| 48      | 99.98  | 1.40  | 99.90 | 3.14  |
| 50      | 99.98  | 1.45  | 99.90 | 3.20  |
| 52      | 99.98  | 1.51  | 99.89 | 3.26  |
| 54      | 99.98  | 1.57  | 99.89 | 3.31  |
| 56      | 99.97  | 1.63  | 99.89 | 3.37  |
| 58      | 99.97  | 1.69  | 99.88 | 3.43  |
| 60      | 99.97  | 1.74  | 99.88 | 3.49  |

*These tables are adequate for use in both feet and meters.


|         | 4    | 5    | 6    | 7    |
|---------|-------|-------|-------|-------|
| Minutes |       |       |       |       |
|         | Hor.  |       |       |       |
| dist.   |       |       |       |       |
| Diff    |       |       |       |       |
| elev.   |       |       |       |       |
| Hor.    |       |       |       |       |
| dist.   |       |       |       |       |
| Diff.   |       |       |       |       |
| elev.   |       |       |       |       |
| Hor.    |       |       |       |       |
| dist.   |       |       |       |       |
| Diff.   |       |       |       |       |
| elev.   |       |       |       |       |
| Hor.    |       |       |       |       |
| dist.   |       |       |       |       |
| Diff.   |       |       |       |       |
| elev.   |       |       |       |       |
| 0       | 99.51 | 6.69  | 99.24 | 8.68  |
| 2       | 99.61 | 7.02  | 99.23 | 8.74  |
| 4       | 99.60 | 7.07  | 99.22 | 8.80  |
| 6       | 99.49 | 7.13  | 99.21 | 8.85  |
| 8       | 99.48 | 7 19  | 99.20 | 8.91  |
| 10      | 99.47 | 7.25  | 99.19 | 8.97  |
|         |       |       |       |       |
| 12      | 99.46 | 7.30  | 99.18 | 9.03  |
| 14      | 99.46 | 7.36  | 99.17 | 9.08  |
| 16      | 99.45 | 7.42  | 99.16 | 9.14  |
| 18      | 99.44 | 7.48  | 98.15 | 9.20  |
| 20      | 99.43 | 7.53  | 99.14 | 9.25  |
|         |       |       |       |       |
| 22      | 99.42 | 7.59  | 99.13 | 9.31  |
| 24      | 99.41 | 7.65  | 99.11 | 9.37  |
| 26      | 99.40 | 7.71  | 99.10 | 9.43  |
| 28      | 99.39 | 7.76  | 99.09 | 9.48  |
| 30      | 99.38 | 7.82  | 99.08 | 9.54  |
|         |       |       |       |       |
| 32      | 99.38 | 7.88  | 99.07 | 9.60  |
| 34      | 99.37 | 7.94  | 99.06 | 9.65  |
| 36      | 99.36 | 7.99  | 99.05 | 9.71  |
| 38      | 99.35 | 8.05  | 99.04 | 9.77  |
| 40      | 99.34 | 8.11  | 99.03 | 9.83  |
|         |       |       |       |       |
| 42      | 99.33 | 8.17  | 99.01 | 9.88  |
| 44      | 99.32 | 8.22  | 99.00 | 9.94  |
| 46      | 99.31 | 8.28  | 98.99 | 10.00 |
| 48      | 99.30 | 8.34  | 98.98 | 10.05 |
| 50      | 99.29 | 8.40  | 98.97 | 10.11 |
|         |       |       |       |       |
| 52      | 99.28 | 8.45  | 98.96 | 10.17 |
| 54      | 99.27 | 8.51  | 98.94 | 10.22 |
| 56      | 99.26 | 8.57  | 99.93 | 10 28 |
| 58      | 99.25 | 8.63  | 98.92 | 10.34 |
| 60      | 99.24 | 8.68  | 98.91 | 10.40 |
|         |       |       |       |       |
|         |       |       |       |       |
|         | 8    | 9    | 10    | 11    |
|---------|-------|-------|--------|--------|
| Minutes |       |       |        |        |
|         | Hor.  |       |        |        |
| dist.   |       |       |        |        |
| Diff.   |       |       |        |        |
| elev.   |       |       |        |        |
| Hor.    |       |       |        |        |
| dist.   |       |       |        |        |
| Diff.   |       |       |        |        |
| elev.   |       |       |        |        |
| Hor.    |       |       |        |        |
| dist.   |       |       |        |        |
| Diff.   |       |       |        |        |
| elev.   |       |       |        |        |
| Hor.    |       |       |        |        |
| dist.   |       |       |        |        |
| Diff.   |       |       |        |        |
| elev.   |       |       |        |        |
| 0       | 98.06 | 13.78 | 97.55  | 15.45  |
| 2       | 98.05 | 13.84 | 97.53  | 15.51  |
| 4       | 98.03 | 13.89 | 97.52  | 15.56  |
| 6       | 98.01 | 13.95 | 97.50  | 15.62  |
| 8       | 98.00 | 14.01 | 97.48  | 15.67  |
| 10      | 97.98 | 14.06 | 97.46  | 15.73  |
| 12      | 97.97 | 14.12 | 97.44  | 15.78  |
| 14      | 97.95 | 14.17 | 97.43  | 15.84  |
| 16      | 97.93 | 14 23 | 87 41  | 15.89  |
| 18      | 97.92 | 14.28 | 97.39  | 15.95  |
| 20      | 97.90 | 14.34 | 97.37  | 16.00  |
| 22      | 97.88 | 14.40 | 97.35  | 16.06  |
| 24      | 97.87 | 14.45 | 97.33  | 16.11  |
| 26      | 97.85 | 14.51 | 97.31  | 16.17  |
| 28      | 97.83 | 14.56 | 97.29  | 16.22  |
| 30      | 97.82 | 14.62 | 97.28  | 16.28  |
| 32      | 97.80 | 14.67 | 97.26  | 16.33  |
| 34      | 97.78 | 14.73 | 97.24  | 16.39  |
| 36      | 97.76 | 14.79 | 97.22  | 16.44  |
| 38      | 97.75 | 14.84 | 97.20  | 16.50  |
| 40      | 97.73 | 14.90 | 97.18  | 16.55  |
| 42      | 97.71 | 14.95 | 97.16  | 16.61  |
| 44      | 97.69 | 15.01 | 97.14  | 16.66  |
| 46      | 97.68 | 15.06 | 97.12  | 16.72  |
| 48      | 97.66 | 15.12 | 97.10  | 16.77  |
| 50      | 97.64 | 15.17 | 97.08  | 16.83  |
| 52      | 97.62 | 15.23 | 97.06  | 16.88  |
| 54      | 97.61 | 15.28 | 97.04  | 16.94  |
| 56      | 97.59 | 15.34 | 97.02  | 16.99  |
| 58      | 97.57 | 15.40 | 97.00  | 17.05  |
| 60      | 97.55 | 15.45 | 96.98  | 17.10  |
|         |       |       |        |        |
|         |       |       |        |        |
|         | 12    | 13    | 14    | 15    |
|---------|--------|--------|--------|--------|
| Minutes |        |        |        |        |
|         | Hor.   |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| 0       | 95.68  | 20.34  | 94.94  | 21.92  |
| 2       | 95.65  | 20.39  | 94.91  | 21.97  |
| 4       | 95.63  | 20.44  | 94.89  | 22.02  |
| 6       | 95.61  | 20.50  | 94 86  | 22.08  |
| 8       | 95.58  | 20.55  | 94.84  | 22.13  |
| 10      | 95.56  | 20.60  | 94.81  | 22.18  |
| 12      | 95.53  | 20.66  | 94.79  | 22.23  |
| 14      | 95.51  | 20.71  | 94.76  | 22.28  |
| 16      | 95.49  | 20.76  | 94.73  | 22.34  |
| 18      | 95.46  | 20.81  | 94.71  | 22.39  |
| 20      | 95.44  | 20.87  | 94.68  | 22.44  |
| 22      | 95.41  | 20.92  | 94.66  | 22.49  |
| 24      | 95.39  | 20.97  | 94.63  | 22.54  |
| 26      | 95.36  | 21.03  | 94.60  | 22.60  |
| 28      | 95.34  | 21.08  | 94.58  | 22.65  |
| 30      | 95.32  | 21.13  | 94.55  | 22.70  |
| 32      | 95.29  | 21.18  | 94.52  | 22.75  |
| 34      | 95.27  | 21.24  | 94.50  | 22.80  |
| 36      | 95.24  | 21.29  | 94.47  | 22.85  |
| 38      | 95.22  | 21.34  | 94.44  | 22.91  |
| 40      | 95.19  | 21.39  | 94.42  | 22.96  |
| 42      | 95.17  | 21.45  | 94.39  | 23.01  |
| 44      | 95.14  | 21.50  | 94.36  | 23.06  |
| 46      | 95.12  | 21.55  | 94.34  | 23.11  |
| 48      | 95.09  | 21.60  | 94.31  | 23.16  |
| 50      | 95.07  | 21.66  | 94.28  | 23.22  |
| 52      | 95.04  | 21.71  | 94.26  | 23.27  |
| 54      | 95.02  | 21.76  | 94.23  | 23.32  |
| 56      | 94.99  | 21.81  | 94.20  | 23.37  |
| 58      | 94.97  | 21.87  | 94.17  | 23.42  |
| 60      | 94.94  | 21.92  | 94.15  | 23.47  |


|         | 16    | 17    | 18    | 19    |
|---------|--------|--------|--------|--------|
| Minutes |        |        |        |        |
|         | Hor.   |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| 0       | 92.40  | 26.50  | 91.45  | 27.96  |
| 2       | 92.37  | 26.55  | 91.42  | 28.01  |
| 4       | 92.34  | 26.59  | 91.39  | 28.06  |
| 6       | 92.31  | 26.64  | 91.35  | 28 10  |
| 8       | 92.28  | 26.69  | 91.32  | 28.15  |
| 10      | 92.25  | 26.74  | 91.29  | 28.20  |
| 12      | 92.22  | 26.79  | 91.26  | 28.25  |
| 14      | 92.19  | 26.84  | 91.22  | 28.30  |
| 16      | 92.15  | 26.89  | 91.19  | 28.34  |
| 18      | 92.12  | 26.94  | 91.16  | 28.39  |
| 20      | 92.09  | 26.99  | 91.12  | 28.44  |
| 22      | 92.06  | 27.04  | 91.09  | 28.49  |
| 24      | 92.03  | 27.09  | 91.06  | 28.54  |
| 26      | 92.00  | 27.13  | 91.02  | 28.58  |
| 28      | 91.97  | 27.18  | 90.99  | 28.63  |
| 30      | 91.93  | 27.23  | 90.96  | 28.68  |
| 32      | 91.90  | 27.28  | 90.92  | 28.73  |
| 34      | 91.87  | 27.33  | 90.89  | 28.77  |
| 36      | 91.84  | 27.38  | 90.86  | 28.82  |
| 38      | 91.81  | 27.43  | 90.82  | 28.87  |
| 40      | 91.77  | 27.48  | 90.79  | 28.92  |
| 42      | 91.74  | 27.52  | 90.76  | 28.96  |
| 44      | 91.71  | 27.57  | 90.72  | 29.01  |
| 46      | 91.68  | 27.62  | 90.69  | 29.06  |
| 48      | 91.65  | 27.67  | 90.66  | 29.11  |
| 50      | 91.61  | 27.72  | 90.62  | 29.15  |
| 52      | 91.58  | 27.77  | 90.59  | 29.20  |
| 54      | 91.55  | 27.81  | 90.55  | 29.25  |
| 56      | 91.52  | 27.86  | 90.52  | 29.30  |
| 58      | 91.48  | 27.91  | 90.48  | 29.34  |
| 60      | 91.45  | 27.96  | 90.45  | 29.39  |
|         |        |        |        |        |
|         |        |        |        |        |
|         | 20    | 21    | 22    | 23    |
|---------|--------|--------|--------|--------|
| Minutes |        |        |        |        |
|         | Hor.   |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff.   |        |        |        |        |
| elev.   |        |        |        |        |
| 0       | 88.30  | 32.14  | 87.16  | 33.46  |
| 2       | 88.26  | 32.18  | 87.12  | 33.50  |
| 4       | 88.23  | 32.23  | 87.08  | 33.54  |
| 6       | 88 19  | 32.27  | 87.04  | 33.69  |
| 8       | 88.15  | 32.32  | 87.00  | 33.63  |
| 10      | 88.11  | 32.36  | 86.96  | 33.67  |
| 12      | 88.08  | 32.41  | 86.92  | 33.72  |
| 14      | 88.04  | 32.45  | 86.88  | 33.76  |
| 16      | 88.00  | 32.49  | 86.84  | 33.80  |
| 18      | 87.96  | 32.54  | 86.80  | 33.84  |
| 20      | 87.93  | 32.58  | 86.77  | 33.89  |
| 22      | 87.89  | 32.63  | 86.73  | 33.93  |
| 24      | 87.85  | 32.67  | 86.69  | 33.97  |
| 26      | 87.81  | 32.72  | 86.65  | 34.01  |
| 28      | 87.77  | 32.76  | 86.61  | 34.06  |
| 30      | 87.74  | 32.80  | 86.57  | 34.10  |
| 32      | 87.70  | 32.85  | 86.53  | 34.14  |
| 34      | 87.66  | 32.89  | 86.49  | 34.18  |
| 36      | 87.62  | 32.93  | 86.45  | 34.23  |
| 38      | 87.58  | 32.98  | 86.41  | 34.27  |
| 40      | 87.54  | 33.02  | 86.37  | 34.31  |
| 42      | 87.51  | 33.07  | 86.33  | 34.35  |
| 44      | 87.47  | 33.11  | 86.29  | 34.40  |
| 46      | 87.43  | 33.15  | 86.25  | 34.44  |
| 48      | 87.39  | 33.20  | 86.21  | 34.48  |
| 50      | 87.35  | 33.24  | 86.17  | 34.52  |
| 52      | 87.31  | 33.28  | 86.13  | 34.57  |
| 54      | 87.27  | 33.33  | 86.09  | 34.61  |
| 56      | 87.24  | 33.37  | 86.05  | 34.65  |
| 58      | 87.20  | 33.41  | 86.01  | 34.69  |
| 60      | 87.16  | 33.46  | 85.97  | 34.73  |
|         |        |        |        |        |
|         |        |        |        |        |
|         | 24    | 25    | 26    | 27    |
|---------|--------|--------|--------|--------|
| Minutes |        |        |        |        |
|         | Hor.   |        |        |        |
| dist.   |        |        |        |        |
| Diff    |        |        |        |        |
| elev.   |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff    |        |        |        |        |
| elev    |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff    |        |        |        |        |
| elev.   |        |        |        |        |
| Hor.    |        |        |        |        |
| dist.   |        |        |        |        |
| Diff    |        |        |        |        |
| elev.   |        |        |        |        |
| 0       | 83.46  | 37.16  | 82.14  | 38.30  |
| 2       | 83.41  | 37.20  | 82.09  | 38.34  |
| 4       | 83.37  | 37.23  | 82.05  | 38.38  |
| 6       | 83.33  | 37.27  | 82.01  | 38.41  |
| 8       | 83.28  | 37.31  | 81.96  | 38.45  |
| 10      | 83.24  | 37.35  | 81.92  | 38.49  |
| 12      | 83.20  | 37.39  | 81.87  | 38.53  |
| 14      | 83.15  | 37.43  | 81.83  | 38.56  |
| 16      | 83.11  | 37.47  | 81.78  | 38.60  |
| 18      | 83.07  | 37.51  | 81.74  | 38.64  |
| 20      | 83.02  | 37.54  | 81.69  | 38.67  |
| 22      | 82.98  | 37.58  | 81.65  | 38.71  |
| 24      | 82.93  | 37.62  | 81.60  | 38.75  |
| 26      | 82.89  | 37.66  | 81.56  | 38.78  |
| 28      | 82.85  | 37.70  | 81.51  | 38.82  |
| 30      | 82.80  | 37.74  | 81.47  | 38.86  |
| 32      | 82.76  | 37.77  | 81.42  | 38.89  |
| 34      | 82.72  | 37.81  | 81.38  | 38.93  |
| 36      | 82.67  | 37.85  | 81.33  | 38.97  |
| 38      | 82.63  | 37.89  | 81.28  | 39.00  |
| 40      | 82.58  | 37.93  | 81.24  | 39.04  |
| 42      | 82.54  | 37.96  | 81.19  | 39.08  |
| 44      | 82.49  | 38.00  | 81.15  | 39.11  |
| 46      | 82.45  | 38.04  | 81.10  | 39.15  |
| 48      | 82.41  | 38.08  | 81.06  | 39.18  |
| 50      | 82.36  | 38.11  | 81.01  | 39.22  |
| 52      | 82.32  | 38.15  | 80.97  | 39.26  |
| 54      | 82.27  | 38.19  | 80.92  | 39.29  |
| 56      | 82.23  | 38.23  | 80.87  | 39.33  |
| 58      | 82.18  | 38.26  | 80.83  | 39.36  |
| 60      | 82.14  | 38.30  | 80.78  | 39.40  |
|         |        |        |        |        |
|         |        |        |        |        |
|         | 28    | 29    | 30    |
|---------|--------|--------|--------|
| Minutes |        |        |        |
|         | Hor.   |        |        |
| dist.   |        |        |        |
| Diff.   |        |        |        |
| elev.   |        |        |        |
| Hor.    |        |        |        |
| dist.   |        |        |        |
| Diff.   |        |        |        |
| elev.   |        |        |        |
| Hor.    |        |        |        |
| dist.   |        |        |        |
| Diff.   |        |        |        |
| elev.   |        |        |        |
| 0       | 77.96  | 41.45  | 76.50  |
| 2       | 77.91  | 41.48  | 76.45  |
| 4       | 77.86  | 41.52  | 76.40  |
| 6       | 77.81  | 41.55  | 76.35  |
| 8       | 77.77  | 41.58  | 76.30  |
| 10      | 77.72  | 41.61  | 76.25  |
|         |        |        |        |
| 12      | 77.67  | 41.65  | 76.20  |
| 14      | 77.62  | 41.68  | 76.15  |
| 16      | 77.57  | 41.71  | 76.10  |
| 18      | 77.52  | 41.74  | 76.05  |
| 20      | 77.48  | 41.77  | 76.00  |
|         |        |        |        |
| 22      | 77.42  | 41.81  | 75.95  |
| 24      | 77.38  | 41.84  | 75.90  |
| 26      | 77.33  | 41.87  | 75.85  |
| 28      | 77.28  | 41.90  | 75.80  |
| 30      | 77.23  | 41.93  | 75.75  |
|         |        |        |        |
| 32      | 77.18  | 41.97  | 75.70  |
| 34      | 77.13  | 42.00  | 75.65  |
| 36      | 77.09  | 42.03  | 75.60  |
| 38      | 77.04  | 42.06  | 75.55  |
| 40      | 76.99  | 42.09  | 75.50  |
|         |        |        |        |
| 42      | 76.94  | 42.12  | 75.45  |
| 44      | 76.89  | 42.15  | 75.40  |
| 46      | 76.84  | 42.19  | 75.35  |
| 48      | 76.79  | 42.22  | 75.30  |
| 50      | 76.74  | 42.25  | 75.25  |
|         |        |        |        |
| 52      | 76.69  | 42.28  | 75.20  |
| 54      | 76.64  | 42.31  | 75.15  |
| 56      | 76.59  | 42.34  | 75.10  |
| 58      | 76.55  | 42.37  | 75.05  |
| 60      | 76.50  | 42.40  | 75.00  |
|         |        |        |        |
|         |        |        |        |

0"
10"
15"
20"
30"
40"
45"
50"

0
.00000
.00278
.00417
.00556
.00833
.01111
.01250
.01389
0
1
.01667
.01944
.02083
.02222
.02500
.02778
.02917
.03056
1
2
.03333
.03611
.03750
.03889
.04167
.04444
.04583
.04722
2
3
.05000
.05278
.05417
05556
.05833
.06111
.06250
.06389
3
4
.06667
.06944
.07083
.07222
.07500
.07778
.07917
.08056
4
5
.08333
.08611
.08750
.08889
.09167
.09444
.09583
.09722
5
6
.10000
.10278
.10417
.10556
.10833
.11111
.11250
.11389
6
7
.11667
.11944
.12083
.12222
.12500
.12778
.12917
.13056
7
8
.13333
.13611
.13750
.13889
.14167
.14444
.14583
.14722
8
9
.15000
.15278
.15417
.15556
.15833
.16111
.16250
.16389
9
10
.16667
.16944
.17083
.17222
.17500
.17778
.17917
.18056
10
11
.18333
.18611
.18750
.18889
.19167
.19444
.19583
.19722
11
12
.20000
.20278
.20417
.20556
.20833
.21111
.21250
.21389
12
13
.21667
.21944
.22083
.22222
.22500
.22778
.22917
.23056
13
14
.23333
.23611
.23750
.23889
.24167
.24444
.24583
.24722
14
15
.25000
.25278
.25417
.25556
.25833
.26111
.26250
.26389
15
16
.26667
.26944
.27083
.27222
.27500
.27778
.27917
.28056
16
17
.28333
.28611
.28750
.28889
.29167
.29444
.29583
.29722
17
18
.30000
.30278
.30417
.30556
.30833
.31111
.31250
.31389
18
19
.31667
.31944
.32083
.32222
.32500
.32778
.32917
.33056
19
20
.33333
.33611
.33750
.33889
.34167
.34444
.34583
.34722
20
21
.35000
.35278
.35417
.35556
.35833
.36111
.36250
.36389
21
22
.36667
.36944
.37083
.37222
.37500
.37778
.37917
.38056
22
23
.38333
.38611
.38750
.38889
.39167
.39444
.39583
.39722
23
24
.40000
.40278
.40417
.40556
.40833
.41111
.41250
.41389
24
25
.41667
.41944
.42083
.42222
.42500
.42778
.42917
.43056
25
26
.43333
.43611
.43750
.43889
.44167
.44444
.44583
.44722
26
27
.45000
.45278
.45417
.45556
.45883
.46111
.46250
.46389
27
28
.46667
.46944
.47083
.47222
.47500
.47778
.47917
.48056
28
29
.48333
.48611
.48750
.48889
.49167
.49444
.49583
.49722
29
30
.50000
.50278
.50417
.50556
.50833
.51111
.51250
.51389
30


0"
10"
15"
20"
30"
40"
46"
50"

31
.51667
.51944
.52083
.52222
.52500
.52778
.52917
.53056
31
32
.53333
.53611
.53750
.53889
.54167
.54444
.54583
.54722
32
33
.55000
.55278
.55417
.55556
.55833
.56111
.56250
.56389
33
34
.56667
.56944
.57083
.57222
.57500
.57778
.57917
.58056
34
35
.58333
.58611
.58750
.58889
.59167
.59444
.59583
.59722
35
36
.60000
.60278
.60417
.60556
.60833
.61111
.61250
.61389
36
37
.61667
.61944
.62083
.62222
.62500
.62778
.62917
.63056
37
38
.63333
.63611
.63750
.63889
.64167
.64444
.64583
.64722
38
39
.65000
.65278
.65417
.65556
.65833
.66111
.66250
.66389
39
40
.66667
.66944
.67083
.67222
.67500
.67778
.67917
.68056
40
41
.68333
.68611
.68750
.68889
.69167
.69444
.69583
.69722
41
42
.70000
.70278
.70417
.70556
.70883
.71111
.71250
.71389
42
43
.71687
.71944
.72083
.72222
.72500
.72778
.72917
.73056
43
44
.73333
.73611
.73750
.73889
.74167
.74444
.74583
.74722
44
45
.75000
.75278
.75417
.75556
.75833
.76111
.76250
.76389
45
46
.76667
.76944
.77083
.77222
.77500
.77778
.77917
.78056
46
47
.78333
.78611
.78750
.78889
.79167
.79444
.79583
.79722
47
48
.80000
.80278
.80417
.80556
.80833
.81111
.81250
.81389
48
49
.81667
.81944
.82083
.82222
.82500
.82778
.82917
.83056
49
50
.83333
.83611
.83750
.83889
.84167
.84444
.84583
.84722
50
51
.85000
.85278
85417
.85556
.85833
.86111
.86250
.86389
51
52
.86667
.86944
.87088
.87222
.87500
.87778
.87917
.88056
52
53
.83333
.88611
.88750
.88889
.89167
.89444
.89583
.89722
53
54
.90000
.90278
.90417
.90556
.90833
.91111
.91250
.91389
54
55
.91667
.91944
.92083
.92222
.92500
.92778
.92917
.93056
55
56
.93333
.93611
.93750
.93889
.94167
.94444
.94583
.94722
56
57
.95000
.95278
.95417
.95556
.95833
.96111
.96250
.96389
57
58
.96667
.96944
.97083
.97222
.97500
.97778
.97917
.98056
58
59
.98333
.98611
.98750
.98889
.99167
.99444
.99583
.99722
59


## Table A-4. Useful Constants And Formulas

a. Trigonometrical formulas. - The six most usual trigonometrical functions are the ratios defined for a right-angled triangle, as follows:

sine = opposite side
hypotenuse



| cosine =      | adjacent side   |
|---------------|-----------------|
| hypotenuse    |                 |
|               |                 |
| tangent =     | opposite side   |
| adjacent side |                 |
|               |                 |
| cotangent =   | adjacent side   |
| opposite side |                 |
|               |                 |
| secant =      |                 |
| hypotenuse    |                 |
| adjacent side |                 |
|               |                 |

## Abstract

In this thesis we present a new method for constructing the \(\mathcal{O}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}( \log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}( \log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2}(\log^{2 }(\log^{2}(\log^{
Right-angled triangles can be solved by the above and oblique triangles may be solved by the use of the additional relationship for any triangle

a sin A = b sin B = c sin C  a  b a + b = tan 12(A  B) tan 12(A + B)
and the group

a2 = b2 + c2 2bc cos A b2 = a2 + c2 2ac cos B  c2 = a2 + b2 2ab cos C

where A, B, and C are the angles and a, b. and c are the sides opposite to these angles, respectively.


## Table A-4. Useful Constants And Formulas

b. Fundamental relations.

sin A =
         1
       csc  A ; cos  A =
                        1
                       sec A ; tan A =
                                       1
                                     cot A = sin A
                                             cos A

csc A =
         1
       sin  A ; sec A =
                        1
                      cos  A ; cot  A =
                                       1
                                     tan A = cos A
                                             sin A

sin
2 A + cos
2 A=1; sec
2 A - tan
2 A = 1; cot
2 A = 1
c. Functions of multiple angles.

sin 2 A = 2 sin A cos A cos 2 A = 2 cos
2 A- 1 = 1 - 2 sin
2 A = cos
2 A - sin
2A
sin 3 A = 3 sin A - 4 sin
3 A;
cos 3 A = 4 cos
3 A - 3 cos A
d. Functions of half angles.

$$\sin\frac{A}{2}=\pm\sqrt{\frac{1-\cos A}{2}}\qquad\qquad\qquad\qquad\qquad \qquad\cos\frac{A}{2}=\pm\sqrt{\frac{1+\cos A}{2}}$$

$$\tan\frac{A}{2}=\pm\ \frac{1-\cos A}{\sin A}=\frac{\sin A}{1+\cos A}=\pm\sqrt{ \frac{1-\cos A}{1+\cos A}}$$
e. Powers of functions.

sin
2 A = 12(1 - cos 2 A);
cos
2 A = 12(1 - cos 2 A)
sin
3 A = 14(3 sin A - sin 3 A);
A = 14(cos 3 A + 3 cos A)
f. Sum end difference of angles.

sin (A  B) = sin A cos B cos A sin B cos (A ) = cos A cos B  sin A sin B
tan(A  B) = tan A  tan B
1  tan A tan B
sin A  sin B = 2 sin 12(A  B) cos 12(A  B)
cos A + cos B = 2 cos 12(A + B) cos 12(A - B)
cos A - cos B = -2 sin 12(A + B) sin 12(A - B)

tan A  tan B = sin A  B cos A cos B


0
30
45
60
90
120
135
150
180
270


Sine ........ 0
12

12  2 12
3
1
12 3
12
2
12

0
-1
Cosine ........ 1
12
3 12
 2 12
0
-12

12
2
12
3
-1
0
Tangent ...... 0
13
3
1


3

 3
-1

13
3
0

Cotangent ..
3
1

13
3
0
13
3
-1


3

0
Secant ........ 1
23
3
2 2


-2


2
23
3
-1

Cosecant ....   2


2 23
3
1
23  3

2
2


-1


Lineal feet
x
.00019
=
miles
1 radian
=

 = 57.2957790 = 5717' 44.8" (nearly)
Lineal yards
x
.006
=
miles
Square inches
x
.007
=
square feet
1 radian
=
1018.6 mile
Square feel
x
.111
=
square yards
1 degree
=
0.0174633 radians
Square yards
x
.0002067
=
acres
1 minute
=
0.0002909 radians
Acres
x
4840.0
=
square yards
1 mil
=
0.00009817 radians
Cubic inches
x
.00058
=
cubic feet
 radians
=
180
Cubic feet
x
.03704
=
cubic yards


Links
x
.22
=
yards

 radians
=
90
Links
x
.66
=
feet


Feet
x
.15
-
links


360 =21600' = 1295000" Circumference of circle ( r = radius) = 2r, or d Radius = arc of 57.2957790 Arc of 1 (radius = 1) = .017453292 Arc of 1' (radius = 1) = .000290888 Arc of 1" (radius = 1) = .000004848 Area of circle (r = radius) ........ r
2
Area of sector of circle (length of arc = L; r = radius) ........ 1/2Lr Ares of segment of parabola (c = chord; m = mid.ord)........ 2/3 cm
Area of segment of circle (ap) ........ 2/3 cm

= 1.240700982.

= 3.141592654.
6


4
= 0.785398163.
2
= 9.869604401.

6
= 0.523598776.
1

= 0.101321184.
4

= 1.128379167.

= 1.772453851
4
3
= 4.188790205.
1

= 0.3183099.



## Table A-5. Functions Of 1 Curves Functions Of A 1 Curve

A-5. The long chords, mid-ordinates, externals, and tangent distances of this table are for a curve of 5730
feet radius. To find the corresponding functions of any other curve, divide the tabular values by the degree of curve. Values obtained from this table can be converted to the metric system by multiplying by 0.3048.

##

|    |        |       |       |        |        |       |       | 0      | 1    |
|----|--------|-------|-------|--------|--------|-------|-------|---------|-------|
|    | LC     | M     | E     | T      | LC     | M     | E     | T       |       |
| 0  | 0.00   | 0.000 | 0.000 | 0.00   | 100.00 | 0.218 | 0.218 | 50.00   | 0     |
| 2  | 3.33   | 0.000 | 0.000 | 1.67   | 103.33 | 0.233 | 0.233 | 51.67   | 2     |
| 4  | 6.67   | 0.001 | 0.001 | 3.33   | 106.66 | 0.248 | 0.248 | 53.33   | 4     |
| 6  | 10.00  | 0.002 | 0.002 | 5.00   | 110.00 | 0.264 | 0.264 | 55.00   | 6     |
| 8  | 13.33  | 0.004 | 0.004 | 6.67   | 113.33 | 0.280 | 0.280 | 56.67   | 8     |
| 10 | 16.67  | 0.006 | 0.006 | 8.33   | 116.66 | 0.297 | 0.297 | 58.33   | 10    |
| 12 | 20.00  | 0.009 | 0.009 | 10.00  | 120.00 | 0.314 | 0.314 | 60.00   | 12    |
| 14 | 23.33  | 0.012 | 0.012 | 11.67  | 123.33 | 0.332 | 0.332 | 61.67   | 14    |
| 16 | 26.67  | 0.015 | 0.015 | 13.33  | 126.66 | 0.350 | 0.350 | 63.33   | 16    |
| 18 | 30.00  | 0.019 | 0.019 | 15.00  | 130.00 | 0.368 | 0.368 | 65.00   | 18    |
| 20 | 33.33  | 0.024 | 0.024 | 16.67  | 133.33 | 0.388 | 0.388 | 66.67   | 20    |
| 22 | 36.67  | 0.029 | 0.029 | 18.33  | 136.66 | 0.407 | 0.407 | 68.33   | 22    |
| 24 | 40.00  | 0.035 | 0.035 | 20.00  | 140.00 | 0.427 | 0.427 | 70.00   | 24    |
| 26 | 43.33  | 0.041 | 0.041 | 21.67  | 143.33 | 0.448 | 0.448 | 71.67   | 26    |
| 28 | 46.67  | 0.048 | 0.048 | 23.33  | 146.66 | 0.469 | 0.469 | 73.33   | 28    |
| 30 | 50.00  | 0.054 | 0.054 | 25.00  | 150.00 | 0.491 | 0.491 | 75.00   | 30    |
| 32 | 53.33  | 0.062 | 0.062 | 26.67  | 153.33 | 0.513 | 0.513 | 76.67   | 32    |
| 34 | 56.67  | 0.070 | 0.070 | 28.33  | 156.66 | 0.536 | 0.536 | 78.33   | 34    |
| 36 | 60.00  | 0.079 | 0.079 | 30.00  | 160.00 | 0.559 | 0.559 | 80.00   | 36    |
| 38 | 63.33  | 0.088 | 0.088 | 31.67  | 163.33 | 0.582 | 0.582 | 81.67   | 38    |
| 40 | 66.67  | 0.097 | 0.097 | 33.33  | 166.66 | 0.606 | 0.606 | 83.33   | 40    |
| 42 | 70.00  | 0.107 | 0.107 | 35.00  | 170.00 | 0.630 | 0.630 | 85.00   | 42    |
| 44 | 73.33  | 0.117 | 0.117 | 36.67  | 173.33 | 0.655 | 0.655 | 86.67   | 44    |
| 46 | 76.67  | 0.128 | 0 128 | 38.33  | 176.66 | 0.681 | 0.681 | 88.33   | 46    |
| 48 | 80.00  | 0.140 | 0.140 | 40.00  | 180.00 | 0.706 | 0.706 | 90.00   | 48    |
| 50 | 83.33  | 0.151 | 0.151 | 41.67  | 183.33 | 0.733 | 0.733 | 91.67   | 50    |
| 52 | 86.67  | 0.164 | 0.164 | 43.33  | 186.66 | 0.760 | 0.760 | 93.33   | 52    |
| 54 | 90.00  | 0.176 | 0.176 | 45.00  | 190.00 | 0.788 | 0.788 | 95.00   | 54    |
| 56 | 93.33  | 0.190 | 0.190 | 46.67  | 193.33 | 0.815 | 0.815 | 96.67   | 56    |
| 58 | 96.67  | 0.204 | 0.204 | 48.33  | 196.66 | 0.844 | 0.844 | 98.33   | 58    |
| 60 | 100.00 | 0.218 | 0.218 | 50.00  | 199.98 | 0.873 | 0.873 | 100.00  | 60    |
| 2 | 3     |       |       |        |        |       |       |         |       |
|    |        |       |       |        |        |       |       |         |       |
| LC | M      | E     | T     | LC     | M      | E     | T     |         |       |
| 0  | 199.98 | 0.873 | 0.873 | 100.00 | 299.96 | 1.964 | 1.964 | 150.07  | 0     |
| 2  | 203.31 | 0.902 | 0.902 | 101.67 | 303.29 | 2.008 | 2.009 | 151.74  | 2     |
| 4  | 206.64 | 0.932 | 0.932 | 103.34 | 306.62 | 2.053 | 2.054 | 153.41  | 4     |
| 6  | 209.97 | 0.962 | 0.962 | 105.01 | 309.95 | 2.098 | 2.099 | 155.08  | 6     |
| 8  | 213.31 | 0.993 | 0.993 | 106.68 | 313.29 | 2.143 | 2.144 | 156.75  | 8     |
| 10 | 216.64 | 1.024 | 1.024 | 108.35 | 316.62 | 2.188 | 2.189 | 158.42  | 10    |
| 12 | 219.97 | 1.056 | 1.056 | 110.02 | 319.95 | 2.225 | 2.236 | 160.09  | 12    |
| 14 | 223.30 | 1.088 | 1.088 | 111.69 | 323.28 | 2.282 | 2.283 | 161.76  | 14    |
| 16 | 226 64 | 1.121 | 1.121 | 113.36 | 326 62 | 2.329 | 2.330 | 163.43  | 16    |
| 18 | 229.97 | 1.154 | 1.154 | 115.02 | 329.95 | 2.376 | 2.377 | 165.09  | 18    |
| 20 | 233.30 | 1.188 | 1.188 | 116.69 | 333.28 | 2.424 | 2.425 | 166.76  | 20    |
| 22 | 236.63 | 1.222 | 1.222 | 118.36 | 336.61 | 2.473 | 2.474 | 168,43  | 22    |
| 24 | 239.97 | 1.256 | 1.256 | 120.03 | 339.95 | 2.523 | 2.523 | 170.10  | 24    |
| 26 | 243.30 | 1.292 | 1.282 | 121.70 | 343.28 | 2.572 | 2.573 | 171.77  | 26    |
| 28 | 246.63 | 1.328 | 1.328 | 123.37 | 346.61 | 2.622 | 2.623 | 1 73.44 | 28    |
| 30 | 249.95 | 1.364 | 1.364 | 125.03 | 349 94 | 2.672 | 2.673 | 175.10  | 30    |
| 32 | 253.29 | 1.399 | 1.399 | 126.70 | 353.27 | 2.724 | 2.725 | 176.72  | 32    |
| 34 | 256.62 | 1.437 | 1.437 | 128.37 | 356.60 | 2.776 | 2.777 | 178.39  | 34    |
| 36 | 259.96 | 1.475 | 1.475 | 130.04 | 359.94 | 2.828 | 2.829 | 180.06  | 36    |
| 2    | 3     |
|-------|--------|
|       |        |
| LC    | M      |
| 38    | 263.29 |
| 40    | 266.62 |
| 42    | 269.96 |
| 44    | 273.29 |
| 46    | 276.62 |
| 48    | 279.96 |
| 50    | 283.29 |
| 52    | 286.62 |
| 54    | 289.96 |
| 56    | 293.29 |
| 58    | 296.62 |
| 60    | 299.96 |
| 4    | 5     |
|       | LC     |
| 0     | 399.94 |
| 2     | 403.27 |
| 4     | 406.60 |
| 6     | 409.93 |
| 8     | 413.26 |
| 10    | 416.59 |
| 12    | 419.92 |
| 14    | 423.26 |
| 16    | 426.59 |
| 18    | 429.92 |
| 20    | 433.25 |
| 22    | 436.58 |
| 24    | 439.91 |
| 26    | 443.24 |
| 28    | 446.58 |
| 30    | 449.91 |
| 32    | 453.24 |
| 34    | 456.57 |
| 36    | 459.90 |
| 38    | 463.23 |
| 40    | 466.56 |
| 42    | 469.89 |
| 44    | 473.23 |
| 46    | 476.56 |
| 48    | 479.89 |
| 50    | 483.22 |
| 52    | 486.55 |
| 54    | 48988  |
| 56    | 493.21 |
| 58    | 496.54 |
| 60    | 499.88 |
| 6    | 7     |
|       | LC     |
| 0     | 599.80 |
| 2     | 603.13 |
| 4     | 606.46 |
| 6     | 609.78 |
|    |        |       |       |        |        |       |       | 6     | 7    |
|----|--------|-------|-------|--------|--------|-------|-------|--------|-------|
|    | LC     | M     | E     | T      | LC     | M     | E     | T      |       |
| 8  | 613.11 | 8.210 | 8.221 | 306.98 | 712.91 | 11.11 | 11.13 | 357.13 | 8     |
| 10 | 616.44 | 8.300 | 8.311 | 308.65 | 716.24 | 11.21 | 11.23 | 358.81 | 10    |
| 12 | 619.76 | 8.390 | 8.401 | 310.32 | 719.56 | 11.31 | 11.33 | 360.48 | 12    |
| 14 | 623.09 | 8.480 | 8.491 | 311.99 | 722.89 | 11.42 | 11.44 | 362.15 | 14    |
| 16 | 626.42 | 8.570 | 8.581 | 313.66 | 726.21 | 11.52 | 11.54 | 363.83 | 16    |
| 18 | 629.74 | 8.660 | 8.671 | 315.33 | 729.53 | 11.63 | 11.65 | 365.50 | 18    |
| 20 | 633.07 | 8.750 | 8.761 | 317.00 | 732.86 | 11.73 | 11.75 | 367.17 | 20    |
| 22 | 636.40 | 8.844 | 8.856 | 318.67 | 736.19 | 11.84 | 11.86 | 368.85 | 22    |
| 24 | 639.72 | 8.939 | 8.951 | 320.34 | 739.51 | 11.95 | 11.97 | 370.52 | 24    |
| 26 | 643.05 | 9.033 | 9.046 | 322.01 | 742.84 | 12.06 | 12.08 | 372.19 | 26    |
| 28 | 646.38 | 9.128 | 9.141 | 323.68 | 746.17 | 12.17 | 12.19 | 373.86 | 28    |
| 30 | 649.70 | 9.222 | 9.236 | 325.35 | 749.49 | 12.27 | 12.30 | 375.54 | 30    |
| 32 | 653.03 | 9.317 | 9.331 | 327.02 | 752.82 | 12.38 | 12.41 | 377.22 | 32    |
| 34 | 656.36 | 9.411 | 9.426 | 328.69 | 756.15 | 12.49 | 12.52 | 378.89 | 34    |
| 36 | 659.69 | 9.506 | 9.521 | 330.37 | 759.47 | 12.60 | 12.63 | 380.57 | 36    |
| 38 | 663.02 | 9.600 | 9.616 | 332.04 | 762.80 | 12.71 | 12.74 | 382.24 | 38    |
| 40 | 666.34 | 9.695 | 9.712 | 333.71 | 766.13 | 12.82 | 12.85 | 383.92 | 40    |
| 42 | 669.67 | 9.794 | 9.812 | 335.38 | 769.45 | 12.93 | 12.96 | 385.60 | 42    |
| 44 | 673.00 | 9.894 | 9.912 | 337.05 | 772.78 | 13.04 | 13.08 | 387.27 | 44    |
| 46 | 676.32 | 9.993 | 10.01 | 338.73 | 776.11 | 13.15 | 13.19 | 388.95 | 46    |
| 48 | 679.65 | 10.09 | 10.11 | 340.40 | 779.43 | 13.26 | 13.31 | 390.62 | 48    |
| 50 | 682.98 | 10.19 | 10.21 | 342.07 | 782.76 | 13.37 | 13.42 | 392.30 | 50    |
| 52 | 686.30 | 10.29 | 10.31 | 343.74 | 786.09 | 13.48 | 13.53 | 393.98 | 52    |
| 54 | 689.63 | 10.39 | 10.41 | 345.41 | 789.41 | 13.59 | 13.65 | 395.65 | 54    |
| 56 | 692.96 | 10.49 | 10.51 | 347.08 | 792.74 | 13.70 | 13.76 | 397.33 | 56    |
| 58 | 696.28 | 10.59 | 10.61 | 348.76 | 796.07 | 13.81 | 13.88 | 399.01 | 58    |
| 60 | 699.60 | 10.69 | 10.71 | 350.44 | 799.40 | 13.96 | 13.99 | 400.70 | 60    |
| 8 | 9     |       |       |        |        |       |       |        |       |
|    | LC     | M     | E     | T      | LC     | M     | E     | T      |       |
| 0  | 799.40 | 13.96 | 13.99 | 400.70 | 899.10 | 17.66 | 17.71 | 450.95 | 0     |
| 2  | 802.72 | 14.07 | 14.10 | 402.37 | 902.42 | 17.79 | 17.84 | 452.63 | 2     |
| 4  | 806.04 | 14.19 | 14.22 | 404.05 | 905.74 | 17.92 | 17.98 | 454.31 | 4     |
| 6  | 809.37 | 14 31 | 14 34 | 405 72 | 909.07 | 18.06 | 18.11 | 455.98 | 6     |
| 8  | 812.69 | 14.43 | 14.46 | 407.39 | 912.39 | 18.19 | 18.25 | 457.66 | 8     |
| 10 | 816.01 | 14.55 | 14.58 | 409.06 | 915.71 | 18.32 | 18.38 | 459.34 | 10    |
| 12 | 819.34 | 14.66 | 14.70 | 410.74 | 919.04 | 18.46 | 18.52 | 461.02 | 12    |
| 14 | 822.66 | 14.78 | 14.82 | 412.41 | 922.36 | 18.59 | 18.65 | 462.70 | 14    |
| 16 | 825.98 | 14.90 | 14.94 | 414.08 | 925.68 | 18.72 | 18.79 | 464.37 | 16    |
| 18 | 829.31 | 15.02 | 15.06 | 415.75 | 929.01 | 18.86 | 18.92 | 466.05 | 18    |
| 20 | 832.63 | 15.14 | 15.18 | 417.43 | 932.33 | 18.99 | 19.06 | 467.73 | 20    |
| 22 | 835.95 | 15.26 | 15.30 | 419.10 | 935.65 | 19.12 | 19.19 | 469.41 | 22    |
| 24 | 839.28 | 15.38 | 15.43 | 420.77 | 938.98 | 19.26 | 19.33 | 471.08 | 24    |
| 26 | 842.60 | 15.51 | 15.55 | 422.45 | 942.30 | 19.40 | 19.47 | 472.76 | 26    |
| 28 | 845.92 | 15.63 | 15.68 | 424.12 | 945.62 | 19.54 | 19.61 | 474.43 | 28    |
| 30 | 849.25 | 15.75 | 15.80 | 425.79 | 948.95 | 19.68 | 19.75 | 476.10 | 30    |
| 32 | 852.57 | 15.88 | 15.93 | 427.47 | 952.27 | 19.82 | 19.89 | 477.78 | 32    |
| 34 | 855.89 | 16.00 | 16.05 | 429.15 | 955.59 | 19.96 | 20.03 | 479.46 | 34    |
| 36 | 859.22 | 16.12 | 16.18 | 430.82 | 958.92 | 20.10 | 20.17 | 481.14 | 36    |
| 38 | 862.54 | 16.25 | 16.30 | 432.50 | 962.24 | 20.24 | 20.31 | 482.83 | 38    |
| 40 | 865.86 | 16.38 | 16.43 | 434.18 | 965.56 | 20.38 | 20.45 | 484.51 | 40    |
| 42 | 869.19 | 16.50 | 16.55 | 435.86 | 968.89 | 20.52 | 20.59 | 486.19 | 42    |
|     |        |       |       |        |        |       |       | 8     | 9    |
|-----|--------|-------|-------|--------|--------|-------|-------|--------|-------|
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |       |
| 44  | 872.51 | 16.63 | 16.68 | 437.54 | 972.21 | 20.66 | 20.74 | 487.87 | 44    |
| 46  | 875.83 | 16.76 | 16.81 | 439.21 | 975.53 | 20.80 | 20.88 | 469.56 | 46    |
| 48  | 879.16 | 16.89 | 16.94 | 440.89 | 978.86 | 20.94 | 21.03 | 491.24 | 48    |
| 50  | 882.48 | 17.02 | 17.07 | 442.57 | 982.18 | 21.09 | 21.17 | 492.92 | 50    |
| 52  | 885.80 | 17.14 | 17.19 | 444.45 | 985.50 | 21.23 | 21.31 | 494.60 | 52    |
| 54  | 889.13 | 17.27 | 17.32 | 445.93 | 988.83 | 21.37 | 21.46 | 496.28 | 54    |
| 56  | 892.45 | 17.40 | 17.45 | 447.60 | 992.15 | 21.51 | 21.60 | 497.96 | 56    |
| 58  | 895.77 | 17.53 | 17.58 | 449.28 | 995.47 | 21.65 | 21.75 | 499.65 | 58    |
| 60  | 899.10 | 17.66 | 17.71 | 450.95 | 998.80 | 21.80 | 21.89 | 501.32 | 60    |
| 10 | 11    |       |       |        |        |       |       |        |       |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |       |
| 0   | 998.8  | 21.80 | 21.89 | 501.32 | 1098.4 | 26.38 | 26.50 | 551.74 | 0     |
| 2   | 1002.1 | 21.94 | 22.03 | 503.00 | 1101.7 | 26.54 | 26.66 | 553.42 | 2     |
| 4   | 1005.4 | 22.09 | 22.18 | 504.68 | 1105.0 | 26.70 | 26.83 | 555.10 | 4     |
| 6   | 1008.8 | 22.24 | 22.33 | 506.36 | 1108.3 | 26.86 | 26.99 | 556.78 | 6     |
| 8   | 1012.1 | 22.39 | 22.48 | 508.04 | 1111.7 | 27.02 | 27.16 | 558.46 | 8     |
| 10  | 1015.4 | 22.54 | 22.63 | 509.72 | 1115.0 | 27.19 | 27.32 | 560.14 | 10    |
| 12  | 1018.7 | 22.68 | 22.78 | 511.40 | 1118.3 | 27.35 | 17.48 | 561.82 | 12    |
| 14  | 1022.0 | 22.83 | 22.93 | 513.08 | 1121.6 | 27.51 | 27.65 | 563.50 | 14    |
| 16  | 1025.4 | 22.98 | 23.08 | 514.76 | 1124.9 | 27.67 | 27.81 | 565.18 | 16    |
| 18  | 1028.7 | 23.13 | 23.23 | 516.44 | 1128.2 | 27.83 | 27.98 | 566.86 | 18    |
| 20  | 1032.0 | 23.28 | 23.38 | 518.12 | 1131.6 | 28.00 | 28.14 | 568.54 | 20    |
| 22  | 1035.3 | 23.43 | 23.53 | 519.80 | 1134.9 | 28.17 | 28.30 | 570.22 | 22    |
| 24  | 1038.6 | 25.58 | 23.68 | 521.48 | 1138.2 | 28.34 | 28.47 | 571.90 | 24    |
| 26  | 1042.0 | 23.73 | 23.84 | 523.16 | 1141.5 | 28.50 | 28.64 | 573.58 | 26    |
| 28  | 1045.3 | 23.83 | 23.33 | 524.85 | 1144.8 | 28.67 | 28.81 | 575.27 | 28    |
| 30  | 1048.6 | 24.04 | 24.14 | 526.53 | 1148.1 | 28.84 | 28.98 | 576.95 | 30    |
| 32  | 1051.9 | 24.19 | 24.30 | 528.21 | 1151.5 | 29.00 | 29.14 | 578.63 | 32    |
| 34  | 1055.2 | 24.34 | 24.45 | 529.89 | 1154.8 | 29.17 | 29.31 | 580.32 | 34    |
| 36  | 1058.6 | 24.49 | 24.60 | 531.57 | 1158.1 | 29.34 | 29.48 | 582.00 | 36    |
| 38  | 1061.9 | 24.64 | 24.76 | 533.25 | 1161.4 | 29.50 | 29.65 | 583.69 | 38    |
| 40  | 1065.2 | 24.80 | 24.91 | 534.93 | 1164.7 | 29.67 | 29.82 | 585.37 | 40    |
| 42  | 1068.5 | 24.95 | 25.06 | 536.61 | 1168.0 | 23.84 | 29.99 | 587.05 | 42    |
| 44  | 1071.8 | 25.11 | 25.22 | 538.29 | 1171.4 | 30.01 | 30.17 | 588.74 | 44    |
| 46  | 1075.2 | 25.27 | 25.38 | 539.97 | 1174.7 | 30.18 | 30.34 | 590.42 | 46    |
| 48  | 1078.5 | 25.43 | 25.54 | 541.65 | 1178.0 | 30.35 | 30.52 | 592.11 | 48    |
| 50  | 1081.8 | 25.59 | 25.70 | 543.33 | 1181.3 | 30.53 | 30.69 | 593.79 | 50    |
| 52  | 1085.1 | 25.74 | 25.86 | 545.01 | 1184.6 | 30.70 | 30.86 | 595.47 | 52    |
| 54  | 1088.4 | 25.90 | 26.02 | 546.69 | 1187.9 | 30.87 | 31.04 | 597.16 | 54    |
| 56  | 1091.8 | 26.06 | 26.18 | 548.37 | 1191.3 | 31.04 | 31.21 | 598.84 | 56    |
| 58  | 1095.1 | 26.22 | 26.34 | 550.06 | 1194.6 | 31.21 | 31.39 | 600.53 | 58    |
| 60  | 1098.4 | 26.38 | 26.50 | 551.74 | 1197.9 | 31.39 | 31.56 | 602.22 | 60    |
| 12 | 13    |       |       |        |        |       |       |        |       |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |       |
| 0   | 1197.9 | 31.39 | 31.56 | 602.22 | 1297.3 | 36.83 | 37.07 | 652.87 | 0     |
| 2   | 1201.2 | 31.57 | 31.73 | 603.91 | 1300.6 | 37.02 | 37.26 | 654.56 | 2     |
| 4   | 1204.5 | 31.74 | 31.91 | 605.60 | 1303.9 | 37.21 | 37.46 | 656.25 | 4     |
| 6   | 1207.8 | 31.92 | 32.09 | 607.28 | 1307.2 | 37.40 | 37.65 | 657.93 | 6     |
| 8   | 1211.1 | 32.09 | 32.37 | 608.97 | 1310.5 | 37.59 | 37.85 | 659.62 | 8     |
| 10  | 1214.5 | 32.27 | 32.45 | 610.66 | 1313.8 | 37.79 | 38.04 | 661.31 | 10    |
| 12  | 1217.8 | 32.45 | 32.63 | 612.35 | 1317.2 | 37 98 | 38.23 | 663.00 | 12    |
| 14  | 1221.1 | 32.62 | 32.81 | 614.04 | 1320.5 | 38.17 | 38.43 | 664.69 | 14    |
|     |         |       |       |        |         |       |       | 12    | 13    |
|-----|---------|-------|-------|--------|---------|-------|-------|--------|--------|
|     | LC      | M     | E     | T      | LC      | M     | E     | T      |        |
| 16  | 1224.4  | 32.80 | 32.99 | 615.72 | 1323.8  | 38.36 | 38.62 | 666.37 | 16     |
| 18  | 1227.7  | 32.97 | 33.17 | 617.41 | 1327.1  | 38.55 | 38.82 | 668.06 | 18     |
| 20  | 1231.0  | 33.15 | 33.35 | 619.10 | 1330.4  | 38.75 | 39.01 | 669.75 | 20     |
| 22  | 1234.3  | 33.33 | 33.53 | 620.79 | 1333.7  | 38.95 | 39.20 | 671.44 | 22     |
| 24  | 1237.7  | 33.51 | 33.72 | 622.48 | 1337.0  | 39.15 | 39.40 | 673.13 | 24     |
| 26  | 1241 0  | 33 59 | 33 90 | 524 16 | 1340.3  | 39.35 | 39.60 | 674 81 | 26     |
| 28  | 1244.3  | 33.87 | 34.09 | 625.85 | 1343.6  | 39.54 | 39.80 | 676.51 | 28     |
| 30  | 1247.6  | 34.06 | 34.27 | 627.55 | 1346.9  | 39.74 | 40.00 | 678,20 | 30     |
| 32  | 1250.9  | 34.24 | 34.45 | 629.24 | 1350.3  | 39.94 | 40.19 | 679.89 | 32     |
| 34  | 1254.2  | 34.42 | 34 64 | 630.93 | 1353.6  | 40.13 | 40,39 | 681.58 | 34     |
| 36  | 1257.5  | 34.60 | 34.82 | 632.61 | 1356.9  | 40.23 | 40.59 | 683.26 | 36     |
| 38  | 1 260.8 | 34.78 | 35.01 | 634.30 | 1360.2  | 40.52 | 40.79 | 684.95 | 38     |
| 40  | 1264.2  | 34.97 | 35.19 | 635.99 | 1363.5  | 40.71 | 40.99 | 686.64 | 40     |
| 42  | 1267.5  | 35.16 | 35.37 | 637.68 | 1366.8  | 40.91 | 41.19 | 688.33 | 42     |
| 44  | 1270.8  | 35.34 | 35.56 | 639.37 | 1370.1  | 41.11 | 41.40 | 690.02 | 44     |
| 46  | 1274.1  | 35.53 | 35.75 | 641.05 | 1373.4  | 41.31 | 41.60 | 631.70 | 46     |
| 48  | 1277.4  | 35.71 | 35.94 | 642.74 | 1376.7  | 41.51 | 41.81 | 693.39 | 48     |
| 50  | 1280.7  | 35.90 | 38.13 | 644.43 | 1380.0  | 41.71 | 42.01 | 695.08 | 50     |
| 52  | 1284.0  | 36.09 | 36.31 | 646.12 | 1383.4  | 41.91 | 42.21 | 696.77 | 52     |
| 54  | 1287.4  | 36.27 | 36.50 | 647.81 | 1386.7  | 42.11 | 42.42 | 698.46 | 54     |
| 56  | 1290.7  | 36.46 | 36.69 | 649.49 | 1390.0  | 42.31 | 42.62 | 700.14 | 56     |
| 58  | 1294 0  | 38 84 | 36 88 | 651.18 | 1393.3  | 42.51 | 42.83 | 701.83 | 58     |
| 60  | 1297.3  | 36.83 | 37.07 | 652.87 | 1396.6  | 42.71 | 43.03 | 703.53 | 60     |
| 14 |         | 15   |       |        |         |       |       |        |        |
|     | LC      | M     | E     | T      | LC      | M     | E     | T      |        |
| 0   | 1396.6  | 42.71 | 43.03 | 703.53 | 1495.9  | 49.02 | 49.44 | 754.35 | 0      |
| 2   | 1399.9  | 42.92 | 43.23 | 705.23 | 1499.2  | 49.24 | 49.66 | 756.05 | 2      |
| 4   | 1403.2  | 43.12 | 43.44 | 706.92 | 1502.5  | 49.46 | 49.89 | 757.74 | 4      |
| 6   | 1406.5  | 43.33 | 43.65 | 708.62 | 1505.8  | 49.68 | 50.11 | 759.44 | 6      |
| 8   | 1409.8  | 43.53 | 43.86 | 710.31 | 1509.1  | 49.90 | 50.34 | 761.13 | 8      |
| 10  | 1413.1  | 43.74 | 44.07 | 712.01 | 1512.4  | 50.12 | 50.56 | 762.83 | 10     |
| 12  | 1416.5  | 43.94 | 44.28 | 713.71 | 1515.7  | 50.34 | 50.78 | 764.53 | 12     |
| 14  | 1419.8  | 44.15 | 44.49 | 715.40 | 1519.0  | 50.56 | 51.01 | 766.22 | 14     |
| 16  | 1423.1  | 44.35 | 44.70 | 717.10 | 1522.3  | 50.78 | 51.23 | 767.92 | 16     |
| 18  | 1426.4  | 44.56 | 44.91 | 718.79 | 1525.6  | 51.00 | 51.46 | 769.61 | 18     |
| 20  | 1429.7  | 44.77 | 45.12 | 720.49 | 1528.9  | 51.22 | 51.68 | 771.31 | 20     |
| 22  | 1433.0  | 44.98 | 45.33 | 722.20 | 1532.2  | 51.44 | 51.90 | 773.01 | 22     |
| 24  | 1436.3  | 45.19 | 45.54 | 723.89 | 1535.5  | 51.67 | 52.13 | 774.70 | 24     |
| 26  | 1439.6  | 45.40 | 45.76 | 725.59 | 1538.8  | 51.89 | 52.36 | 776.40 | 26     |
| 28  | 1442.9  | 45,61 | 45.97 | 727.28 | 1542.1  | 52.12 | 52.59 | 778.09 | 28     |
| 30  | 1446.2  | 45.82 | 46.18 | 728.97 | 1545.4  | 52.34 | 52.82 | 779.79 | 30     |
| 32  | 1449.6  | 46.03 | 46.60 | 730.66 | 1 548.7 | 52.57 | 53.05 | 781.49 | 32     |
| 34  | 1452.9  | 46.24 | 46.61 | 732.35 | 1552.0  | 52.79 | 53.28 | 783.19 | 34     |
| 36  | 1456.2  | 46.45 | 46.82 | 734.05 | 1555.3  | 53.02 | 53.51 | 784.89 | 36     |
| 38  | 1459.5  | 46.66 | 47.04 | 735.74 | 1558.6  | 53.24 | 53.74 | 786.59 | 38     |
| 40  | 1462.8  | 46.87 | 47.25 | 737.43 | 1561.9  | 53.47 | 53.97 | 788.29 | 40     |
| 42  | 1466.1  | 47.08 | 47.46 | 739.12 | 1565.2  | 53.69 | 54.20 | 789.99 | 42     |
| 44  | 1469.4  | 47.30 | 47.68 | 740.81 | 1568.5  | 53.32 | 54.44 | 731.63 | 44     |
| 46  | 1472.7  | 47.51 | 47.90 | 742.51 | 1571.8  | 54.15 | 54.67 | 793.39 | 46     |
| 48  | 1476.0  | 47.73 | 48.12 | 744.20 | 1575.1  | 54.38 | 54.94 | 735.03 | 48     |
| 50  | 1479.3  | 47.94 | 48.34 | 745.89 | 1578.4  | 54.61 | 55.14 | 796.79 | 50     |
|     |        |       |       |        |        |       | 14    |        | 15    |
|-----|--------|-------|-------|--------|--------|-------|--------|--------|--------|
|     | LC     | M     | E     | T      | LC     | M     | E      | T      |        |
| 52  | 1482.7 | 48.16 | 48.56 | 747.58 | 1581.7 | 54.84 | 55.37  | 798.49 | 52     |
| 54  | 1486.0 | 48.37 | 48.78 | 749.27 | 1585.0 | 55.07 | 55.61  | 800.19 | 54     |
| 56  | 1489.3 | 48 59 | 49.00 | 750.97 | 1588.3 | 55.30 | 55.84  | 801.89 | 56     |
| 58  | 1492.6 | 48.80 | 49.22 | 752.66 | 1591.6 | 55.53 | 56.08  | 803.59 | 58     |
| 60  | 1495.9 | 49.02 | 49.44 | 754.35 | 1594.9 | 55.76 | 56.31  | 605.29 | 60     |
| 16 |        | 17   |       |        |        |       |        |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E      | T      |        |
| 0   | 1594.9 | 55.76 | 56.31 | 805.29 | 1693.9 | 62.94 | 63.64  | 856.35 | 0      |
| 2   | 1598.2 | 55.99 | 56.54 | 806.99 | 1697.2 | 63.18 | 63.89  | 858.05 | 2      |
| 4   | 1601.5 | 56.23 | 56.78 | 808.64 | 1700.5 | 63.43 | 64.15  | 859.76 | 4      |
| 6   | 1604.8 | 56.46 | 57.02 | 810.39 | 1703.8 | 63.68 | 64.40  | 861.46 | 6      |
| 8   | 1608.1 | 56.70 | 57.26 | 812.09 | 1707.1 | 63.93 | 64.66  | 863.16 | 8      |
| 10  | 1611.4 | 56.93 | 57.50 | 813.79 | 1710.4 | 64.18 | 64.91  | 864.87 | 10     |
| 12  | 1614.7 | 57.17 | 57.74 | 815.49 | 1713.7 | 64.42 | 65.16  | 866.57 | 12     |
| 14  | 1618.0 | 57.40 | 57.98 | 817.19 | 1716.9 | 64.67 | 65.42  | 868.27 | 14     |
| 16  | 1621.3 | 57.64 | 58.22 | 818.89 | 1720.2 | 64.92 | 65.67  | 869.98 | 16     |
| 18  | 1624.6 | 57.87 | 58.46 | 820.59 | 1723.5 | 65.17 | 65.93  | 871.68 | 18     |
| 20  | 1627.9 | 58.11 | 58.70 | 822.29 | 1726.8 | 65.42 | 66.18  | 873.38 | 20     |
| 22  | 1631.2 | 58.34 | 58.94 | 823.99 | 1730.1 | 65.67 | 66.43  | 875.09 | 22     |
| 24  | 1634.5 | 58.58 | 59.19 | 825.69 | 1733.4 | 65.93 | 66.69  | 876.79 | 24     |
| 26  | 1637.8 | 58.82 | 59.43 | 827.39 | 1736.7 | 66.18 | 66.95  | 878.49 | 26     |
| 28  | 1641.1 | 59.06 | 59.68 | 829.09 | 1740.0 | 66.44 | 67.21  | 880.20 | 28     |
| 30  | 1644.4 | 59.30 | 59.92 | 830.79 | 1743.3 | 66.69 | 67.47  | 881.90 | 30     |
| 32  | 1647.7 | 59.54 | 60.16 | 832.49 | 1746.6 | 66.94 | 67.72  | 883.61 | 32     |
| 34  | 1651.0 | 59.78 | 60.41 | 834.20 | 1749.9 | 67.20 | 67.98  | 885.32 | 34     |
| 36  | 1654.3 | 60.02 | 60.85 | 835.00 | 1753.2 | 67.45 | 68.24  | 887.02 | 38     |
| 38  | 1657.6 | 60.26 | 60.90 | 837.61 | 1756.5 | 67.71 | 68.50  | 888.73 | 38     |
| 40  | 1660.9 | 60.50 | 61.14 | 839.31 | 1759.8 | 67.96 | 68.76  | 890.44 | 40     |
| 42  | 1664.2 | 60.74 | 61.39 | 841.01 | 1763.1 | 68.21 | 69.03  | 892.15 | 42     |
| 44  | 1667.5 | 60.99 | 61.64 | 842.72 | 1766.3 | 68.47 | 69.29  | 893.86 | 44     |
| 46  | 1670.8 | 61.23 | 61.89 | 844.42 | 1769.6 | 68.73 | 69.56  | 895.56 | 46     |
| 48  | 1674.1 | 61.48 | 62.14 | 846.13 | 1772.9 | 68.99 | 69.82  | 897.27 | 48     |
| 50  | 1677.4 | 61.72 | 62.39 | 847.83 | 1776.2 | 69.25 | 70.09  | 898.98 | 50     |
| 52  | 1680.7 | 61.96 | 62.64 | 849.53 | 1779.5 | 69.50 | 70.36  | 900.69 | 52     |
| 54  | 1684.0 | 62.21 | 62.89 | 851.24 | 1782.8 | 69.76 | 70.62  | 902.40 | 54     |
| 56  | 1687.3 | 62.45 | 63.14 | 852.94 | 1786.1 | 70.02 | 70.89  | 904.10 | 56     |
| 58  | 1690.6 | 62.70 | 63.39 | 854.65 | 1789.4 | 70.28 | 71.17  | 905.81 | 58     |
| 60  | 1693.9 | 62.94 | 63.64 | 856.35 | 1792.7 | 70.54 | 71.42  | 907.52 | 60     |
| 18 |        | 19   |       |        |        |       |        |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E      | T      |        |
| 0   | 1792.7 | 70.54 | 71.42 | 907.52 | 1891.5 | 78.58 | 79.65  | 958.86 | 0      |
| 2   | 1796.0 | 70.80 | 71.69 | 909.23 | 1894.8 | 78.86 | 79.94  | 960.57 | 2      |
| 4   | 1799.3 | 71.06 | 71.96 | 910.94 | 1898.1 | 79.13 | 80.22  | 962.30 | 4      |
| 6   | 1802.6 | 71.33 | 72.23 | 912.65 | 1901.3 | 79.41 | 80.51  | 964.00 | 6      |
| 8   | 1805.9 | 71.59 | 72.50 | 914.36 | 1904.6 | 79.68 | 80.79  | 965.72 | 8      |
| 10  | 1809.2 | 71.85 | 72.77 | 916.07 | 1907.9 | 79.96 | 81.08  | 967.43 | 10     |
| 12  | 1812.5 | 72.12 | 73.04 | 917.78 | 1911.2 | 80.24 | 81.37  | 969.15 | 12     |
| 14  | 1815.7 | 72.38 | 73.31 | 919.49 | 1914.5 | 80.51 | 81.65  | 970.86 | 14     |
| 16  | 1819.0 | 72.64 | 73.58 | 921.20 | 1917.8 | 80.79 | 81.94  | 972.58 | 16     |
| 18  | 1822.3 | 72.91 | 73.85 | 922.91 | 1921.0 | 81.07 | 82.22  | 974.29 | 18     |
| 20  | 1825.6 | 73.17 | 74.12 | 924.63 | 1924.3 | 81.35 | 82.51  | 976.01 | 20     |
| 22  | 1828.9 | 73.43 | 74.39 | 926.34 | 1927.6 | 81.63 | 82.80  | 977.72 | 22     |
|    |        |       |       |        |        |       | 18    |        | 19    |
|----|--------|-------|-------|--------|--------|-------|--------|--------|--------|
|    | LC     | M     | E     | T      | LC     | M     | E      | T      |        |
| 24 | 1832.2 | 73.70 | 74.67 | 928.05 | 1930.9 | 81.91 | 83.09  | 979.44 | 24     |
| 26 | 1835.5 | 73.97 | 74.94 | 929.76 | 1934.2 | 82.20 | 83.38  | 981.15 | 26     |
| 28 | 1838.8 | 74.24 | 75.22 | 931.47 | 1937.5 | 82.48 | 83.67  | 982.86 | 28     |
| 30 | 1842.1 | 74.51 | 75.49 | 933.18 | 1940.7 | 82.76 | 83.97  | 984.58 | 30     |
| 32 | 1845.4 | 74.77 | 75.77 | 934.89 | 1944.0 | 83.05 | 84.26  | 986.30 | 32     |
| 34 | 1848.7 | 75.04 | 76.04 | 936.60 | 1947.3 | 83.33 | 84.55  | 988.02 | 34     |
| 36 | 1852.0 | 75.31 | 76.32 | 938.32 | 1950.6 | 83.61 | 84.84  | 989.74 | 36     |
| 38 | 1855.3 | 75.58 | 76.59 | 940.03 | 1953.9 | 83.90 | 85.13  | 991.46 | 38     |
| 40 | 1858.6 | 75.85 | 76.87 | 941.74 | 1957.2 | 84.18 | 85.43  | 993.18 | 40     |
| 42 | 1861.9 | 76.12 | 77.14 | 943.45 | 1960.4 | 84.47 | 85.73  | 994.90 | 42     |
| 44 | 1865.1 | 76.39 | 77.42 | 945.16 | 1963.7 | 84.75 | 86.02  | 996.62 | 44     |
| 46 | 1868.4 | 76.67 | 77.70 | 946.88 | 1967.0 | 85.04 | 86.32  | 998.34 | 46     |
| 48 | 1871.1 | 76.94 | 77.98 | 948.59 | 1970.3 | 85.32 | 86.61  | 1000.0 | 48     |
| 50 | 1875.0 | 77.21 | 78.26 | 950.30 | 1973.6 | 85.61 | 86.91  | 1001.8 | 50     |
| 52 | 1878.3 | 77.49 | 78.53 | 952.01 | 1976.9 | 85.90 | 87.21  | 1003.5 | 52     |
| 54 | 1881.6 | 77.76 | 78.81 | 953.72 | 1980.1 | 86.19 | 87.50  | 1005.2 | 54     |
| 56 | 1884.9 | 78.03 | 79.09 | 955.44 | 1983.4 | 86.47 | 87.80  | 1006.9 | 56     |
| 58 | 1888.2 | 78.31 | 79.37 | 957.15 | 1986.7 | 86.76 | 88.09  | 1008.6 | 58     |
| 60 | 1891.5 | 78.58 | 79.65 | 958.86 | 1990.0 | 87.05 | 88.39  | 1010.4 | 60     |

## 20 21


LC
M
E
T
LC
M
E
T

0
1990.0
87.50
88.39
1010.4
2088.5
95.95
97.58
1062.0
0
2
1993.3
87.34
88.69
1012.1
2091.8
96.26
97.90
1063.7
2
4
1996.6
87.63
88.99
1013.8
2095.0
96.56
98.21
1065.4
4
6
1999.8
87.92
89.29
1015.5
2098.3
96.87
98.53
1067.2
6
8
2003.1
88.21
89.59
1017.2
2101.6
97.17
98.84
1068.9
8
10
2006.4
88.50
89.89
1019.0
2104.9
97.48
99.16
1070.6
10
12
2009.7
88.79
90.19
1020.7
2108.1
97.79
99.48
1072.4
12
14
2013.0
83.08
90.48
1022.4
2111.4
98.09
99.73
1074.1
14
16
2016.3
89.37
90.79
1024.1
2114.7
98.40
100.1
1075.8
16
18
2019.5
89.66
91.09
1025.8
2118.0
98.70
100.4
1077.5
18
20
2022.8
89.96
91.40
1027.6
2121.2
99.00
100.7
1079.3
20
22
2026.1
90.25
91.71
1029.3
2124.5
99.39
101.1
1081.0
22
24
2029.4
90.55
92.01
1031.0
2127.8
99.60
101.4
1082.7
24
26
2032.7
90.85
92.32
1032.7
2131.0
99.90
101.7
1084.4
26
28
2036.0
91.15
92.62
1034.4
2134.3
100.2
102.0
1086.2
28
30
2039.2
91.45
92.93
1036.1
2137.6
100.5
102.3
1087.9
30
32
2042.5
91.74
93.24
1037.9
2140.9
100.8
102.7
1089.6
32
34
2045.8
92.04
93.54
1039.6
2144.1
101.1
103.0
1091.3
34
36
2049.1
92.34
93.85
1041.3
2147.4
101.4
103.3
1093.1
36
38
2052.4
92.64
94.15
1043.0
2150.7
101.7
103.6
1094.8
38
40
2055.7
92.94
94.46
1044.8
2154.0
102.1
104.0
1096.5
40
42
2058.9
93.24
94.78
1046.5
2157.2
102.4
104.3
1098.3
42
44
2062.2
93.54
95.09
1048.2
2160.5
102.7
104.6
1100.0
44
46
2065.5
93.84
95.40
1049.9
2153.8
103,0
104.9
1101.7
46
48
2068.8
94.14
95.71
1051.7
2167.1
103.3
105.3
1103.4
48
50
2072.1
94.44
96.03
1053.4
2170.3
103.6
105.6
1105.2
50
52
2075.4
94.74
96.34
1055.1
2173.6
103.9
105.9
1106.9
52
54
2078.6
95.04
96.65
1056.8
2176.9
104.2
106.3
1108.6
54
56
2081.9
95.34
96.96
1056.6
2180.1
104.5
106.6
1110.3
56
58
2085.2
95.64
97.27
1060.3
2183.4
104.8
106.9
1112.1
58
60
2088.5
95.95
97.58
1062.0
2186.7
105.2
107.2
1113.8
60
|     |        |       |       |        |        | 22   |       | 23    |     |
|-----|--------|-------|-------|--------|--------|-------|-------|--------|-----|
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |     |
| 0   | 2186.7 | 105.2 | 107.2 | 1113.8 | 2284.8 | 115.0 | 117.4 | 1165.8 | 0   |
| 2   | 2190,0 | 105.5 | 107.8 | 1115.5 | 2288,1 | 115.3 | 117 7 | 1167.5 | 2   |
| 4   | 2193 2 | 105.9 | 107.9 | 1117.3 | 2297.3 | 115.7 | 118.1 | 1169.2 | 4   |
| 6   | 2196.5 | 106.2 | 108.2 | 1119.0 | 2294.6 | 116.0 | 118.4 | 1171.0 | 6   |
| 8   | 2199.8 | 106.5 | 108.6 | 1120.7 | 2297.8 | 116.4 | 118.8 | 1172.7 | 8   |
| 10  | 2203.0 | 106.8 | 108.9 | 1122.4 | 2301.1 | 116.7 | 119.1 | 1174.4 | 10  |
| 12  | 2206.3 | 107.1 | 109.2 | 1124.2 | 2304.4 | 117.0 | 119.5 | 1176.5 | 12  |
| 14  | 2209.6 | 107.4 | 109.6 | 1125.9 | 2307.6 | 117.4 | 119.8 | 1177.9 | 14  |
| 16  | 2212.9 | 107.7 | 109.9 | 1127.6 | 2310.9 | 117.7 | 120.4 | 1179.7 | 16  |
| 18  | 2216.1 | 108.0 | 110.2 | 1129.4 | 2314.1 | 118.1 | 120.5 | 1181.4 | 18  |
| 20  | 2219.4 | 108.4 | 110.6 | 1131.1 | 2317.4 | 118.4 | 120.9 | 1183.1 | 20  |
| 22  | 2222.7 | 108.7 | 110.9 | 1132.8 | 23207  | 118.7 | 121.2 | 1184.9 | 22  |
| 24  | 2225.9 | 109.0 | 111.2 | 1134.6 | 2323.9 | 119.1 | 121.6 | 1186.6 | 24  |
| 26  | 2229.2 | 109.4 | 111.6 | 1136.3 | 2327.2 | 119.4 | 121.9 | 1188.4 | 26  |
| 28  | 2232.5 | 109.7 | 111.9 | 1138.0 | 2330.4 | 119.8 | 122.3 | 1190.1 | 28  |
| 30  | 2235.7 | 110.0 | 112.3 | 1139.7 | 2333.7 | 120.1 | 122.6 | 1191.8 | 30  |
| 32  | 2239.0 | 110.4 | 112.6 | 1141.5 | 2337.0 | 120.4 | 123.0 | 1193.6 | 32  |
| 34  | 2242.3 | 110.7 | 112.9 | 1143.2 | 2340.2 | 120.8 | 123.3 | 1195.3 | 34  |
| 36  | 2245.6 | 111.0 | 113.3 | 1144.9 | 2343.5 | 121.1 | 123.7 | 1197.1 | 36  |
| 38  | 2248.8 | 111.4 | 113.6 | 1146.7 | 2346.7 | 121.5 | 124.1 | 1198.8 | 38  |
| 40  | 2252.1 | 111.7 | 113.9 | 1148.4 | 2350.0 | 121.8 | 124.4 | 1200.5 | 40  |
| 42  | 2255.4 | 112.0 | 114.3 | 1150.1 | 2353.3 | 122.1 | 124.8 | 1202.3 | 42  |
| 44  | 2258.6 | 112.3 | 114.6 | 1151.9 | 2356.5 | 122.5 | 125.1 | 1204.0 | 44  |
| 46  | 2261.9 | 112.7 | 115.0 | 1153.6 | 2359.8 | 122.8 | 125.5 | 1205.8 | 46  |
| 48  | 2265.2 | 113.0 | 115.3 | 1155.4 | 2363.0 | 123.2 | 125.8 | 1207.5 | 48  |
| 50  | 2268.4 | 113.3 | 115.7 | 1157.1 | 2366.3 | 123.5 | 126.2 | 1209.2 | 50  |
| 52  | 2271.7 | 113,7 | 116,0 | 1158.8 | 2369.6 | 123.8 | 126.6 | 1211.0 | 52  |
| 54  | 2275.0 | 114.0 | 116.3 | 1160.6 | 2372.8 | 124.2 | 126.9 | 1212.7 | 54  |
| 56  | 2278.3 | 114.3 | 116.7 | 1162.3 | 2376.1 | 124.5 | 127.3 | 1214.5 | 56  |
| 58  | 2281.5 | 114.7 | 117.0 | 1164.0 | 2379.3 | 124.9 | 127.6 | 1216.2 | 58  |
| 60  | 2284.8 | 115.0 | 117.4 | 1165.8 | 2382.6 | 125.2 | 128.0 | 1218.0 | 60  |
| 24 | 25    |       |       |        |        |       |       |        |     |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |     |
| 0   | 2382.6 | 125.2 | 128.0 | 1218.0 | 2480.4 | 135.8 | 139.1 | 1270.3 | 0   |
| 2   | 2385.9 | 125.5 | 128.4 | 1219.7 | 2483.6 | 136.2 | 139.5 | 1272.0 | 2   |
| 4   | 2389.1 | 125.9 | 128.7 | 1221.4 | 2486.9 | 136.5 | 139.9 | 1273.8 | 4   |
| 6   | 2392.4 | 126.2 | 129.1 | 1223.2 | 2490.1 | 136.9 | 140.3 | 1275.5 | 6   |
| 8   | 2395.6 | 126.6 | 129.5 | 1224.9 | 2493.4 | 137.2 | 140.6 | 1277.3 | 8   |
| 10  | 2398.9 | 126.9 | 129.8 | 1226.7 | 2496.6 | 137.6 | 121.0 | 1279.0 | 10  |
| 12  | 2402.2 | 127.3 | 130.2 | 1228.4 | 2499.9 | 138.0 | 121.4 | 1280.8 | 12  |
| 14  | 2405.4 | 127.6 | 130.6 | 1230.2 | 2503.1 | 138.3 | 121.8 | 1282.5 | 14  |
| 16  | 2408.7 | 128.0 | 130.9 | 1231.9 | 2506.4 | 138.7 | 142.2 | 1284.3 | 16  |
| 18  | 2411.9 | 128.3 | 131.3 | 1233.6 | 2509.6 | 139.0 | 142.5 | 1286.1 | 18  |
| 20  | 2415.2 | 128.7 | 131.7 | 1235.4 | 2512.9 | 139.4 | 142.9 | 1287.8 | 20  |
| 22  | 2418.5 | 129.0 | 132.0 | 1237.1 | 2516.1 | 139.8 | 143.3 | 1289.6 | 22  |
| 24  | 2421.7 | 123.4 | 132.4 | 1233.9 | 2519.4 | 140.1 | 143.7 | 1291.3 | 24  |
| 26  | 2425.0 | 129.7 | 132.8 | 1240.6 | 2522.6 | 140.5 | 144.1 | 1293.1 | 26  |
| 28  | 2428.2 | 130.1 | 133.1 | 1242.4 | 2525.9 | 140.8 | 144.5 | 1294.8 | 28  |
| 30  | 2431.5 | 130.4 | 133.5 | 1244.1 | 2529.1 | 141.2 | 144.9 | 1296.6 | 30  |
| 32  | 2434.8 | 130.8 | 133.9 | 1245.8 | 2532.4 | 141.6 | 145.3 | 1298.3 | 32  |
| 34  | 2438.0 | 131.1 | 134.2 | 1247.6 | 2535.6 | 142.0 | 145.6 | 1300.1 | 34  |
| 36  | 2441.3 | 131.5 | 134.6 | 1249.3 | 2538.9 | 142.3 | 146.0 | 1301.8 | 36  |
|     |        |       |       |        |        |       |       | 24    | 25    |
|-----|--------|-------|-------|--------|--------|-------|-------|--------|--------|
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 38  | 2444.5 | 131.8 | 135.0 | 1251.1 | 2542.1 | 142.7 | 146.4 | 1303.6 | 38     |
| 40  | 2447.8 | 132.2 | 135.4 | 1252.8 | 2545.4 | 143.1 | 146.8 | 1305.3 | 40     |
| 42  | 2451.1 | 132.6 | 135.7 | 1254.8 | 2548.6 | 143.5 | 147.2 | 1307.1 | 42     |
| 44  | 2454.3 | 132.9 | 136.1 | 1256.3 | 2551.9 | 143.8 | 147.6 | 1308.8 | 44     |
| 46  | 2457.6 | 133.3 | 136.5 | 1258.1 | 2555.1 | 144.2 | 148.0 | 1310.6 | 46     |
| 48  | 2460.8 | 133.6 | 136.9 | 1259.8 | 2558.4 | 144.5 | 148.4 | 1312.4 | 48     |
| 50  | 2464.1 | 134.0 | 137.2 | 1261.5 | 2561.6 | 144.9 | 148.8 | 1314.1 | 50     |
| 52  | 2467.4 | 134.4 | 137.6 | 1263.3 | 2564.9 | 146.3 | 149.2 | 1315.9 | 52     |
| 54  | 2470.6 | 134.7 | 138.0 | 1265.0 | 2568.1 | 146.7 | 149.5 | 1317.6 | 54     |
| 56  | 2473.9 | 135.1 | 138.4 | 1266.8 | 2571.4 | 146.0 | 149.9 | 1319.4 | 56     |
| 58  | 2477.1 | 135.4 | 138.7 | 1268.5 | 2574.6 | 146.4 | 150.3 | 1321.1 | 58     |
| 60  | 2480.4 | 135.8 | 139.1 | 1270.3 | 2577.9 | 146.8 | 150.7 | 1322.9 | 60     |
| 26 | 27    |       |       |        |        |       |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 2577.9 | 146.8 | 150.7 | 1322.9 | 2675.3 | 158.3 | 162.8 | 1376.6 | 0      |
| 2   | 2581.1 | 147.1 | 151.1 | 1324.6 | 2678.5 | 158.6 | 163.2 | 1377.4 | 2      |
| 4   | 2584.4 | 147.5 | 151.5 | 1326.4 | 2681.8 | 159.0 | 163.7 | 1379.2 | 4      |
| 6   | 2587.6 | 147.9 | 151.9 | 1328.1 | 2685.0 | 159.4 | 164.1 | 1380.9 | 6      |
| 8   | 2590.9 | 148.3 | 152.3 | 1329.9 | 2688.2 | 159.8 | 164.6 | 1382.7 | 8      |
| 10  | 2594.1 | 148.7 | 152.7 | 1331.6 | 2691.5 | 160.2 | 164.9 | 1384.5 | 10     |
| 12  | 2597.4 | 149.1 | 153.1 | 1333.4 | 2694.7 | 160.6 | 165.3 | 1386.2 | 12     |
| 14  | 2600.6 | 149.4 | 153.5 | 1335.2 | 2698.0 | 161.0 | 165.7 | 1388.0 | 14     |
| 16  | 2603.9 | 149.8 | 153.9 | 1336.9 | 2701.2 | 161.4 | 166.1 | 1389.8 | 16     |
| 18  | 2607.1 | 150.2 | 154.3 | 1338.7 | 2704.4 | 161.8 | 166.5 | 1391.5 | 18     |
| 20  | 2610.4 | 150.6 | 154.7 | 1340.4 | 2707.7 | 162.2 | 167.0 | 1393.3 | 20     |
| 22  | 2613.6 | 151.0 | 155.1 | 1342.2 | 2710.9 | 162.6 | 167.4 | 1395.0 | 22     |
| 24  | 2616.9 | 151.4 | 155.5 | 1343.9 | 2714.1 | 163.0 | 167.8 | 1396.8 | 24     |
| 26  | 2620.1 | 151.7 | 155.9 | 1345.7 | 2717.4 | 163.4 | 168.2 | 1398.6 | 26     |
| 28  | 2623.4 | 152.1 | 156.3 | 1347.4 | 2720.6 | 163.8 | 168.6 | 1400.3 | 28     |
| 30  | 2626.6 | 152.5 | 156.7 | 1349.2 | 2723.8 | 164.2 | 169.1 | 1402.1 | 30     |
| 32  | 2629.8 | 152.9 | 157.1 | 1351.0 | 2727.1 | 164.6 | 169.5 | 1403.9 | 32     |
| 34  | 2633.1 | 153.3 | 157.5 | 1352.7 | 2730.3 | 165.0 | 169.9 | 1405.6 | 34     |
| 36  | 2636.3 | 153.7 | 157.9 | 1354.5 | 2733.6 | 165.4 | 170.3 | 1407.4 | 36     |
| 38  | 2639.6 | 154.0 | 158.3 | 1356.2 | 2736.8 | 165.8 | 170.8 | 1409.2 | 38     |
| 40  | 2642.8 | 154.4 | 158.7 | 1358.0 | 2740.0 | 166.2 | 171.2 | 1410.9 | 40     |
| 42  | 2646.1 | 154.8 | 159.1 | 1359.8 | 2743.3 | 166.6 | 171.6 | 1412.7 | 42     |
| 44  | 2649.3 | 155.2 | 159.5 | 1361.5 | 2746.5 | 167.0 | 172.0 | 1414.5 | 44     |
| 46  | 2652.6 | 155.6 | 160.0 | 1363.3 | 2749.7 | 167.4 | 172.5 | 1416.3 | 46     |
| 48  | 2655.8 | 156.0 | 160.4 | 1365.1 | 2753.0 | 167.8 | 172.9 | 1418.0 | 48     |
| 50  | 2659.1 | 156.3 | 160.8 | 1366.8 | 2756.2 | 168.2 | 173.3 | 1419.8 | 50     |
| 52  | 2662.3 | 156.7 | 161.2 | 1368.6 | 2759.5 | 168.6 | 173.7 | 1421.6 | 52     |
| 54  | 2665.6 | 157.1 | 161.6 | 1370.4 | 2762.7 | 169.0 | 174.1 | 1423.3 | 54     |
| 56  | 2668.8 | 157.5 | 162.0 | 1372.1 | 2765.9 | 169.4 | 174.6 | 1425.1 | 56     |
| 58  | 2672.1 | 157.9 | 162.4 | 1373.9 | 2769.2 | 169.8 | 175.0 | 1426.9 | 58     |
| 60  | 2675.3 | 158.3 | 162.8 | 1375.6 | 2772.4 | 170.2 | 175.4 | 1428.6 | 60     |
| 28 | 29    |       |       |        |        |       |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 2772.4 | 170.2 | 175.4 | 1428.6 | 2869.4 | 182.5 | 188.5 | 1481.9 | 0      |
| 2   | 2775.6 | 170.6 | 175.8 | 1430.4 | 2872.6 | 182.9 | 189.0 | 1483 7 | 2      |
| 4   | 2778.9 | 171.0 | 176.3 | 1432.2 | 2875.8 | 183.3 | 189.4 | 1485.4 | 4      |
| 6   | 2782.1 | 171.4 | 178.7 | 1434.0 | 2879.1 | 183.7 | 189.9 | 1487.2 | 6      |
| 8   | 2785.3 | 171.8 | 177.1 | 1435.7 | 2882.3 | 184.2 | 190.3 | 1489.0 | 8      |
|     |        |       |       |        |        |       |       | 28     | 29    |
|-----|--------|-------|-------|--------|--------|-------|-------|---------|--------|
|     | LC     | M     | E     | T      | LC     | M     | E     | T       |        |
| 10  | 2788.6 | 172.2 | 177.6 | 1437.5 | 2885.5 | 184.6 | 190.8 | 1490.8  | 10     |
| 12  | 2791.8 | 172.6 | 178.0 | 1439.3 | 2888.7 | 186.0 | 191.2 | 1492.6  | 12     |
| 14  | 2795.0 | 173.0 | 178.4 | 1441.1 | 2892.0 | 185.4 | 191.7 | 1494.3  | 14     |
| 16  | 2798.3 | 173.4 | 178.9 | 1442.8 | 2895.2 | 185.8 | 192.1 | 1496.1  | 16     |
| 18  | 2801.5 | 173.8 | 179.3 | 1444.6 | 2898.4 | 186.3 | 192.6 | 1497.9  | 18     |
| 20  | 2804.7 | 174.3 | 179.7 | 1446.4 | 2901.6 | 186.7 | 193.0 | 1499.7  | 20     |
| 22  | 2808.0 | 174.7 | 180.2 | 1448.2 | 2904.8 | 187.1 | 193.6 | 1501.5  | 22     |
| 24  | 2811.2 | 175.1 | 180.6 | 1449.9 | 2908.1 | 187.5 | 193.9 | 1503 2  | 24     |
| 26  | 2814.4 | 175.5 | 181.0 | 1451.7 | 2911.3 | 188.0 | 194.4 | 1505.0  | 26     |
| 28  | 2817.7 | 175.9 | 181.5 | 1453.5 | 2914.5 | 188.4 | 194.8 | 1506.8  | 28     |
| 30  | 2820.9 | 176.3 | 181.9 | 1455.2 | 2917.7 | 188.8 | 196.3 | 1508.6  | 30     |
| 32  | 2824.1 | 176.7 | 182.3 | 1457.0 | 2921.0 | 189.2 | 195.7 | 1510.4  | 32     |
| 34  | 2827.4 | 177.1 | 182.8 | 1458.8 | 2924.2 | 189.7 | 196.2 | 1512.1  | 34     |
| 36  | 2830.6 | 177.5 | 183.2 | 1460.6 | 2927.4 | 190.1 | 196 7 | 1513.9  | 36     |
| 38  | 2833.8 | 177.9 | 183.6 | 1462.3 | 2930.6 | 190.5 | 197.1 | 1515.7  | 38     |
| 40  | 2837.1 | 178.4 | 184.1 | 1464.1 | 2933.9 | 190.9 | 197.6 | 1517.6  | 40     |
| 42  | 2840.3 | 178.8 | 184.5 | 1465.9 | 2937.1 | 191.4 | 198.0 | 1519.3  | 42     |
| 44  | 2843.6 | 179.2 | 185.0 | 1467.7 | 2940.3 | 191.9 | 198.6 | 1621.0  | 44     |
| 46  | 2846.8 | 179.6 | 185.4 | 1469.5 | 2943.5 | 192.4 | 198.9 | 1622.8  | 46     |
| 48  | 2850.0 | 180.0 | 185.9 | 1471.2 | 2946.8 | 192.8 | 199.4 | 1524.6  | 48     |
| 50  | 2853.2 | 180.4 | 186.3 | 1473.0 | 2950.0 | 193.2 | 199.8 | 1526.4  | 50     |
| 52  | 2656.5 | 180.8 | 186.8 | 1474.8 | 2953.2 | 193.6 | 200.3 | 1628.2  | 52     |
| 54  | 2859.7 | 181.2 | 187.2 | 1476.6 | 2956.4 | 194.0 | 200.8 | 1 630.0 | 54     |
| 56  | 2862.9 | 181.6 | 187.6 | 1478.3 | 2959.6 | 194.4 | 201.2 | 1531.7  | 56     |
| 58  | 2866.2 | 182.0 | 188.1 | 1480.1 | 2962.9 | 194.8 | 201.7 | 1533.6  | 58     |
| 60  | 2869.4 | 182 5 | 188.5 | 1481.9 | 2966.1 | 195.2 | 202.1 | 1535.3  | 60     |
| 30 | 31    |       |       |        |        |       |       |         |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T       |        |
| 0   | 2966.1 | 195.2 | 202.1 | 1535.3 | 3062.6 | 208.4 | 216.3 | 1689.0  | 0      |
| 2   | 2969.3 | 195.6 | 202.6 | 1537.1 | 3065.8 | 208.8 | 216.8 | 1590.8  | 2      |
| 4   | 2972.5 | 196.1 | 203 1 | 1538.9 | 3069.0 | 209.3 | 217.2 | 1592.6  | 4      |
| 6   | 2975.7 | 196.5 | 203.5 | 1540.7 | 3072.2 | 209.7 | 217.7 | 1694.4  | 6      |
| 8   | 2979.0 | 197.0 | 204.0 | 1542.5 | 3075.4 | 210.2 | 218.2 | 1596.2  | 8      |
| 10  | 2982.2 | 197.4 | 204.5 | 1544.3 | 3078.6 | 210.6 | 218.7 | 1598.0  | 10     |
| 12  | 2985.4 | 197.8 | 204.9 | 1546.0 | 3081.8 | 211.1 | 219.2 | 1599.9  | 12     |
| 14  | 2988.6 | 198.2 | 205.4 | 1547.8 | 3085.0 | 211.5 | 219.6 | 1601.6  | 14     |
| 16  | 2991.8 | 198.6 | 205.9 | 1549.6 | 3088.3 | 212.0 | 220.1 | 1603.4  | 16     |
| 18  | 2995.0 | 199.1 | 206 3 | 1551.4 | 3091.5 | 212.4 | 220 6 | 1605.2  | 18     |
| 20  | 2998.3 | 199.5 | 206.8 | 1553.2 | 3094.7 | 212.9 | 221.1 | 1607.0  | 20     |
| 22  | 3001.5 | 199.9 | 207.3 | 1555.0 | 3097.9 | 213.3 | 221 6 | 1608.8  | 22     |
| 24  | 3004.7 | 200.4 | 207.7 | 1556.8 | 3101.1 | 213.8 | 222.1 | 1610.6  | 24     |
| 26  | 3007.9 | 200.8 | 208.2 | 1558.6 | 3104.3 | 214.2 | 222.6 | 1612.4  | 26     |
| 28  | 3011.1 | 201.3 | 208.7 | 1560.4 | 3107.5 | 214.7 | 223.0 | 1614.2  | 28     |
| 30  | 3014.3 | 201.7 | 209.1 | 1562.2 | 3110.7 | 215.1 | 223.5 | 1616.0  | 30     |
| 32  | 3017.6 | 202.1 | 209.6 | 1564.0 | 3113.9 | 215.6 | 224.0 | 1617.8  | 32     |
| 34  | 3020.8 | 202.6 | 210.1 | 1565.7 | 3117.1 | 216.0 | 224.5 | 1619.6  | 34     |
| 36  | 3024.0 | 203.0 | 210.5 | 1567.5 | 3120.3 | 216.5 | 225.0 | 1621.4  | 36     |
| 38  | 3027.2 | 203.5 | 211.0 | 1569.3 | 3123.5 | 216.9 | 225.5 | 1623.2  | 38     |
| 40  | 3030.4 | 203.9 | 211.5 | 1571.1 | 3126.7 | 217.4 | 226.0 | 1625.0  | 40     |
| 42  | 3033.6 | 204.3 | 212.0 | 1572.9 | 3129.9 | 217.8 | 226.5 | 1626.8  | 42     |
| 44  | 3036.9 | 204.8 | 212.4 | 1574.7 | 3133.1 | 218.3 | 227.0 | 1628.6  | 44     |
|     |        |       |       |        |        |       |       | 30    | 31    |
|-----|--------|-------|-------|--------|--------|-------|-------|--------|--------|
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 46  | 3040.1 | 205.2 | 212.9 | 1576.5 | 3136.4 | 218.7 | 227.5 | 1630.5 | 46     |
| 48  | 3043.3 | 205.7 | 213.4 | 1578.3 | 3139.6 | 219.2 | 228.0 | 1632.3 | 48     |
| 50  | 3046.5 | 206.1 | 213.9 | 1580.1 | 3142.8 | 219.6 | 228.4 | 1634.1 | 50     |
| 52  | 3049.7 | 206 5 | 214.4 | 1581.9 | 3146.0 | 220.1 | 228.9 | 1635.9 | 52     |
| 54  | 3052.9 | 207 0 | 214.8 | 1583.7 | 3149.2 | 220.5 | 229 4 | 1637.7 | 54     |
| 56  | 3056.2 | 207.4 | 215.3 | 1585.5 | 3152.4 | 221.0 | 229.9 | 1639.5 | 56     |
| 58  | 3059.4 | 207.9 | 215.8 | 1587.2 | 3155.6 | 221.5 | 230.4 | 1641.3 | 58     |
| 60  | 3062.6 | 208.4 | 216.3 | 1589.0 | 3158.8 | 222.0 | 230.9 | 1643.1 | 60     |
| 32 | 33    |       |       |        |        |       |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 3158.6 | 222.0 | 230.9 | 1643.1 | 3245.9 | 236.0 | 246.1 | 1697.3 | 0      |
| 2   | 3162.0 | 222.5 | 231.4 | 1644.9 | 3258.1 | 236.4 | 246.6 | 1699,1 | 2      |
| 4   | 3165.2 | 222.9 | 231.9 | 1646.7 | 3261.3 | 236.9 | 247.1 | 1700.9 | 4      |
| 6   | 3168.4 | 223.4 | 232.4 | 1648.5 | 3264.5 | 237.4 | 247.7 | 1702.7 | 6      |
| 8   | 3171.6 | 223.8 | 232.9 | 1650.3 | 3267.7 | 237.9 | 248.2 | 1704.5 | 8      |
| 10  | 3174.8 | 224.3 | 233.4 | 1652.1 | 3270.8 | 238.4 | 248.7 | 1706.4 | 10     |
| 12  | 3178.0 | 224.8 | 233.9 | 1653.9 | 3274.0 | 238.9 | 249.2 | 1708.2 | 12     |
| 14  | 3181.2 | 225.2 | 234.4 | 1655.7 | 3277.2 | 239.3 | 249.7 | 1710.0 | 14     |
| 16  | 3184.4 | 225.7 | 234.9 | 1657.5 | 3280.4 | 239.8 | 250.2 | 1711.8 | 16     |
| 18  | 3187.6 | 226.1 | 235.4 | 1659.3 | 3283.6 | 240.3 | 250.8 | 1713.6 | 18     |
| 20  | 3190.8 | 226.6 | 235 9 | 1661.1 | 3286.8 | 240.8 | 251.3 | 1715.5 | 20     |
| 22  | 3194.0 | 227.1 | 236.4 | 1662.9 | 3290.0 | 241.2 | 251.3 | 1717.3 | 22     |
| 24  | 3197.2 | 227.5 | 236.9 | 1664.7 | 3293.2 | 241.7 | 252.3 | 1719.1 | 24     |
| 26  | 3200.4 | 228.0 | 237.4 | 1666.5 | 3296.4 | 242.2 | 252.9 | 1720.9 | 26     |
| 28  | 3203.6 | 228.4 | 237.9 | 1668.3 | 3299.6 | 242.7 | 253.4 | 1722.7 | 28     |
| 30  | 3206.8 | 228.3 | 236 4 | 1670.1 | 3302.7 | 243,2 | 253.9 | 1724.6 | 30     |
| 32  | 3210.0 | 229.4 | 239.0 | 1671.9 | 3305.9 | 243.6 | 254.4 | 1726.4 | 32     |
| 34  | 3213.2 | 229.8 | 239.5 | 1673.7 | 3309.1 | 244.1 | 255.0 | 1728.2 | 34     |
| 36  | 3216.5 | 230.3 | 240.0 | 1675.5 | 3312.3 | 244.6 | 255.5 | 1730.0 | 36     |
| 38  | 3219.7 | 230.7 | 240.5 | 1677.4 | 3315.5 | 245.1 | 256.0 | 1731.8 | 38     |
| 40  | 3222.9 | 231.2 | 241.0 | 1679.2 | 3318.7 | 245.6 | 256.5 | 1733.6 | 40     |
| 42  | 3226.1 | 231.7 | 241.5 | 1681.0 | 3321.9 | 246.0 | 257.1 | 1735.5 | 42     |
| 44  | 3229.3 | 232.2 | 242.0 | 1682.8 | 3325.1 | 246.5 | 257.6 | 1737.3 | 44     |
| 46  | 3232.5 | 232.6 | 242.5 | 1384.6 | 3328.3 | 247.0 | 258.1 | 1738.1 | 46     |
| 48  | 3235.7 | 233.1 | 243.0 | 1686 4 | 3331.5 | 247.5 | 258.6 | 1740.9 | 48     |
| 50  | 3289.9 | 233.5 | 243.5 | 1688.2 | 3334.6 | 248.0 | 259.2 | 1742.7 | 50     |
| 52  | 3242.1 | 234.0 | 244.1 | 1690.0 | 3337.8 | 248.4 | 259.7 | 1744.6 | 52     |
| 54  | 3245.3 | 234.5 | 244.6 | 1691.8 | 3341 o | 248.9 | 260.2 | 1745.4 | 54     |
| 56  | 3248.5 | 235.0 | 245.1 | 1693.7 | 3344.2 | 249.4 | 260.8 | 1748.2 | 56     |
| 58  | 3251.7 | 235.5 | 245.6 | 1695.5 | 3347.4 | 249.9 | 261.3 | 1750.0 | 58     |
| 60  | 3254.9 | 236.0 | 246.1 | 1697.3 | 3350.6 | 250.4 | 261.8 | 1751.8 | 60     |
| 34 | 35    |       |       |        |        |       |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 3350.6 | 250.4 | 261.8 | 1751.8 | 3446.1 | 265.2 | 278.1 | 1806.7 | 0      |
| 2   | 3353.8 | 250.8 | 262.3 | 1753.7 | 3449.3 | 265.7 | 278.6 | 1808.5 | 2      |
| 4   | 3357.0 | 251.2 | 262.9 | 1755.5 | 3452.5 | 266.2 | 279.2 | 1810.3 | 4      |
| 6   | 3360.1 | 251.7 | 263.4 | 1757.3 | 3455.6 | 266.7 | 279.7 | 1812.2 | 6      |
| 8   | 3363.3 | 252.2 | 264.0 | 1759.1 | 3458 8 | 267.2 | 280.3 | 1814.0 | 8      |
| 10  | 3366.5 | 252.7 | 264.5 | 1761.0 | 3462.0 | 267.7 | 280.8 | 1815.8 | 10     |
| 12  | 3369.7 | 253.2 | 265.0 | 1762.8 | 3465.2 | 268.2 | 281.4 | 1817.7 | 12     |
| 14  | 3372.9 | 253.7 | 265.6 | 1764.6 | 3468.3 | 268.7 | 281.9 | 1819.5 | 14     |
| 16  | 3376.1 | 254.2 | 266.1 | 1766.4 | 3471.5 | 269.2 | 282.5 | 1821.3 | 16     |
|     |        |       |       |        |        |       |       | 34    | 35    |
|-----|--------|-------|-------|--------|--------|-------|-------|--------|--------|
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 18  | 3379.2 | 254.7 | 266.7 | 1768.3 | 3474.7 | 269.7 | 283.0 | 1823.2 | 18     |
| 20  | 3382.4 | 255.2 | 267.2 | 1770.1 | 3477.9 | 270.2 | 283.6 | 1825.0 | 20     |
| 22  | 3385.6 | 255.7 | 267.7 | 1771.9 | 3481.0 | 270.7 | 284.2 | 1826.8 | 22     |
| 24  | 3388 8 | 256.2 | 268.3 | 1773.7 | 3484.2 | 271.2 | 284.7 | 1828.7 | 24     |
| 26  | 3392.0 | 256.7 | 268.8 | 1775.6 | 3487.4 | 271.7 | 285.3 | 1830.5 | 26     |
| 28  | 3395.2 | 257.2 | 269.3 | 1777.4 | 3490.6 | 272.2 | 285.9 | 1832.3 | 28     |
| 30  | 3398.3 | 257.7 | 269.9 | 1779.2 | 3493.7 | 272.7 | 286.4 | 1834.2 | 30     |
| 32  | 3401.5 | 258.2 | 270.4 | 1781.0 | 3496.9 | 273.2 | 287.0 | 1836.0 | 32     |
| 34  | 3404.7 | 258.7 | 271.0 | 1782.9 | 3500.1 | 273.7 | 287.5 | 1837.8 | 34     |
| 36  | 3407.9 | 259.2 | 271.5 | 1784.7 | 3503.3 | 274.2 | 288.1 | 1839.7 | 36     |
| 38  | 3411.1 | 259.7 | 272.0 | 1786.5 | 3506.5 | 274.7 | 288.7 | 1841.5 | 38     |
| 40  | 3414.3 | 260.2 | 272.6 | 1788.4 | 3503.6 | 275.2 | 289.2 | 1843.4 | 40     |
| 42  | 3417.4 | 260.7 | 273.1 | 1790.2 | 3512.8 | 275.7 | 289.8 | 1845.2 | 42     |
| 44  | 3420.6 | 261.2 | 273.7 | 1792.0 | 3516.0 | 276.2 | 290.4 | 1847.1 | 44     |
| 46  | 3423.8 | 261.7 | 274.2 | 1793.9 | 3519.2 | 276.7 | 290.9 | 1848.9 | 46     |
| 48  | 3427.0 | 262.2 | 274.8 | 1795.7 | 3522.3 | 277.2 | 291.5 | 1850.7 | 48     |
| 50  | 3430.2 | 262.7 | 275.3 | 1797.5 | 3525.5 | 277.7 | 292.0 | 1852.6 | 50     |
| 52  | 3433.4 | 263.2 | 275.9 | 1799.3 | 3528.7 | 278.2 | 292.6 | 1854.4 | 52     |
| 54  | 3436.5 | 263.7 | 276.4 | 1801.2 | 3531.9 | 278.7 | 293.2 | 1856.3 | 54     |
| 56  | 3439.7 | 264.2 | 277.0 | 1803.0 | 3535.0 | 279.2 | 293.7 | 1858.1 | 56     |
| 58  | 3442.9 | 264.7 | 277.5 | 1804.8 | 3538.2 | 279.8 | 294.3 | 1859.9 | 58     |
| 60  | 3446.1 | 265.2 | 278.1 | 1806.7 | 3241.4 | 280.4 | 294.9 | 1861.8 | 60     |
| 36 | 37    |       |       |        |        |       |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 3541.4 | 280.4 | 294.9 | 1861.8 | 3636.3 | 296.1 | 312.3 | 1917.3 | 0      |
| 2   | 3544.6 | 280.9 | 295.4 | 1863.6 | 3639.5 | 296.6 | 312.8 | 1919.1 | 2      |
| 4   | 3547.7 | 281.4 | 296.0 | 1865.5 | 3642.6 | 297.1 | 313.4 | 1921.0 | 4      |
| 6   | 3550.9 | 281.9 | 296.6 | 1867.3 | 3645.8 | 297.7 | 314.0 | 1922.8 | 6      |
| 8   | 3554.0 | 282.5 | 297.2 | 1869.2 | 3648.9 | 298.2 | 314.6 | 1924.7 | 8      |
| 10  | 3557.2 | 283.0 | 297.7 | 1871.0 | 3652.1 | 298.7 | 315.2 | 1926.5 | 10     |
| 12  | 3560.4 | 283.5 | 298.3 | 1872.9 | 3655.2 | 299.3 | 315.8 | 1928.4 | 12     |
| 14  | 3563.5 | 234.0 | 298.9 | 1874.7 | 3658.4 | 299.8 | 316.4 | 1930.2 | 14     |
| 16  | 3566.7 | 284.6 | 299.5 | 1876.5 | 3661.6 | 300.3 | 317.0 | 1932.1 | 16     |
| 18  | 3583.9 | 285.1 | 300.0 | 1878.4 | 3664.7 | 300.9 | 317.5 | 1933.9 | 18     |
| 20  | 3573.0 | 285.6 | 300.6 | 1880.2 | 3667.9 | 301.4 | 318.1 | 1935.8 | 20     |
| 22  | 3576.2 | 286.1 | 301.2 | 1882.1 | 3671.0 | 301.9 | 318.7 | 1937.6 | 22     |
| 24  | 3579.4 | 286.7 | 301.8 | 1883.9 | 3674.2 | 302.5 | 319.3 | 1939.5 | 24     |
| 26  | 3582.5 | 287.2 | 302.3 | 1885.8 | 3677.3 | 303.0 | 319.9 | 1941.3 | 26     |
| 28  | 3585.7 | 287.7 | 302.9 | 1887.6 | 3680.5 | 303.5 | 320.5 | 1943.2 | 28     |
| 30  | 3588.8 | 288.2 | 303.5 | 1889.5 | 3683.6 | 304.1 | 321.1 | 1945.0 | 30     |
| 32  | 3592.0 | 288.8 | 304.1 | 1891.3 | 3686.8 | 304.6 | 321.7 | 1946.9 | 32     |
| 34  | 3535.2 | 283.3 | 304.6 | 1833.2 | 3630.0 | 305.1 | 322.3 | 1343.8 | 34     |
| 36  | 3598.3 | 289.8 | 305.2 | 1895.0 | 3633.1 | 305.7 | 322.9 | 1950.6 | 36     |
| 38  | 3601.5 | 290.3 | 305.8 | 1836.3 | 3686.3 | 306.2 | 323.5 | 1952.5 | 38     |
| 40  | 3604.7 | 290.9 | 306.4 | 1898.7 | 3699.4 | 306.7 | 324.2 | 1954.4 | 40     |
| 42  | 3607.8 | 291.4 | 307.0 | 1900.6 | 3702.6 | 307.3 | 324.8 | 1956.2 | 42     |
| 44  | 3611.0 | 291.9 | 307.5 | 1902.4 | 3705.7 | 307.8 | 325.4 | 1958.1 | 44     |
| 46  | 3614.1 | 292.4 | 308.1 | 1904.3 | 3708.9 | 308.3 | 326.0 | 1960.0 | 46     |
| 48  | 3617.3 | 293.0 | 308 7 | 1906.1 | 3712.1 | 308.9 | 326.6 | 1961.8 | 48     |
| 50  | 3620.5 | 293.5 | 309.3 | 1908.0 | 3715.2 | 309.4 | 327.2 | 1963.7 | 50     |
| 52  | 3623.6 | 294.0 | 309.9 | 1909.8 | 3718.4 | 309.9 | 327.8 | 1965.5 | 52     |
|     |        |       |       |        |        |       |       | 36    | 37    |
|-----|--------|-------|-------|--------|--------|-------|-------|--------|--------|
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 54  | 3626.8 | 294.5 | 310.5 | 19117  | 3721.5 | 310.5 | 328.4 | 1967.4 | 54     |
| 56  | 3630.0 | 295.1 | 311.1 | 1913.5 | 3724.7 | 311.0 | 329.0 | 1969.3 | 56     |
| 58  | 3633.1 | 295.6 | 311.7 | 1915.4 | 3727.8 | 311.6 | 329.6 | 1971.1 | 58     |
| 60  | 3636.3 | 296.1 | 312.3 | 1917.3 | 3731.0 | 312.2 | 330.2 | 1973.0 | 60     |
| 38 | 39    |       |       |        |        |       |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 3731.0 | 312.2 | 330.2 | 1973.0 | 3825.5 | 328.7 | 348.7 | 2029.1 | 0      |
| 2   | 3734 1 | 312.7 | 330.8 | 1974.3 | 3828.6 | 323.2 | 349.3 | 2031.0 | 2      |
| 4   | 3737.3 | 313.3 | 331.4 | 1976.7 | 3831.8 | 329.8 | 343.8 | 2032.9 | 4      |
| 6   | 3740.4 | 313.8 | 332.0 | 1978.6 | 3834.9 | 330.3 | 350.6 | 2034.7 | 6      |
| 8   | 3743.6 | 314.4 | 332.6 | 1980.5 | 3838.0 | 330.9 | 351.2 | 2036.6 | 8      |
| 10  | 3746.7 | 314.8 | 333.2 | 1982.3 | 3841.2 | 331.5 | 351.8 | 2038.5 | 10     |
| 12  | 3749.9 | 315.5 | 333.8 | 1984.2 | 3844.3 | 332.0 | 352.4 | 2040.4 | 12     |
| 14  | 3753.0 | 316.0 | 334.5 | 1986.1 | 3847.4 | 332.6 | 353.1 | 2042.3 | 14     |
| 16  | 3756.2 | 316.6 | 335.1 | 1987.9 | 3850.6 | 333.2 | 353.7 | 2044.1 | 16     |
| 18  | 3759.3 | 317.1 | 335.7 | 1989.8 | 3853.7 | 333.7 | 354.3 | 2046.0 | 18     |
| 20  | 3762.5 | 317.7 | 336.3 | 1991.7 | 3856.8 | 334.3 | 354.0 | 2047.9 | 20     |
| 22  | 3765.6 | 318.2 | 336.5 | 1993.6 | 3860.0 | 334.3 | 355.6 | 2043.3 | 22     |
| 24  | 3768.8 | 318.8 | 337.5 | 1995.4 | 3863.1 | 335.4 | 356.2 | 2051.7 | 24     |
| 26  | 3771.9 | 319.3 | 338.1 | 1997.3 | 3866.2 | 336.0 | 356.3 | 2053.5 | 26     |
| 28  | 3775.1 | 319.9 | 338.7 | 1999.2 | 3869.4 | 336.6 | 357.5 | 2055.4 | 28     |
| 30  | 3778.2 | 320.4 | 339.4 | 2001.0 | 3872.5 | 337.1 | 358.1 | 2057.3 | 30     |
| 32  | 3781.4 | 321.0 | 340.0 | 2002.9 | 3875.6 | 337.7 | 358.8 | 2059.2 | 32     |
| 34  | 3784.5 | 321.5 | 340.6 | 2004.8 | 3878.8 | 338.3 | 353.4 | 2061.1 | 34     |
| 36  | 3787.7 | 322.1 | 341.2 | 2006.6 | 3881.9 | 338.8 | 360.1 | 2063.0 | 36     |
| 38  | 3790.8 | 322.6 | 341.8 | 2008 5 | 3885.0 | 339.4 | 360.7 | 2064.8 | 38     |
| 40  | 3794.0 | 323.2 | 342.4 | 2010.4 | 3888.2 | 340.0 | 361.3 | 2066.7 | 40     |
| 42  | 3797.1 | 323.7 | 343.1 | 2012.3 | 3891.3 | 340.5 | 362.0 | 2068.6 | 42     |
| 44  | 3800.3 | 324.3 | 343.7 | 2014.1 | 3894.4 | 341.1 | 362.6 | 2070.5 | 44     |
| 46  | 3803.4 | 324.8 | 344.3 | 2016.0 | 3897.6 | 341.7 | 363.3 | 2072.4 | 46     |
| 48  | 3806.6 | 325.4 | 344.9 | 2017.9 | 3900.7 | 342.2 | 363.9 | 2074.2 | 48     |
| 50  | 3809.7 | 325.9 | 345.6 | 2019.7 | 3903.8 | 342.8 | 364.5 | 2076.1 | 50     |
| 52  | 3812.9 | 326.5 | 346.2 | 2021.6 | 3907.0 | 343.4 | 365.2 | 2078.0 | 52     |
| 54  | 3816.0 | 327.0 | 346.8 | 2023.5 | 3910.1 | 343.9 | 365.8 | 2079.9 | 54     |
| 56  | 3819.2 | 327.6 | 347.4 | 2025.4 | 3913.2 | 344.5 | 366.5 | 2081.8 | 56     |
| 58  | 3822.3 | 328.1 | 348.1 | 2027.2 | 3916.4 | 345.1 | 367.1 | 2083.7 | 58     |
| 60  | 3825.5 | 328.7 | 348.7 | 2029.1 | 3919.5 | 345.6 | 367.7 | 2035.5 | 60     |
| 40 | 41    |       |       |        |        |       |       |        |        |
|     | LC     | m     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 3919.5 | 345.6 | 367.7 | 2085.5 | 4013.4 | 362.9 | 387.4 | 2142.3 | 0      |
| 2   | 3922.6 | 346 1 | 368.4 | 2087.4 | 4016.5 | 363.4 | 388.1 | 2144.2 | 2      |
| 4   | 3925.8 | 346.7 | 369.0 | 2089.3 | 4019.6 | 364.0 | 388.8 | 2146.1 | 4      |
| 6   | 3928.9 | 347.2 | 369.7 | 2091.2 | 4022.7 | 364.5 | 389.4 | 2148.0 | 6      |
| 8   | 3932.0 | 347.8 | 370.3 | 2093.1 | 4025.9 | 365.1 | 390.1 | 2149.9 | 8      |
| 10  | 3935.1 | 348.4 | 371.0 | 2095.0 | 4029.0 | 365.6 | 390.7 | 2151.9 | 10     |
| 12  | 3938.3 | 348.9 | 371.6 | 2096.9 | 4032.1 | 366.2 | 391.4 | 2153.8 | 12     |
| 14  | 3941.4 | 349.5 | 372.3 | 2098.8 | 4035.2 | 366.8 | 392.1 | 2155.7 | 14     |
| 16  | 3944.5 | 350.1 | 372.9 | 2100.7 | 4038.3 | 367.4 | 392.7 | 2157.6 | 16     |
| 18  | 3947.7 | 350.7 | 373.6 | 2102.6 | 4041.4 | 368.0 | 393.4 | 2159.5 | 18     |
| 20  | 3950.8 | 351.3 | 374.3 | 2104.5 | 4044.6 | 368.6 | 394.1 | 2161.4 | 20     |
| 22  | 3953.9 | 351.8 | 374.9 | 2106.3 | 4047.7 | 369.2 | 394.7 | 2163.3 | 22     |
|     |        |       |       |        |        |       |       | 40    | 41    |
|-----|--------|-------|-------|--------|--------|-------|-------|--------|--------|
|     | LC     | m     | E     | T      | LC     | M     | E     | T      |        |
| 24  | 3957.1 | 352.4 | 375.6 | 2108.2 | 4050.8 | 369.8 | 395.4 | 2165.2 | 24     |
| 26  | 3960.2 | 353.0 | 376.2 | 2110.1 | 4053.9 | 370.4 | 396.1 | 2167.1 | 26     |
| 28  | 3963.3 | 353.6 | 376.9 | 2112.0 | 4057.0 | 371.0 | 396.8 | 2169.0 | 28     |
| 30  | 3966.4 | 354.2 | 377.5 | 2113.9 | 4060.1 | 371.6 | 397.5 | 2170.9 | 30     |
| 32  | 3969.6 | 354.7 | 378.2 | 2115.8 | 4063.3 | 372.2 | 398.1 | 2172.8 | 32     |
| 34  | 3972.7 | 355.3 | 378.8 | 2117.7 | 4066.4 | 372.8 | 398.8 | 2174.7 | 34     |
| 36  | 3975.8 | 355.9 | 379.5 | 2119.6 | 4069.5 | 373.4 | 399.5 | 2176.6 | 36     |
| 38  | 3979.0 | 356.5 | 380.1 | 2121.5 | 4072.6 | 374.0 | 400.2 | 2178.5 | 38     |
| 40  | 3982.1 | 357.1 | 380 8 | 2123.4 | 4075.7 | 374.6 | 400.9 | 2180.4 | 40     |
| 42  | 3985.2 | 357.6 | 381.4 | 2125.3 | 4078.8 | 375.2 | 401.5 | 2182.4 | 42     |
| 44  | 3988.4 | 358.2 | 382.1 | 2127.2 | 4082.0 | 375.8 | 402.2 | 2184.3 | 44     |
| 46  | 3991.5 | 358.6 | 382.8 | 2129.1 | 4085.1 | 376.4 | 402.9 | 2186.2 | 46     |
| 48  | 3994.6 | 359.4 | 383.4 | 2131.0 | 4088.2 | 377.0 | 403.6 | 2188.1 | 48     |
| 50  | 3997.7 | 360.0 | 384.1 | 2132.9 | 4091.3 | 377.6 | 404.3 | 2190.0 | 50     |
| 52  | 4000.9 | 360.5 | 384.8 | 2134.7 | 4094.4 | 378.2 | 404.9 | 2191.9 | 52     |
| 54  | 4004.0 | 361.1 | 385.4 | 2136.6 | 4097.5 | 378.8 | 405.6 | 2193.8 | 54     |
| 56  | 4007.1 | 361.7 | 386.1 | 2138.5 | 4100.7 | 379.4 | 406.3 | 2195.7 | 56     |
| 58  | 4010.3 | 362.3 | 386.8 | 2140.4 | 4103.8 | 380.0 | 407.0 | 2197.6 | 58     |
| 60  | 4013.4 | 362.9 | 387.4 | 2142.3 | 4106.9 | 380.6 | 407.7 | 2199.5 | 60     |
| 42 | 43    |       |       |        |        |       |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 4106.9 | 380.6 | 407.7 | 2199.5 | 4200.1 | 398.7 | 428.6 | 2257.1 | 0      |
| 2   | 4110.0 | 381.2 | 408.3 | 2201.4 | 4203.2 | 399.3 | 429.3 | 2259.0 | 2      |
| 4   | 4113.1 | 381.8 | 409.0 | 2203.3 | 4206.3 | 399.9 | 430.0 | 2261.0 | 4      |
| 6   | 4116 2 | 382 4 | 409.7 | 2205 3 | 4209.4 | 400.5 | 430.7 | 2262.9 | 6      |
| 8   | 4119.3 | 383.0 | 410.4 | 2207.2 | 4212.5 | 401.1 | 431.4 | 2264.8 | 8      |
| 10  | 4122 4 | 383 6 | 411.1 | 2209.1 | 4215.6 | 401.7 | 432.1 | 2266.7 | 10     |
| 12  | 4125.5 | 384.2 | 411.8 | 2211.0 | 4218.7 | 402.4 | 432.8 | 2268.7 | 12     |
| 14  | 4128 6 | 384 8 | 412.5 | 2212 9 | 4221.8 | 403.0 | 433.5 | 2270.6 | 14     |
| 16  | 4131.8 | 385.4 | 413.2 | 2214.9 | 4224.9 | 403.6 | 434.2 | 2272.5 | 16     |
| 18  | 4134 9 | 386.0 | 413.9 | 2216.8 | 4228.0 | 404.2 | 434.9 | 2274.5 | 18     |
| 20  | 4138.0 | 386.6 | 414.6 | 2218.7 | 4231.0 | 404.8 | 435.6 | 2276.4 | 20     |
| 22  | 4141.1 | 387.2 | 415.3 | 2220.6 | 4234.2 | 405.4 | 436.3 | 2278.3 | 22     |
| 24  | 4144.2 | 387.8 | 416.0 | 2222.5 | 4237.3 | 406.1 | 437.0 | 2280.2 | 24     |
| 26  | 4147.3 | 388.4 | 416.6 | 2224.4 | 4240.4 | 406.7 | 437.8 | 2282.2 | 26     |
| 28  | 4150.4 | 389.0 | 417.3 | 2226.4 | 4243.5 | 407.3 | 438.5 | 2284.1 | 28     |
| 30  | 4153.5 | 389.6 | 418.0 | 2228.3 | 4246.5 | 407.9 | 439.2 | 2286.0 | 30     |
| 32  | 4156.6 | 390.2 | 418.7 | 2230.2 | 4249.6 | 408.5 | 439.9 | 2288.0 | 32     |
| 34  | 4159.7 | 390.8 | 419.4 | 2232.1 | 4252.7 | 409.1 | 440.6 | 2289.9 | 34     |
| 36  | 4162.8 | 391.4 | 420.1 | 2234.0 | 4255.8 | 409.8 | 441.4 | 2291.8 | 36     |
| 38  | 4165.9 | 392.0 | 420.8 | 2236.0 | 4258.9 | 410.4 | 442.1 | 2293.8 | 38     |
| 40  | 4169.0 | 392.6 | 421.5 | 2237.9 | 4262.0 | 411.0 | 442.8 | 2295.7 | 40     |
| 42  | 4172.1 | 393.2 | 422.2 | 2239.8 | 4265.1 | 411.6 | 443.5 | 2297.7 | 42     |
| 44  | 4175.2 | 393.8 | 422.9 | 2241.7 | 4268.2 | 412.2 | 444.2 | 2299.6 | 44     |
| 46  | 4178.4 | 394.4 | 423.6 | 2243.6 | 4271.3 | 412.8 | 445.0 | 2301.5 | 46     |
| 48  | 4181.5 | 395.0 | 424.3 | 2245.6 | 4274.4 | 413.5 | 445.7 | 2303.5 | 48     |
| 50  | 4184.6 | 395.6 | 425.0 | 2247.5 | 4277.5 | 414.1 | 446.4 | 2305.4 | 50     |
| 52  | 4187.7 | 396.2 | 425.7 | 2249.4 | 4280.6 | 414.7 | 447.1 | 2307.3 | 52     |
| 54  | 4190.8 | 396.8 | 426.4 | 2251.3 | 4283.7 | 415.3 | 447.8 | 2309.3 | 54     |
| 56  | 4193.9 | 397.4 | 427.1 | 2253.3 | 4286.8 | 415.9 | 448.6 | 2311.2 | 56     |
| 58  | 4197.0 | 398.0 | 427.8 | 2255.2 | 4289.9 | 416.5 | 449.3 | 2313.1 | 58     |
| 60  | 4200.1 | 398.7 | 428.6 | 2257.1 | 4293.0 | 417.2 | 450.0 | 2315.1 | 60     |
|     |        |       |       |        |        |       |       | 44    | 45    |
|-----|--------|-------|-------|--------|--------|-------|-------|--------|--------|
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 4293.0 | 417.2 | 450.0 | 2315.1 | 4385.5 | 436.2 | 472.1 | 2373.4 | 0      |
| 2   | 4296.1 | 417.8 | 450.7 | 2317.0 | 4388.6 | 436.8 | 472.9 | 2375.4 | 2      |
| 4   | 4299.2 | 418.4 | 451.5 | 2319.0 | 4331.7 | 437.5 | 473.6 | 2377.3 | 4      |
| 6   | 4302.2 | 419.1 | 452.2 | 2320.9 | 4394.7 | 438.1 | 474.4 | 2379.3 | 6      |
| 8   | 4305.3 | 419.7 | 452.9 | 2322.8 | 4397.8 | 438.8 | 475.1 | 2381.2 | 8      |
| 10  | 4308.4 | 420.3 | 453.7 | 2324.8 | 4400.9 | 439.4 | 475.9 | 2383.2 | 10     |
| 12  | 4311.5 | 421.0 | 454.4 | 2326.7 | 4404.0 | 440.0 | 476.6 | 2385.2 | 12     |
| 14  | 4314.6 | 421.6 | 455.1 | 2328.7 | 4407.0 | 440.7 | 477.4 | 2387.1 | 14     |
| 16  | 4317.7 | 422.2 | 455.9 | 2330.6 | 4410.1 | 441.3 | 478.1 | 2389.1 | 16     |
| 18  | 4320.7 | 422.9 | 456.6 | 2332.6 | 4413.2 | 442.0 | 478.9 | 2391.0 | 18     |
| 20  | 4323.8 | 423.5 | 457.3 | 2334.5 | 4416.3 | 442.6 | 479.6 | 2393.0 | 20     |
| 22  | 4326.9 | 424.1 | 458.1 | 2336.4 | 4419.3 | 443.2 | 480.4 | 2394.9 | 22     |
| 24  | 4330.0 | 424.8 | 458.8 | 2338.4 | 4422.4 | 443.9 | 481.1 | 2396.9 | 24     |
| 26  | 4333.1 | 425.4 | 459.5 | 2340.3 | 4425.5 | 444.5 | 481.9 | 2398.8 | 26     |
| 28  | 4336.2 | 426.0 | 460.3 | 2342.3 | 4428.6 | 445.2 | 482.6 | 2400.8 | 28     |
| 30  | 4339.2 | 426.7 | 461.0 | 2344.2 | 4431.6 | 445.8 | 483.4 | 2402.8 | 30     |
| 32  | 4342.3 | 427.3 | 461.7 | 2346.1 | 4434.7 | 446.4 | 484.2 | 2404.7 | 32     |
| 34  | 4345.4 | 427.9 | 462.5 | 2348.1 | 4437.8 | 447.1 | 484.9 | 2406.7 | 34     |
| 36  | 4348.5 | 428.6 | 463.2 | 2350.0 | 4440.9 | 447.7 | 485.7 | 2408.6 | 36     |
| 38  | 4351.6 | 429.2 | 463.9 | 2352.0 | 4444.0 | 448.3 | 486.5 | 2410.6 | 38     |
| 40  | 4354.7 | 429.8 | 464.7 | 2353.9 | 4447.0 | 448.9 | 487.2 | 2412.6 | 40     |
| 42  | 4357.7 | 430.5 | 465.4 | 2355.9 | 4450.1 | 449.5 | 488.0 | 2414.5 | 42     |
| 44  | 4360.8 | 431.1 | 466.2 | 2357.8 | 4453.2 | 450.2 | 488.7 | 2416.5 | 44     |
| 46  | 4363.9 | 431.7 | 466.9 | 2359.8 | 4456.3 | 450.8 | 489.5 | 2418.5 | 46     |
| 48  | 4367.0 | 432.4 | 467.7 | 2361.7 | 4459.3 | 451.5 | 490.3 | 2420.4 | 48     |
| 50  | 4370.1 | 433.0 | 468.4 | 2363.7 | 4462.4 | 452.1 | 491.0 | 2422.4 | 50     |
| 52  | 4373.2 | 433.6 | 469.1 | 2365.5 | 4465.5 | 452.7 | 491.8 | 2424.4 | 52     |
| 54  | 4376.2 | 434.3 | 469.9 | 2367.6 | 4468.6 | 453.4 | 492.5 | 2426.3 | 54     |
| 56  | 4379.3 | 434.9 | 470.6 | 2369.5 | 4471.6 | 454.1 | 493.3 | 2428.3 | 56     |
| 58  | 4382.4 | 435.6 | 471.4 | 2371.5 | 4474.7 | 454.8 | 494.1 | 2430.2 | 58     |
| 60  | 4385.5 | 436.2 | 472.1 | 2373.4 | 4477.8 | 455.5 | 494.8 | 2432.2 | 60     |
| 46 | 47    |       |       |        |        |       |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 4477.8 | 455.5 | 494.8 | 2432.2 | 4569.7 | 475.2 | 518.3 | 2491.5 | 0      |
| 2   | 4480.9 | 456.1 | 4S5.6 | 2434.2 | 4572.7 | 475.8 | 513.0 | 2483.4 | 2      |
| 4   | 4483.9 | 456.8 | 496.5 | 2436.1 | 4575.8 | 476.5 | 519.8 | 2495.4 | 4      |
| 6   | 4487.0 | 457.4 | 497.2 | 2438.1 | 4578.8 | 477.2 | 520.5 | 2437.4 | 6      |
| 8   | 4490.0 | 458.1 | 497.9 | 2440.1 | 4581.9 | 477.8 | 521.4 | 2499.4 | 8      |
| 10  | 4493.1 | 458.7 | 498.7 | 2442.1 | 4584.9 | 478.5 | 522.2 | 2501.4 | 10     |
| 12  | 4496.2 | 459.4 | 499.5 | 2444.0 | 4588.0 | 479.2 | 523.0 | 2503.4 | 12     |
| 14  | 4499.2 | 460.0 | 500.3 | 2446.0 | 4591.0 | 479.8 | 523.8 | 2505.4 | 14     |
| 16  | 4502.3 | 460.7 | 501.0 | 2448.0 | 4594.1 | 480.5 | 524.6 | 2507.3 | 16     |
| 18  | 4505.4 | 461.3 | 501.8 | 2449.9 | 4597.1 | 481.1 | 525.4 | 2509.3 | 18     |
| 20  | 4508.4 | 462.0 | 502.6 | 2451.9 | 4600.2 | 481.7 | 526.2 | 2511.3 | 20     |
| 22  | 4511.5 | 462.7 | 503.4 | 2453.9 | 4603.2 | 482.3 | 527.0 | 2513.3 | 22     |
| 24  | 4514.6 | 463.3 | 504.1 | 2455.9 | 4606.3 | 483.0 | 527.8 | 2515.3 | 24     |
| 26  | 4517.6 | 464.0 | 504.9 | 2457.8 | 4609.3 | 483.7 | 528.6 | 2517.3 | 26     |
| 28  | 4520.7 | 464.6 | 505.7 | 2459.8 | 4612.4 | 484.3 | 529.4 | 2519.3 | 28     |
| 30  | 4523.7 | 465.3 | 506.5 | 2461.8 | 4615.4 | 485.0 | 530.2 | 2521.2 | 30     |
| 32  | 4526.8 | 466.0 | 507.3 | 2463.8 | 4618.5 | 485.7 | 531.0 | 2523.2 | 32     |
| 34  | 4529.9 | 466.6 | 508.0 | 2465.7 | 4621.5 | 486.3 | 531.8 | 2525.2 | 34     |
|     |        |       |       |        |        |       |       | 46    | 47    |
|-----|--------|-------|-------|--------|--------|-------|-------|--------|--------|
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 36  | 4532.9 | 467.3 | 508.8 | 2467.7 | 4624.6 | 487.0 | 532.6 | 2527.2 | 36     |
| 38  | 4536.0 | 467.9 | 508.6 | 2468.7 | 4627.6 | 487.7 | 533.4 | 2523.2 | 38     |
| 40  | 4539.1 | 468.6 | 510.4 | 2471.7 | 4630.7 | 488.4 | 534.2 | 2531.2 | 40     |
| 42  | 4542.1 | 469.3 | 511.1 | 2473.6 | 4633.7 | 489.1 | 535.0 | 2533.2 | 42     |
| 44  | 4545.2 | 469.9 | 511 9 | 2475.6 | 4636.8 | 489.8 | 535.8 | 2535.2 | 44     |
| 46  | 4548.2 | 470.6 | 512.7 | 2477.6 | 4639.8 | 490.5 | 536.6 | 2537.2 | 46     |
| 48  | 4551.3 | 471.2 | 513.5 | 2479.6 | 4642.9 | 491.2 | 537.4 | 2539.2 | 48     |
| 50  | 4554.4 | 471.9 | 514.3 | 2481.6 | 4645.9 | 491.9 | 538.2 | 2541.2 | 50     |
| 52  | 4557.4 | 472.6 | 515.1 | 2483.5 | 4649.0 | 492.6 | 539.0 | 2543.1 | 52     |
| 54  | 4566.5 | 473.2 | 515.9 | 2485.5 | 4652.0 | 493.3 | 539.8 | 2545.1 | 54     |
| 56  | 4563.6 | 473.9 | 516.7 | 2487.5 | 4655.1 | 494.0 | 540.6 | 2547.1 | 56     |
| 58  | 4566.6 | 474.5 | 517.5 | 2489.5 | 4658.1 | 494.7 | 541.4 | 2549.1 | 58     |
| 60  | 4569.7 | 475.2 | 518.3 | 2491.5 | 4661.2 | 495.4 | 542.3 | 2551.1 | 60     |
| 48 | 49    |       |       |        |        |       |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 4661.2 | 495.4 | 542.3 | 2551.1 | 4752.3 | 515.9 | 567.0 | 2611.3 | 0      |
| 2   | 4664.2 | 496.0 | 543.1 | 2553.1 | 4755.3 | 516.5 | 567.8 | 2613.3 | 2      |
| 4   | 4667.3 | 496.7 | 543.9 | 2555.1 | 4758.4 | 517.2 | 568.7 | 2615.3 | 4      |
| 6   | 4670.3 | 497.4 | 544.7 | 2557.1 | 4761.4 | 517.9 | 569.5 | 2617.3 | 6      |
| 8   | 4673.3 | 488.1 | 545.5 | 2559.1 | 4764.4 | 516.6 | 570.3 | 2619.3 | 8      |
| 10  | 4676.4 | 498.8 | 546.4 | 2561.1 | 4767.4 | 519.3 | 571.2 | 2621.4 | 10     |
| 12  | 4679.4 | 499.4 | 547.2 | 2563.1 | 4770.5 | 520.0 | 572.0 | 2623.4 | 12     |
| 14  | 4682.5 | 500.1 | 548.0 | 2565.1 | 4773.5 | 520.7 | 572.8 | 2625.4 | 14     |
| 16  | 4685.5 | 500.8 | 548.8 | 2567.1 | 4776.5 | 521.4 | 573.7 | 2627.4 | 16     |
| 18  | 4688.5 | 501.5 | 549.6 | 2569.1 | 4779.6 | 522.1 | 574.5 | 2629.4 | 18     |
| 20  | 4691.6 | 502.2 | 550.5 | 2571.1 | 4782.6 | 522.8 | 575.3 | 2631.4 | 20     |
| 22  | 4594.6 | 502.8 | 551.3 | 2573.1 | 4735 5 | 523 5 | 576.2 | 2633.5 | 22     |
| 24  | 4697.6 | 503.5 | 552.1 | 2575.1 | 4788.7 | 524.2 | 577.0 | 2635.5 | 24     |
| 26  | 4700.7 | 504.2 | 552.9 | 2577.1 | 4791.7 | 524.9 | 577.9 | 2637.5 | 26     |
| 28  | 4703.7 | 504.9 | 553.7 | 2579.1 | 4794.7 | 525.6 | 578.7 | 2639.5 | 28     |
| 30  | 4706.7 | 505.6 | 554.6 | 2581.1 | 4797.7 | 526 3 | 579 6 | 2641.5 | 30     |
| 32  | 4709.8 | 506.2 | 555.4 | 2583.1 | 4800.8 | 527.0 | 580.4 | 2543.5 | 32     |
| 34  | 4712.8 | 506.9 | 556.2 | 2585.1 | 4803.8 | 527 7 | 581.3 | 2545.6 | 34     |
| 36  | 4715.9 | 507.6 | 557.0 | 2587.2 | 4806.8 | 528.4 | 582.1 | 2647.6 | 36     |
| 38  | 4718.9 | 508.3 | 557.8 | 2589.2 | 4809.9 | 529.1 | 583.0 | 2549.6 | 38     |
| 40  | 4721.9 | 509.0 | 558.7 | 2591.2 | 4812.9 | 529.8 | 583.8 | 2651.6 | 40     |
| 42  | 4725.0 | 509.6 | 559.5 | 2593.2 | 4815.9 | 530.5 | 584.7 | 2653.7 | 42     |
| 44  | 4728.0 | 510.3 | 560.3 | 2595.2 | 4819.0 | 531.2 | 585.5 | 2655.7 | 44     |
| 46  | 4731.0 | 511.0 | 561.2 | 2597 2 | 4822.0 | 531.9 | 586.4 | 2657.7 | 46     |
| 48  | 4734.1 | 511.7 | 562.0 | 2599.2 | 4825.0 | 532.6 | 587.2 | 2659.7 | 48     |
| 50  | 4737.1 | 512.4 | 562.8 | 2601.2 | 4828.0 | 533.3 | 588.1 | 2661.8 | 50     |
| 52  | 4740.2 | 513.1 | 563.7 | 2603.2 | 4831.1 | 534.0 | 588.9 | 2663.8 | 52     |
| 54  | 4743.2 | 513.8 | 564.5 | 2605.2 | 4834.1 | 534.7 | 589.8 | 2665.8 | 54     |
| 56  | 4746.2 | 514.5 | 565.3 | 2607.2 | 4837.1 | 535.4 | 590.6 | 2667.8 | 56     |
| 58  | 4749.3 | 515.2 | 566.2 | 2609.3 | 4840.2 | 536.1 | 591.5 | 2669.9 | 58     |
| 60  | 4752.3 | 515.9 | 567.0 | 2611.3 | 4843.2 | 536.8 | 592.4 | 2671.9 | 60     |
| 50 | 51    |       |       |        |        |       |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 4843.2 | 536.8 | 592.4 | 2671.9 | 4933.6 | 558.2 | 618.5 | 2733.0 | 0      |
| 2   | 4846.2 | 537.5 | 593.2 | 2673.9 | 4936.6 | 558.9 | 619.3 | 2735.1 | 2      |
| 4   | 4849.2 | 538.2 | 594.1 | 2676.0 | 4933.6 | 559.7 | 620.2 | 2737.1 | 4      |
| 6   | 4852.2 | 538.9 | 594.9 | 2678.0 | 4942.6 | 560.4 | 621.1 | 2739.2 | 6      |
|     |        |       |       |        |        |       |       | 50    | 51    |
|-----|--------|-------|-------|--------|--------|-------|-------|--------|--------|
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 8   | 4855.2 | 539.6 | 595.8 | 2680.0 | 4945.6 | 561.1 | 622.0 | 2741.2 | 8      |
| 10  | 4858.3 | 540.3 | 596.7 | 2682.1 | 4948.6 | 561.8 | 622.9 | 2743.3 | 10     |
| 12  | 4861.3 | 541.0 | 597.5 | 2684.1 | 4951.6 | 562.5 | 623.7 | 2745.3 | 12     |
| 14  | 4864.3 | 541.7 | 598.4 | 2686.1 | 4954.6 | 563.3 | 624.6 | 2747.4 | 14     |
| 16  | 4867.3 | 542.4 | 599.3 | 2688.2 | 4957.6 | 564.0 | 625.5 | 2749.4 | 16     |
| 18  | 4870.3 | 543.1 | 600.1 | 2690.2 | 4960.6 | 564.7 | 626.4 | 2751.5 | 18     |
| 20  | 4873.3 | 543.9 | 601.0 | 2692.3 | 4963.6 | 565.4 | 627.3 | 2753.5 | 20     |
| 22  | 4876.3 | 544.6 | 601.9 | 2694.3 | 4966.6 | 566.2 | 628.2 | 2755.6 | 22     |
| 24  | 4879.4 | 545.3 | 602.7 | 2696.3 | 4969.6 | 566.9 | 629.9 | 2757.7 | 24     |
| 26  | 4882.4 | 546.0 | 603.6 | 2698.4 | 4972.6 | 567.6 | 630.0 | 2759.7 | 26     |
| 28  | 4885.4 | 546.7 | 604.5 | 2700.4 | 4975.6 | 568.3 | 630.9 | 2761.8 | 28     |
| 30  | 4888.4 | 547.4 | 605.3 | 2702.4 | 4978.6 | 569.1 | 631.8 | 2763.8 | 30     |
| 32  | 4891.4 | 548.1 | 606.2 | 2704.5 | 4981.8 | 569.8 | 632.7 | 2765.9 | 32     |
| 34  | 4894.4 | 548,8 | 607.0 | 2706,5 | 4984.6 | 570.5 | 633 6 | 2767.9 | 34     |
| 36  | 4897.4 | 549.5 | 607.9 | 2708.6 | 4987.7 | 571.2 | 634.5 | 2770.0 | 36     |
| 38  | 4900.4 | 550.2 | 608.8 | 2710.6 | 4990.7 | 572.0 | 635.3 | 2772.0 | 38     |
| 40  | 4903.5 | 551.0 | 609.7 | 2712.6 | 4993.7 | 572.7 | 636.2 | 2774.1 | 40     |
| 42  | 4906.5 | 551.7 | 610.5 | 2714.7 | 4996.7 | 573.4 | 637.1 | 2776.2 | 42     |
| 44  | 4909.5 | 552.4 | 611.4 | 2716.7 | 4999.7 | 574.1 | 638.0 | 2778.2 | 44     |
| 46  | 4912.5 | 553.1 | 612.3 | 2718.8 | 5002.7 | 574.9 | 638.9 | 2780.3 | 46     |
| 48  | 4915.5 | 553.8 | 613.2 | 2720.8 | 5005.7 | 575.6 | 639.8 | 2782.3 | 48     |
| 50  | 4918.5 | 554.5 | 614.1 | 2722.8 | 5008.7 | 576.3 | 640.7 | 2784.4 | 50     |
| 52  | 4921.5 | 555.2 | 614.9 | 2724.9 | 5011.7 | 577.0 | 641.6 | 2786.4 | 52     |
| 54  | 4924.6 | 555.9 | 615.8 | 2726.9 | 5014.7 | 577.8 | 642.5 | 2788.5 | 54     |
| 56  | 4927.6 | 556.6 | 616.7 | 2729.0 | 5017.7 | 578.5 | 643.4 | 2790.6 | 56     |
| 58  | 4930.6 | 557.4 | 617.6 | 2731.0 | 5020.7 | 579.2 | 644.3 | 2792.6 | 58     |
| 60  | 4933.6 | 558.2 | 618.5 | 2733.0 | 5023.7 | 579.9 | 645.2 | 2794.7 | 60     |
| 52 | 53    |       |       |        |        |       |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 5023.7 | 579.9 | 645.2 | 2794.7 | 5113.5 | 602.0 | 672.7 | 2856.9 | 0      |
| 2   | 5026.7 | 580.6 | 646.1 | 2796.8 | 5116.5 | 602.8 | 673.7 | 2858.9 | 2      |
| 4   | 5029.7 | 581.3 | 647.0 | 2798.8 | 5119.4 | 603.5 | 674.6 | 2861.0 | 4      |
| 6   | 5032.7 | 582.1 | 647.9 | 2800.9 | 5122.4 | 604.3 | 675.5 | 2863.1 | 6      |
| 8   | 5035.7 | 582.8 | 648.9 | 2803.0 | 5125.4 | 605.0 | 676.4 | 2865.2 | 8      |
| 10  | 5038.7 | 583.5 | 649.8 | 2805.0 | 5128.4 | 605.8 | 677.4 | 2867.3 | 10     |
| 12  | 5041.7 | 584.3 | 650.7 | 2807.1 | 5131.3 | 606.5 | 678.3 | 2869.4 | 12     |
| 14  | 5044.7 | 585.0 | 651.6 | 2809.2 | 5134.3 | 607.3 | 673.2 | 2871.5 | 14     |
| 16  | 5047.7 | 585.7 | 652.5 | 2811.2 | 5137.3 | 608.0 | 680.2 | 2873.5 | 16     |
| 18  | 5050.7 | 586 5 | 653.4 | 2813.3 | 5140.3 | 608.8 | 681.1 | 2875.6 | 18     |
| 20  | 5053.6 | 587.2 | 654.3 | 2815.4 | 5143.2 | 609.5 | 682.0 | 2877.7 | 20     |
| 22  | 5056.6 | 587.9 | 655.2 | 2817.4 | 5146.2 | 610.3 | 883.0 | 2873.8 | 22     |
| 24  | 5059.6 | 588.7 | 656.2 | 2819.5 | 5149.2 | 611.0 | 683.9 | 2881.9 | 24     |
| 26  | 5062.6 | 589.4 | 657.1 | 2821.6 | 5152.1 | 611.8 | 684.9 | 2884.0 | 26     |
| 28  | 5065.6 | 590.1 | 658.0 | 2823.6 | 5155.1 | 612.5 | 685.8 | 2886.1 | 28     |
| 30  | 5068.6 | 590.3 | 658.9 | 2825.7 | 5158.1 | 613.3 | 686.7 | 2333.1 | 30     |
| 32  | 5071.6 | 591.6 | 659.8 | 2827.8 | 5161.1 | 614.0 | 687.7 | 2890.2 | 32     |
| 34  | 5074.6 | 532.3 | 660.7 | 2823.8 | 5164.0 | 814.3 | 888.6 | 2832.3 | 34     |
| 36  | 5077.6 | 593.1 | 661.6 | 2831.3 | 5167.0 | 615.5 | 689.6 | 2894.4 | 36     |
| 38  | 5080.6 | 533.8 | 662.5 | 2834.0 | 5170.0 | 616.3 | 690.5 | 2896.5 | 38     |
| 40  | 5083.6 | 594.5 | 663.5 | 2836.1 | 5173,0 | 617,0 | 691.5 | 2898.6 | 40     |
| 42  | 5086.6 | 595.3 | 664.4 | 2838.2 | 5175.9 | 617.8 | 692.4 | 2900.7 | 42     |
|     |        |       |       |        |        |       |       | 52    | 53    |
|-----|--------|-------|-------|--------|--------|-------|-------|--------|--------|
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 44  | 5089.6 | 596.0 | 665.3 | 2840.2 | 5178.9 | 618.5 | 693.4 | 2902.8 | 44     |
| 46  | 5092.6 | 596.7 | 666.2 | 2842.3 | 5181.9 | 619.3 | 694.3 | 2904.9 | 46     |
| 48  | 5095.6 | 597.5 | 667.2 | 2844.4 | 5184.9 | 620.1 | 695.3 | 2907.0 | 48     |
| 50  | 5098.6 | 598.2 | 668.1 | 2846.5 | 5187.8 | 620.8 | 696.2 | 2909.1 | 50     |
| 52  | 5101.6 | 598.9 | 669.0 | 2848.5 | 5190.8 | 621.5 | 897.1 | 2911.2 | 52     |
| 54  | 5104.6 | 599.7 | 699.9 | 2850.6 | 6193.8 | 622.3 | 698.1 | 2913.3 | 54     |
| 56  | 5107.6 | 600.4 | 670.9 | 2852.7 | 6196.7 | 623.0 | 699.0 | 2915.4 | 56     |
| 58  | 5110.6 | 601.2 | 671.8 | 2854.8 | 5199.7 | 623.8 | 700.0 | 2917.5 | 58     |
| 60  | 5113.5 | 602.0 | 672.7 | 2856.9 | 5202.7 | 624.6 | 700.9 | 2919.5 | 60     |
|     |        |       | 54   |        |        | 55   |       |        |        |
|     | LC     | M     | E     | T      | LC     | M     | E     | T      |        |
| 0   | 5202.7 | 624.6 | 700.9 | 2919.6 | 5291.7 | 647.4 | 729.9 | 2982.8 | 0      |
| 2   | 5205.7 | 625.4 | 701.9 | 2921.6 | 5294.6 | 648.1 | 730.9 | 2984.9 | 2      |
| 4   | 5208.6 | 626.1 | 702.8 | 2923.8 | 5297.6 | 648.9 | 731.9 | 2987.1 | 4      |
| 6   | 5211.6 | 626.9 | 703.8 | 2925.9 | 5300.5 | 649.6 | 732.9 | 2989.2 | 6      |
| 8   | 5214.6 | 627.6 | 704.8 | 2928.0 | 5303.5 | 650.4 | 733.8 | 2991.3 | 8      |
| 10  | 5217.6 | 628.4 | 705.7 | 2930.1 | 5306.4 | 651.2 | 734.8 | 2993.4 | 10     |
| 12  | 5220.5 | 629.2 | 706.7 | 2932.2 | 5309.4 | 652.0 | 735.8 | 2995.5 | 12     |
| 14  | 5223.5 | 629.9 | 707.7 | 2934.3 | 5312.3 | 652.7 | 736.8 | 2097.7 | 14     |
| 16  | 5226.4 | 630.7 | 708.6 | 2936.4 | 5315.3 | 653.5 | 737.8 | 2999.8 | 16     |
| 18  | 5229.4 | 631.4 | 709.6 | 2938.5 | 5318.2 | 654.3 | 738.7 | 3001.9 | 18     |
| 20  | 5232.4 | 632.2 | 710.5 | 2940.6 | 5321.2 | 655.1 | 739.7 | 3004.0 | 20     |
| 22  | 5235.3 | 633.0 | 711.5 | 2942.7 | 5324.1 | 655.8 | 740.7 | 3006.2 | 22     |
| 24  | 5238.3 | 633.7 | 712.5 | 2944.8 | 5327.1 | 656.6 | 741.7 | 3008.3 | 24     |
| 26  | 5241.3 | 634.5 | 713.4 | 2346.9 | 5330.0 | 657.4 | 742.7 | 3010.4 | 26     |
| 28  | 5244.2 | 635.2 | 714.4 | 2949.0 | 5333.0 | 658.2 | 743.7 | 3012.5 | 28     |
| 30  | 5247.2 | 636.0 | 715.3 | 2951.1 | 5335.9 | 658.9 | 744.7 | 3014.7 | 30     |
| 32  | 5250.2 | 636.8 | 716.3 | 2953.2 | 5338.8 | 659.7 | 745.7 | 3016.8 | 32     |
| 34  | 5253.1 | 637.5 | 717.3 | 2955.3 | 5341.8 | 660.5 | 746.7 | 3018.9 | 34     |
| 36  | 5256.1 | 638.3 | 718.2 | 2957.5 | 5344.7 | 661.3 | 747.7 | 3021.1 | 36     |
| 38  | 5259.1 | 639.0 | 719.2 | 2959.6 | 5347.7 | 662.0 | 748.7 | 3023.2 | 38     |
| 40  | 5262.0 | 63S.8 | 720.7 | 2861.7 | 5350.5 | 662.8 | 749.7 | 3025.3 | 40     |
| 42  | 5265.0 | 640.6 | 721.1 | 2963.8 | 5353.6 | 663.6 | 750.7 | 3027.5 | 42     |
| 44  | 5268.0 | 641.3 | 722.1 | 2965.0 | 5356.5 | 664.4 | 751.7 | 3029.6 | 44     |
| 46  | 5270.9 | 642.1 | 723.1 | 2968.0 | 5359.5 | 665.1 | 752.6 | 3031.7 | 46     |
| 48  | 5273.3 | 642.8 | 724.1 | 2970.1 | 5362.4 | 665.3 | 753.6 | 3033.8 | 48     |
| 50  | 5276.9 | 643.6 | 725.0 | 2972.2 | 5365.4 | 666.7 | 754.6 | 3036.0 | 50     |
| 52  | 5278.8 | 644.4 | 726.0 | 2374.4 | 5368.3 | 667.5 | 755.6 | 3038.1 | 52     |
| 54  | 5282.8 | 645.1 | 727.0 | 2976.5 | 5371.3 | 668.3 | 756.6 | 3040.2 | 54     |
| 56  | 5285.8 | 645.9 | 728.0 | 2978.6 | 5374.2 | 668.1 | 757.6 | 3042.4 | 56     |
| 58  | 5288.7 | 646.6 | 729.0 | 2980.7 | 5377.2 | 668.3 | 758.6 | 3044.5 | 58     |
| 60  | 5291.7 | 647.4 | 729.8 | 2982.8 | 5380.1 | 670.7 | 759.6 | 3046.6 | 60     |
| 56 | 57    |       |       |        |        |       |       |        |        |
|     |        |       |       |        |        |       |       |        |        |
| LC  | M      | E     | T     | LC     | M      | E     | T     |        |        |
|     |        |       |       |        |        |       |       |        |        |
| 0   | 5380.1 | 670.7 | 759.6 | 3046.6 | 5468.2 | 694.4 | 790.2 | 3111.1 | 0      |
| 2   | 5383.0 | 671.4 | 760.6 | 3048.8 | 5471.1 | 695.2 | 791.2 | 3113.3 | 2      |
| 4   | 5386.0 | 672.2 | 761.6 | 3050.9 | 5474.0 | 696.0 | 792.2 | 3115.4 | 4      |
| 6   | 5388.9 | 672.9 | 762.7 | 3053.1 | 5477.0 | 696.8 | 793.3 | 3117.6 | 6      |
| 8   | 5391.8 | 673.7 | 763.7 | 3055.2 | 5479.9 | 697.6 | 794.3 | 3119.7 | 8      |
| 10  | 5394.8 | 674.4 | 764.7 | 3057.4 | 5482.8 | 698.4 | 795.3 | 3121.9 | 10     |
| 12  | 5397.7 | 675.2 | 765.7 | 3059.5 | 5485.7 | 699.2 | 796.3 | 3124.1 | 12     |
| 14  | 5400.7 | 676.0 | 766.7 | 3061.6 | 5488.7 | 700.0 | 797.4 | 3126.2 | 14     |
| 56    | 57    |
|--------|--------|
|        |        |
| LC     | M      |
|        |        |
| 16     | 5403.6 |
| 18     | 5406.5 |
| 20     | 5409.5 |
| 22     | 5412.4 |
| 24     | 5415.3 |
| 26     | 5418.3 |
| 28     | 5421.2 |
| 30     | 5424.1 |
| 32     | 5427.1 |
| 34     | 5430.0 |
| 36     | 5433.0 |
| 38     | 5435.9 |
| 40     | 5438.8 |
| 42     | 5441.8 |
| 44     | 5444.7 |
| 46     | 5447.6 |
| 48     | 5450.6 |
| 50     | 5453.5 |
| 52     | 5456.5 |
| 54     | 5459.4 |
| 56     | 5462.3 |
| 58     | 5465.3 |
| 60     | 5468.2 |
| 58    | 59    |
|        | LC     |
| 0      | 5555.9 |
| 2      | 5558.8 |
| 4      | 5561.7 |
| 6      | 5564.6 |
| 8      | 5567.5 |
| 10     | 5570.4 |
| 12     | 5573.3 |
| 14     | 5576.2 |
| 16     | 5579.2 |
| 18     | 5582.1 |
| 20     | 5585.0 |
| 22     | 5587.9 |
| 24     | 5590 8 |
| 26     | 5593.7 |
| 28     | 5596.6 |
| 30     | 5599.5 |
| 32     | 5602.4 |
| 34     | 5605.3 |
| 36     | 5608.2 |
| 38     | 5611.1 |
| 40     | 5614.0 |
| 42     | 5616.9 |
| 44     | 5619.8 |
| 46     | 5622.8 |
| 48     | 5625.7 |
| 50     | 5628.6 |
|     |        |       |       |        |        |       |        | 58     | 59    |
|-----|--------|-------|-------|--------|--------|-------|--------|---------|--------|
|     | LC     | M     | E     | T      | LC     | M     | E      | T       |        |
| 52  | 5631.5 | 738.4 | 849.2 | 3233.1 | 5718.4 | 764.4 | 882.0  | 3299.3  | 52     |
| 54  | 5634.4 | 740.2 | 850.3 | 3235.3 | 5721.3 | 765.2 | 883.1  | 3301.5  | 54     |
| 56  | 5637.3 | 741.0 | 851.4 | 3237.5 | 5724.2 | 766.0 | 884.2  | 3303.8  | 56     |
| 58  | 5640.2 | 741.9 | 852.5 | 3239.7 | 5727.1 | 766.8 | 885.3  | 3306.0  | 58     |
| 60  | 5643.1 | 742.8 | 853.5 | 3241.9 | 5730.0 | 767.7 | 886.4  | 3308.2  | 60     |
| 60 | 61    |       |       |        |        |       |        |         |        |
|     |        |       |       |        |        |       |        |         |        |
| LC  | M      | E     | T     | LC     | M      | E     | T      |         |        |
|     |        |       |       |        |        |       |        |         |        |
| 0   | 5730.0 | 767.7 | 886.4 | 3308.2 | 5816.4 | 732.8 | 920.2  | 3375.2. | 0      |
| 2   | 5732.9 | 768.5 | 887.5 | 3310.4 | 5819.3 | 733.7 | 921.4  | 3377.4  | 2      |
| 4   | 5735.3 | 768.4 | 333.7 | 3312.7 | 5822.1 | 784.6 | 922.5  | 337S.7  | 4      |
| 6   | 5738.6 | 770.2 | 889.8 | 3314.9 | 5825.0 | 735.4 | 923.6  | 3381.9  | 6      |
| 8   | 5741.5 | 771.1 | 890.9 | 3317.1 | 5827.9 | 736.3 | 924.8  | 3384.2  | 8      |
| 10  | 5744.4 | 771.9 | 892.0 | 3319.3 | 5830.7 | 737.1 | 925.9  | 3386.4  | 10     |
| 12  | 5747.3 | 772.7 | 893.1 | 3321.6 | 5833.6 | 798.0 | 927.1  | 3388.7  | 12     |
| 14  | 5750.2 | 773.6 | 894.3 | 3323.8 | 5836.5 | 738.8 | 928.2  | 3390.9  | 14     |
| 16  | 5753.0 | 774.4 | 895.4 | 3326.0 | 5839.3 | 799.7 | 929.3  | 3393.2  | 16     |
| 18  | 5755.9 | 775.3 | 896.5 | 3328.3 | 5842.2 | 800.5 | 930.5  | 3395.4  | 18     |
| 20  | 5758.8 | 776.1 | 897.6 | 3330.5 | 5845.1 | 801.4 | 931.6  | 3397.7  | 20     |
| 22  | 5761.7 | 776.9 | 898.8 | 3332.7 | 5847.9 | 802.2 | 932.8  | 3399.9  | 22     |
| 24  | 5764.6 | 777.8 | 899.9 | 3334.9 | 5850.8 | 803.1 | 933.9  | 3402.2  | 24     |
| 26  | 5767.4 | 778.6 | 901.0 | 3337.2 | 5853.7 | 803.9 | 935.1  | 3404.4  | 26     |
| 23  | 5770.3 | 779.5 | 902.1 | 3339.4 | 5356.5 | 304.8 | 936.3  | 3406.7  | 28     |
| 30  | 5773.2 | 780.3 | 903.2 | 3341.6 | 5859.4 | 805.6 | 937.4  | 3408.9  | 30     |
| 32  | 5776.1 | 781.1 | 904.4 | 3343.9 | 5862.3 | 806.5 | 938.6  | 3411.2  | 32     |
| 34  | 5779.0 | 782.0 | 905.5 | 3346.1 | 5865.1 | 807.3 | 939.7  | 3413.5  | 34     |
| 36  | 5781.8 | 782.8 | 906.6 | 3348.3 | 5868.0 | 808.2 | 940.9  | 3415.7  | 36     |
| 38  | 5784.7 | 783.7 | 907.7 | 3350.6 | 5870.9 | 809.0 | 942.1  | 3418.0  | 38     |
| 40  | 5787.6 | 784.5 | 908.8 | 3352.8 | 5873.7 | 809.9 | 943.2  | 3420.3  | 40     |
| 42  | 5790.5 | 785.3 | 910.0 | 3355.0 | 5876.6 | 810.7 | 944.4  | 3422.5  | 42     |
| 44  | 5793.4 | 786.2 | 911.1 | 3357.3 | 5879.5 | 811.6 | 945.5  | 3424.8  | 44     |
| 46  | 5796.6 | 787.0 | 918.8 | 3359.5 | 5882.3 | 812.4 | 946.7  | 3427.1  | 46     |
| 48  | 5799.1 | 787.9 | 913.4 | 3361.8 | 5885.2 | 813.3 | 947.8  | 3429.3  | 48     |
| 50  | 5802.0 | 788.7 | 914.5 | 3364.0 | 5888.1 | 814.1 | 949.0  | 3431.6  | 50     |
| 52  | 5804.9 | 789.5 | 915.7 | 3366.2 | 5890.9 | 815.0 | 950.2  | 3433.9  | 52     |
| 54  | 5807.8 | 790.4 | 916.8 | 3368.5 | 5893.8 | 815.8 | 951.3  | 3436.1  | 54     |
| 56  | 5810.6 | 791.2 | 918.0 | 3370.7 | 5896.7 | 816.7 | 952.5  | 3438.4  | 56     |
| 58  | 5813.5 | 792.1 | 919.1 | 3373.0 | 5899.5 | 817.5 | 953.6  | 3440.7  | 58     |
| 60  | 5816.4 | 792.9 | 920.2 | 3375.2 | 5302.4 | 818.4 | 954.8  | 3442.9  | 60     |
| 62 | 63    |       |       |        |        |       |        |         |        |
|     | LC     | M     | E     | T      | LC     | M     | E      | T       |        |
| 0   | 5902.4 | 818.4 | 954.8 | 3442.9 | 5987.8 | 844.4 | 990.3  | 3511.3  | 0      |
| 2   | 5905.2 | 819.3 | 956.0 | 3445.2 | 5990.6 | 845.3 | 991.5  | 3513.6  | 2      |
| 4   | 5908.1 | 820.1 | 957.2 | 3447.5 | 5993.5 | 846.2 | 992.7  | 3515.9  | 4      |
| 6   | 5910.9 | 821.0 | 958.3 | 3449.7 | 5996.3 | 847.1 | 993.9  | 3518.2  | 6      |
| 8   | 5913.8 | 821.8 | 959.5 | 3452.0 | 5999.1 | 847.9 | 995.1  | 3520.5  | 8      |
| 10  | 5916.6 | 822.7 | 960.7 | 3454.3 | 6002.0 | 848.8 | 996.3  | 3522.8  | 10     |
| 12  | 5919.5 | 823.6 | 961.9 | 3456.6 | 6004.8 | 849.7 | 997.5  | 3525.1  | 12     |
| 14  | 5922.3 | 824.4 | 963.0 | 3458.8 | 6007.7 | 850.6 | 988.7  | 3527.4  | 14     |
| 16  | 5925.2 | 825.3 | 964.2 | 3461.1 | 6010.5 | 851.4 | 999.9  | 3529.7  | 16     |
| 18  | 5928.0 | 826.1 | 965.4 | 3463.4 | 6013.3 | 852.3 | 1001.1 | 3532.0  | 18     |
| 20  | 5930.9 | 827.0 | 966.6 | 3465.7 | 6016.2 | 853.2 | 1002.3 | 3534.3  | 20     |
|     |        |       |        |        |        |       |        | 62    | 63    |
|-----|--------|-------|--------|--------|--------|-------|--------|--------|--------|
|     | LC     | M     | E      | T      | LC     | M     | E      | T      |        |
| 22  | 5933.7 | 827.9 | 967.8  | 3467.9 | 6019.0 | 854.1 | 1003.5 | 3536.6 | 22     |
| 24  | 5936.6 | 828.7 | 968.9  | 3470.2 | 6021.8 | 854.9 | 1004.7 | 3538.9 | 24     |
| 26  | 5939.4 | 829.6 | 970.1  | 3472.5 | 6024.7 | 855.8 | 1005.9 | 3541.2 | 26     |
| 28  | 5942.3 | 830.4 | 971.3  | 3474.7 | 6027.5 | 856.7 | 1007.1 | 3543.5 | 28     |
| 30  | 5945.1 | 831.3 | 972 5  | 3477.0 | 6030.3 | 857.6 | 1008.4 | 3545.8 | 30     |
| 32  | 5847.9 | 832.2 | 973.6  | 3479.3 | 6033.2 | 858.4 | 1009.6 | 3548.1 | 32     |
| 34  | 5950.8 | 833.0 | 974.8  | 3481.6 | 6036.0 | 8593  | 1010.8 | 3550.4 | 34     |
| 36  | 5953.6 | 833.9 | 976.0  | 3483.9 | 6038.9 | 860.2 | 1012.0 | 3552.7 | 36     |
| 38  | 5956.5 | 834.7 | 977.2  | 3486.2 | 6041.7 | 861.1 | 1013.2 | 3555.0 | 38     |
| 40  | 5959.3 | 835.6 | 978.4  | 3488.5 | 6044.5 | 861.9 | 1014.5 | 3557.3 | 40     |
| 42  | 5962.2 | 836.5 | 979.6  | 3430.7 | 6047.4 | 862.8 | 1015.7 | 3559.0 | 42     |
| 44  | 5965.0 | 837.4 | 980.8  | 3493.0 | 6050.2 | 863.7 | 1016.9 | 3562.0 | 44     |
| 46  | 5967.9 | 838.3 | 982.0  | 3495.3 | 6053.0 | 864.6 | 1018.1 | 3564.3 | 46     |
| 48  | 5970.7 | 839.1 | 983.2  | 3497.6 | 6055.9 | 865.4 | 1019.3 | 3566.6 | 48     |
| 50  | 5873.6 | 840.0 | 984.4  | 3499.9 | 6058.7 | 866.3 | 1020.6 | 3568.9 | 50     |
| 52  | 5976.4 | 840.9 | 985.5  | 3502.2 | 6061.6 | 867.2 | 1021.8 | 3571.2 | 52     |
| 54  | 5979.3 | 841.7 | 936.7  | 3504.5 | 6064,4 | 868.1 | 1023.0 | 3573 5 | 54     |
| 56  | 5982.1 | 842.6 | 987.9  | 3506.8 | 6067.2 | 868.9 | 1024.2 | 3575.8 | 56     |
| 58  | 5985.0 | 843.5 | 989.1  | 3509.0 | 6070.1 | 869.8 | 1025.4 | 3578.1 | 58     |
| 60  | 5987.8 | 844.4 | 990.3  | 3511.3 | 6072.9 | 870.7 | 1026.7 | 3580.4 | 60     |
| 64 | 65    |       |        |        |        |       |        |        |        |
|     |        |       |        |        |        |       |        |        |        |
| LC  | M      | E     | T      | LC     | M      | E     | T      |        |        |
| 0   | 6072.9 | 870.7 | 1026.7 | 3580.4 | 6157.5 | 897.3 | 1064.0 | 3650.4 | 0      |
| 2   | 6075.7 | 871.5 | 1027.9 | 3582.8 | 6160.3 | 898.2 | 1065.2 | 3652.8 | 2      |
| 4   | 6078.5 | 872.4 | 1029.2 | 3585.1 | 6163.1 | 899.1 | 1066.5 | 3655.1 | 4      |
| 6   | 6081.4 | 873.3 | 1030.4 | 3587.4 | 6165.9 | 900.0 | 1067.7 | 3657.5 | 6      |
| 8   | 6084.2 | 874.2 | 1031.7 | 3589.7 | 6168.7 | 900.9 | 1069.0 | 3659.8 | 8      |
| 10  | 6087.0 | 875.1 | 1032.9 | 3592.1 | 6171.5 | 901.8 | 1070.2 | 3662.2 | 10     |
| 12  | 6089.8 | 875.9 | 1034.1 | 3594.4 | 6174.3 | 902.7 | 1071.5 | 3664.5 | 12     |
| 14  | 6092.6 | 876.8 | 1035.4 | 3596.7 | 6177.1 | 903.6 | 1072.7 | 3666.9 | 14     |
| 16  | 6095.5 | 877.7 | 1036.6 | 3599.1 | 6179.9 | 904 5 | 1074.0 | 3669.2 | 16     |
| 18  | 6098.3 | 878.6 | 1037.9 | 3601.4 | 6182.7 | 905.4 | 1075.2 | 3671.6 | 18     |
| 20  | 6101.1 | 879.5 | 1039.1 | 3603.7 | 6185.5 | 906.3 | 1076.6 | 3673.9 | 20     |
| 22  | 6103.9 | 880.3 | 1040.3 | 3606.0 | 6188.3 | 907.2 | 1077.8 | 3676.2 | 22     |
| 24  | 6106.7 | 881.2 | 1041.6 | 3608.4 | 6191.1 | 908.1 | 1079.1 | 3678.6 | 24     |
| 26  | 6109.6 | 882.1 | 1042.8 | 3610.7 | 6193.9 | 909.0 | 1080.4 | 3680.9 | 26     |
| 28  | 6112.4 | 883.0 | 1044.1 | 3613.0 | 6196.7 | 909.9 | 1081.7 | 3683.3 | 28     |
| 30  | 6115.2 | 883.9 | 1045.3 | 3615.3 | 6199.5 | 910.8 | 1083.0 | 3685.6 | 30     |
| 32  | 6118.0 | 884.7 | 1046.5 | 3617.7 | 6202.3 | 911.7 | 1084.2 | 3688.0 | 32     |
| 34  | 6120.8 | 885.6 | 1047.8 | 3620.0 | 6205.1 | 912.6 | 1085.5 | 3690.4 | 34     |
| 36  | 6123.7 | 886.5 | 1049.0 | 3622.3 | 6208.0 | 913.5 | 1086.8 | 3692.7 | 36     |
| 38  | 6126.5 | 887.4 | 1050.3 | 3624.7 | 6210.8 | 914.4 | 1088.1 | 3695.1 | 38     |
| 40  | 6129.3 | 888.3 | 1051.5 | 3627.0 | 6213.6 | 915.3 | 1089.4 | 3697.4 | 40     |
| 42  | 6132.1 | 889.2 | 1052.7 | 3629.4 | 6216.4 | 916.2 | 1090.6 | 3699.8 | 42     |
| 44  | 6134.9 | 890.1 | 1054.0 | 3631.7 | 6219.2 | 917.1 | 1091.9 | 3702.2 | 44     |
| 46  | 6137.8 | 891.0 | 1055.2 | 3634.0 | 6222.0 | 918.0 | 1093.2 | 3704.5 | 46     |
| 48  | 6140.6 | 891.9 | 1056.5 | 3636.4 | 6224.8 | 918.9 | 1094.5 | 3706.9 | 48     |
| 50  | 6143.4 | 892.8 | 1057.7 | 3638.7 | 6227.6 | 919.8 | 1095.8 | 3709.3 | 50     |
| 52  | 6146.2 | 893.7 | 1059.0 | 3641.1 | 6230.4 | 920.7 | 1097.0 | 3711.6 | 52     |
| 54  | 6149.0 | 894.6 | 1060.2 | 3643.4 | 6233.2 | 921.6 | 1098.3 | 3714.0 | 54     |
| 56  | 6151.9 | 895.5 | 1061.5 | 3645.7 | 6236.0 | 922.5 | 1099.6 | 3716.3 | 56     |
| 64    | 65    |
|--------|--------|
|        |        |
| LC     | M      |
| 58     | 6154.7 |
| 60     | 6157.5 |
| 66    | 67    |
|        | LC     |
| 0      | 6241.6 |
| 2      | 6244.4 |
| 4      | 6247.2 |
| 6      | 6250 0 |
| 8      | 6252.7 |
| 10     | 6255.5 |
| 12     | 6258.3 |
| 14     | 6261.1 |
| 16     | 6263.9 |
| 18     | 6266.7 |
| 20     | 6269.5 |
| 22     | 6272.3 |
| 24     | 6275.0 |
| 26     | 6277.8 |
| 28     | 6280.6 |
| 30     | 6283.4 |
| 32     | 6286.2 |
| 34     | 6289.0 |
| 36     | 6291.8 |
| 38     | 6294.5 |
| 40     | 6297.3 |
| 42     | 6300.1 |
| 44     | 6302.9 |
| 46     | 6305.7 |
| 48     | 6308.5 |
| 50     | 6311.3 |
| 52     | 6314.1 |
| 54     | 6316.8 |
| 56     | 6319.6 |
| 58     | 6322.4 |
| 60     | 6325.2 |
| 68    | 69    |
|        |        |
| LC     | M      |
|        |        |
| 0      | 6408.3 |
| 2      | 6411.1 |
| 4      | 6413.8 |
| 6      | 6416.6 |
| 8      | 6419.3 |
| 10     | 6422.1 |
| 12     | 6424.8 |
| 14     | 6427.6 |
| 16     | 6430.4 |
| 18     | 6433.1 |
| 20     | 6435.9 |
| 22     | 6438.7 |
| 24     | 6441.4 |
| 26     | 6444.2 |
| 68    | 69    |
|--------|--------|
|        |        |
| LC     | M      |
|        |        |
| 28     | 6446.9 |
| 30     | 6449.7 |
| 32     | 6452.5 |
| 34     | 6455.2 |
| 36     | 6458.0 |
| 38     | 6460.7 |
| 40     | 6463.7 |
| 42     | 6466.3 |
| 44     | 6469.0 |
| 46     | 6471.8 |
| 48     | 6474.5 |
| 50     | 6477.3 |
| 52     | 6480.1 |
| 54     | 6482.8 |
| 56     | 6485.6 |
| 58     | 6488.3 |
| 60     | 6491.1 |
| 70    | 71    |
|        | LC     |
| 0      | 6573.3 |
| 2      | 6576.0 |
| 4      | 6578.7 |
| 6      | 6581.5 |
| 8      | 6584.2 |
| 10     | 6586.9 |
| 12     | 6589.6 |
| 14     | 6532.3 |
| 16     | 6595.1 |
| 18     | 6537.8 |
| 20     | 6600.5 |
| 22     | 6603.2 |
| 24     | 6605.9 |
| 26     | 6608.7 |
| 28     | 6611.4 |
| 30     | 6614.1 |
| 32     | 6616.8 |
| 34     | 6619.5 |
| 36     | 6622.3 |
| 38     | 6625.0 |
| 40     | 6627.7 |
| 42     | 6630.4 |
| 44     | 6633.1 |
| 46     | 6635.9 |
| 48     | 6638.6 |
| 50     | 6641.1 |
| 52     | 6644.0 |
| 54     | 6646.7 |
| 56     | 6649.5 |
| 58     | 6652.2 |
| 60     | 6654.9 |
|        |        |
| 72    | 73    |
|--------|--------|
|        |        |
| LC     | M      |
|        |        |
| 0      | 6736.1 |
| 2      | 6738.8 |
| 4      | 6741.5 |
| 6      | 6744.1 |
| 8      | 6746.8 |
| 10     | 6749.5 |
| 12     | 6752.2 |
| 14     | 6754.9 |
| 16     | 6757.6 |
| 18     | 6760.2 |
| 20     | 6762.9 |
| 22     | 6765.6 |
| 24     | 6768.3 |
| 26     | 6771.0 |
| 28     | 6773.7 |
| 30     | 6776.3 |
| 32     | 6779.0 |
| 34     | 6781.7 |
| 36     | 6784.4 |
| 38     | 6787.1 |
| 40     | 6789.8 |
| 42     | 6792.4 |
| 44     | 6795,1 |
| 46     | 6797.8 |
| 48     | 6800.5 |
| 50     | 6803.2 |
| 52     | 6805.9 |
| 54     | 6808.5 |
| 56     | 6811.2 |
| 58     | 6813.9 |
| 60     | 6816.6 |
| 74    | 75    |
|        | LC     |
| 0      | 6896.8 |
| 2      | 6899.4 |
| 4      | 6902.1 |
| 6      | 6904.8 |
| 8      | 6907.4 |
| 10     | 6910.1 |
| 12     | 6912.7 |
| 14     | 6915.4 |
| 16     | 6918.0 |
| 18     | 6920.7 |
| 20     | 6923.3 |
| 22     | 6926.0 |
| 24     | 6928.6 |
| 26     | 6931.3 |
| 28     | 6933.9 |
| 30     | 6336.8 |
| 32     | 6939.2 |
| 34     | 6941.9 |
|     |        |         |        |        |        |        |        | 74    | 75    |
|-----|--------|---------|--------|--------|--------|--------|--------|--------|--------|
|     | LC     | M       | E      | T      | LC     | M      | E      | T      |        |
| 36  | 6944.6 | 1171.9  | 1473.1 | 4365.1 | 7023.9 | 1202.4 | 1521.8 | 4444.6 | 36     |
| 38  | 6947.2 | 1172.9  | 1474.7 | 4367.7 | 7026.5 | 1203.4 | 1523.5 | 4447.3 | 38     |
| 40  | 6949.9 | 1174.0  | 1476.4 | 4370.3 | 7029.1 | 1204.5 | 1525.1 | 4450.0 | 40     |
| 42  | 6952.5 | 1175.0  | 1478.0 | 4373.0 | 7031.8 | 1205.5 | 1526.7 | 4452.7 | 42     |
| 44  | 6955.2 | 1176.0  | 1479.6 | 4375.6 | 7034.4 | 1206.5 | 1528.4 | 4455.3 | 44     |
| 46  | 6957.8 | 1177.0  | 1481.2 | 4378.3 | 7037.0 | 1207.5 | 1530.0 | 4458.0 | 46     |
| 48  | 6960.5 | 1178.0  | 1482.8 | 4380.9 | 7039.7 | 1208.5 | 1531.7 | 4460.7 | 48     |
| 50  | 6963.1 | 1179.0  | 1484.4 | 4383.5 | 7042.3 | 1209.6 | 1533.3 | 4463.4 | 50     |
| 52  | 6965.8 | 1180.0  | 1486.0 | 4386.2 | 7045.0 | 1210.6 | 1534.9 | 4466.0 | 52     |
| 54  | 6968.4 | 1181.0  | 1487.7 | 4388.8 | 7047.6 | 1211.6 | 1536.6 | 4468.7 | 54     |
| 56  | 6971.1 | 1182.0  | 1489.3 | 4391.5 | 7050.2 | 1212.6 | 1538.2 | 4471.4 | 56     |
| 58  | 6973.7 | 1183.0  | 1490.9 | 4394.1 | 7052.9 | 1213.6 | 1539.9 | 4474.1 | 58     |
| 60  | 6976.4 | 1184.1  | 1492.5 | 4396.7 | 7055.5 | 1214.7 | 1541.5 | 4476.7 | 60     |
| 76 | 77    |         |        |        |        |        |        |        |        |
|     |        |         |        |        |        |        |        |        |        |
| LC  | M      | E       | T      | LC     | M      | E      | T      |        |        |
|     |        |         |        |        |        |        |        |        |        |
| 0   | 7055.5 | 1214.7  | 1541.5 | 4476.7 | 7134.0 | 1245.6 | 1591.7 | 4557.8 | 0      |
| 2   | 7058.1 | 1215.7  | 1543.2 | 4479.4 | 7136.6 | 1246.6 | 1593.4 | 4560.5 | 2      |
| 4   | 7060.7 | 1216.7  | 1544.9 | 4482.1 | 7139.2 | 1247.7 | 1595.1 | 4563.3 | 4      |
| 6   | 7063.3 | 1217.8  | 1546.5 | 4484.8 | 7141.8 | 1248.7 | 1596.8 | 4566.0 | 6      |
| 8   | 7066.0 | 1218.8  | 1548.2 | 4487.5 | 7144.4 | 1249.8 | 1598.5 | 4568.7 | 8      |
| 10  | 7068.6 | 1219.8  | 1549.9 | 4490.2 | 7147.0 | 1250.8 | 1600.2 | 4571.5 | 10     |
| 12  | 7071.2 | 1220.9  | 1551.5 | 4492.9 | 7149.6 | 1251.8 | 1601.9 | 4574.2 | 12     |
| 14  | 7073.8 | 1221.9  | 1553.2 | 4495.6 | 7152.2 | 1252.9 | 1603.6 | 4576.9 | 14     |
| 16  | 7076.4 | 1222.9  | 1554.9 | 4498.3 | 7154.8 | 1253.9 | 1605.3 | 4579.7 | 16     |
| 18  | 7079.0 | 1224.0  | 1556.5 | 4501.0 | 7157.4 | 1255.0 | 1607.0 | 4582.4 | 18     |
| 20  | 7081.7 | 1225.0  | 1558.2 | 4503.7 | 7160.0 | 1256.0 | 1608.7 | 4585.1 | 20     |
| 22  | 7084.3 | 1226.0  | 1559.9 | 4506.3 | 7162.6 | 1257.0 | 1610.4 | 4B87.9 | 22     |
| 24  | 7086.9 | 1227.1  | 1561.5 | 4509.0 | 7165.2 | 1258.1 | 1612.1 | 4590.2 | 24     |
| 26  | 7089.5 | 1228.1  | 1563.2 | 4511.7 | 7167.8 | 1259.1 | 1613.8 | 4593.3 | 26     |
| 28  | 7092.1 | 1229.1  | 1564.9 | 4514.4 | 7170.4 | 1260.2 | 1615.5 | 4596.0 | 28     |
| 30  | 7094.7 | 1230.2  | 1566.5 | 4517.1 | 7173.0 | 1261.2 | 1617.3 | 4598.8 | 30     |
| 32  | 7097.4 | 1231.2  | 1568.2 | 4519.8 | 7175.6 | 1262.2 | 1619.0 | 4601.5 | 32     |
| 34  | 7100.0 | 1232.2  | 1569.9 | 4522.5 | 7178.2 | 1263.3 | 1620.7 | 4604.3 | 34     |
| 36  | 7102.6 | 1233.3  | 1571.5 | 4525.3 | 7180.8 | 1264.3 | 1622.4 | 4607.0 | 36     |
| 38  | 7105.2 | 1234.3  | 1573.2 | 4528.0 | 7183.4 | 1265.4 | 1624.1 | 4609.8 | 38     |
| 40  | 7107.8 | 1235.3  | 1574.8 | 4530.7 | 7186.0 | 1266.4 | 1625.9 | 4612.5 | 40     |
| 42  | 7110.4 | 1236.4  | 1576.4 | 4533.4 | 7188.6 | 1267.4 | 1627.6 | 4615.3 | 42     |
| 44  | 7113.1 | 1237.4  | 1578.1 | 4536.1 | 7191.2 | 1268.5 | 1629.3 | 4618.0 | 44     |
| 46  | 7115.7 | 1 238.4 | 1579.8 | 4538.8 | 7193.8 | 1269.5 | 1631.0 | 4620.8 | 46     |
| 48  | 7118.3 | 1239.5  | 1581.5 | 4541.5 | 7196.4 | 1270.6 | 1632.7 | 4623.5 | 48     |
| 50  | 7120.9 | 1240.5  | 1583.2 | 4544.2 | 7199.0 | 1271.6 | 1634.5 | 4626.3 | 50     |
| 52  | 7123.5 | 1241.5  | 1584.9 | 4547.0 | 7201.6 | 1272.7 | 1636.2 | 4629.0 | 52     |
| 54  | 7126.1 | 1242.6  | 1586.6 | 4549.7 | 7204.2 | 1273.7 | 1637.9 | 4631.8 | 54     |
| 56  | 7128.8 | 1243.6  | 1588.3 | 4552.4 | 7206.8 | 1274.8 | 1639.6 | 4634.5 | 56     |
| 58  | 7131.4 | 1244.6  | 1590.0 | 4555.1 | 7209.4 | 1275.8 | 1641.3 | 4637.3 | 58     |
| 60  | 7134.0 | 1245.6  | 1591.7 | 4557.8 | 7212.0 | 1276.9 | 1643.1 | 4640.0 | 60     |
| 78 | 79    |         |        |        |        |        |        |        |        |
|     | LC     | M       | E      | T      | LC     | M      | E      | T      |        |
| 0   | 7212.0 | 1276.9  | 1643.1 | 4640.0 | 7289.5 | 1308.5 | 1696.0 | 4723.4 | 0      |
| 2   | 7214.6 | 1278.0  | 1644.8 | 4642.8 | 7292.1 | 1309.5 | 1697.7 | 4726.2 | 2      |
| 4   | 7217.2 | 1279.0  | 1646.6 | 4645.6 | 7294.6 | 1310.6 | 1699.5 | 4729.0 | 4      |
|     |        |        |         |        |        |        |        | 78    | 79    |
|-----|--------|--------|---------|--------|--------|--------|--------|--------|--------|
|     | LC     | M      | E       | T      | LC     | M      | E      | T      |        |
| 6   | 7219.7 | 1280.1 | 1648.3  | 4648.3 | 7297.2 | 1311.7 | 1701.3 | 4731.8 | 6      |
| 8   | 7222.3 | 1281.1 | 1650.1  | 4651.1 | 7299.7 | 1312.7 | 1703.1 | 4734.7 | 8      |
| 10  | 7224.9 | 1282.2 | 1651.8  | 4653.9 | 7302.3 | 1313.8 | 1704.9 | 4737.5 | 10     |
| 12  | 7227.5 | 1283.2 | 1653.6  | 4656.7 | 7304.9 | 1314.9 | 1706.6 | 4740.3 | 12     |
| 14  | 7230.1 | 1284.3 | 1655.3  | 4659.4 | 7307.4 | 1315.9 | 1708.4 | 4743.1 | 14     |
| 16  | 7232.7 | 1285.3 | 1657.1  | 4662.2 | 7310.0 | 1317.0 | 1710.2 | 4745.9 | 16     |
| 18  | 7235.2 | 1286.4 | 1658.8  | 4665.0 | 7312.6 | 1318.1 | 1712.0 | 4748.7 | 18     |
| 20  | 7237.8 | 1287.4 | 1 660.6 | 4667.7 | 7315.1 | 1319.1 | 1713.8 | 4751.5 | 20     |
| 22  | 7240.4 | 1288.5 | 1662.3  | 4670.5 | 7317.7 | 1320.2 | 1715.6 | 4754.3 | 22     |
| 24  | 7243.0 | 1289.5 | 1664.1  | 4673.3 | 7320.3 | 1321.3 | 1717.4 | 4757.1 | 24     |
| 26  | 7245.6 | 1290.6 | 1665.8  | 46760  | 7322.8 | 1322.3 | 1719.2 | 4760.0 | 26     |
| 28  | 7248.2 | 1291.6 | 1667.6  | 4678.8 | 7325.4 | 1323.4 | 1721.0 | 4762.8 | 28     |
| 30  | 7250.7 | 1292.7 | 1669.3  | 4681.6 | 7327.9 | 1324.5 | 1722.8 | 4765.6 | 30     |
| 32  | 7253.3 | 1293.7 | 1671.1  | 4684.4 | 7330.5 | 1325.5 | 1724.6 | 4768.4 | 32     |
| 34  | 7255.9 | 1294.8 | 1672.8  | 4687.2 | 7333.1 | 1326.6 | 1726.4 | 4771.2 | 34     |
| 36  | 7258.5 | 1295.8 | 1674.6  | 4689.9 | 7335.6 | 1327.7 | 1728.2 | 4774.1 | 36     |
| 38  | 7261.1 | 1296.9 | 1676.3  | 4692.7 | 7338.2 | 1328.7 | 1730.0 | 4776.9 | 38     |
| 40  | 7263.7 | 1297.9 | 1678.2  | 4695.5 | 7340.8 | 1328.8 | 1731.3 | 4773.7 | 40     |
| 42  | 7266.2 | 1299.0 | 1679.9  | 4698.3 | 7343.3 | 1330.8 | 1733.7 | 4782.6 | 42     |
| 44  | 7268.8 | 1300.0 | 1681.7  | 4701.1 | 7345.9 | 1331.9 | 1735.5 | 4785.4 | 44     |
| 46  | 7271.4 | 1301.1 | 1683.5  | 4703.9 | 7348.4 | 1333.0 | 1737.3 | 4788.2 | 46     |
| 48  | 7274.0 | 1302.1 | 1685.3  | 4706.7 | 7351.0 | 1334.1 | 1739.1 | 4791.0 | 48     |
| 50  | 7276.6 | 1303.2 | 1687.1  | 4709.5 | 7353.6 | 1335.2 | 1740.9 | 4793.9 | 50     |
| 52  | 7279.2 | 1304.2 | 1688.8  | 4712.2 | 7356.1 | 1336.2 | 1742.7 | 4796.7 | 52     |
| 54  | 7281.7 | 1305.3 | 1690.6  | 4715.0 | 7358.7 | 1337.3 | 1744.5 | 4739.5 | 54     |
| 56  | 7284.3 | 1306.3 | 1692.4  | 4717.8 | 7361.3 | 1338.4 | 1746.3 | 4802.4 | 56     |
| 58  | 7286.9 | 1307.4 | 1694.2  | 4720.6 | 7363.8 | 1339.5 | 1748.1 | 4805.2 | 58     |
| 60  | 7289.5 | 1308.5 | 1696.0  | 4723.4 | 7366.4 | 1340.6 | 1750.0 | 4808.0 | 60     |
| 80 | 81    |        |         |        |        |        |        |        |        |
|     |        |        |         |        |        |        |        |        |        |
| LC  | M      | E      | T       | LC     | M      | E      | T      |        |        |
|     |        |        |         |        |        |        |        |        |        |
| 0   | 7366.4 | 1340.6 | 1750.0  | 4808.0 | 7442.7 | 1372.8 | 1805.5 | 4893.9 | 0      |
| 2   | 7368.9 | 1341.7 | 1751.8  | 4810.9 | 7445.2 | 1373.9 | 1807.3 | 4896.8 | 2      |
| 4   | 7371.5 | 1342.7 | 1753.7  | 4813.7 | 7447.7 | 1375.0 | 1809.2 | 4899.7 | 4      |
| 6   | 7374.0 | 1343.8 | 1755.5  | 4816.6 | 7450.3 | 1376.1 | 1811.1 | 4902.6 | 6      |
| 8   | 7376.6 | 1344.9 | 1757.4  | 4819.4 | 7452.8 | 1377.1 | 1813.0 | 4905.4 | 8      |
| 10  | 7379.1 | 1346.0 | 1759.2  | 4822.3 | 7455.3 | 1378.2 | 1814.9 | 4908.3 | 10     |
| 12  | 7381.7 | 1347.0 | 1761.0  | 4825.1 | 7457.8 | 1379.3 | 1816.8 | 4911.2 | 12     |
| 14  | 7384.2 | 1348.1 | 1762.9  | 4828.0 | 7460.4 | 1380.4 | 1818.6 | 4914.1 | 14     |
| 16  | 7386.7 | 1349.2 | 1764.7  | 4830.8 | 7462.9 | 1381.4 | 1820.5 | 4917.0 | 16     |
| 18  | 7389.3 | 1350.3 | 1766.6  | 4833.7 | 7465.4 | 1382.5 | 1822.4 | 4919.9 | 18     |
| 20  | 7391.8 | 1351.3 | 1768.4  | 4836.5 | 7467.9 | 1383.6 | 1824.2 | 4922.8 | 20     |
| 22  | 7394.4 | 1352.4 | 1770.2  | 4839.4 | 7470.4 | 1384.7 | 1826.1 | 4925.7 | 22     |
| 24  | 7396.9 | 1353.5 | 1772.1  | 4842.2 | 7473.0 | 1385.7 | 1828.0 | 4928.6 | 24     |
| 26  | 7399.5 | 1354.6 | 1773.9  | 4845.1 | 7475.5 | 1386.8 | 1829.9 | 4931.5 | 26     |
| 28  | 7402.0 | 1355.6 | 1775.8  | 4847.9 | 7478.0 | 1387.9 | 1831.8 | 4934.4 | 28     |
| 30  | 7404.5 | 1356.7 | 1777.6  | 4850.8 | 7480.5 | 1389.0 | 1833.7 | 4937.2 | 30     |
| 32  | 7407.1 | 1357.8 | 1779.4  | 4853.7 | 7483.1 | 1390.1 | 1835.6 | 4940.2 | 32     |
| 34  | 7409.6 | 1358.9 | 1781.3  | 4856.5 | 7485.6 | 1391.2 | 1837.5 | 4943.1 | 34     |
| 36  | 7412.2 | 1359.9 | 1783.1  | 4859.4 | 7488.1 | 1392.3 | 1839.4 | 4649.0 | 36     |
| 38  | 7414.7 | 1361.0 | 1785.0  | 4862.3 | 7490.6 | 1393.4 | 1841.3 | 4948.9 | 38     |
| 40  | 7417.3 | 1362.1 | 1786.8  | 4865.1 | 7493.2 | 1394.5 | 1843.2 | 4951 8 | 40     |
| 80    | 81    |
|--------|--------|
|        |        |
| LC     | M      |
|        |        |
| 42     | 7419.8 |
| 44     | 7422.3 |
| 46     | 7424.9 |
| 48     | 7427.4 |
| 50     | 7430.0 |
| 52     | 7432.5 |
| 54     | 7435.1 |
| 56     | 7437.6 |
| 58     | 7440.1 |
| 60     | 7442.7 |
| 82    | 83    |
|        | LC     |
| 0      | 7518.4 |
| 2      | 7520.9 |
| 4      | 7523.4 |
| 6      | 7525.9 |
| 8      | 7528.4 |
| 10     | 7530.9 |
| 12     | 7533.4 |
| 14     | 7535.9 |
| 16     | 7538.5 |
| 18     | 7541.0 |
| 20     | 7543.5 |
| 22     | 7546.0 |
| 24     | 7548.5 |
| 26     | 7551.0 |
| 28     | 7553.5 |
| 30     | 7556.0 |
| 32     | 7558.5 |
| 34     | 7561.0 |
| 36     | 7563.5 |
| 38     | 7566.0 |
| 40     | 7568.5 |
| 42     | 7571.0 |
| 44     | 7573.5 |
| 46     | 7576.1 |
| 48     | 7578.6 |
| 50     | 7581.1 |
| 52     | 7583.6 |
| 54     | 7586.1 |
| 56     | 7588.6 |
| 58     | 7591.1 |
| 60     | 7593.6 |
| 84    | 85    |
|        |        |
| LC     | M      |
|        |        |
| 0      | 7668.3 |
| 2      | 76708  |
| 4      | 7673.2 |
| 6      | 7675.7 |
| 8      | 7678.2 |
| 10     | 7680.6 |
| 12     | 7683 1 |
| 84    | 85    |
|--------|--------|
|        |        |
| LC     | M      |
|        |        |
| 14     | 7685.6 |
| 16     | 7688.1 |
| 18     | 7690.5 |
| 20     | 7693.0 |
| 22     | 7695.5 |
| 24     | 7697.9 |
| 26     | 7700.4 |
| 28     | 7702.9 |
| 30     | 7705.3 |
| 32     | 7707.8 |
| 34     | 7710.3 |
| 36     | 7712.8 |
| 38     | 7715.2 |
| 40     | 7717.7 |
| 42     | 7720.2 |
| 44     | 7722.6 |
| 46     | 7725.1 |
| 48     | 7727.6 |
| 50     | 7730.0 |
| 52     | 7732.5 |
| 54     | 7735.0 |
| 56     | 7737.5 |
| 58     | 7739.9 |
| 60     | 7742.4 |
| 86    | 87    |
|        | LC     |
| 0      | 7815.8 |
| 2      | 7818.2 |
| 4      | 7820.6 |
| 6      | 7823.1 |
| 8      | 7825.5 |
| 10     | 7827.9 |
| 12     | 7830.3 |
| 14     | 7832.8 |
| 16     | 7835.2 |
| 18     | 7837.6 |
| 20     | 7840.0 |
| 22     | 7842.4 |
| 24     | 7844.9 |
| 26     | 7847.3 |
| 28     | 7849.7 |
| 30     | 7852.1 |
| 32     | 7854.6 |
| 34     | 7857.0 |
| 36     | 7859.4 |
| 38     | 7861.8 |
| 40     | 7864.3 |
| 42     | 7866.7 |
| 44     | 7869.1 |
| 46     | 7871.5 |
| 48     | 7874.0 |
|     |        |        |        |        |        |        |        | 86    | 87    |
|-----|--------|--------|--------|--------|--------|--------|--------|--------|--------|
|     | LC     | M      | E      | T      | LC     | M      | E      | T      |        |
| 50  | 7876.4 | 1567.8 | 2158.6 | 5421.8 | 7948.7 | 1602.4 | 2224.5 | 5517.3 | 50     |
| 52  | 7878.8 | 1568.9 | 2160.7 | 5424.9 | 7951.2 | 16035  | 2226.7 | 5520.5 | 52     |
| 54  | 7881.2 | 1570.1 | 2162.9 | 5428.1 | 7953.6 | 1604.7 | 2228.9 | 5523.7 | 54     |
| 56  | 7883.6 | 1571.2 | 2165.1 | 5431.2 | 7956.0 | 1605.8 | 2231.1 | 5526.9 | 56     |
| 58  | 7886.1 | 1572.4 | 2167.3 | 5434.4 | 7958.4 | 1607.0 | 2233.3 | 5530.1 | 58     |
| 60  | 7888.5 | 1573.6 | 2169.5 | 5437.5 | 7960.8 | 1608.2 | 2235.6 | 5533.3 | 60     |
| 88 | 89    |        |        |        |        |        |        |        |        |
|     |        |        |        |        |        |        |        |        |        |
| LC  | M      | E      | T      | LC     | M      | E      | T      |        |        |
|     |        |        |        |        |        |        |        |        |        |
| 0   | 7960.8 | 1608.2 | 2235.6 | 5533.3 | 8032.4 | 1643.0 | 2303.6 | 5630.8 | 0      |
| 2   | 7963.2 | 1609.4 | 2237.8 | 5536.6 | 8034.8 | 1644.1 | 2305.9 | 5634.1 | 2      |
| 4   | 7965.6 | 1610.5 | 2240.1 | 5539.8 | 8037.1 | 1645.3 | 2308.2 | 5637.4 | 4      |
| 6   | 7968.0 | 1611.7 | 2242.3 | 5543.1 | 8039.5 | 1646.5 | 2310.5 | 5640.7 | 6      |
| 8   | 7970.3 | 1612.8 | 2244.6 | 5546.3 | 8041.9 | 1647.7 | 2312.8 | 5644.0 | 8      |
| 10  | 7972.7 | 1614.0 | 2246.8 | 5549.5 | 8044.2 | 1648.9 | 2315.1 | 5647.3 | 10     |
| 12  | 7975.1 | 1615.2 | 2249.1 | 5552.8 | 8046.6 | 1650.0 | 2317.4 | 5650.6 | 12     |
| 14  | 7977.5 | 1616.3 | 2251.3 | 5556.0 | 8049.0 | 1651.2 | 2319.7 | 5653.9 | 14     |
| 16  | 7979.9 | 1617.5 | 2253.6 | 5559.2 | 8051.4 | 1652.4 | 2322.0 | 5657.1 | 16     |
| 18  | 7982.3 | 1618.6 | 2255.8 | 5562.5 | 8053.7 | 1653.6 | 2324.3 | 5660.4 | 18     |
| 20  | 7984.7 | 1619.8 | 2258.1 | 5565.7 | 8056.1 | 1654.8 | 2326.7 | 5663.7 | 20     |
| 22  | 7987.1 | 1621.0 | 2260.4 | 5568.9 | 8058.5 | 1655.9 | 2329.0 | 5667.0 | 22     |
| 24  | 7989.4 | 1622.1 | 2262.7 | 5572.2 | 8060.8 | 1657.1 | 2331.3 | 5670.3 | 24     |
| 26  | 7991.8 | 1623.3 | 2264.9 | 5575.4 | 8063.2 | 1658.3 | 2333.7 | 5673.6 | 26     |
| 28  | 7994.2 | 1624.4 | 2267.2 | 5578.6 | 8065.6 | 1659.5 | 2336.0 | 5676.9 | 28     |
| 30  | 7996.6 | 1625.6 | 2269.5 | 5581.9 | 8067.9 | 1660.7 | 2338.3 | 5680.2 | 30     |
| 32  | 7999.0 | 1626.8 | 2271.7 | 5585.1 | 8070.3 | 1661.8 | 2340.7 | 5683.5 | 32     |
| 34  | 8001.4 | 1627.9 | 2273.9 | 5588.4 | 8073.7 | 1663.0 | 2343.0 | 5686.8 | 34     |
| 36  | 8003.8 | 1629.1 | 2276.2 | 5591.7 | 8075.1 | 1664.2 | 2345.3 | 5690.2 | 36     |
| 38  | 8006.1 | 1630.2 | 2278.5 | 5594.9 | 8077.4 | 1665.4 | 2347.7 | 5693.5 | 38     |
| 40  | 8008.5 | 1631.4 | 2280.8 | 5598.2 | 8079.8 | 1666.6 | 2350.0 | 5696.8 | 40     |
| 42  | 8010.9 | 1632.6 | 2283.0 | 5601.4 | 8082.2 | 1667.7 | 2352.3 | 5700.1 | 42     |
| 44  | 8013.3 | 1633.7 | 2285.3 | 5604.7 | 8084.5 | 1668.8 | 2354.7 | 5703.4 | 44     |
| 46  | 8015.7 | 1634.9 | 2287.6 | 5608.0 | 8086.9 | 1670.0 | 2357.0 | 5706.8 | 46     |
| 48  | 8018.1 | 1636.0 | 2289.9 | 5611.2 | 8089.3 | 1671.2 | 2359.3 | 5710.1 | 48     |
| 50  | 8020.5 | 1637.2 | 2292.2 | 5614.5 | 8091.6 | 1672.4 | 2361.7 | 5713.4 | 50     |
| 52  | 8022.9 | 1638.4 | 2294.4 | 5617.8 | 8094.0 | 1673.5 | 2364.0 | 5716.7 | 52     |
| 54  | 8025.2 | 1639.5 | 2296.7 | 5621.0 | 8096.4 | 1674.7 | 2366.3 | 5720.0 | 54     |
| 56  | 8027.6 | 1640.7 | 2299.0 | 5624.3 | 8098.8 | 1675.9 | 2368.7 | 5723.4 | 56     |
| 58  | 8030.0 | 1641.8 | 2301.3 | 5627.5 | 8101.1 | 1677.1 | 2371.0 | 5726.7 | 58     |
| 60  | 8032.4 | 1643.0 | 2303.6 | 5630.8 | 8103.5 | 1678.3 | 2373.4 | 5730.0 | 60     |
| 90 | 91    |        |        |        |        |        |        |        |        |
|     | LC     | M      | E      | T      | LC     | M      | E      | T      |        |
| 0   | 8103.5 | 1678.3 | 2373.4 | 5730.0 | 8173.9 | 1713.8 | 2445.1 | 5830.9 | 0      |
| 2   | 8105.8 | 1679.5 | 2375.8 | 5733.3 | 8176.2 | 1715.0 | 2447.5 | 5834.3 | 2      |
| 4   | 8108.2 | 1680.6 | 2378.2 | 5736.7 | 8178.5 | 1716.2 | 2450.0 | 5837.7 | 4      |
| 6   | 8110.5 | 1681.8 | 2380.5 | 5740.0 | 8180.9 | 1717.4 | 2452.4 | 5841.1 | 6      |
| 8   | 8112.9 | 1683.0 | 2382.9 | 5743.4 | 8183.2 | 1718.6 | 2454.8 | 5844.5 | 8      |
| 10  | 8115.2 | 1684.2 | 2385.3 | 5746.7 | 8185.5 | 1719.7 | 2457.2 | 5847.9 | 10     |
| 12  | 8117.6 | 1685.4 | 2387.6 | 5750.0 | 8187.9 | 1720.9 | 2459.7 | 5851.3 | 12     |
| 14  | 8119.9 | 1686.5 | 2390.0 | 5753.4 | 8190.2 | 1722.1 | 2462.1 | 5854.7 | 14     |
| 16  | 8122.3 | 1687.7 | 2392.4 | 5756.7 | 8192.5 | 1723.3 | 2464.5 | 5858.1 | 16     |
| 18  | 8124.6 | 1688.9 | 2394.7 | 5760.1 | 8194.8 | 1724.5 | 2467.0 | 5861.5 | 18     |
|     |        |        |        |        |        |        |        | 90    | 91    |
|-----|--------|--------|--------|--------|--------|--------|--------|--------|--------|
|     | LC     | M      | E      | T      | LC     | M      | E      | T      |        |
| 20  | 8127.0 | 1690.1 | 2397.1 | 5763.4 | 8197.2 | 1725.7 | 2469.4 | 5864.9 | 20     |
| 22  | 8129.3 | 1691.3 | 2399.5 | 5766.8 | 8199.5 | 1726.9 | 2471.9 | 5668.3 | 22     |
| 24  | 8131.7 | 1692.5 | 2401.9 | 5770.1 | 8201.8 | 1728.1 | 2474.3 | 5871.8 | 24     |
| 26  | 8134.0 | 1693.6 | 2404.3 | 5773.5 | 8204.2 | 1729.3 | 2476.7 | 5875.2 | 26     |
| 28  | 8136.4 | 1694.8 | 2406.6 | 5776.9 | 8206.5 | 1730.5 | 2479.2 | 5878.6 | 28     |
| 30  | 8138.7 | 1696.0 | 2409.0 | 5780.2 | 8208.8 | 1731.7 | 2481.6 | 5882.0 | 30     |
| 32  | 8141.1 | 1697.2 | 2411.4 | 5783.6 | 8211.1 | 1732.9 | 2484.1 | 5885.4 | 32     |
| 34  | 8143.4 | 1698.4 | 2413.8 | 5787.0 | 8213.5 | 1734.1 | 2486.5 | 5888.9 | 34     |
| 36  | 8145.8 | 1699.6 | 2416.2 | 5790.3 | 8215.8 | 1735.3 | 2489.0 | 5892.3 | 36     |
| 38  | 8148.1 | 1700.7 | 2418.6 | 5793.7 | 8218.1 | 1736.4 | 2491.5 | 5895.7 | 38     |
| 40  | 81504  | 1701.9 | 2421.0 | 5797.1 | 8220.4 | 1737.6 | 2493.9 | 5899.2 | 40     |
| 42  | 8152.8 | 1703.1 | 2423.4 | 5800.4 | 8222.8 | 1738.8 | 2496.4 | 5902.6 | 42     |
| 44  | 8155.1 | 1704.3 | 2425.8 | 5803.8 | 8225.1 | 1740.0 | 2498.9 | 5906.0 | 44     |
| 46  | 8157.5 | 1705.5 | 2428.2 | 5807.2 | 8227.4 | 1741.2 | 2501.3 | 5909.4 | 46     |
| 48  | 8159.8 | 1706.7 | 2430.6 | 5810.6 | 8229.7 | 1742.4 | 2503.8 | 5912.9 | 48     |
| 50  | 8162.2 | 1707.9 | 2433.0 | 5814.0 | 8232.0 | 1743.6 | 2506.3 | 5916.3 | 50     |
| 52  | 8164.5 | 1709.0 | 2435.4 | 5817.3 | 8234.3 | 1744.8 | 2508.7 | 5919.8 | 52     |
| 54  | 8166.8 | 1710.2 | 2437.9 | 5820.7 | 8236.7 | 1746.0 | 2511.2 | 5923.2 | 54     |
| 56  | 8169.2 | 1711.4 | 2440.3 | 5824.1 | 8239.0 | 1747.2 | 2513.7 | 5926.7 | 56     |
| 58  | 8171.5 | 1712.6 | 2442.7 | 5827.5 | 8241.3 | 1748.4 | 2516.2 | 5930.1 | 58     |
| 60  | 8173.9 | 1713.8 | 2445.1 | 5830.9 | 8243.6 | 1749.6 | 2518.7 | 5933.6 | 60     |
| 92 | 93    |        |        |        |        |        |        |        |        |
|     |        |        |        |        |        |        |        |        |        |
| LC  | M      | E      | T      | LC     | M      | E      | T      |        |        |
|     |        |        |        |        |        |        |        |        |        |
| 0   | 8243.6 | 1749.6 | 2518.7 | 5933.6 | 8312.8 | 1785.7 | 2594.2 | 6038.2 | 0      |
| 2   | 8245.9 | 1750.8 | 2521.2 | 5937.0 | 8315.1 | 1786.9 | 2596.8 | 6041.7 | 2      |
| 4   | 8248.2 | 1752.0 | 2523.6 | 5940.5 | 8317.4 | 1788.2 | 2599.3 | 6045.2 | 4      |
| 6   | 8250.6 | 1753.2 | 2526.1 | 5944.0 | 8319.7 | 1789.4 | 2601.9 | 6048.7 | 6      |
| 8   | 8252.9 | 1754.4 | 2528.6 | 5947.4 | 8322.0 | 1790.6 | 2604.4 | 6052.2 | 8      |
| 10  | 8255.2 | 1755.6 | 2531.1 | 5950.9 | 8324.3 | 1791.8 | 2607.0 | 6055.8 | 10     |
| 12  | 8257.5 | 1756.8 | 2533.6 | 5954.4 | 8326.6 | 1793.0 | 2609.6 | 6059.3 | 12     |
| 14  | 8259.8 | 1758.0 | 2536.1 | 5957.8 | 8328.8 | 1794.2 | 2612.1 | 6062.8 | 14     |
| 16  | 8262.2 | 1759.2 | 2338.6 | 5961.3 | 8331.1 | 1795.4 | 2614.7 | 6066.4 | 16     |
| 18  | 8264.5 | 1760.4 | 2541.1 | 5964.8 | 8333.3 | 1796.6 | 2617.3 | 6069.9 | 18     |
| 20  | 8266.8 | 1761.6 | 2543.6 | 5968.2 | 8335.6 | 1797.8 | 26198  | 6073.4 | 20     |
| 22  | 8269.1 | 1762.8 | 2546.1 | 5971.7 | 8337.9 | 1799.1 | 2622.4 | 6077.0 | 22     |
| 24  | 8271.4 | 1764.0 | 2548.6 | 5975.2 | 8340.2 | 1800.3 | 2625.0 | 6080.5 | 24     |
| 26  | 8273.7 | 1765.2 | 2551.2 | 5978.7 | 8342.5 | 1801.5 | 2627.6 | 6084.1 | 26     |
| 28  | 8276.0 | 1766.4 | 2553.7 | 5982.2 | 8344.8 | 1802.7 | 2630.2 | 6087.6 | 28     |
| 30  | 8278.3 | 1767.6 | 2556.2 | 5985.6 | 8347.1 | 1803.9 | 2632.7 | 6091.2 | 30     |
| 32  | 8280.6 | 1768.8 | 2558.7 | 5989.1 | 8349.4 | 1805.1 | 2635.3 | 6094.7 | 32     |
| 34  | 8282.9 | 1770.0 | 2561.2 | 5992.6 | 8351.7 | 1806.3 | 2637.9 | 6098.3 | 34     |
| 36  | 8285.2 | 1771.2 | 25638  | 5996.1 | 8354.0 | 1807.6 | 2640.5 | 6101.8 | 36     |
| 38  | 8287.5 | 1772.5 | 2566.3 | 5999.6 | 8356.3 | 1808.8 | 2643.1 | 6105.4 | 38     |
| 40  | 8289.8 | 1773.7 | 2568.8 | 6003.1 | 8358.5 | 1810.0 | 2645.7 | 6109.0 | 40     |
| 42  | 8292.1 | 1774.9 | 2571.3 | 6006.6 | 8360.8 | 1811.2 | 2648.3 | 6112.5 | 42     |
| 44  | 8294.4 | 1776.1 | 2573.9 | 6010.1 | 8363.1 | 1812.4 | 2650.9 | 6116.1 | 44     |
| 46  | 8296.7 | 1777.3 | 2576.4 | 6013.6 | 8365.4 | 1813.6 | 2653.5 | 6119.7 | 46     |
| 48  | 8299.0 | 1778.5 | 2578.9 | 6017.1 | 8367.7 | 1814.9 | 2656.1 | 6123.2 | 48     |
| 50  | 8301.3 | 1779.7 | 2581.5 | 6020.6 | 8369.9 | 1816.1 | 2658.7 | 6128.7 | 50     |
| 52  | 8303.6 | 1780.9 | 2584.0 | 6024.1 | 8372.2 | 1817.3 | 2661.3 | 6130.4 | 52     |
| 54  | 8305.9 | 1782.1 | 2586.6 | 6027.6 | 8374.5 | 1818.5 | 2663.9 | 6133.9 | 54     |
| 92    | 93    |
|--------|--------|
|        |        |
| LC     | M      |
|        |        |
| 56     | 8308.2 |
| 58     | 8310.5 |
| 60     | 8312.8 |
| 94    | 95    |
|        | LC     |
| 0      | 8381.3 |
| 2      | 8383.6 |
| 4      | 8385.9 |
| 6      | 8388.1 |
| 8      | 8390.4 |
| 10     | 8392.7 |
| 12     | 8395.0 |
| 14     | 8397.2 |
| 16     | 8399.5 |
| 18     | 8401.7 |
| 20     | 8404.0 |
| 22     | 8406.3 |
| 24     | 8408.5 |
| 26     | 8410.8 |
| 28     | 8413.1 |
| 30     | 8415.3 |
| 32     | 8417.6 |
| 34     | 8413.9 |
| 36     | 8422.1 |
| 38     | 8424.4 |
| 40     | 8426.6 |
| 42     | 8428.9 |
| 44     | 8431.2 |
| 46     | 8433.4 |
| 48     | 8435.7 |
| 50     | 8437.9 |
| 52     | 8440.2 |
| 54     | 8442 4 |
| 56     | 8444.7 |
| 58     | 8447.0 |
| 60     | 8449.2 |
| 96    | 97    |
|        |        |
| LC     | M      |
|        |        |
| 0      | 8516.4 |
| 2      | 85187  |
| 4      | 8520.9 |
| 6      | 8523.1 |
| 8      | 8525.4 |
| 10     | 8527.6 |
| 12     | 8529.8 |
| 14     | 8532.0 |
| 16     | 8534.3 |
| 18     | 8536.5 |
| 20     | 8538.7 |
| 22     | 8540.3 |
| 24     | 8543.2 |
| 96    | 97    |
|--------|--------|
|        |        |
| LC     | M      |
|        |        |
| 26     | 8545.4 |
| 28     | 8547.6 |
| 30     | 8549.8 |
| 32     | 8552.0 |
| 34     | 8554.3 |
| 36     | 8556.5 |
| 38     | 8558.7 |
| 40     | 8560.9 |
| 42     | 8563.1 |
| 44     | 8565.3 |
| 46     | 8567.6 |
| 48     | 8569.8 |
| 50     | 8572.0 |
| 52     | 8574.2 |
| 54     | 8576.4 |
| 56     | 8578.6 |
| 58     | 8580.8 |
| 60     | 8583.0 |
| 98    | 99    |
|        | LC     |
| 0      | 8649.0 |
| 2      | 8651.2 |
| 4      | 8653.3 |
| 6      | 8655.6 |
| 8      | 8667.7 |
| 10     | 8659.9 |
| 12     | 8662.1 |
| 14     | 8664.3 |
| 16     | 8666.4 |
| 18     | 8668.6 |
| 20     | 8670.8 |
| 22     | 8673.0 |
| 24     | 8675.2 |
| 26     | 8677.3 |
| 28     | 8679.5 |
| 30     | 8681.7 |
| 32     | 8683.9 |
| 34     | 8686.0 |
| 36     | 8688.2 |
| 38     | 8690.4 |
| 40     | 8692.6 |
| 42     | 8694.7 |
| 44     | 8696.9 |
| 46     | 8699.1 |
| 48     | 8701.2 |
| 50     | 8703.4 |
| 52     | 8705.6 |
| 54     | 8707.8 |
| 56     | 8709.9 |
| 58     | 8712.1 |
| 60     | 8714.3 |
|        |        |
| 100    | 101    |
|---------|---------|
|         |         |
| LC      | M       |
|         |         |
| 0       | 8778.9  |
| 2       | 8781.0  |
| 4       | 8783.1  |
| 6       | 8785.3  |
| 8       | 8787.4  |
| 10      | 8789.6  |
| 12      | 8791.7  |
| 14      | 8793.9  |
| 16      | 8796.0  |
| 18      | 8798.9  |
| 20      | 8800.3  |
| 22      | 8802.4  |
| 24      | 8804.5  |
| 26      | 8806.7  |
| 28      | 8808.8  |
| 30      | 8810.9  |
| 32      | 8813.1  |
| 34      | 8815.2  |
| 36      | 8817.3  |
| 38      | 8819.5  |
| 40      | 8821.6  |
| 42      | 8823.7  |
| 44      | 8825.8  |
| 46      | 8828.0  |
| 48      | 8830.1  |
| 50      | 8832.2  |
| 52      | 8834.3  |
| 54      | 8836.4  |
| 56      | 8838.6  |
| 58      | 8840.7  |
| 60      | 8842.8  |
| 102    | 103    |
|         | LC      |
| 0       | 8906.1  |
| 2       | 8908.2  |
| 4       | 8910.3  |
| 6       | 8912.4  |
| 8       | 8914.5  |
| 10      | 8916.6  |
| 12      | 8918.7  |
| 14      | 8920.8  |
| 16      | 8922.9  |
| 18      | 8925.0  |
| 20      | 8927.0  |
| 22      | 8929.1  |
| 24      | 8931.2  |
| 26      | 8933.3  |
| 28      | 8935.4  |
| 30      | 8937.5  |
| 32      | 8939.6  |
| 34      | 8941.6  |
|      |        |        |        |        |         |        |        | 102    | 103    |
|------|--------|--------|--------|--------|---------|--------|--------|---------|---------|
|      | LC     | M      | E      | T      | LC      | M      | E      | T       |         |
| 36   | 8943.7 | 2147.4 | 3434.5 | 7152.2 | 9005.9  | 2186.5 | 3535.7 | 7281.5  | 36      |
| 38   | 8945.8 | 2148.7 | 3437.8 | 7156.5 | 9008.0  | 2187.8 | 3539.2 | 7285.9  | 38      |
| 40   | 8947.9 | 2150.0 | 3441.1 | 7160.7 | 9010.0  | 2189.1 | 3542.6 | 7290.3  | 40      |
| 42   | 8950.0 | 2151.3 | 3444.4 | 7165.0 | 9012.1  | 2190.5 | 3546.0 | 7294.6  | 42      |
| 44   | 8952.1 | 2152.6 | 3447.8 | 7169.3 | 9014.2  | 2191.8 | 3549.5 | 7299.0  | 44      |
| 46   | 8954.1 | 2153.9 | 3451.1 | 7173.6 | 9016.2  | 2193.1 | 3552.9 | 7303.4  | 46      |
| 48   | 8956.2 | 21552  | 3454.5 | 7177.9 | 9018.3  | 2194.4 | 3556.3 | 7307.7  | 48      |
| 50   | 8958.3 | 2156.5 | 3457.8 | 7182.1 | 9020.3  | 2195.7 | 3559.8 | 7312.1  | 50      |
| 52   | 8960.4 | 2157.8 | 3461.2 | 7186.4 | 9022.4  | 2197.0 | 3563.2 | 7316.5  | 52      |
| 54   | 8962.5 | 2159.1 | 3464.5 | 7190.7 | 9024.5  | 2198.3 | 3566.7 | 7320.9  | 54      |
| 56   | 8964.5 | 2160.4 | 3467.9 | 7195.0 | 9026.5  | 2199.6 | 3570.2 | 7325.3  | 56      |
| 58   | 8966.6 | 2161.7 | 3471.2 | 7199.3 | 9028.6  | 2200.9 | 3573.6 | 7329.7  | 58      |
| 60   | 8968.7 | 2163.0 | 3474.6 | 7203.6 | 9030.6  | 2202.3 | 3577.1 | 7334.1  | 60      |
| 104 | 105   |        |        |        |         |        |        |         |         |
|      | LC     | M      | E      | T      | LC      | M      | E      | T       |         |
| 0    | 9030.6 | 2202.3 | 3577.1 | 7334.1 | 9091.8  | 2241.8 | 3682.6 | 7467.5  | 0       |
| 2    | 9032.7 | 2203.6 | 3580.5 | 7338.5 | 9093.9  | 2243.1 | 3686.1 | 7472.0  | 2       |
| 4    | 9034.7 | 2204.9 | 3584.0 | 7342.9 | 9095.9  | 2244.4 | 3689.7 | 7476.5  | 4       |
| 6    | 9036.8 | 2206.2 | 3587.5 | 7347.3 | 9097.9  | 2245.8 | 3693.3 | 7481.0  | 6       |
| 8    | 9038.8 | 2207.5 | 3591.0 | 7351.7 | 9033.3  | 2247.1 | 3696.9 | 7485.5  | 8       |
| 10   | 9040.9 | 2208.8 | 3594.4 | 7356.1 | 9102.0  | 2248.4 | 3700.4 | 7490.0  | 10      |
| 12   | 9042.9 | 2210.2 | 3597.9 | 7360.5 | 9104.0  | 2249.7 | 3704.0 | 7494.5  | 12      |
| 14   | 9045.0 | 2211.5 | 3601.4 | 7364.9 | 9106.0  | 2251.1 | 3707.6 | 7499.1  | 14      |
| 16   | 9047.0 | 2212.8 | 3604.9 | 7369.4 | 9108.0  | 2252.4 | 3711.2 | 7503.6  | 16      |
| 18   | 9049.1 | 2214.1 | 3608.4 | 7373.8 | 9110.1  | 2253.7 | 3714.8 | 7508.1  | 18      |
| 20   | 9051.1 | 2215.4 | 3611.9 | 7378.2 | 9112.1  | 2255.0 | 3718.4 | 7512.6  | 20      |
| 22   | 9053.1 | 2216.7 | 3615.4 | 7382.6 | 9114.1  | 2256.4 | 3722.0 | 7517.2  | 22      |
| 24   | 9055.2 | 2218.0 | 3618.9 | 7387.1 | 9116.1  | 2257.7 | 3725.6 | 7521.7  | 24      |
| 26   | 9057.2 | 2219.4 | 3622.4 | 7391.5 | 9118.1  | 2259.0 | 3729.3 | 7526.3  | 26      |
| 28   | 9059.3 | 2220.7 | 3625.9 | 7396.0 | 9120.2  | 2260.3 | 3732.9 | 7530.8  | 28      |
| 30   | 9061.3 | 2222.0 | 3629.4 | 7400.4 | 9122.2  | 2261.7 | 3736.5 | 7535.3  | 30      |
| 32   | 9063.3 | 2223.3 | 3633.0 | 7404.8 | 9124.2  | 2263.0 | 3740.1 | 7539.9  | 32      |
| 34   | 9065.4 | 2224.6 | 3636.5 | 7409.3 | 9126.2  | 2264.3 | 3743.7 | 7544.4  | 34      |
| 36   | 9067.4 | 2226.0 | 3640.0 | 7413.8 | 9128.2  | 2265.7 | 3747.4 | 7549.0  | 36      |
| 38   | 9069.5 | 2227.3 | 3643.5 | 7418.2 | 9130.2  | 2267.0 | 3751.0 | 7553.6  | 38      |
| 40   | 3071.5 | 2228.6 | 3647.1 | 7422.7 | SI 32.3 | 2268.3 | 3754.6 | 7558.1  | 40      |
| 42   | 9073.5 | 2229.9 | 3650.6 | 7427.1 | 9134.3  | 2269.6 | 3758.3 | 7562.7  | 42      |
| 44   | 3075.6 | 2231.2 | 3654.1 | 7431.6 | 9136.3  | 2271.0 | 3761.9 | 7567.3  | 44      |
| 46   | 9077.6 | 2232.6 | 3657.7 | 7436.1 | 9138.3  | 2272.3 | 3765.6 | 7571.8  | 46      |
| 48   | 9079.6 | 2233.9 | 3661.2 | 7440.6 | 9140.3  | 2273.6 | 3769.2 | 7576.4  | 48      |
| 50   | 9081.7 | 2235.2 | 3664.8 | 7445.0 | 9142.3  | 2275.0 | 3772.9 | 7581.0  | 50      |
| 52   | 9083.7 | 2236.5 | 3668.3 | 7449.5 | 9144.3  | 2276.3 | 3776.5 | 7585.6  | 52      |
| 54   | 9085.7 | 2237.8 | 3671.9 | 7454.0 | 9146.3  | 2277.6 | 3780.2 | 7590.2  | 54      |
| 56   | 9087.8 | 2233.2 | 3675.4 | 7458.5 | 9148.3  | 2278.8 | 3783.8 | 7594.8  | 56      |
| 58   | 9089.8 | 2240.5 | 3679.0 | 7463.0 | 9150.4  | 2280.3 | 3787.5 | 7599.4  | 58      |
| 60   | 9091.8 | 2241.8 | 3682.6 | 7467.5 | 9152.4  | 2281.6 | 3791.2 | 7604.0  | 60      |
|      |        |        |        |        |         |        |        |         |         |

## Table A-6. Corrections For Tangent And External Distances

A-6. (Table A-6, page A-146, is to convert tabular values in table A-5, page A-110, to the chord definition.)

## A-7. Example

Required are the tangent, external distance, and length of curve for a curve of 18${}^{\circ}$ 20' and an I angle of 9${}^{\circ}$ 46'.

$$Tangent\ T\ =\frac{Tabluar\ Entry}{Degree\ of\ Curve}-\frac{489.56}{18.333}=\ 26.70$$

$+$ (correction to be added from table A-6 for 18${}^{\circ}$ 20' and 9${}^{\circ}$ 46') 0.12' = 26.82'

$$External\ Distance\ =\frac{Tabluar\ Entry}{Degree\ of\ Curve}=\frac{20.88}{18.333}=\ 1.139$$


                  + (correction to be added from table A-6 for 18 20' and 9 46') 0.005 = 1.14'


Angle
Curve
5
10
15
20
25
30
35
40
45
50
55
60
65
5
.02
.03
.05
.06
.08
10
.11
.13
.15
.16
.18
.20
.21
10
.03
.06
.09
.13
.16
.19
.22
.25
.28
.31
.34
.38
.42
15
.04
.10
.14
.19
.24
.29
.34
.39
.45
.51
.53
.58
.63
20
.06
.13
.19
.26
.32
.39
.45
.51
.58
.65
.72
.79
.84
25
.08
.16
.24
.33
.40
.49
.58
.67
.75
.83
.90
.99
1.06
30
.10
.19
.29
.39
.49
.59
.69
.79
.89
.99
1.09
1.20
1.29
35
.11
.22
.34
.47
.58
.69
.80
.93
1.05
1.17
1.29
1.42
1.54
40
.13
.26
.40
.53
.67
.80
.93
1.06
1.20
1.34
1.49
1.64
1.79
45
.15
.30
.44
.60
.76
.91
1.06
1.21
1.37
1.52
1.70
1.87
2.04
50
.17
.34
.51
.68
.85
1.02
1.19
1.36
1.54
1.72
1.91
2.10
2.29
55
.19
.38
.57
.76
.95
1.14
1.32
1.52
1.72
1.92
2.14
2.35
2.56
60
.21
.42
.63
.84
1.05
1.27
1.49
1.71
1.92
2.17
2.38
2.60
2.83
65
.23
.46
.69
.93
1.16
1.40
1.64
1.88
2.13
2.38
2.63
2.88
3.13
70
.25
.51
.76
1.02
1.28
1.54
1 80
2.06
2.33
2.60
2.88
3.16
3.44
75
.27
.56
.83
1 12
1.40
1.69
1.98
2.27
2.57
2.87
3.16
3.47
3.78
80
.30
.61
.91
1.22
1.53
1.84
2.15
2.46
2.78
310
3.44
3.78
4.12
85
.33
.86
1.00
1.33
1.68
2.02
2.36
2.70
3.05
3.40
3.77
4.14
4.55
90
.36
.72
1.09
1.45
1.83
2.20
2.57
2.94
3.32
3.70
4.10
4.60
4.91
95
.39
.79
1.19
1.55
2.00
2.40
2.80
3.20
3.61
4.02
4.49
4.98
5.38
100
.43
.86
1.30
1.74
2.18
2.62
3.06
3.60
3.95
4.40
4.88
5.37
5.85
105
.46
.94
1.42
1.90
2.38
2.37
3.34
3.84
4.36
4.84
535
5.87
6.40
110
.50
1.03
1.55
2.08
2.60
3.14
3.66
4.21
4.76
5.31
586
6.43
7.01
115
.54
1.13
1.70
2.29
2.86
3.45
4.03
4.63
5.23
5.83
6.44
7.07
7.70
120
.61
1.25
1.89
2.52
3.16
3.81
4.44
5.11
5.78
6.44
7.11
7.80
8.51
Angle
Curve
5
10
15
20
25
30
35
40
45
50
55
60
65
5
.000
.000
.001
.001
.002
.002
.002
.003
.003
.004
.004
.004
.005
10
.001
.003
.004
.006
.007
.008
.009
.011
.012
.014
.015
.017
.018
15
.003
.007
.010
.014
.018
.023
.027
.029
.032
.035
.039
.043
.047
20
.006
.011
.017
.022
.028
.034
.038
.045
.051
.057
.063
.070
.076
25
.005
.018
.027
.036
.046
.056
.065
.074
.083
.093
.106
.120
.127
30
.013
.025
.038
.051
.065
.078
.090
.103
.116
.129
.149
.170
.179
35
.018
.035
.054
.072
.086
.109
.131
.153
.175
.197
.213
.230
.247
40
.023
.046
.070
.093
.117
.141
.172
.203
.234
.265
.277
.290
.315
45
.030
.060
.093
.119
.153
.184
.216
.254
.289
.325
.351
.378
.411
50
.037
.075
.116
.151
.189
.227
.266
.305
.345
.384
.425
.467
.508
55
.046
.093
.142
.188
.236
.283
.332
.381
.420
.479
.530
.582
.641
60
.056
.112
.168
.225
.283
.340
.398
.457
.516
.575
.636
.697
.774
65
.067
.135
.204
.273
.343
.412
.483
.554
.625
.697
.711
.845
.922
70
.080
.159
.240
.321
.403
.485
.568
.652
.735
.819
.906
.994
1.08
75
.095
.182
.286
.383
.480
.578
.678
.777
.877
.977
1.07
1.18
1.29
80
.110
.220
.332
.445
.558
.671
.787
.903
1.02
1.13
1.25
1.38
1.50
85
.128
.259
.391
.524
.657
.790
.926
1.06
1.20
1.34
1.47
1.62
1.76
90
.149
.299
.450
.603
.756
.910
1.07
1.22
1.38
1.54
1.70
1.87
2.03
95
.174
.350
.522
.706
.985
1.06
1.25
1.43
1.62
1.80
1.99
2.18
2.38
100
.200
.401
.604
.809
1.01
1.22
1.43
1.64
1.85
2.06
2.28
2.50
2.73
105
.230
.470
.700
.938
1.17
1.42
1.65
1.90
2.14
2.39
2.64
2.90
3.16
110
.260
.535
.808
1.08
1.36
1.63
1.91
2.19
2.49
2.61
3.05
3.35
3.65
115
.307
.624
.939
1 26
1 57
1 89
2.21
2.54
2.87
3.20
3.53
3.88
4.23
120
.339
.720
1.08
1.45
1.82
2.20
2.56
2.95
3.33
3.72
4.10
4.50
4.91

| Deflection =              | 1718. 873            |
|---------------------------|----------------------|
| R                         |                      |
| arc length                |                      |
|                           |                      |
| Chord = 2R sin definition |                      |
|                           |                      |
| Radius                    |                      |
| Deflection for arc length | Chord for arc length |
| Degree of curve. Arc      |                      |
| definition                |                      |
| 25'                       | 50'                  |
| 150                       | 4 46.48'            |
| 200                       | 3 34.86'            |
| 225                       | 3 10.98'            |
| 250                       | 2 51.89'            |
| 275                       | 2 36.36'            |
| 300                       | 2 23.24'            |
| 325                       | 2 12 22'            |
| 350                       | 2 02.78'            |
| 375                       | 1 54.59'            |
| 400                       | 1 47.43'            |
| 450                       | 1 35.49'            |
| 500                       | 1 25.94'            |
| 550                       | 1 18.13'            |
| 600                       | 1 11.62'            |
| 650                       | 1 06.11'            |
| 700                       | 1 01.39'            |
| 750                       | 0 57.30'            |
| 800                       | 0 53.71'            |
| 850                       | 0 50.56'            |
| 900                       | 0 47.75'            |
| 950                       | 0 45.23'            |
| 1000                      | 0 42.97'            |
| 1050                      | 0 40.93'            |
| 1100                      | 0 39.07'            |
| 1150                      | 0 37.37'            |
| 1200                      | 0 35.81'            |
| 1300                      | 0 33.06'            |
| 1400                      | 0 30.69'            |
| 1500                      | 0 28 65'            |
| 1600                      | 0 26.86'            |
| 1700                      | 0 25.28'            |
| 1800                      | 0 23.87'            |
| 1900                      | 0 2262'             |
| 2000                      | 0 21.49'            |
| 2100                      | 0 20.46'            |
| 2200                      | 0 19.53'            |
| 2300                      | 0 18.68'            |
| 2400                      | 0 17.91'            |
| 2500                      | 0 17.19             |
| 3000                      | 0 14.32'            |
| 3500                      | 0 12.28'            |
| 4000                      | 0 10.74'            |
| 4500                      | 0 09.55'            |
| 5000                      | 0 08.59             |
| 6000                      | 0 07 16'            |
| 7000                      | 0 06.14'            |
| 7500                      | 0 06.73'            |
| 8000                      | 0 05 37'            |
| 9000                      | 0 04.77'            |
| 10000                     | 0 04.30'            |

## Table A-8. Squares, Cubes, Square Roots, And Cube Roots

A-8. Example; The square of 26 = 676; the cube of 26 = 17,576; the square root of 26 = 5.0990; the cube root of 26 = 2.9625.

A-9. To find the square root of a decimal or mixed number, first multiply the number by either 100
or 10,000 to eliminate as many of the decimals as possible. Round the result off to the nearest whole number. Locate this number in the square column. Determine the desired square root by taking the corresponding number from the number column and moving the decimal point. If the original number was multiplied by 100, move the decimal one place to the left; if it was multiplied by 10,000, move the decimal two places to the left.

A-10. Example:
A-11. Find the square root of 5.246 to the first decimal place. Multiply by 100. The result is 524. The nearest number in the column of squares is 529, which is opposite 23 in the column of numbers. Move the decimal point one place to the left. This gives 2.3 as the desired root to the first place of decimals.

A-12. Find the square root of 5.246 to the second decimal place. Multiply by 10,000. The result is
52,460. The nearest number in the column of squares is 52,441, which is opposite 229 in the column of numbers.

A-13. Move the decimal point two places to the left. The result is 2.29 A-14. To find the cube root of a similar number, multiply by 1,000 or by 1,000,000, and find the nearest number in the column of cubes. The corresponding number in the column of numbers with a decimal point one or two places to the left is the required root. Perform similarly to preceding example.


To find the square root or cube root of number greater than 1,000, find the nearest number in the column of squares or cubes and take the corresponding number in the first column. The number thus found is correct for the number of figures it contains.

To find various roots: For the fourth root, take the square root of the square root. For the sixth root, take the square root of the cube root or vice versa. Higher roots, whose indices can be factored into 2s and 3s, may be obtained in a similar manner.


No.

Square

Cube
Square
Root
Cube
Root

No.

Square

Cube
Square
Root
Cube
Root
1
1
1
1.0000
1.
21
441
9261
4.5826
2.7589
2
4
8
1.4142
1.2599
22
484
10648
4.6904
2.8020
3
9
27
1.7321
1.4422
23
529
12167
4.7958
2.8439
4
16
64
2.0000
1.5874
24
576
13824
4.8990
2.8845
5
25
125
2.2361
1.7100
25
625
15625
5.0000
2.9240
6
36
216
2.4495
1.8171
26
676
17576
5.0990
2.9625
7
49
343
2.6468
1.9129
27
729
19683
5.1962
3.0000
8
64
512
2.8284
2.0000
28
784
21952
5.2915
3.0366
9
81
729
3.0000
2.0801
29
841
24389
5.3852
3 0723
10
100
1000
3.1623
2.1544
30
900
27000
5.4772
3.1072
11
121
1331
3.3166
2.2240
31
961
29791
5.5678
3.1414
12
144
1728
3.4641
2.2894
32
1024
32768
5.6569
3.1748
13
169
2197
3.6056
2.3513
33
1089
35937
5.7446
3.2075
14
196
2744
3.7417
2.4101
34
1156
39304
5.8310
3.2396
15
225
3375
3.8730
2.4662
35
1225
42875
5.9161
3.2711
16
256
4096
4.0000
2.5198
36
1296
46656
6.0000
3.3019
17
289
4913
4.1231
2.5713
37
1369
50653
6.0828
3.3322
18
324
5832
4.2426
2.6207
38
1444
548 72
6.1644
3.3620
19
361
6859
4.3569
2.6884
39
1521
59315
6.2450
3.3912
20
400
8000
4.4721
2.7144
40
1600
64000
6.3246
3.4200



No.

Square

Cube
Square
Root
Cube
Root

No.

Square

Cube
Square
Root
Cube
Root
41
1681
68921
6.4031
3.4482
91
8281
753571
9.5394
4.4979
42
1764
74088
8.4807
3.4760
92
8464
778688
9.5917
4.5144
43
1849
79507
6.5574
3.5034
93
8649
804357
9.6437
4.5307
44
1936
85184
6.6332
3.5303
94
8836
830584
9.6954
4.5468
45
2025
91125
6.7082
3.5569
95
9025
857375
9.7468
4.5629
46
2116
97336
6.7823
3.5830
96
9216
884736
9.7980
4.5789
47
2209
103823
6.8557
3.6088
97
9409
912673
9.8489
4.5947
48
2304
110592
6.9282
3.6342
98
9604
941192
9.8995
4.6104
49
2401
117649
7.0000
3.6593
99
9801
970299
9.9499
4.6261
50
2500
125000
7.0711
3.6840
100
10000
1000000
10.0000
4.6416
51
2601
132651
7.1414
3.7084
101
10201
1030301
10.0499
4.6570
52
2704
140608
7.2111
37325
102
10404
1061208
10.0995
4.6723
53
2809
148877
7.2801
3.7563
103
10609
1092727
10.1489
4.6875
54
2916
157464
7.3485
3.7798
104
10816
1124864
10.1980
4.7027
55
3025
166375
7.4162
3.8030
105
11025
1157625
10.2470
4.7177
56
3136
175616
7.4833
3.8259
106
11236
1191016
10.2956
4.7326
57
3249
185193
7.5498
3.8485
10?
11449
1225043
10.3441
4.7475
58
3364
195112
7.6158
3.8709
108
11664
1259712
10.3923
4.7622
59
3481
205379
7.6811
3.8930
109
11881
1295023
10.4403
4.7769
60
3600
216000
7.7460
3.9149
110
12100
1331000
10.4881
4.7914
61
3721
228981
7.8102
3.9365
111
12321
1367631
10.5357
4.8059
62
3844
238328
7.8740
3.9579
112
12544
1404928
10.5830
4.8203
63
3969
250047
7.9373
3.9791
113
12769
1442896
10.6301
4.8346
64
4096
262144
8.0000
4.0000
114
12996
1481544
10.6771
4.8488
65
4225
274625
8.0623
4.0207
115
13225
1520875
10.7238
4.8629
66
4356
287496
8.1240
4.0412
116
13456
1560896
10.7703
4.8770
67
4489
300763
8.1854
4.0615
117
13689
1601613
10.8167
4.8910
68
4624
314432
8.2462
4.0817
118
13924
1643032
10.8628
4.9049
69
4761
328509
8.3066
4.1016
119
14161
1685169
10.9087
4.9187
70
4900
343000
8.3666
4.1213
120
14400
1728000
10.9545
4.9324
71
5041
357911
8.4261
4.1408
121
14641
1771561
11.0000
4.9461
72
5184
373248
8.4853
4.1602
122
14884
1815848
11.0464
4.9597
73
5329
389017
8.5440
4.1793
123
15129
1860867
11.0905
4.9732
74
5476
405224
8.6023
4.1983
124
15376
1906624
11.1355
4.9866
75
5625
421875
8.6603
4.2172
125
16625
1953125
11.1803
5.0000
76
5776
438976
8.7178
4.2358
126
15876
2000376
11.2250
5.0133
77
5929
456533
8.7750
4.2543
127
16129
2048383
11.2694
5.0266
78
6084
474552
8.8318
4.2727
128
16384
2097152
11.3137
5.0397
79
6241
493039
8.8882
4.2908
129
16641
2146689
11.3578
5.0528
80
6400
512000
8.9443
4.3089
130
16900
2197000
11.4018
5.0658
81
6561
531441
9.0000
4.3267
131
17161
2248091
11.4455
5.0788
82
6724
551368
9.0554
4.3445
132
17424
2299968
11.4891
5.0916
83
6889
571787
9.1104
4.3621
133
17689
2352637
11.5326
5.1045
84
7056
592704
9.1652
4.3795
134
17956
2406104
11.5758
5.1172
85
7225
614125
9.2195
4.3968
135
18225
2460375
11.6190
5.1299
86
7396
636056
9.2736
4.4140
136
18496
2515456
11.6619
5.1426
87
7569
658503
9.3274
4.4310
137
18769
2671353
11.7047
5.1551
88
7744
681472
9.3808
4.4480
138
19044
2628072
11.7473
5.1676
89
7821
704969
9.4340
4.4647
139
19321
2685619
11.7898
5.1801
90
8100
729000
9.4868
4.4814
140
19600
2744000
11.8322
5.1925


No.

Square

Cube
Square
Root
Cube
Root

No.

Square

Cube
Square
Root
Cube
Root
141
19881
2803221
11.8743
5.2048
191
36481
6967871
13.8203
5.7590
142
20164
2863288
11.9164
5.2171
192
36864
7077888
13.8564
5.7690
143
20449
2924207
11.9583
5.2293
193
37249
7189057
13.8924
5.7790
144
20736
2985984
12.0000
5.2415
194
37636
7301384
13.9284
5.7890
145
21025
3048625
12.0416
5.2536
195
38025
7414875
13.9642
5.7989
146
21316
3112136
12.0830
5.2666
196
38416
7529536
14.0000
5.8088
147
21609
3176523
12.1244
5.2776
197
38809
7645373
14.0357
5.8186
148
21904
3241792
12.1655
5.2896
198
39204
7762392
14.0712
5.8285
149
22201
3307949
12.2066
5.3015
199
39601
7880599
14.1067
5.8383
150
22500
3375000
12.2474
5.3133
200
40000
8000000
14.1421
5.8480
151
22801
3442951
12.2882
5.3251
201
40401
8120601
14.1774
5.8578
152
23104
3611808
12.3288
5.3368
202
40804
8242408
14.2127
5.8675
153
23409
3581577
12.3693
5.3485
203
41209
8365427
14.2478
5.8771
154
23716
36S2264
12.4097
5.3601
204
41616
8489664
14.2829
5.8868
155
24025
3723875
12.4499
5.3717
205
42025
8615125
14.3178
5.8964
156
24336
3796416
12.4900
5.3832
206
42436
8741816
14.3527
5.9059
157
24649
3869893
12.5300
5.3947
207
42849
8869743
14.3875
5.9155
158
24964
3944312
12.5698
5.4061
208
43264
8998912
14.4222
5.9250
159
26281
4019679
12.6095
5.4175
209
43681
9129329
14.4568
5.9345
160
26600
4096000
12.6491
5.4288
210
44100
9261000
14.4914
5.9439
161
25921
4173281
12.6886
5.4401
211
44521
9393931
14.5258
5.9533
162
26244
4251528
12.7279
5.4514
212
44944
9528128
14.5602
6.9627
163
26569
4330747
12.7671
5.4626
213
45369
9663597
14.5945
5.9721
164
26896
4410944
12.8062
5.4737
214
45796
9800344
14.6287
5.9814
165
27225
4492125
12.8452
5.4848
215
46225
9938375
14.6629
5.9907
166
27556
4574296
12.8841
5.4959
216
46656
10077696
14.6969
6.0000
167
27889
4657463
12.9228
5.5069
217
47089
10218313
14.7309
6.0082
168
28224
4741631
12.9615
5.5178
218
47524
10360232
14.7648
6.0185
169
28561
4826809
13.0000
5.5288
219
47961
10503459
14.7986
6.0277
170
28900
4913000
13.0334
5.5397
220
48400
10648000
14.8324
6.0368
171
29241
5000211
13.0767
5.6505
221
48841
10793861
14.8661
6.0459
172
29584
5088448
13.1149
5.5613
222
49284
10941048
14.8997
6.0550
173
29929
5177717
131529
5.5721
223
49729
11089567
14.9332
6.0641
174
30276
5268024
13.1909
5.5828
224
50176
11239424
14.9666
6.0732
175
30625
5359375
13.2288
5.5934
225
50625
11390626
15.0000
6.0822
176
30976
5451776
13.2665
5.6041
226
51076
11543176
15.0333
6.0912
177
31329
5545233
13.3041
5.6147
227
51529
11697083
15.0666
6.1002
178
31684
5639752
13.3417
5.6252
228
51984
11852352
150997
6.1091
179
32041
5735339
13.3791
5.6357
229
52441
12008989
15.1327
6.1180
180
32400
5832000
13.4164
5.6462
230
52900
12167000
151658
6.1269
181
32761
5929741
13.4536
5.6567
231
53361
12326391
15.1987
6.1358
182
33124
6028568
13.4907
5.6671
232
53824
12487168
15.2315
6.1446
183
33489
6128487
13.5277
5.6774
233
54289
12649337
15.2643
6.1534
184
33856
6229504
13.5647
5.6877
234
54756
12812904
15.2971
6.1622
185
34225
6331625
13.6015
5.6980
235
55225
12977875
15.3297
6.1710
186
34596
6434856
13.6382
5.7083
236
56696
13144256
15.3623
6.1797
187
34969
6539203
13.6748
5.7185
237
56169
13312053
15.3948
6.1885
188
35344
6644672
13.7113
5.7287
238
56644
13481272
15.4272
6.1972
189
35721
6751269
13.7477
5.7388
239
57121
13651919
15.4596
6.2058
190
36100
6859000
13.7840
5.7489
240
57600
13824000
15.4919
6.2145

No.

Square

Cube
Square
Root
Cube
Root

No.

Square

Cube
Square
Root
Cube
Root
241
58081
13997521
15.5242
6.2231
291
84681
24642171
17.0587
6.6267
242
58564
14172488
15.5563
6.2317
292
85264
24897088
17.0880
6.6343
243
59049
14348907
15.5885
6.2403
293
85849
25153757
17.1172
6.6419
244
58536
14526784
15.6205
6.2488
294
86436
25412184
17.1464
6.6494
245
60025
14706125
15.6525
6.2573
295
87025
25672375
17.1756
6.6569
246
60616
14886936
15.6844
6.2658
296
87616
25934336
17.2047
6.6644
247
61098
16069223
15.7162
6.2743
297
88209
26198073
17.2337
6.6719
248
61504
15252992
15.7480
6.2828
298
88804
26463592
17.2627
6.6794
249
62001
15438249
15.7797
6.2912
299
89401
26730899
17.2916
6.6869
250
62500
15625000
15.8114
6.2996
300
90000
27000000
17 3205
6.6943
251
63001
15813251
15.8430
6.3080
301
90601
27270901
17.3494
6.7018
252
63504
16003008
15.8745
6.3164
302
91204
27543608
17.3781
6.7092
253
64009
16194277
15.9060
6.3247
303
91808
27818127
17.4069
6.7166
254
64516
16387064
15.9374
6.3330
304
92416
28034464
17.4356
6.7240
255
65025
16581375
15.9687
6.3413
305
93025
28372625
17.4642
6.7313
256
66636
16777216
16.0000
6.3496
306
93636
28652616
17.4929
6.7387
257
66049
16974593
16.0312
6.3579
307
94249
28934443
17.5214
6.7460
258
66564
17173512
16.0624
6.3661
308
94864
29218112
17.5499
6.7533
259
67081
17373979
16.0935
6.3743
309
95481
29503629
17.5784
6.7606
260
67600
17576000
16.1245
6.3825
310
96100
29791000
17.6068
6.7679
261
68121
17779581
16.1555
6.3907
311
96721
30080231
17.6352
6.7752
262
68644
17984728
16.1864
6.3988
312
97344
30371328
17.6635
6.7824
263
69169
18191447
16.2173
6.4070
313
97969
30664287
17.6918
6.7897
264
69696
18399744
16.2481
6.4151
314
98596
30959144
17.7200
6.7969
265
70225
18609625
16.2788
6.4232
315
99225
31255875
17 7482
6.8041
266
70756
18821096
16.3095
6.4312
316
99856
31554496
17.7764
6.8113
267
71289
19034163
16.3401
6.4393
317
100489
31855013
17 8045
6.8185
268
71824
19248832
16.3707
6.4473
318
101124
32157432
17.8326
6.8256
269
72361
19465109
16.4012
6.4553
319
101761
32461759
17 8606
6.8328
270
72900
19683000
16.4317
6.4633
320
102400
32768000
17.8885
6.8399
271
73441
19902511
16.4621
6.4713
321
103041
33076161
17 9165
6.8470
272
73984
20123648
16.4924
6.4792
322
103684
33386248
17 9444
6.8541
273
74529
20346417
16.5227
6.4872
323
104329
33698267
17.9722
6.8612
274
75076
20570824
16.5529
6.4951
324
104976
34012224
18.0000
6.8683
275
75625
20796875
16.5831
6.5030
325
105625
34328125
18.0278
6.8753
276
76176
21024576
16.6132
6.5108
326
106276
34845976
18.0555
6.8824
277
76729
21253933
16.6433
6.5187
327
106929
34965783
18.0831
6.8894
278
77284
21484952
16.6733
6.5265
328
107584
36287552
18.1108
6.8964
279
77841
21717639
16 7033
6.5343
329
108241
35611289
18.1384
6.9034
280
78400
21952000
16.7332
6.5421
330
108900
35937000
18.1659
6.9104
281
78961
22188041
16.7631
6.5499
331
109561
36264691
18.1934
6.9174
282
79524
22425768
16.7929
6.5577
332
110224
36694368
18.2209
6.9244
283
80089
22665187
16.8226
6.5654
333
110889
36926037
18.2483
6.9313
284
80656
22906304
16.8523
6.5731
334
111556
37259704
18.2757
6.9382
285
81225
23148125
16.8819
6.5808
335
112225
37595375
18.3030
6.9451
286
81796
23393656
16.9115
6.5885
336
112896
37933056
18.3303
6.9521
287
82369
23639903
16.9411
6.5962
337
113569
38272753
18.3576
6.9589
288
82944
23887872
16.9706
6.6039
338
114244
38614472
18.3848
6.9668
289
83521
24137569
17.0000
6.6115
339
114921
38958219
18.4120
6.9727
290
84100
24389000
17.0294
6.6191
340
115600
39304000
18.4391
6.9795


No.

Square

Cube
Square
Root
Cube
Root

No.

Square

Cube
Square
Root
Cube
Root
341
116281
39651821
18.4662
6.9864
391
152881
59776471
19.7737
7.3124
342
116964
40001688
18.4932
6.9932
392
153664
60236288
19.7990
7.3186
343
117649
40353607
18.5203
7.0000
393
154449
60698457
19.8242
7.3248
344
118336
40707584
18.5472
7.0068
394
155236
61162984
19.8494
7.3310
345
119025
41063625
18.5742
7.0136
395
156025
61629875
19.8746
7.3372
346
119716
41421736
18.6011
7.0203
396
156816
62099136
19.8997
7.3434
347
120409
41781923
18.6279
7.0271
397
157609
62570773
19.9249
7.3496
348
121104
42144192
18.6548
7.0338
398
158404
63044792
19.9499
7.3558
349
121801
42508549
18.6815
7.0406
399
159201
63521199
19.9750
7.3619
350
122500
42875000
18.7083
7.0473
400
160000
64000000
20.0000
7.3681
351
123201
43243551
18.7350
7.0540
401
160801
64481201
20.0250
7.3742
352
123904
43614208
18.7617
7.0607
402
161604
64964808
20.0499
7.3803
353
124609
43986977
18.7883
7.0674
403
162409
65450827
20.0749
7.3864
354
125316
44361864
18.8149
7.0740
404
163216
65939264
20.0998
7.3925
355
126025
44738875
18.8414
7.0807
405
164025
66430125
20.1246
7.3986
356
126736
45118016
18.8680
7.0873
406
164836
66923416
20.1494
7.4047
357
127449
45499293
18.8944
7.0940
407
165649
67410143
20.1742
7.4108
358
128164
45882712
18.9209
7.1006
408
166464
67917312
20.1990
7.4169
359
128881
46268279
18.9473
7.1072
409
167281
68417929
20.2237
7.4229
360
129600
46656000
18.9737
7.1138
410
168100
68921000
20.2485
7.4290
361
130321
47045881
19.0000
7.1204
411
168921
69426531
20.2731
7.4350
362
131044
47437928
19.0263
7.1269
412
169744
69934528
20.2978
7.4410
363
131769
47832147
19.0526
7.1335
413
170569
70444997
20.3224
7.4470
364
132496
48228544
19.0788
7.1400
414
171396
70957944
20.3470
7.4530
365
133225
48627125
19.1050
7.1466
415
172225
71473375
20.3715
7.4590
366
133956
49027896
19.1311
7.1531
416
173056
71991296
20.3961
7.4650
367
134689
49430863
19.1572
7.1596
417
173889
72511713
20.4206
7.4710
368
135424
49836032
19.1833
7.1661
418
174724
73034632
20.4450
7.4770
369
136161
50243409
19.2094
7.1726
419
175561
73560059
20.4695
7.4829
370
136900
50653000
19.2354
7.1791
420
176400
74088000
20.4939
7.4889
371
137641
51064811
19.2614
7.1855
421
177241
74618461
20.5183
7.4948
372
138384
51478848
19.2873
7.1920
422
178084
75151448
20.5426
7.5007
373
139129
51895117
19.3132
7.1984
423
178929
75686967
20.5670
7.5067
374
139786
52313624
19.3391
7.2048
424
179776
76225024
20.5913
7.5126
375
140625
52734375
19.3649
7.2112
425
180625
76765625
20.6155
7.5185
376
141376
53157376
19.3907
7.2177
426
181476
77308776
20.6398
7.5244
377
142129
53582633
19.4165
7.2240
427
182329
77854483
20.6640
7.5302
378
142884
54010152
19.4422
7.2304
428
183184
78402752
20.6882
7.5361
379
143641
54439939
19.4679
7.2368
429
184041
78953589
20.7123
7.5420
380
144400
54872000
19.4936
7.2432
430
184900
79507000
20.7364
7.5478
381
145161
55306341
19.5192
7.2495
431
185761
80062991
20.7605
7.5537
382
145924
55742968
19.5448
7.2558
432
186624
80621568
20.7846
7.5595
383
146689
56181887
19.5704
7.2622
433
187489
81182737
20.8087
7.5654
384
147456
56623104
19.5959
7.2685
434
188356
81746504
20.8327
7.5712
385
148225
57066625
19.6214
7.2748
435
189225
82312875
20.8567
7.5770
386
148996
57512456
1 9.6469
7.2811
436
190096
82881856
20.8806
7.5828
387
149769
57960603
19.6723
7.2874
437
190969
83453453
20.9045
7.5886
388
150544
58411072
19.6977
7.2936
438
191844
84027672
20.9284
7.5944
389
151321
58863869
19.7231
7.2999
439
192721
84604519
20.9523
7.6001
390
152100
59319000
19.7484
7.3061
440
193600
85184000
20.9762
7.6059


No.

Square

Cube
Square
Root
Cube
Root

No.

Square

Cube
Square
Root
Cube
Root
441
194481
85766121
21.0000
7.6117
491
241081
118370771
22.1585
7.8891
442
195364
86350888
21.0238
7.6174
492
242064
119895488
22.1811
7.8944
443
196249
86938307
21.0476
7.6232
493
243049
119823157
22.2036
7.8998
444
197136
87528384
21.0713
7.6289
494
244036
120553784
22.2261
7.9051
445
198025
88121125
21.0950
7.6346
495
245025
121287375
22.2486
7.9105
446
198916
88716536
211187
7.6403
496
246016
122023936
22.2711
7.9158
447
198809
89314623
21.1424
7.6460
497
247009
122763473
22.2935
7.9211
448
200704
89915392
21.1660
7.6517
498
248004
123505992
22.3159
7.9264
449
201601
90518849
21.1896
7.6574
499
249001
124251499
22.3383
7.9317
450
202500
91125000
21.2132
7.6631
500
250000
125000000
22.3607
7.9370
451
203401
91733851
21.2368
7.6688
501
251001
125751501
22.3830
7.9423
452
204304
92345408
21.2603
7.6744
502
252004
126506008
22.4054
7.9476
453
205209
92959677
21.2838
7.6801
503
253009
127263527
22.4277
7.9528
454
206116
93576664
21.3073
7.6857
504
254016
128024064
22.4499
7.9581
455
207025
94196375
21.3307
7.6914
505
255025
128787625
22.4722
7.9634
456
207936
94818816
21.3542
7.6970
506
256036
129554216
22.4944
7.9686
457
208849
95443993
21.3776
7.7026
507
257049
130323843
22.5167
7.9739
458
209764
96071912
21.4009
7.7082
508
258064
131096512
22.5389
7.9791
459
210681
96702579
21.4243
7.7138
509
259081
131872229
22.5610
7.9843
460
211600
97336000
21.4476
7.7194
510
260100
132651000
22.5832
7.9896
461
212521
97972181
21.4709
7.7250
511
261121
133432831
22.6053
7.9948
462
213444
98611128
21.4942
7.7306
512
262144
134217728
22.6274
8.0000
463
214369
99252847
21.5174
7.7362
513
263169
135005697
22.6495
8.0052
464
215296
99897344
21.5407
7.7418
514
264196
135796744
22.6716
8.0104
465
216225
100544625
21.5639
7.7473
515
265225
136590875
22.6936
8.0156
466
217156
101194696
21.5870
7.7529
516
266256
137388096
22.7156
8.0208
467
218089
101847563
21.6102
7.7584
517
267289
138188413
22.7376
80206
468
219024
102503232
21.6333
7.7639
518
268324
138991832
22.7596
8.0311
469
219961
103161709
21.6564
7.7695
519
269361
139798359
22.7816
8.0363
470
220900
103823000
21.6795
7.7750
520
270400
140608000
22.8035
8.0415
471
221841
104487111
21.7025
7.7805
521
271441
141420761
22.8254
8.0466
472
222784
105154048
21.7256
7.7860
522
272484
142236648
22.8473
8.0517
473
223729
105823817
21.7486
7.7915
523
273529
143055667
22.8692
8.0569
474
224676
106496424
21.7715
7.7970
524
274576
143877824
22.8910
8.0620
475
225625
107171875
21.7945
7.8025
525
275625
144703125
22.9129
8.0671
476
226576
107850176
21.8174
7.8079
526
276676
145531576
22.9347
8.0723
477
227529
108531333
21.8403
7.8134
527
277729
146363183
22.9565
8.0774
478
228484
109215352
21.8632
7.8188
528
278784
147197952
22.9783
8.0825
479
229441
109902239
21.8861
7.8243
529
279841
148035889
23.0000
8.0876
480
230400
110592000
21.9089
7.8297
530
280900
148877000
23.0217
8.0927
481
231361
111284641
21.9317
7.8352
531
281961
149721291
23.0434
8.0978
482
232324
111980168
21.9545
7.8406
532
283024
150568768
23.0651
8.1028
483
233289
112678587
21.9773
7.8460
533
284089
151419437
23.0868
8.1079
484
234256
113379904
22.0000
7.8514
534
285156
152273304
23.1084
8.1130
485
235225
114084125
22.0227
7.8568
535
286225
153130375
23.1301
8.1180
486
236196
114791256
22.0454
7.8622
536
287296
153990656
23.1517
8.1231
487
237169
115501303
22.0681
7.8676
537
288369
154854153
23.1733
8.1281
488
238144
116214272
22.0907
7.8730
538
289444
155720872
23.1948
8.1332
489
239121
116930169
22.1133
7.8784
539
290521
156590819
23.2164
8.1382
490
240100
177649000
22.1359
7.8837
540
291600
157464000
23.2379
8.1433


No.

Square

Cube
Square
Root
Cube
Root

No.

Square

Cube
Square
Root
Cube
Root
541
292681
138340421
23.2594
8.1483
591
349281
206425071
24.3105
8.3919
542
293764
149220088
23.2809
8.1533
592
350464
207474688
24.3311
8.3967
543
294849
160103007
23.3024
8.1583
593
351649
208527857
24.3516
8.4014
544
295936
160989184
23.3238
8.1633
594
352836
209584584
24.3721
8.4061
545
297025
161878625
23.3452
8.1683
595
354025
210644875
24.3926
8.4108
546
298116
162771336
23.3666
8.1733
596
355216
211708736
24.4131
8.4155
547
299209
163667323
23.3880
8.1783
597
356409
212776173
24.4336
8.4202
548
300304
164566592
23.4094
8.1833
598
357604
213847192
24.4540
8.4249
549
301401
165469149
23.4307
8.1882
599
358801
214921799
24.4745
8.4296
550
302500
166375000
23.4521
8.1932
600
360000
216000000
24.4949
8.4343
551
303601
167284151
23.4734
8.1982
601
361201
217081801
24.5153
8.4390
552
304704
168196608
23.4947
8.2031
602
362404
218167208
24.5357
8.4437
553
305809
169112377
23.5160
8.2081
603
363609
219256227
24.5561
8.4484
554
306916
170031464
23.5372
8.2130
604
364816
220348864
24.5764
8.4530
555
308025
170953875
23.5584
8.2180
605
366025
221445125
24.5967
8.4577
556
309136
171879616
23.5797
8.2229
606
367236
222545016
24.6171
8.4623
557
310249
172808693
23.6008
8.2278
607
368449
233648543
24.6374
8.4670
558
311364
173741112
23.6220
8.2327
608
369664
224755712
24.6577
8.4716
559
312481
174676879
23.6432
8.2377
609
370881
225866529
24.6779
8.4763
560
313600
175616000
23.6643
8.2426
610
372100
226981000
24.6982
8.4809
561
314721
176558481
23.6854
8.2475
611
373321
228099131
24.7184
8.4856
562
315844
177504328
23.7065
8.2524
612
374544
229220928
24.7386
8.4902
563
316969
178453547
23.7276
8.2573
613
375769
230346397
24.7588
8.4948
564
318096
179406144
23.7487
8.2621
614
376996
231475544
24.7790
8.4994
565
319225
180362125
23.7697
8.2670
615
378225
232608375
24.7992
8.5040
566
320356
181321496
23.7908
8.2719
616
379456
233744896
24.8193
8.5086
567
321489
182284263
23.8118
8.2768
617
380689
234885113
24.8395
8.5132
568
322624
183250432
23.8328
8.2816
618
381924
236029032
24.8596
8.5178
569
323761
184220009
23.8537
8.2865
619
383161
237176659
24.8797
8.5224
570
324900
185193000
23.8747
8.2913
620
384400
238328000
24.8998
8.5270
571
326041
186169411
23.8956
8.2962
621
385641
239483061
24.9199
8.5316
572
327184
187149248
23.9165
8.3010
622
386884
240641848
24.9399
8.5362
573
328329
188132517
23.9374
8.3059
623
388129
241804367
24.9600
8.5408
574
329476
189119224
23.9583
8.3107
624
389376
242970624
24.9800
8.5453
575
330625
190109375
23.9792
8.3155
625
390625
244140625
25.0000
8.5499
576
331776
191102976
24.0000
8.3203
626
391876
245314376
25.0200
8.5544
577
332929
192100033
24.0209
8.3251
627
393129
246491883
25.0400
8.5590
578
334084
193100552
24.0416
8.3300
628
394384
247673152
25.0599
8.5635
579
335241
194104539
24.0624
8.3348
629
395641
248858189
25.0799
8.5681
580
336400
195112000
24.0832
8.3396
630
396900
250047000
25.0998
8.5726
581
337561
196122941
24.1039
8.3443
631
398161
251239591
25.1197
8.5772
582
338724
197137368
24.1247
8.3491
632
399424
252435968
25.1396
8.5817
583
339889
198155287
24.1454
8.3539
633
400689
253636137
25.1595
8 5862
584
341056
199176704
24.1661
8.3587
634
401956
254840104
25.1794
8.5907
585
342225
200201625
24.1868
8.3634
635
403225
256047875
25.1992
8.5952
586
343396
201230056
24.2074
8.3682
636
404496
257259456
25.2190
8.5997
587
344569
202262003
24.2281
8.3730
637
405769
258474853
25.2389
8.6043
588
345744
203297472
24.2487
8.3777
638
407044
259694072
25.2587
8.6088
589
346921
204336469
24.2693
8.3825
639
408321
260917119
25.2784
8.6132
590
348100
205379000
24.2899
8.3872
640
409600
262144000
25.2982
8.6177


No.

Square

Cube
Square
Root
Cube
Root

No.

Square

Cube
Square
Root
Cube
Root
641
410881
263374721
25.3180
8.6222
691
477481
329939371
26.2869
8.8408
642
412164
264608288
25.3377
8.6267
692
478864
331373888
26.3059
8.8451
643
413449
265847707
25.3574
8.6312
693
480249
332812557
26.3249
8.8493
644
414736
267089984
25.3772
8.6357
694
481636
334255384
26.3439
8.8536
645
416025
268336125
25.3969
8.6401
695
483025
335702375
26.3629
8.8578
646
417316
269586136
25.4165
8.6446
696
484416
337153536
26.3818
8.8621
647
418609
270840023
25.4362
8.6490
697
485809
338608873
26.4008
8.8663
648
419904
272097792
25.4558
8.6535
698
487204
340068392
26.4197
8.8706
649
421201
273359449
25.4755
8.6579
699
488601
341532099
26.4386
8.8748
650
422500
274625000
25.4951
8.6624
700
490000
343000000
26.4575
8.8790
651
423801
275894451
25.5147
8.6668
701
491401
344472101
26.4764
8.8833
652
425104
277167808
25.5343
8.6713
702
492804
345948408
26.4953
8.8875
653
426408
278445077
25.5533
8.6757
703
484209
347428927
26.5141
8.8817
654
427716
278726264
25.5734
8.6801
704
485616
348913664
26.5330
8.8853
655
429025
281011375
25.5930
8.6845
705
497025
350402625
26.5518
8.9001
656
430336
282300416
25.6125
8.6890
706
498436
351895816
26.5707
8.9043
657
431649
283583393
25.6320
8.6934
707
499849
353393243
26.5895
8.9085
658
432964
284890312
25.6515
8.6978
708
501264
354894912
26.6083
8.9127
659
434281
286191179
25.6710
8.7022
709
502681
356400829
26.6271
8.9169
660
435600
287496000
25.6905
8.7066
710
504100
357911000
26.6458
8.9211
661
436921
288804781
25.7099
8.7110
711
505521
359425431
26.6646
8.9253
662
438244
290117528
25.7294
8.7154
712
506344
360344128
26.6833
8.8285
663
439569
291434247
25.7488
8.7198
713
508369
362467097
26.7021
8.9337
664
440836
292754944
25.7682
8.7241
714
509796
363994344
26.7208
8.9378
665
442225
294079625
25.7876
8.7285
715
511225
365525875
26.7395
8.9420
666
443556
295408296
25.8070
8.7329
716
512656
367061696
26.7582
8.9462
667
444889
296740863
25.8263
8.7373
717
514089
368601813
26.7769
8.9503
668
446224
298077632
25.8457
8.7416
718
515524
370146232
26.7955
8.9545
669
447561
299418309
25.8650
8.7460
719
516961
371694959
26.8142
8.9587
670
448900
300763000
25.8844
8.7503
720
518400
373248000
26.8328
8.9628
671
450241
302111711
25.9037
8.7547
721
519841
374805361
26.8514
8.3670
672
451584
303464448
25.9230
8.7590
722
521284
376367048
26.8701
8.9711
673
452928
304821217
25.3422
8.7634
723
522729
377333067
26.8887
8.8752
674
454276
306182024
25.9615
8.7677
724
524176
379503424
26.9072
8.9794
675
455625
307546875
25.9808
8.7721
725
525625
381078125
26.9258
8.9835
676
456976
308915776
26.0000
8.7764
726
527076
382657176
26.9444
8.9876
677
458329
310288733
26.0192
8.7807
727
528529
384240583
26.9629
8.9918
678
459684
311665752
26.0384
8.7850
728
529984
385828352
26.9815
8.9959
679
461041
313046839
26.0576
8.7893
729
531441
387420489
27.0000
9.0000
680
462400
314432000
26.0768
8.7937
730
532900
389017000
27.0185
9.0041
681
463761
315821241
26.0960
8.7980
731
534361
390617891
27.0370
9.0082
682
465124
317214568
26.1151
8.8023
732
535824
332223168
27.0555
9.0123
683
466489
318611987
26.1343
8.8066
733
537289
393832837
27.0740
9.0164
684
467856
320013504
26.1543
8.8109
734
538756
395446904
27.0924
9.0205
685
469225
321419125
26.1725
8.8152
735
540225
397065375
27.1109
9.0246
686
470596
322828856
26.1916
8.8194
736
541696
398688256
27.1293
9.0287
687
471969
324242703
26.2107
8.8237
737
543169
400315553
27.1477
9.0328
688
473344
325660673
26.2298
8.8280
738
544644
401947272
27 1662
9.0369
689
474721
327083769
26.2488
8.8323
739
546121
403583419
27.1846
9.0410
690
476100
328509000
26.2679
8.8366
740
547600
405224000
27.2029
9.0450


No.

Square

Cube
Square
Root
Cube
Root

No.

Square

Cube
Square
Root
Cube
Root
741
549081
406869021
27.2213
9.0491
791
625681
494313671
28.1247
9.2482
742
550564
408518488
272397
9.0532
792
626264
496733088
28.1425
9.2521
743
552049
410172407
27.2580
9.0572
793
628849
498677257
28.1603
9.2560
744
553536
41183078?
27.2764
9.0613
794
630436
500566184
28.1780
9.2539
745
555025
413493625
27.2947
9.0654
795
632025
502459875
28.1957
9.2638
746
556516
415160936
27.3130
9.0694
796
633616
504358836
28.2135
9.2677
747
558009
416832723
27.3313
9.0735
797
635209
506261573
28.2312
9.2716
748
559504
418508992
27.3496
9.0775
798
636804
508169592
28.2489
9.2754
749
561001
420189749
27.3679
9.0816
799
638401
510082399
28.2666
9.2733
750
562500
421875000
27.3861
3.0856
800
640000
512000000
28.2843
9.2832
751
564001
423564751
27.4044
9.0896
801
641601
513922401
28.3019
9.2870
752
565504
425259008
27.4226
9.0937
802
643204
515849608
28.3196
9.2909
753
567009
426957777
27.4408
9.0977
803
644809
517781627
28.3373
9.2948
754
568516
428661064
27.4591
9.1017
804
646416
519718464
28.3549
9.2986
755
570025
430368875
27.4773
9.1057
805
648025
521660125
28.3725
9.3025
756
571536
432081216
27.4955
9.1098
806
649636
523606616
28.3901
9.3063
757
573049
433798093
27.5136
9.1138
807
651249
525557943
28.4077
9.3102
758
574564
435519512
27.5318
9.1178
808
652864
527414112
28.4253
9.3140
759
576081
437245479
27.5500
9.1218
809
654481
529475129
28.4429
9.3179
760
577600
438976000
27.5681
9.1258
810
656100
531441000
28.4605
9.3217
761
579121
440711081
27.5862
9.1298
811
657721
533411731
28.4781
9.3255
762
580644
442450728
27.6043
9.1338
812
659344
535387328
28.4956
9.3294
763
582169
444194947
27.6225
9.1378
813
660969
537367797
28.5132
9.3332
764
583696
445943744
27.6405
9.1418
814
662596
539351344
28.5307
9.3370
765
585225
447697125
27.6586
9.1458
815
664225
541343375
28.5482
9.3408
766
586756
449455096
27.6767
9.1498
816
665856
543338496
28.5657
9.3447
767
588289
451217663
27.6948
9.1537
817
667489
545338513
28.5832
9.3485
768
589824
452984832
27.7128
9.1577
818
669124
547343432
28.6007
9 3523
769
591361
454756609
27.7308
9.1617
819
670761
549353259
28.6182
9.3561
770
592900
456533000
27.7489
9.1657
820
672400
551368000
28.6356
9.3599
771
594441
458314011
27.7669
9.1696
821
674041
553387661
28.6531
9.3637
772
595984
460099648
27.7849
9.1736
822
675684
555412248
28.6705
9.3675
773
597529
461889917
27.8029
9.1775
823
677329
557441767
28.6880
9.3713
774
599076
463684824
27.8209
9.1815
824
678976
559476224
28.7054
9.3751
775
600625
465484375
27.8388
9.1855
825
680625
561515625
28.7228
9.3789
776
602176
467288576
27.8568
9.1894
826
682276
563559976
28.7402
9.3827
777
603729
469097433
27.8747
9.1933
827
683929
565609283
28.7576
9.3865
778
605284
470910952
27.8927
9.1973
828
685584
567663552
28.7750
9.3902
779
606841
472729139
27.9106
9.2012
829
687241
569722789
28.7924
9.3940
780
608400
474552000
27.9285
9.2052
830
688900
571787000
28.8097
9.3978
781
609961
476379541
27.9464
9.2091
831
690561
573856191
28.8271
9.4016
782
611524
478211768
27.9643
9.2130
832
692224
575930368
28.8444
9.4053
783
613089
480048687
27.9821
9.2170
833
693889
578009537
28.8617
9.4091
784
614656
481890304
28.0000
9.2209
834
695556
580093704
28.8791
9.4129
785
616225
483736625
28.0179
9.2248
835
697225
582182875
28.8964
9.4166
786
617796
485587656
28.0357
9.2287
836
698896
584277056
28.9137
9.4204
787
619369
487443403
28.0535
9.2326
837
700569
586376253
28.9310
9.4241
788
620944
489303872
28.0713
9.2365
838
702244
588480472
28.9482
9.4279
789
622521
491169069
28.0891
9.2404
839
703921
590589719
28.9655
9.4316
790
624100
493039000
28.1069
9.2443
840
705600
592704000
28.9828
9.4354


No.

Square

Cube
Square
Root
Cube
Root

No.

Square

Cube
Square
Root
Cube
Root
841
707281
594823321
29.0000
9.4391
891
793881
707347971
29.8496
9.6226
842
708964
596947688
29.0172
9.4429
892
795664
709732288
29.8664
9.6262
843
710649
599077107
29.0345
9.4465
893
797449
712121957
23 8831
9.8238
844
712336
601211584
29.0517
9.4503
894
799236
714516984
29.8998
9.8334
845
714025
603351125
29.0689
9.4541
895
801025
716917375
29.9166
9.6370
846
715716
605495736
29.0861
9.4578
896
802816
719323136
29.9333
9.6406
847
717409
607645423
29.1033
9.4615
897
804609
721734273
29.9500
9.6442
848
719104
609800192
29.1204
9.4652
898
806404
724150792
29.9666
9.6477
849
720801
611960049
29.1376
9.4690
899
808201
726572699
29.9833
9.6513
850
722500
614125000
29.1548
9.4727
900
810000
729000000
30.0000
9.6549
851
724201
616295051
29.1719
9.4764
901
811801
731432701
30.0167
9.6585
852
725904
618470208
29.1890
9.4801
902
813604
733870808
30.0333
9.6620
853
727609
620650477
29.2062
9.4838
903
815409
736314327
30.0500
9.6656
854
729316
622835864
29.2233
9.4875
904
817216
738763264
30.0666
9.6692
855
731025
625026375
29.2204
9.4912
905
819025
741217625
30.0832
9.6727
856
732736
627222016
29.2575
9.4949
906
820836
743677416
30.0998
9.6763
857
734449
629422793
29.2746
9.4986
907
822649
746142643
30.1164
9.6799
858
736164
631628712
29.2916
9.5023
908
824464
748613312
30.1330
9.6834
859
737881
633839779
29.3087
9.5060
909
826281
751089429
30.1496
9.6870
860
739600
636056000
29.3258
9.5097
910
828100
753571000
30.1662
9.6905
861
741321
638277381
29.3428
9.5134
911
829921
756058031
30.1828
9.6941
862
743044
640503928
29.3598
9.5171
912
831744
758550528
30.1993
9.6976
863
744769
642735647
29.3769
9.5207
913
833569
761048497
30.2159
9.7012
864
746496
644972544
29.3339
9.5244
914
835396
763551944
30.2324
9 7047
865
748225
647214625
29.4109
9.5281
915
837225
766060875
30.2490
9.7082
866
749956
649461896
29.4279
9.5317
916
839056
768575296
30.2655
9.7118
867
751689
651714363
29.4449
9.5354
917
840889
771095213
30.2820
9.7153
868
753424
653972032
29.4618
9.5291
918
842724
773620632
30.2985
9.7188
869
755161
656234909
29.4788
9.5427
919
844561
776151559
30.3150
9.7224
870
756900
658503000
29.4958
9.5464
920
846400
778688000
30.3315
9.7259
871
758641
660776311
29.5127
9.5501
921
848241
781229961
30.3480
9.7294
872
760384
663054848
29.5296
9.5537
922
850084
783777448
30.3645
9.7329
873
762129
665338617
295466
9.5574
923
851929
786330467
30.3809
9.7364
874
763876
667627624
29.5635
9.5610
924
853776
788889024
30.3974
9.7400
875
765625
669921875
29.5804
9.5647
925
855625
791453125
30.4138
9.7435
876
767376
672221376
29.5973
9.5683
926
857476
794022776
30.4302
9.7470
877
769129
674526133
29.6142
9.5719
927
859329
796597983
30.4467
9.7505
878
770884
676836152
29.6311
9.5756
928
861184
799178752
30 4631
9.7540
879
772641
579151439
29.6478
9.5782
929
863041
801765089
30.4795
9.7575
880
774400
681472000
29.6648
9.5828
930
864900
804357000
30.4959
9.7610
881
776161
683797841
29.6816
9.5865
931
866761
806954491
30.5123
9.7645
882
777924
686128968
29.6985
9.5901
932
868624
809557568
30.5287
9.7680
883
779689
688465387
29.7153
9.5937
933
870489
812166237
30.5450
9.7715
884
781456
690807104
29.7321
9.5973
934
872356
841780504
30.5614
9.7750
885
783225
693154125
29.7489
9.6010
935
874225
817400375
30.5778
9.7785
886
784996
695506456
29.7658
9.6046
936
876096
820025856
30.5941
9.7819
887
786769
697864103
29.7825
9.6082
937
877969
822656953
30.6105
9.7854
888
788544
700227072
29.7993
9.6118
938
879844
825293672
30.6268
9.7889
889
790321
702595369
29.8161
9.6154
939
881721
827936019
30.6431
9.7924
890
792100
704969000
29.8329
9.6190
940
883600
830584000
30.6594
9.7959


No.

Square

Cube
Square
Root
Cube
Root

No.

Square

Cube
Square
Root
Cube
Root
941
885481
833237621
30.6757
9.7993
971
942841
915498611
31.1609
9.9024
942
887364
835896888
30.6920
9.8028
972
944784
918330048
31.1769
9.9058
943
889249
838561807
30.7083
9.8063
973
946729
921167317
31.1929
9.9092
944
891136
841232384
30.7246
9.8097
974
948676
924010424
31.2090
9.9126
945
893025
843908625
30.7409
9.8132
975
950625
926859375
31.2250
9.9160
946
894916
846590536
30.7571
9.8167
976
952576
929714176
31.2410
9.9194
947
896809
849278123
30.7734
9.8201
977
954529
932574833
31.2570
9.9227
948
898704
851971392
30.7896
9.8236
978
956484
935441352
31.2730
9.9261
949
900601
854670349
30.8058
9.8270
979
958441
938313739
31.2890
9.9295
950
902500
857375000
30.8221
9.8305
980
960400
941192000
31.3050
9.9329
951
904401
860085351
30.8383
9.8339
981
962361
944076141
31.3209
9.9363
952
906304
862801408
30.3545
9.8374
982
964324
946966168
31,3369
9,9396
953
908209
865523177
30.8707
9.8408
983
966289
949862087
31.3528
9.9430
954
910116
868250664
30.8869
9.8443
984
968256
952763904
31.3688
9.9464
955
912025
870983875
30.9031
9.8477
985
970225
955671625
31.3847
9.9497
956
913936
873722816
30.9192
9.8511
986
972196
958585256
31.4006
9.9531
957
915849
876467493
30.9354
9.8546
987
974169
961504803
31.4166
9.9565
958
917764
879217912
30.9516
9.8580
988
976144
964439272
31.4325
9.9598
959
919681
881974079
30.9677
9.8614
989
978121
967361669
31.4484
9.9632
960
921600
884736000
30.9839
9.8648
990
980100
970299000
31.4643
9.9666
961
923521
887503681
31.0000
9.8683
991
982081
973242271
31.4802
9.9699
962
925444
890277128
31.0161
9.8717
992
984064
976191488
31.4960
9.9733
963
927369
893056347
31.0332
9.8751
993
986049
979146657
31.5119
9.9766
964
929296
895841344
31.0483
9.8785
994
988036
982107784
31.5278
9.9800
965
931225
898632125
31.0644
9.8819
995
990025
985074875
31.5436
9.9833
966
933156
901428696
31.0805
9.8854
996
992016
988047936
31.5595
9.9866
967
935089
904231063
31.0966
9.8888
997
994009
991026973
31.5753
9.9900
968
937024
907039232
31.1127
9.8922
998
996004
994011992
31.5911
9.9933
969
938961
909853209
31.1288
9.8956
999
998001
997002999
31.6070
9.9967
970
940900
912673000
31.1448
9.8990
1000
1000000
1000000000
31.6228
10.0000

##

A-15. (To use table, locate the angle in the left column.)
A-16. The valve for angle A is in the second column.

A-17. To compute the value of C, X or Y, multiply the appropriate value times the length of the spiral
(Ls).



|     | A          |
|------|------------|
| C    |            |
| L.   |            |
|      |            |
| X    |            |
| L.   |            |
|      |            |
| Y    |            |
| L.   |            |
|      |            |
|     | A          |
| C    |            |
| L.   |            |
|      |            |
| X    |            |
| L.   |            |
|      |            |
| Y    |            |
| L.   |            |
|      |            |
| 0.0 | 0 00' 00" |
| 0.1 | 0 02' 00" |
| 0.2 | 0 04' 00" |
| 0.3 | 0 06' 00" |
| 0.4 | 0 08' 00" |
| 0.5 | 0 10' 00" |
| 0.6 | 0 12' 00" |
| 0.7 | 0 14' 00" |
| 0.8 | 0 16' 00" |
| 0.9 | 0 18' 00" |
| 1.0 | 0 20' 00" |
| 1.1 | 0 22' 00" |
| 1.2 | 0 24' 00" |
| 1.3 | 0 26' 00" |
| 1.4 | 0 28' 00" |
| 1.5 | 0 30' 00" |
| 1.6 | 0 32' 00" |
| 1.7 | 0 34' 00" |
| 1.8 | 0 36' 00" |
| 1.9 | 0 38' 00" |
| 2.0 | 0 40' 00" |
| 2.1 | 0 42' 00" |
| 2.2 | 0 44' 00" |
| 2.3 | 0 46' 00" |
| 2.4 | 0 48' 00" |
| 2.5 | 0 50' 00" |
| 2.6 | 0 52' 00" |
| 2.7 | 0 54' 00" |
| 2.8 | 0 56' 00" |
| 2.9 | 0 58' 00" |
| 3.0 | 1 00' 00" |
| 3.1 | 1 02' 00" |
| 3.2 | 1 04' 00" |
| 3.3 | 1 06' 00" |
| 3.4 | 1 08' 00" |
| 3.5 | 1 10' 00" |
| 3.6 | 1 12' 00" |
| 3.7 | 1 14' 00" |
| 3.8 | 1 16' 00" |
| 3.9 | 1 18' 00" |
| 4.0 | 1 20' 00" |
| 4.1 | 1 22' 00" |
| 4.2 | 1 24' 00" |
| 4.3 | 1 26' 00" |
| 4.4 | 1 28' 00" |
| 4.5 | 1 30' 00" |
| 4.6 | 1 32' 00" |
| 4.7 | 1 34' 00" |
| 4.8 | 1 36' 00" |
| 4.9 | 1 38' 00" |
|      |            |
|      | A          |
|-------|------------|
| C     |            |
| L.    |            |
|       |            |
| X     |            |
| L.    |            |
|       |            |
| Y     |            |
| L.    |            |
|       |            |
|      | A          |
| C     |            |
| L.    |            |
|       |            |
| X     |            |
| L.    |            |
|       |            |
| Y     |            |
| L.    |            |
|       |            |
| 10.0 | 3 19' 57" |
| 10.1 | 3 21' 57" |
| 10.2 | 3 23' 57" |
| 10.3 | 3 25' 57" |
| 10.4 | 3 27' 57" |
| 10.5 | 3 29' 57" |
| 10.6 | 3 31' 56" |
| 107  | 3 33' 56" |
| 10.8 | 3 35' 56" |
| 10.9 | 3 37' 56" |
| 11.0 | 3 33' 56" |
| 11.1 | 3 41' 56" |
| 11.2 | 3 43' 56" |
| 11.3 | 3 45' 56" |
| 114  | 3 47' 56" |
| 11.5 | 3 49' 55" |
| 11.6 | 3 51' 55" |
| 11.7 | 3 53' 55" |
| 11.8 | 3 55' 55" |
| 11.9 | 3 57' 55" |
| 12.0 | 3 59' 55" |
| 12 1 | 4 01' 55" |
| 12.2 | 4 03' 55" |
| 12.3 | 4 05' 54" |
| 12.4 | 4 07' 54" |
| 12.5 | 4 09' 54" |
| 12.6 | 4 11' 54" |
| 12.7 | 4 13' 54" |
| 12.8 | 4 15' 54" |
| 12.9 | 4 17' 54" |
| 13.0 | 4 19' 53" |
| 13.1 | 4 21' 53" |
| 13.2 | 4 23' 53" |
| 13.3 | 4 25' 53" |
| 13.4 | 4 27' 53" |
| 13.5 | 4 29' 53" |
| 13.6 | 4 31' 53" |
| 13.7 | 4 33' 52" |
| 13.8 | 4 35' 52" |
| 13.9 | 4 37' 52" |
| 14.0 | 4 39' 52" |
| 14.1 | 4 41' 52" |
| 14.2 | 4 43' 51" |
| 14.3 | 445' 51"  |
| 14.4 | 4 47' 51" |
| 14.5 | 4 49' 51" |
| 14.6 | 4 51' 51" |
| 14.7 | 4 53' 51" |
| 14.8 | 4 55' 50" |
| 14.9 | 4 57' 50" |
|       |            |
|      | A          |
|-------|------------|
| C     |            |
| L.    |            |
|       |            |
| X     |            |
| L.    |            |
|       |            |
| Y     |            |
| L.    |            |
|       |            |
|      | A          |
| C     |            |
| L.    |            |
|       |            |
| X     |            |
| L.    |            |
|       |            |
| Y     |            |
| L.    |            |
|       |            |
| 20.0 | 6 39' 36" |
| 20.1 | 6 41' 36" |
| 20.2 | 6 43' 36" |
| 20.3 | 6 45' 35" |
| 20.4 | 6 47' 35" |
| 20.5 | 6 49' 34" |
| 20.6 | 6 51' 34" |
| 20.7 | 6 53' 34" |
| 20.8 | 6 55' 33" |
| 20.9 | 6 57' 33" |
| 21.0 | 6 59' 32" |
| 21.1 | 7 01' 32" |
| 21.2 | 7 03' 32" |
| 21.3 | 7 05' 31" |
| 21.4 | 7 07' 31" |
| 21.5 | 7 09' 30" |
| 21.6 | 7 11' 30" |
| 21.7 | 7 13' 30" |
| 21.8 | 7 15' 29" |
| 21.9 | 7 17' 29" |
| 22.0 | 7 19' 28" |
| 22.1 | 7 21' 28" |
| 22.2 | 7 23' 28" |
| 22.3 | 7 25' 27" |
| 22.4 | 7 27' 27" |
| 22.5 | 7 29' 26" |
| 22.6 | 7 31' 26" |
| 22.7 | 7 33' 25" |
| 22.8 | 7 35' 25" |
| 22.9 | 7 37' 24" |
| 23.0 | 7 39' 24" |
| 23.1 | 7 41' 23" |
| 23.2 | 7 43' 23" |
| 23.3 | 7 45' 22" |
| 23.4 | 7 47' 22" |
| 23.5 | 7 49' 21" |
| 23.6 | 7 51' 21" |
| 23.7 | 7 53' 20" |
| 23.8 | 7 55' 20" |
| 23.9 | 7 57' 19" |
| 24.0 | 7 59' 19" |
| 24.1 | 8 01' 18" |
| 24.2 | 8 03' 18" |
| 24.3 | 8 05' 17" |
| 24.4 | 8 07' 17" |
| 24.5 | 8 09' 16" |
| 24.6 | 8 11' 16" |
| 24.7 | 8 13' 15" |
| 24.8 | 8 15' 15" |
| 24.9 | 8 17' 14" |
|       |            |
|      | A           |
|-------|-------------|
| C     |             |
| L.    |             |
|       |             |
| X     |             |
| L.    |             |
|       |             |
| Y     |             |
| L.    |             |
|       |             |
|      | A           |
| C     |             |
| L.    |             |
|       |             |
| X     |             |
| L.    |             |
|       |             |
| Y     |             |
| L.    |             |
|       |             |
| 30.0 | 9 58' 40"  |
| 30.1 | 10 00' 39" |
| 30.2 | 10 02' 38" |
| 30.3 | 10 04' 37" |
| 30.4 | 10 06' 37" |
| 30.5 | 10 08' 36" |
| 30.6 | 10 10' 35" |
| 30.7 | 10 12' 34" |
| 30.8 | 10 14' 33" |
| 30.9 | 10 16' 32" |
| 31.0 | 10 18' 32" |
| 31.1 | 10 20' 31" |
| 31.2 | 10 22' 30" |
| 31.3 | 10 24' 29" |
| 31.4 | 10 26' 28" |
| 31.5 | 10 28' 27" |
| 31.6 | 10 30' 26" |
| 31.7 | 10 32' 25" |
| 31.8 | 10 34' 24" |
| 31.9 | 10 36' 24" |
| 32.0 | 10 38' 23" |
| 32.1 | 10 40' 22" |
| 32.2 | 10 42' 21" |
| 32.3 | 10 44' 20" |
| 32.4 | 10 46' 19" |
| 32.5 | 10 48' 18" |
| 32.6 | 10 50' 17" |
| 32.7 | 10 52' 16" |
| 32.8 | 10 54' 15" |
| 32.9 | 10 56' 14" |
| 33.0 | 10 58' 13" |
| 33.1 | 11 00' 12" |
| 33.2 | 11 02' 11" |
| 33.3 | 11 04' 10" |
| 33.4 | 11 06' 09" |
| 33.5 | 11 08' 08" |
| 33.6 | 11 10' 07" |
| 33.7 | 11 12' 06" |
| 33.8 | 11 14' 05" |
| 33.9 | 11 16' 04" |
| 34.0 | 11 18' 03" |
| 34.1 | 11 20' 02" |
| 34.2 | 11 22' 01" |
| 34.3 | 11 24' 00" |
| 34.4 | 11 25' 59" |
| 34.5 | 1127' 58"  |
| 34.6 | 11 29' 57" |
| 34.7 | 11 31' 56" |
| 34.8 | 11 33' 55" |
| 34.9 | 11 35' 54" |
|       |             |
|      | A            |
|-------|--------------|
| C     |              |
| L.    |              |
|       |              |
| X     |              |
| L.    |              |
|       |              |
| Y     |              |
| L.    |              |
|       |              |
|      | A            |
| C     |              |
| L.    |              |
|       |              |
| X     |              |
| L.    |              |
|       |              |
| Y     |              |
| L.    |              |
|       |              |
| 40.0 | 13 16' 50"  |
| 40.1 | 13 18' 48"  |
| 40.2 | 13 20' 47"  |
| 40.3 | 13 22' 46"  |
| 40.4 | 13 24' 44"  |
| 40.5 | 13 26' 43"  |
| 40.6 | 13 28' 41"  |
| 40.7 | 13 30' 40"  |
| 40.8 | 13 32' 38"  |
| 40.9 | 13 34' 37"  |
| 41.0 | 13 36' 35"  |
| 41.1 | 13 38' 34"  |
| 41.2 | 13 40' 32"  |
| 41.3 | 13 42' 31"  |
| 41.4 | 13 44' 29"  |
| 41.5 | 13 46' 28"  |
| 41.6 | 13 48' 26"  |
| 41.7 | 13 50' 25"' |
| 41.8 | 13 52' 23"  |
| 41.9 | 13 54' 22"  |
| 42.0 | 13 56' 20"  |
| 42.1 | 13 58' 18"  |
| 42.2 | 14 00' 17"  |
| 42.3 | 14 02' 15"  |
| 42.4 | 14 04' 14"  |
| 42.5 | 14 06' 12"  |
| 42.6 | 14 08' 10"  |
| 42.7 | 14 10' 09"  |
| 42.8 | 14 12' 07"  |
| 42.9 | 14 14' 06"  |
|       |              |

To use the table, look in the middle column for the temperature reading you have. If the reading you have is in degrees Centigrade, read the Fahrenheit equivalent in the right-hand column. If the reading you have is in degree Fahrenheit, read the Centigrade equivalent in the left-hand-column.

FORMULAS. C =  5/9 (F  32) or F = 9/5 (C + 32)
-80 to 34
35 to 77
78 to 290
C

F
C

F
C

F
-62
-80
-112
1.7
35
95.0
25.6
78
172.4
-57
-70
-94
2.2
36
96.8
26.1
79
174.2
-51
-60
-76
2.8
37
98.6
26.7
80
176.0
-46
-50
-58
3.3
38
100.4
27.2
81
177.8
-40
-40
-40
3.9
39
102.4
27.8
82
179.6
-34
-30
-22
4.4
40
104.0
28.3
83
181.4
-29
-20
-4
5.0
41
105.8
28.9
84
183.2
-23
-10
14
5.6
42
107.6
29.4
85
185.0
-17.8
0
32
6.1
43
109.4
30.0
86
186.8
-17.2
1
33.8
6.7
44
111.2
30.6
87
188.6
-16.7
2
35.6
7.2
45
113.0
31.1
88
190.6
-16.1
3
37.4
7.8
46
114.8
31.7
89
192.2
-15.6
4
39.2
8.3
47
116.6
32.2
90
194.0
-15.0
5
41.0
8.9
48
118.4
32.8
91
195.8
-14.4
6
42.8
9.4
49
120.2
33.3
92
197.6
-13.9
7
44.6
10.0
50
122.0
33.9
93
199.4
-13.3
8
46.4
10.6
51
123.8
34.4
94
201 2
-12.8
9
48.2
11.1
52
125.6
35.0
95
203.0
-12.2
10
50.0
11.7
53
127.4
35.6
96
204.8
-11.7
11
51.8
12.2
54
129.2
36.1
97
206.6
-11.1
12
53.6
12.8
55
131.0
36.7
98
208.4
-10.6
13
55.4
13.3
56
132.8
37.2
99
210.2
-10.0
14
57.2
13.9
57
134.6
37.8
100
212.0
-9.4
15
59.0
14.4
58
136.4
43
110
230
-8.9
16
60.8
15.0
59
138.2
49
120
248
-8.3
17
62.6
15.6
60
140.0
54
130
260
-7.8
18
64.4
16.1
61
141.8
60
140
284
-7.2
19
66.2
16.7
62
143.6
66
150
302
-6.7
20
68.0
17.2
63
145.4
71
160
320
-6.1
21
69.8
17.8
64
147.2
77
170
338
-5.6
22
71.6
18.3
65
149.0
82
180
356
-5.0
23
73.4
18.9
66
150.8
88
190
374
-4.4
24
75.2
19.4
67
152.6
93
200
392
-3.9
25
77.0
20.0
68
154.4
99
210
410
-3.3
26
78.8
20.6
69
156.2
100
212
413.6
-2.8
27
80.6
21.1
70
158.0
104
220
428
-2.2
28
82.4
21.7
71
159.8
110
230
446
-1.7
29
84.2
22.2
72
161.6
116
240
464
-1.1
30
86.0
22.8
73
163.4
121
250
482
-0.6
31
87.8
23.3
74
165.2
127
260
500
0.0
32
89.6
23.9
75
167.0
132
270
518
0.6
33
91.4
24.4
76
168.8
138
280
536
1.1
34
93.2
25.0
77
170.6
143
290
554
Meters
Feet
Meters
Feet
Meters
Feet
Meters
Feet
Meters
Feet
0

50
164.04167
100
328.08333
150
492.12500
200
656.16667
1
3.28083
1
167.32250
1
331.36417
1
495.40583
1
659.44750
2
6.56167
2
170.60333
2
334.64500
2
498.68667
2
662.72833
3
9.84250
3
173.88417
3
337.92583
3
501.96750
3
666.00917
4
13.12333
4
177.16500
4
341.20667
4
505.24833
4
669.2900
5
16.40417
5
180.44583
5
344.48750
5
508.52917
5
672.57083
6
19.68500
6
183.72667
6
347.76833
6
511.81000
6
675.85167
7
22.96583
7
187.00750
7
351.04917
7
515.09083
7
679.13250
8
26.24667
8
190.28833
8
354.33000
8
518.37167
8
682.41333
9
29.52750
9
193.56917
9
357.61083
9
521.65250
9
685.69417
10
32.80833
60
196.85000
110
360.89167
160
524.93333
210
688.97500
1
36.08917
1
200.13083
1
364.17250
1
528.21417
1
692.25583
2
39.37000
2
203.41167
2
367.45333
2
531.49500
2
695.53667
3
42.65083
3
206.69250
3
370.73417
3
534.77583
3
698.81750
4
45.93167
4
209.97333
4
374.01500
4
538.05667
4
702.09833
5
49.21250
5
213.25417
5
377.29583
5
541.33750
5
705.37917
6
52.49333
6
216.53500
6
380.57667
6
544.61833
6
708.66000
7
55.77417
7
219.81583
7
383.85750
7
547.89917
7
711.94083
8
59.05500
8
223.09667
8
387.13833
8
551.18000
8
715.22167
9
62.33583
9
226.37750
9
390.41917
9
554.46083
9
718.50250
20
65.61667
70
229.65833
120
393.70000
170
557.74167
220
721.78333
1
68.89750
1
232.93917
1
396.98083
1
561.02250
1
725.06417
2
72.17822
2
236.22000
2
400.26167
2
564.30333
2
728.34500
3
75.45917
3
239.50083
3
403.54250
3
567.58417
3
731.62583
4
78.74000
4
242.78167
4
406.82333
4
570.86500
4
734.90667
5
82.02083
5
246.06250
5
410.10417
5
574.14583
5
738.18750
6
85.30167
6
249.34333
6
413.38500
6
577.42667
6
741.46833
7
88.58250
7
252.62417
7
416.66583
7
580.70750
7
744.74917
8
91.86333
8
255.90500
8
419.94667
8
583.98833
8
748.03000
9
95.14417
9
259.18583
9
423.22750
9
587.26917
9
751.31083
30
98.42500
80
262.46667
130
426.50833
180
590.55000
230
754.59167
1
101.70583
1
265.74750
1
429.78917
1
593.83083
1
757.87250
2
104.98667
2
269.02833
2
433.07000
2
597.11167
2
761.15333
3
108.26750
3
272.30917
3
436.35083
3
600.39250
3
764.43417
4
111.54833
4
275.59000
4
439.63167
4
603.67333
4
767.71500
5
114.82917
5
278.87083
5
442.91250
5
606.95417
5
770.99583
6
118.11000
6
282.15167
6
446.19333
6
610.23500
6
774.27667
7
121.39083
7
285.43250
7
449.47417
7
613.51583
7
777.55750
8
124.67167
8
288.71333
8
452.75500
8
616.79667
8
780.83833
9
127.95250
9
291.99417
9
456.03583
9
620.07750
9
784.11917
40
131.23333
90
295.27500
140
459.31667
190
623.35833
240
787.40000
1
134.51417
1
298.55583
1
462.59750
1
626.63917
1
790.68083
2
137.79500
2
301.83667
2
465.87833
2
629.92000
2
793.96167
3
141.07583
3
305.11750
3
469.15917
3
633.20083
3
797.24250
4
144.35667
4
308.39833
4
472.44000
4
636.48167
4
800.52333
5
147.63750
5
311.67917
5
475.72083
5
639.76250
5
803.80417
6
150.91833
6
314.96000
6
479.00167
6
643.04333
6
807.08500
7
154.19917
7
318.24083
7
482.28250
7
646.32417
7
810.36583
8
157.48000
8
321.52167
8
485.56333
8
649.60500
8
813.64667
9
160.76083
9
324.80250
9
488.84417
9
652.88583
9
816.92750

Meters
Feet
Meters
Feet
Meters
Feet
Meters
Feet
Meters
Feet
250
820.20833
300
984.25000
350
1,148.29167
400
1,312.33333
450
1,476.37500
1
823.48917
1
987.53083
1
1,151.57250
1
1,315.61417
1
1,479.65583
2
826.77000
2
990.81167
2
1,154.85333
2
1,318.89500
2
1,482.93667
3
830.05083
3
994.09250
3
1,158.13417
3
1,322.17583
3
1,486.21750
4
833.33167
4
997.37333
4
1,161.41500
4
1,325.45667
4
1,489.49833
5
836.61250
5
1,000.66417
5
1,164.69583
5
1,328.73750
5
1,492.77917
6
839.89333
6
1,003.93500
6
1,167.97667
6
1,332.01833
6
1,496.06000
7
843.17417
7
1,007.21583
7
1,171.25750
7
1,335.29917
7
1,499.34083
8
846.45500
8
1,010.49667
8
1,174.53833
8
1,338.68000
8
1,502.62167
9
849.73583
9
1,013.77750
9
1,177.81917
9
1,341.86083
9
1,505.90250
260
853.01667
310
1,017.06833
360
1,181.10000
410
1,346.14167
460
1,509.18333
1
856.29750
1
1,020.33917
1
1,184.38083
1
1,348.42250
1
1,512.46417
2
859.57833
2
1,023.62000
2
1,187.66167
2
1,351.70333
2
1,516.74500
3
862.85317
3
1,026.90083
3
1,190.94250
3
1,354.33417
3
1,519.02583
4
866.14000
4
1,030.18167
4
1,194.22333
4
1,358.26500
4
1,522.30667
5
869.42083
5
1,033.46250
5
1,197.50417
5
1,361.54583
5
1,525.58750
6
873 70167
6
1,036.74333
6
1,200.78500
6
1,364.82667
6
1,528.86833
7
876.98250
7
1,040.02417
7
1,204.06583
7
1,368.10750
7
1,532.14917
8
879.26333
8
1,043.30500
8
1,207.34667
8
1,371.38833
8
1,535.43000
9
882.54417
9
1,046.58583
9
1,210.62750
9
1,374.66917
9
1,538.71083
270
885.82500
320
1,049.86667
370
1,213.90833
420
1,377.95000
470
1,541.99167
1
889.10583
1
1,053.14750
1
1,217.18917
1
1,381.23083
1
1,545.27250
2
892.38667
2
1,056.42833
2
1,220.47000
2
1,384.51167
2
1,548.65333
3
895.66750
3
1,059.70917
3
1,223.75083
3
1,387.79250
3
1,551.83417
4
898.94833
4
1,062.99000
4
1,227.03167
4
1,391.07333
4
1,555.11500
5
902.22917
5
1,066.27083
5
1,230.31250
5
1,394.35417
5
1,558 39583
6
906.51000
6
1,069.55167
6
1,233.59333
6
1,397.63500
6
1,561.67667
7
908.79083
7
1,072.83250
7
1,236.87417
7
1,400.91583
7
1,564.95750
8
912.07167
8
1,076.11333
8
1,240.15500
8
1,404.19667
8
1,568.23833
9
915.35250
9
1,079.39417
9
1,243.43583
9
1,407.47750
9
1,571.51917
280
918.63333
330
1.082.67500
380
1.246.71667
430
1.410.75833
480
1.574.80000
1
921.91417
1
1,085.95583
1
1,249.99750
1
1,414.03917
1
1,578.08083
2
925.19500
2
1,089.23667
2
1,253.27833
2
1,417.32000
2
1,581.36167
3
928.47583
3
1,092.51750
3
1,256.55917
3
1,420.60083
3
1,584.64250
4
931.75667
4
1,095.79833
4
1,259.84000
4
1,423.88167
4
1,587.92333
5
935.03750
5
1.099.07917
5
1,263.12083
5
1,427.16250
5
1,591.20417
6
938.31833
6
1,012.36000
6
1,266.40167
6
1,430.44333
6
1,594.48500
7
941.59917
7
1,105.64083
7
1,269.68250
7
1,433.72417
7
1,597.76583
8
944.88000
8
1,108.92167
8
1,272.96333
8
1,437.00500
8
1,601.04667
9
948.16083
9
1,112.20250
9
1,276.24417
9
1,440.28583
9
1,604.32750
290
951.44167
340
1,115.48333
390
1,279.52500
440
1,443.56667
490
1,607.60833
1
954.72250
1
1,118 76417
1
1,282.80583
1
1,446.84750
1
1,610.88917
2
958.00333
2
1,122.04500
2
1,286.08667
2
1,450.12833
2
1,614.17000
3
961.28417
3
1,125.32583
3
1,289.36750
3
1,453.40917
3
1,617.45083
4
964.56500
4
1,128.60667
4
1,292.64833
4
1,456.69000
4
1,620.73167
5
967.84583
5
1,131.88750
5
1,295.92917
5
1,459.97083
5
1,624.01250
6
971.12667
6
1,135.16833
6
1,299.21000
6
1,463.25167
6
1,627.29333
7
974.40750
7
1,138.44917
7
1,302.49083
7
1,466.53250
7
1,630.57417
8
977.68833
8
1,141.73000
8
1,305.77167
8
1,469.81333
8
1,633.85500
9
980.96917
9
1,145.01083
9
1,309.05250
9
1,473.09417
9
1,637.13583

Meters
Feet
Meters
Feet
Meters
Feet
Meters
Feet
Meters
Feet
500
1,640.41667
550
1,804.45833
600
1,968.50000
650
2,132.54167
700
2,296.58333
1
1,643.69750
1
1,807.73917
1
1,971.78083
1
2,135.82250
1
2,299.86417
2
1,646.97833
2
1,811.02000
2
1,975.06167
2
2,139.10333
2
2,303.14500
3
1,650.25917
3
1,814.30083
3
1,978.34250
3
2,142.38417
3
2,306.42583
4
1,653.54000
4
1,817.58167
4
1,981.62333
4
2,145.66500
4
2,309.70667
5
1,656.82083
5
1,820.86250
5
1,984.90417
5
2,148.94583
5
2,312.98750
6
1,660.10167
6
1,824.14333
6
1.988.18500
6
2,152.22667
6
2,316.26833
7
1,663.38250
7
1,827.42417
7
1.991.46583
7
2,155.50750
7
2,319.54917
8
1,666.66333
8
1,830.70500
8
1.994.74667
8
2,158.78833
8
2,322.83000
9
1,669.94417
9
1,833.98583
9
1,998.02750
9
2,162.06917
9
2,226.11083
510
1,673.22500
560
1,837.26667
610
2,001.30833
660
2,165.35000
710
2,329.39167
1
1,676.50583
1
1,840.54750
1
2,004.58917
1
2,168.63083
1
2,332.67250
2
1,679.78667
2
1,843.82833
2
2,007.87000
2
2,171.91167
2
2,335.95333
3
1,683.06750
3
1,847.10917
3
2,011.15083
3
2,175.19250
3
2,339.23417
4
1,686.34833
4
1,850.39000
4
2,014.43167
4
2,178.47333
4
2,342.51500
5
1,689.62917
5
1,853.67083
5
2,017.71250
5
2,181.75417
5
2,345.79583
6
1,692.91000
6
1,856.95167
6
2,020.99333
6
2,185.03500
6
2,349.07667
7
1,696.19083
7
1,860.23250
7
2,024.27417
7
2,188.31583
7
2,352.35750
8
1,699.47167
8
1,863.51333
8
2,027.55500
8
2,191.59667
8
2,355.63833
9
1,702.75250
9
1,866.79417
9
2,030.83583
9
2,194.87750
9
2,358.91917
520
1,706.03333
570
1,870.07500
620
2,034.11667
670
2,198.15833
720
2,362.20000
1
1,709.31417
1
1,873.35583
1
2,037.39750
1
2,201.43917
1
2,365.48083
2
1,712.59500
2
1,876.63667
2
2,040.67833
2
2,204.72000
2
2,368.76167
3
1,715.87583
3
1,879.91750
3
2,043.95917
3
2,208.00083
3
2,372.04250
4
1,719.15667
4
1,883.19833
4
2,047.24000
4
2,211.28167
4
2,375.32333
5
1,722.43750
5
1,886.47917
5
2,050.52083
5
2,214.56250
5
2,378.60417
6
1,725.71833
6
1,889.76000
6
2,053.80167
6
2,217.84333
6
2,381.88500
7
1,728.99917
7
1,893.04083
7
2,057.08250
7
2,221.12417
7
2,385.16583
8
1,732.28000
8
1,896.32167
8
2,060.36333
8
2,224.40500
8
2,366.44667
9
1,735.56083
9
1,899.60250
9
2,063.64417
9
2,227.68583
9
2,391.72750
530
1,738.84167
580
1,902.88333
630
2,066.92500
680
2,230.96667
730
2,395.00833
1
1,742.12250
1
1,906.16417
1
2,070.20583
1
2,234.24750
1
2,398.28917
2
1,745.40333
2
1,909.44500
2
2,073.48667
2
2,237.52833
2
2,401.57000
3
1.748.68417
3
1,912.72583
3
2,076.76750
3
2,240.80917
3
2,404.85083
4
1,751.96500
4
1,916.00667
4
2,080.04833
4
2,244.09000
4
2,408.13167
5
1,755.24583
5
1,919.28750
5
2,083.32917
5
2,247.37083
5
2,411.41250
6
1,758.52667
6
1,922.56833
6
2,086.61000
6
2,250.65167
6
2,414.69333
7
1,761.80750
7
1,925.84917
7
2,088.83083
7
2,253.83250
7
2,417.97417
8
1,765.08833
8
1,929.13000
8
2,093.17167
8
2,257.21333
8
2,421.25500
9
1,768.36917
9
1,932.41083
9
2,086.45250
9
2,260.48417
9
2,424.53583
540
1,771.65000
590
1,935.69167
640
2,099.73333
690
2,263.77500
740
2,427.81667
1
1,774.93083
1
1,938.97250
1
2,103.01417
1
2,267.05583
1
2,431.09750
2
1,778.21167
2
1,942.25333
2
2,106.29500
2
2,270.33667
2
2,434.37833
3
1,781.49250
3
1,945.53417
3
2,109.57583
3
2,273.61750
3
2,437.65917
4
1,784.77333
4
1,948.81500
4
2,112.85667
4
2,276.83833
4
2,440.94000
5
1,788.05417
5
1,952.09583
5
2,116.13750
5
2,280.17817
5
2,444.22083
6
1,791.33500
6
1,955.37667
6
2,119.41833
6
2.283.46000
6
2,447.50167
7
1,794.61583
7
1,958.65750
7
2,122.69917
7
2,286.74083
7
2,450.78250
8
1,797.89667
8
1,961.93833
8
2,125.98000
8
2,290.02167
8
2,454.06333
9
1,801.17750
9
1,965.21917
9
2,129.26083
9
2,293.30250
9
2,457.34417

Meters
Feet
Meters
Feet
Meters
Feet
Meters
Feet
Meters
Feet
750
2,460.62500
800
2,624.66667
850
2,788.70833
900
2,952.75000
950
3,116.79167
1
2,463.90583
1
2,627.94750
1
2,791.98917
1
2,956.03083
1
3,120.07250
2
2,467.18667
2
2,631.22833
2
2,795.27000
2
2,959.31167
2
3,123.35333
3
2,470.46750
3
2,634.50917
3
2,798.55083
3
2,962.59250
3
3.126.63417
4
2,473.74833
4
2,637.79000
4
2,801.83167
4
2.965.87333
4
3.129.91500
5
2,477.02917
5
2,641.07083
5
2,805.11250
5
2,969.15417
5
3,133.19583
6
2,480.31000
6
2,644.35167
6
2,808.39333
6
2,972.43500
6
3,136.47667
7
2,483.59083
7
2,647.63250
7
2,811.67417
7
2,975.71583
7
3,139.75750
8
2,486.87167
8
2,650.91333
8
2,814.95500
8
2,978.99667
8
3,143.03833
9
2,490.15250
9
2,654.19417
9
2,818.23583
9
2,982.27750
9
3,146.31917
760
2,493.43333
810
2,657.47500
860
2,821.51667
910
2,985.55833
960
3,149.60000
1
2,496.71417
1
2,660.75583
1
2,824.79750
1
2,988.83917
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3,152.88083
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2,499.99500
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2,664.03667
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2,841.20167
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3,005.24333
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2,516.39917
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2,680.44083
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2,844.48250
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3,008.52417
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2,519.68000
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3,011.80500
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3,015.08583
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3,179.12750
770
2,526.24167
820
2,690.28333
870
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920
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970
3,182.40833
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2,529.52250
1
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3,021.64750
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2,696.84500
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3,024.92833
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3,047.89417
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3,211.93583
780
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830
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880
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930
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980
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840
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3,100.38750
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2,611.54333
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2,618.10500
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3,110.23000
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2,621 38583
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Feet
Meters
Feet
Meters
Feet
Meters
Feet
Meters
0
0.0
50
15.24003
100
30.48006
150
45.72009
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60.96012
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30.78486
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46.02489
1
61.26492
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0.60960
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15.84963
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31.08966
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46.32969
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61.56972
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0.91440
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16.15443
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31.39446
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46.63449
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61.87452
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1.21920
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16.45923
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31.69926
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46.93929
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62.17932
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16.76403
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32.00406
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47.24409
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62.48412
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1.82880
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32.30886
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47.54890
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62 78893
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2.13360
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17.37363
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32.61367
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47.85370
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63.09373
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2.43840
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17.67844
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32.91847
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48.15850
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63.39853
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2.74321
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17.98324
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33.22327
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48.46330
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63.70333
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3.04801
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18.38804
110
33.52807
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64.00813
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49.07290
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67 05513
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39 01448
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54.55931
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70.10414
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39.92888
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24.99365
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55.47371
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10.05842
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25.29845
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40.53848
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55.77851
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10.36322
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40.84328
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56.08331
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10.66802
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25.90805
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41.14808
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56.38811
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71.62814
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10.97282
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26.21285
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41.45288
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66.69291
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71.93294
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11.27762
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26.51765
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41.75768
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56.99771
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72.23774
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26.82245
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42.06248
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57.30251
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72.54255
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11.88722
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27.12725
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57.60732
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12.19202
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27.43205
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73.15215
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12.49682
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58.21692
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12.80163
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28.04166
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43.28169
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58.52172
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13.10643
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28.34646
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58.82652
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59.13132
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13.71603
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Meters
Feet
Meters
Feet
Meters
Feet
Meters
Feet
Meters
250
76.20015
300
91.44018
350
106.68021
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121.92024
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137.16027
1
76.50495
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91.74498
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106.98501
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122.22504
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137.46507
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76.80975
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92.04978
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107.28981
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122.52985
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137.76988
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77.11455
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92.35458
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107.59462
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122.83465
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138.07468
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77.41935
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92.65939
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107.89942
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123.13945
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138.37948
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77 72416
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92.96419
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108.20422
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123.44425
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138.68428
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108.81382
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124.05385
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139.29388
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93.87859
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109.11862
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124.35865
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139.59868
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78.94336
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109.42342
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124.66345
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139.90348
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79.24816
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360
109.72822
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124.96825
460
140.20828
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79.55296
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94.79299
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110.03302
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125.27305
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140.51308
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125.57785
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142.95149
270
82.29616
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97.53620
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112.77623
420
128.01626
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143.25629
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128.32106
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145.99949
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146.30429
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152.09550


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Meters
Feet
Meters
Feet
Meters
Feet
Meters
Feet
Meters
500
152.40030
550
167.64034
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182.88037
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198.42520
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213.66523
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183.48997
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216.10363
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155.44831
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185.92837
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201.16840
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216.40843
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186.23317
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201.47320
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213.15164
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620
188.97638
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219.45644
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158.80112
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8
206.65481
8
221.89484
9
161.23952
9
176.47955
9
191.71958
9
206.95961
9
222.19964
530
161.54432
580
176.78435
630
192.02438
680
207.26441
730
222.50445
1
161.84912
1
177.08915
1
182.32818
1
207.56822
1
222.80325
2
162.15392
2
177.39395
2
192.63399
2
207.87402
2
223.11405
3
162.45872
3
177.69876
3
192.93879
3
208.17882
3
223.41885
4
162.76353
4
178.00356
4
193.24359
4
208.48362
4
223.72365
5
163.06833
5
178.30836
5
193.54839
5
208.78842
5
224.02845
6
163.37313
6
178.61316
6
193.85319
6
209.09322
6
224.33325
7
163.67793
7
178.91736
7
194.15733
7
209.39802
7
224.63805
8
163.98273
8
179.22276
8
194.46279
8
209.70282
8
224.94285
9
164.28753
9
173.52756
9
134.76758
9
210.00762
9
225.24765
540
164.59233
590
179.83236
640
195.07239
690
210.31242
740
225.55245
1
164.89713
1
180.13716
1
195.37719
1
210.61722
1
225.85725
2
165.20193
2
180.44196
2
195.68199
2
210.92202
2
226.16205
3
165.50673
3
180.74676
3
195.98679
3
211.22682
3
226.46685
4
165.81153
4
181.05156
4
196.29159
4
211.53162
4
226.77165
5
166.11633
5
181.35636
5
196.59639
5
211.83642
5
227.07645
6
166.42113
6
181.66116
6
196.90119
6
212.14122
6
227.38125
7
166.72593
7
181.96596
7
197.20599
7
212.44602
7
227.68606
8
167.03073
8
182.27076
8
197.51080
8
212.75083
8
227.99086
9
167.33553
9
182.57557
9
197.81560
9
213.05563
9
228.29566


Feet
Meters
Feet
Meters
Feet
Meters
Feet
Meters
Feet
Meters
750
228.60046
800
243.84049
850
259.08052
900
274.32055
950
289.56058
1
228.90526
1
244.14529
1
259.38532
1
274.62535
1
289.86538
2
229.21006
2
244.45009
2
259.69012
2
274.93015
2
290.17018
3
229.51486
3
244.75489
3
259.99492
3
275.23495
3
290.47498
4
229.81966
4
245.95969
4
280.29972
4
275.53975
4
290.77978
5
230.12446
5
245.36449
5
260.60452
5
275.84455
5
291 98458
6
230.42926
6
245.66929
6
260.90932
6
276.14935
6
291.38938
7
230.73406
7
245.97409
7
261.21412
7
276.45415
7
291.69418
8
231.03886
2
246.27889
8
261.51892
8
276 75895
8
291 99898
9
231.34366
9
246.58369
9
261.82372
9
277.06375
9
292.30378
760
231.64846
810
246.88849
860
262.12852
910
277.36855
960
292.60859
1
231.95326
1
247.19329
1
262.43332
1
277.67336
1
292.91339
2
232.25806
2
247.49809
2
262.73813
2
277.97816
2
293.21819
3
232.56287
3
247.80290
3
263.04293
3
278.28296
3
293.52299
4
232.86767
4
248.10770
4
263.34773
4
278.58776
4
293.82779
5
233.17247
5
248.41250
5
263.65253
5
278.89256
5
294.13259
6
233.47727
6
248.71730
6
263.95733
6
279.19736
6
294.43739
7
233.78207
7
249.02210
7
264.26213
7
279.50216
7
294.74219
8
234.08687
8
249.32690
8
264.56693
8
279.80696
8
295.04699
9
234.39167
9
249.63170
9
264.87173
9
280.11176
9
295.35179
770
234.69647
820
249.93650
870
265.17653
920
280.41656
970
295.65659
1
235.00127
1
250.24130
1
265.48133
1
280.72136
1
295.36133
2
235.30607
2
250.54610
2
265.78613
2
281.02616
2
296.26619
3
235.61087
3
250.85090
3
266.09092
3
281.33096
3
296.57099
4
235.91567
4
251.15570
4
266.39573
4
281.63576
4
296.87579
5
236.22047
5
251.46050
5
266.70053
5
281.94056
5
297.18059
6
236.52527
6
251.76530
6
267.00533
6
282.24536
6
297.48539
7
236.83007
7
252.07010
7
267.31013
7
282.55017
7
297.79020
8
237.13487
8
252.37490
8
267.61494
8
282.85497
8
298.09500
9
247.43967
9
252.67971
9
267.91974
9
283.15977
9
298.39980
780
237.74448
830
252.98451
880
268.22454
930
283.46457
980
298.70460
1
238.04928
1
253 28931
1
268.52934
1
283.76937
1
299.00940
2
238 35408
2
253.59411
2
268.83414
2
284.07417
2
299.31420
3
238.65888
3
253.89891
3
269.13894
3
284.37897
3
299.61900
4
238.96368
4
254.20371
4
269.44374
4
284.68377
4
299.92380
5
239.26848
5
254.50851
5
259.74354
5
284.98857
5
300.22860
6
239.57328
6
254.81331
6
270.05334
6
285.29337
6
300.53340
7
239.87808
7
255.11811
7
270.35814
7
285.59817
7
300.83820
8
240.18288
8
255.42291
8
270.66294
8
285.90297
8
301.14300
9
240 48768
9
255.72771
9
270.96774
9
286.20777
9
301.44780
790
240.79248
840
256.03251
890
271.27254
940
286.51257
990
301.75260
1
241.09728
1
256.33731
1
271.57734
1
286.81737
1
302.05740
2
241.40208
2
256.64211
2
271.88214
2
287.12217
2
302.36220
3
241.70688
3
256.94691
3
272.18694
3
287.42697
3
302.66701
4
242.01168
4
257.25171
4
272.49174
4
287.73178
4
302.97181
5
242.31648
5
257.55652
5
272.79655
5
288.03658
5
303.27661
6
242.62129
6
257.86132
6
273.10135
6
288.34138
6
303.58141
7
242.92609
7
258.16612
7
273.40615
7
288.64618
7
303.88621
8
243.23089
8
248.47092
8
273.71095
8
288.95098
8
304.19101
9
243.53569
9
258.77572
9
274.01575
9
289 25578
9
304.49581

## Appendix B Sample Notes (Construction Survey)

List of Figures


Page
B-1.
Mailing label ........ B-2
B-2.
Front page of notebook ........ B-3
B-3.
Index ........ B-4
B-4.
Differential leveling ........ B-5
B-5.
Horizontal taping ........ B-6
B-6.
Station angle traverse ........ B-7
B-7.
Station angle with horizon closure ........ B-8
B-8.
Deflection angle traverse ........ B-9
B-9.
Transit stadia-survey ........ B-10
B-10.
Plane table ........ B-11
B-11.
Profile and cross-section leveling ........ B-12
B-12.
Slope stakes ........ B-13
B-13.
Horizontal curve layout ........ B-14
B-14.
Building layout ........ B-15
B-15.
Sewer line ........ B-16
B-16.
Height of an accessible point ........ B-17
B-17.
Elevation/distance to an inaccessible point ........ B-18

## Introduction

B-1. Keeping good notes is not only an art, it is a science as well. Notes must not only be legible, but also correct and meaningful. You must decide, before you go into the field, how you want to run your survey and how to record your observations. You must also decide which information you must record in order to make your notes meaningful. Keep in mind that extraneous entries in your notes can do just as much harm as omission of pertinent data. Before making any entry in your notebook, make certain that the entry, sketch, or remark is necessary and will contribute to the completeness of the notes. Below are samples of notes which the construction surveyor may be required to keep. They are only samples of how they may be kept, not of how they must be kept. When assigned to a unit in the field, you will determine what to record and how to do it. Most of the time, the chief of the party will prescribe how notes on the project are to be kept. Above all, decide on your notekeeping procedures and format before you go out on your survey. Your headings, members of party, instrument identification, and weatherman all be entered before you leave for the field.

## Labeling And Mailing Procedures

B-2. The surveyor normally fills out the mailing label in front of the notebook to the unit conducting the project(s) (figure B-1, page B-2).

B-3. The front page is to be filled out as required by the unit (figure B-2).

## Survey Notes

B-4. The backsight (BS) and foresight (FS) distances are determined by stadia and should be balanced. A
page check (PC) is made (figure B-3) for each page. REMEMBER: Page checks only check the accuracy of your mathematics, not the accuracy of the survey.

B-5. The error of closure (EC) is equal to the computed elevation minus the starting or fixed elevation.

For total correction (TC), change the sign of the EC. The allowable error (AE) may be given in the project specifications. The following formulas can be used when the BS and FS distances are balanced as near as possible.

B-6. For normal construction work - AE =  0.1 ft miles or  24mm kilometers B-7. Third order (figure B-4) - AE =  0.05 ft miles or  12mm kilometers B-8. Elevations for fixed points are adjusted by dividing the TC by the total distance and multiplying the result by the distance from the beginning station to the station being adjusted. This value is then algebraically added to the station's computed elevation.



B-9. This set of horizontal taping notes (figure B-5, page B-6) shows the proper way to record distances between points. The lines are taped in both the forward (FWD) and backward (BKWD) direction. The difference between the forward and backward total distances equals the error of closure (EC). The allowable error (AE) is computed by dividing the mean distance (MEAN) by 5,000. Do not round the AE up. This AE will give an accuracy ratio of 1 in 5,000 or third order accuracy. The AE must equal or exceed the EC for the taping to be acceptable.

B-10. The station angles in figure B-6 were first measured with the instrument's telescope in the direct (D)
position. The angle is then doubled by measuring it again with the telescope in the reverse (R) position. The mean angle (MEAN) is found by dividing the R value by 2. The mean angle must be within  30 seconds of the D value. The total of the mean angles should equal N-2 (180 degrees); N is the number of station angles within the loop traverse. When using a one-minute instrument, an error of  30 seconds per station angle is acceptable. The distances recorded were obtained by a separate survey and copied here for completeness.

B-11. The station angle in figure B-7, page B-8, was measured as described above. The explement angle is similarly measured and meaned, thus closing the horizon.

Note: When the explement angle was measured in direct (D), its value exceeded 180 degrees. To compute the MEAN first, add 360 degrees to the reverse (R) value and divide the result by 2.

   B-12. Any mean angle must be within  30 seconds of its D value. The total of both MEAN angles for a
   station must be within  30 seconds of 360 degrees to be acceptable.


## Figure B-7. Station Angle With Horizontal Closure

B-13. Figure B-8 shows deflection angles. When the direct (D) value for direction exceeds 180 degrees

The deflection angle is computed by subtracting the D value from 360 degrees. The difference is a left deflection angle and is preceded by the letter L.

The mean deflection angle is computed by subtracting the reverse (R) value from 360 degrees and dividing the difference by 2. The mean deflection angle is also preceded by the letter L.
B-14. When the direct (D) value for direction is less than 180 degrees

The deflection angle is the same as the D value and is preceded by the R for right deflection angle. The mean deflection angle is computed by dividing the reverse (R) value by 2.

The mean deflection angle is also preceded by the letter R. Deflection angles never exceed 180
degrees. Any mean deflection angle must be with 30 seconds of its D value. The distances
(DIST) were obtained from a separate survey.
B-15. The rod intercept (RI) is the difference between the top and bottom stadia crosshairs. The rod correction (RC) is the value of the center crosshair rod reading. Figure B-9, page B-10, shows notes for RI and RC.

B-16. Product (PROD) is determined by multiplying the RI by the difference in elevation value extracted from table A-2, page A-93, using the vertical angle as the argument. For level shots, the PROD is zero. The PROD can also be computed using the formula: PROD = (RI x 100) 12 Sin 2 Vertical Angle. The PROD has the opposite sign of the vertical angle when backlighting and the same sign when foresighting. Difference in elevation (DE) is determined by algebraically adding the RC to the PROD. Height of instrument is determined by making a level backsight to a point and adding the RC to the point' s known elevation or by determining the vertical angle and the RC, computing the PROD and the DE, then algebraically adding the DE to the known elevation. Zenith distance (ZD) is the angular value between zenith and the RC. Vertical angle (VERT ANGLE) is the angular value between a level line of sight and the RC. Its value and sign are determined by subtracting 270 degrees from the ZD. Horizontal angle (HORIZ ANGLE) is the angle from a beginning reference point to the observed point. Horizontal distance (DIST) is determined for level shots by multiplying the RI by 100. For inclined shots, multiply the RI times the horizontal distance value from table A-2 using the vertical angle as the argument. The DIST can also be computed using the formula: Horizontal Distance = (RI x 100) Cos2 Vertical Angle. ELEV is the elevation of the station. When not given, it is determined by algebraically adding the DE to the HI. Remarks (RMKS) is used to give a brief description of the occupied or observed station.

B-17. Correct horizontal distance (CORR H DIST) is determined by multiplying the H SCALE by the RI
(figure B-10).

B-18. Horizontal scale (H SCALE) is read directly on the alidade. Rod intercept (RI) is the difference between the top and bottom crosshairs.


Vertical scale (V SCALE) is read directly on the alidade.

Product (PROD ) is determined by subtracting 50 from the V-SCALE reading and multiplying
the result by the RI.

Rod correction (RC) is the value of the center crosshair rod reading.

The RC is always negative when foresighting.

Difference in elevation (DE) is determined by algebraically adding the (PROD ) to the RC.

Height of instrument (HI) can be determined by measuring the DE above the occupied station or by making a level backsight to station of known elevation. The RC is positive when backlighting.

Elevation (ELEV) is the elevation of the station. When not given, it is determined by algebraically adding the DE to the HI.

Remarks (RMKS) is used to give a brief description of the occupied or observed station.

B-19. Profile and cross-sectional level notes (figure B-11, page B-12) are best recorded from the bottom of
the page up. This method will align the direction of the survey with the notes. The right page shows the
elevations of ground shots and their distance from the road centerline.


Ground Elevation
134.7
Rod reading
     3.5
Distance from Centerline
50

B-20. The ground elevation is determined by subtracting the rod reading from the HI. The distance from the centerline is measured with a tape.

B-21. Slope stake notes (figure B-12) are best recorded from the bottom of the page up. This method aligns the direction of the survey with the notes. Grade elevations are normally given in the construction drawings. The grade rod values are determined by subtracting the grade elevation from the HI. The threepart entries on the right page show the amount of cut (C) or fill (F), the ground rod reading, and the distance of the slope stake from the road centerline. A detailed method of setting slope stakes can be found in chapter 2.

   B-22. The right deflection angles (R DEFL) (figure B-13, page B-14) were extracted from the curve
   computations (chapter 3). When a road curves to the left, the left deflection angles (L DEFL) are
   determined by subtracting the R DEFL from 360 degrees. The R DEFL are used to "back-in" a left curve
   from the point of tangency (PT). When a curve is to the right, the L DEFL need not be computed.


B-23. The building corner numbers in the sketch must agree with the corner numbers on the left page. In this example, (figure B-14) the building foundation is required to be 1.5 feet above the ground at the highest corner. The batter board elevation (BATTER ELEV) is determined by adding 1.5 feet to the ground elevation (ELEV) of the highest corner. The difference between the BATTER ELEV and the HI equals the grade rod. When a batter board elevation is given, the ground shots are not necessary. The grade rod equals the HI minus the given batter board elevation.



B-24. The stations in figure B-15, page B-16, were foresighted on top of their offset stakes. The invert elevations (INVERT ELEV) were computed using the manhole (M. H.) invert elevation at 0+00 and the percent of the slope. The elevation (ELEV) of a station minus the INVERT ELEV equals the amount of CUT at the offset station. The CUT is rounded down to the nearest whole or half foot for the adjusted cut (ADJ CUT). The ADJ CUT assists the construction crew when digging the ditch. The difference between the CUT and ADJ CUT is the distance measured down and marked on the offset stakes. The ADJ CUT
value and the offset distance (OFFSET DIST) is also marked on the offset stakes facing the sewer line. The station values are marked on the opposite side (figure B-16, page B-17, and figure B-17, page B-18).

## Glossary Section I - Definitions

Alidade
The part of a surveying instrument that consists of a sighting device, an index, and reading or recording accessories.

## Azimuth A Horizontal Angle, Measured Clockwise, Between North And A Line To An Observed Or Described Point. Azimuth Mark A Marked Point, Visible From A Survey Station, To Which The Azimuth Has Been Determined. Bearing The Acute Angle Formed By A Line And The North-South Line Through An Occupied Point. Borrow Pit An Excavated Area Whose Material Is Used As Fill At Another Location. Chord A Straight Line Joining Two Points On A Curve.

Closed Traverse A traverse that starts at a point and ends at the same point or at a point whose relative position is known.

## Compound Curve Two Simple Curves Joined Together And Curving In The Same Direction. Easting One Of The Two Values (The Other Being Northing) Indicating The Position Of A Point On A Grid System. External Distance The Distance From A Curve' S Point Of Intersection To Its Midpoint. Invert Curve See Sag Curve. Long Chord The Chord From The Point Of Curvature To The Point Of Tangency. Loop Traverse A Traverse That Starts And Ends At The Same Point And Does Not Cross Itself. Middle Ordinate The Distance From The Midpoint Of The Curve To The Midpoint Of The Long Chord. Northing One Of The Two Values (The Other Being Easting) Indicating The Position Of A Point On A Grid.

Open Traverse
A traverse that starts at a point of known or assumed position and ends at a point whose relative position is unknown.

## Overt Curve See Summit Curve. Parabolic Curve See Vertical Curve. Glossary Point Of Compound Curvature The Point At Which Two Curves Connect. Point Of Curvature The Point Where A Circular Curve Begins. Point Of Intersection The Point Where The Back And Forward Tangents Of A Curve Intersect. Point Of Tangency The End Of A Curve. Reverse Curve Two Simple Curves Joined Together But Curving In Opposite Directions.

Sag Curve
A vertical curve which connects a descending grade with an ascending grade, or with one descending less sharply; also called an invert curve.

## Simple Curve A Horizontal Curve Which Is The Arc Of A Circle; The Most Common Curve.

Spiral Curve
A curve of varying radius used to gradually increase the curvature of a road or railroad. Also known as a transition curve or transition spiral.

Summit Curve
       A vertical curve which connects an ascending grade with a descending grade, or with one ascending
       less sharply; also called an overt curve.
Vertical Curve -
       A curve used to produce a more gradual direction change when two grade lines intersect; also called a
       parabolic curve.

## Wing Walls In Bridge Construction, An Oblique Retaining Wall. Section Ii - Acronyms And Abbreviations

AE
Allowable Angular Error
Az
Azimuth mark
A.R.E.A
American Railway Engineering Association

Centerline
D
Degree of Curv
DMD
Double Meridian Distance
E
External Distance
HI
Height of Instrument
I
Intersecting Angle
L
Length of Curve
LC
Long Chord
M
Middle Ordinate
PC
Point of Curvature
PI
Point of Intersection
PRC
  Point of Reverse Curvature
PT
Point of Tangency
PVC
Point of Vertical Curvature
PVI
Point of Vertical Intersection
PVT
Point of Vertical Tangency
R
Radius
SI
Station Interval
TS
Traverse Station
This page intentionally left blank.


## References

REQUIRED
Required publications are sources that users must read in order to understand or to comply with this publication.

TECHNICAL MANUALS
5-232
Elements of Surveying (superseded by FM 3-34.331)
5-330
Planning and Design of Roads, Airfields, and Heliports in the Theater of Operations
(superseded by FM 5-430-00-1 and FM 5-430-00-2)
RELATED
Related publications are sources of additional information. They are not required in order to understand this publication.

FIELD MANUALS (FM)
5-1
Engineer Troop Organizations and Operations (superseded by FM 5-104)
5-30
Engineer Intelligence (superseded by FM 5-170)
5-34
Engineer Field Data
5-35
Engineer's Reference and Logistical Data (rescinded)
21-26
Map Reading and Land Navigation (superseded by FM 3-25.26)
21-30
Military Symbols (superseded by FM 101-5-1)
21-31
Topographic Symbols (rescinded)
TECHNICAL MANUALS (TM)
5-235
Special Surveys
5-237
Surveying Computer's Manual (superseded by FM 3-34.331)
5-258
Pile Construction (superseded by FM 5-134)
5-302-1 Army Facilities Components System: Design 5-302-2 Army Facilities Components System: Design 5-302-3 Army Facilities Components System: Design 5-302-4 Army Facilities Components System: Design 5-302-5 Army Facilities Components System: Design 5-332
Pits and Quarries (superseded by FM 3-34.465)
5-337
Paving and Surfacing Operations (superseded by FM 5-436)
5-349
Arctic Construction
5-360  Port Construction and Rehabilitation (superseded by FM 5-480) 5-370
Railroad Construction (rescinded)
5-441
Geodetic and Topographic Surveying (superseded by FM 5-232)
This page intentionally left blank.


## Index

Interior transfer of line and grade 6-4
Layout 6-2 Sewer lines 6-4

A
Abutments, staking 5-4 Accuracies and specifications, traverse 7-12
Accuracy of surveys 1-1 Arc and chord:
Accuracy 3-9 Purpose 3-9
Arc definition, degree of curve
3-4
A.R.E.A 10-chord spiral 3-25 Area computations:
Counting-squares 4-4 Double-meridian-distance
4-6
Geometric 4-4 Planimeter 4-8 Stripper 4-4
Azimuth adjustment 7-7 Azimuth-bearing angle 7-8 Azimuth corrections 7-7
C
Calculating a spiral 3-28 - 3-
31
Centerline profile 2-5 Centerline running, road surveys 2-4 - 2-5
Central angle 3-3 Chief of party, traverse 7-4 Chord definition, degree of curve 3-4 - 3-6
Chord length 3-5, 3-10 Closed traverse 7-2 Common excavation 4-9 Compound curvature, point of
3-17
Compound curves 3-17 -
3-20
Computations 3-20 Staking 3-20
Connecting diverging tangents 3-23 - 3-24
Connecting parallel tangents
3-22 - 3-23
Construction layout surveys
2-5
Coordinate computations
7-10
Culvert layout 2-10 Curves:
Compound 3-1, 3-17 -
3-20
Elements 3-2 - 3-4 Formulas 3-6 Horizontal 3-1 - 3-2 Layout 3-9 - 3-17 Length 3-3 Reverse 3-17 - 3-24 Sag 3-35, 3-36 Simple 3-1, 3-11 Spiral 3-2, 3-24 - 3-35 Stations 3-1, 3-2 Summit 3-35 - 3-36 Tables 3-9, 3-11 Through fixed point 3-16 -
3-17
B
Battens, sewer alignment 6-5 Batter boards:
Building construction surveying 6-2
Sewer alignment 6-5
"Blue-tops" 2-6 Borrow pit layout 4-11 Borrow pits 4-10 Bridge surveying: Abutments 5-4 Foundation investigation 5-2 Piers 5-6 Piles 5-7 Reconnaissance 5-1
Access roads 5-1 Bridge length 5-1 Flow character 5-2 Profile 5-2 River banks 5-2 River bottom character 5-2 Use of local materials 5-2
Soundings 5-2 Wing walls 5-5 Building construction surveying:
Batter boards 6-2
Vertical 3-35 - 3-39 Vertical parabolic 3-35
Curvature:
Degree of 3-4 - 3-5 Point of 3-2 Radius 3-2, 3-43-5
D
Deflection angles 3-5, 3-7 Deflection angles, spiral curve 3-33 - 3-34
Diverging tangents, connecting 3-23 - 3-24
Double-meridian-distance method 4-6
Drainage 2-2
E
Earthwork computations:
Borrow pits 4-10 Counting squares 4-4 Double-meridian-distance
4-6
Geometric 4-4 Importance Planimeter 4-8 Stripper 4-4
Elevation of sewer grade 6-5 Excavated material 4-9 Exaggerated vertical scale
4-3
External distance 3-3 Field location of compound curve 3-20
Field notes (see appendix B):
Degree of precision 1-1 Recording procedure 1-2 Spirals 3-35 Traverse 7-4, 7-13
F
Final location survey 2-4 First difference, parabolic curve 3-37
Flow line, sewer 6-5 Formulas:
Compound curve 3-18 Deflection angles 3-6 Simple curve 3-6 Spiral curve 3-27 - 3-28
Vertical curve 3-36
Forward station 7-3 Full station 3-2
Inaccessible PT 3-14 -
3-15
Obstacle on curve 3-15 Terrain restrictions 3-12
Occupied station 7-3 Open traverse 7-2 Organization of traverse parties 7-4
G
Geometric method 4-4 Grade:
Pole 6-5 Rod 2-6 Sewer 6-5 Stakes 2-6
H
High point of vertical curve
3-38
Highway spiral lengths 3-28
I
Inaccessible PC 3-13 Inaccessible PI 3-12 Inaccessible PT 3-14 - 3-15 Instrument operator, traverse
7-4
Instrument setup on a spiral
3-30
Interior transfer of line and grade 6-4
Intermediate setup 3-10 Intersecting angle 3-2
P
Parabolic curve (see Vertical curve)
Parallel tangents, connecting
3-22 - 3-23
Piers, locating 5-6 Piles, locating 5-7 Pipe grade 6-6c Plane table party, road surveying 2-4
Planimeter 4-8 Plus stations 3-2 Point:
Compound curvature 3-17 Curvature 3-2, 3-10 Intersection 3-2 Locating inaccessible
3-12 - 3-15
Reverse curvature 3-20 Tangency 3-2 Vertical intersection 3-36 Vertical tangency 3-35
Polar planimeter 4-8 Preliminary survey, road 2-3 Profile, centerline 2-5
L
Layout surveys (see Road surveying) 2-5
Length of chords 3-5 Level party 2-4 Leveling:
Cross section 2-5 Profile 2-5
Long chord (LC) 3-3 Loose rock, excavation of 4-9 Low point of vertical curve
3-38
M
Measurements, survey 1-1 Metric system 1-2 Middle ordinate (M) 3-3
R
Radius of curvature 3-2,
3-4 - 3-5
Railroad spiral lengths 3-28 Rear station 7-3 Reconnaissance:
Access roads 5-1 Bridge length 5-1 Flow character 5-2 Profile 5-2 River bottom character 5-2 River banks 5-2 Use of local materials 5-2
Reconnaissance survey (see Road surveying) 2-1
Recorder, traverse 7-4 Reference stakes 2-5 Reverse curve:
O
Obstacles to curve location:
Curve through fixed point
3-16
Inaccessible PC 3-13 Inaccessible PI 3-12
Connecting diverging tangents 3-23 - 3-24
Connecting parallel tangents 3-22 - 3-23
Point of 3-20
Road surveying:
Alignment markers 2-6 Centerline running 2-4 Cross sections 2-5 Culvert 2-10 Data collection 2-3 Design 2-1 Drainage 2-10 Grade stakes 2-6 Level party 2-4 Maps 2-3 Plane table 2-4 Preparation 2-1 Reference stakes 2-5 Roadway criteria 2-2 Slope stakes 2-7 Topographic party 2-4 Transit stadia 2-4 Traverse party 2-4
Roadway criteria 2-2 Rock excavation 4-3 Rodman, traverse 7-4
S
Sag curve (see Vertical curve)
Second difference, vertical curves 3-37
Sewer grade 6-6 Sewer lines, building construction 6-5
Short-radius curves 3-1
Side slope 4-3 Sighting cord, sewer alignment 6-5
Simple curves 3-1  - 3-11 Site layout:
Batter boards 6-2 Building layout 6-2 Utilities drainage 6-4
Slope stakes 2-7 Solid rock excavation 4-9 Sounding, bridge surveying
5-2
Spiral calculations:
Chord length 3-30 Circular arc 3-30 Deflection angles 3-30 -
3-31
Computations 7-5 Coordinates 7-10 Fieldwork 7-3 Open 7-2 Organizing party 7-4 Starting control 7-1 Types 7-2
Traverse party 2-4, 7-4  -  7-5 Traverse stations:
Markers 7-4 Selecting 7-4 Signals 7-4

## U Utilities Drainage 6-6

V
Vertical curves 3-35 - 3-39
Function 3-35 Sag 3-35-3-36 Summit 3-35 - 3-36
Vertical offset, formula 3-37

## W Wing Walls, Staking 5-5

Determining Ls 3-29 Determining  3-29
Determining Ts 3-30 Determining Z 3-30
Spiral curves:
Elements 3-25 - 3-27 Field notes 3-35 Formulas 3-28 Staking 3-34 Intermediate setup 3-33
Spiral lengths 3-28 Stakes:
Grade 2-6 Reference 2-5 Slope 2-7
Staking spirals 3-34 Station interval 3-36 Station, traverse:
Forward 7-3 Occupied 7-3 Rear 7-3
Stripper method 4-4 Subchord lengths, calculating
3-10
Summit curve (see Vertical curve)
Superelevation 3-24 Survey:
Accuracy 1-1 Road (see Road surveying)
Survey measurments 1-2 Survey objectives 1-1 Surveyor, construction 1-1
T
Tangency, point of 3-2 Tangents, connecting:
Diverging 3-23 - 3-24 Parallel 3-22 - 3-23
Tangent distance 3-3 Tapeman, traverse 7-4 Terrain restrictions 3-12 -
3-16
Topographic party 2-4 Transition spirals (see Spiral curves)
Transit-stadia party, road surveying 2-4
Trapezoidal method 4-4 Traverse:
Accuracy 7-12 Closed 7-2
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1030903

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