An Improved Instrument for Facilitating Trigonometrical Admeasurements, and "other Calculations.
Year: 1898

page_text: Date of Application, 23rd Nov., 1898-Accepted, 2nd June, 1899
COMPLETE SPECIFICATION.
An Improved Instrument for Facilitating Trigonometrical
Admeasurements, and "other Calculations.
and
We, FRANCIS JOSEPH BAYLDON, Master Mariner, Holder of British Board of
Trade Certificate No. 025035, at present serving as Third Officer on Board the
Canadian Australian Steamship Company's Steamship "Aorangi" and having as
his address Low Toynton Rectory. Horncastle, Lincolnshire, England,
ARNOLD HUDDART ARMSTRONG, at present serving as Fourth Engineer on board the
said Steamship 66
Aorangi" and having as his address No. 152, High Street,
Stockton on Tees, Durham, England, do hereby declare the nature of this inven-
tion and in what manner the same is to be performed, to be particularly described
and ascertained in and by the following statement:―
This invention relates to an improved instrument by which the admeasurements
of the remaining sides and angles of triangles may be ascertained from the usual
data by inspection and thus renders unnecessary the time the burden and the
material of calculation usually employed for such purposes.
or
This invention has been specially devised for the purpose of enabling navigators
to ascertain angles and distances independently of books of tables and calculating
materials and of providing them with a conveniently handled and always
accessible instrument from which they may ascertain by inspection dis-
tances of their vessel either at the moment after the passage of
time from objects ashore with no other data than that which their
compass and the speed of said vessel afford, and by which they may prove
whether their vessel has been travelling on the proper course. But although this.
invention is specially useful to navigators yet land surveyors and the like will
find it of great value as obviating many of their calculations as also will engineers
and others who use angular measurements to compute strains and stresses or
the like.
the
This improved instrument for facilitating trigonometrical admeasurements and
other calculations consists of certain movable parts mounted upon a base plate
of wood or metal or other material upon which plate are engraved (or otherwise
fixed) certain scales of measurements. On a base line or diameter is a graduated
seale preferably termed the "base" from which rises a "protractor." Another
similar graduated scale preferably termed the "vertical" reaches centrally and
at right angles from the base to the circumference. Mounted upon the centre of
'protractor" are two movable radii preferably termed " pointers" each
bearing a graduated scale similar to those before mentioned. Reaching from
side to side and adapted to slide over the "pointers," the scales, and the " pro-
tractor" and vet be always parallel to the base scale is another graduated scale
termed the "bar." This sliding bar has guide blocks in grooves in the base plate
of the instrument and is capable of being clamped in any desired position. A.
central "protractor" termed the ". upper protractor" is carried by this "bar"
and mounted upon its centre is a double-ended "pointer" or indicator capable
of being clamped in any desired position. A graduated scale (similar to those
before mentioned) preferably termed the "parallel" is jointed to this indicator

page_text: Bo as to have a parallel motion therewith and to be clamped at desired distances
therefrom. The scales graduated on the "base" the " vertical," the "pointers,"
the "bar" and the "parallel" can be used to denote any unit such as yards, miles,
furlongs, cables etc. and they are preferably on the decimal system and are used
when necessary as aliquot parts or multiples as well understood.
Upon the base of the instrument there may be engraved two or more clock
faces or compass dials having movable hands or indicators and there may be one
or more scales or the like having movable indicators but these are not necessary
though useful adjuncts for preserving certain notations from time to time.
But in order that this invention may be clearly understood the various parts
of this improved instrument for facilitating trigonometrical admeasurements and
other calculations and their particular uses (including some examples of such
uses), will now be described with reference to the drawings herewith in which
Figure 1 is a plan of said instrument and Figure 2 an edge view from bottom
while Diagrams 1 to 16 on a smaller scale serve to illustrate certain inspections
instead of calculations as hereinafter set forth.
On the plate or baseboard X is engraved a protractor or graduated semi-circle A
having graduated base B and graduated vertical C. On a pivot A¹ at the centre
of the protractor are movable radial pointers D1 and D2 (adapted to be clamped
by thumb nut A2) both bearing graduated scales on an edge which is a true radius.
The bar E bears also graduated scales and is retained in parallelism with the base B
by guide blocks E' (in guide grooves A³) which may be immovably clamped by
thumb nuts E. From this sliding bar E extends upper protractor F at whose
centre is a pivot on which is double ended indicator G adapted to be clamped
to said protractor by thumb nut F. Jointed to the indicator by bars H¹ and
adapted to be clamped by thumb nuts H² 'is the parallel H also bearing similar
graduated scales.
I and J are engraved clock faces with movable hands and K is a graduated
scale having movable indicators K. These are adjuncts not necessary to the
instrument but useful the first for denoting the times of taking observations
et cetera, and the latter for denoting mileage of a log or whatever distance or
number it may be useful to remember.
The protractor A is for laying off any bearings or angles which will be represented
by the pointers D' and D2 whose edges will thus form the one or two sides of a
triangle as necessary and will indicate the length of that particular side or sides.
The bar E is used to give or to find a third side or one or two other angles (or
their sines and co-sines) by being placed across the vertical and one pointer or
both. The upper protractor F enables the parallel H to be placed across the
pointers and the vertical at various angles given or indicated by the pointer G
and at various distances for side of triangle or other figure to enable
other admeasurements of angles or sides to be given or found. The
parallel especially enables readings to be taken from the protractor
A and the other scales which would otherwise
be obscured by the
bar B. By variously combining these movable parts on the fixed scales the
lengths of the sides of triangles and the values of the angles are regulated or
determined.
The scales shown in the drawing are divided into 5, 10, and 50 units say miles
but if the distances be small each smallest unit can be taken to represent ½ of a
mile or a mile or ½ or 10 or 20 of a mile and so on.
To navigators this improved instrument will prove of incalculable value for
kept in its case (or ready mounted for use) on deck or on the bridge it is always
handy. Practically no bad weather or motion of the ship can prevent its use and
it is reliable and accurate and very simple to manipulate and all that it needs to
work it can always be obtained namely a light, a compass and a patent log or
watch while books, charts pencils or paper are not needed; the officer has not to
leave the deck or bridge but when off a coast there and then can obtain his ship's
course and distance difference of latitude and departure, distance off shore or any

page_text: point the distance he has passed or will pass of any particular point, the set and
drift of a current, the course he is making and many more items of vital necessity.
With a little practice with the instrument in a minute can be obtained any par-
ticulars of this sort which otherwise would be neglected altogether or only attained
after laborious calculations or else by drawing the same diagrams on a chart
and then measuring them necessitating leaving the deck. The instrument is not
so especially intended for chart room or fine weather use when other calculations
may easily be made as it is for bad and rainy weather or a heavily straining ship
when it is impossible to use books or papers or pencils on deck or when for other
reasons the officer is unable to leave the deck. The navigator when taking bear-
ings off the land need not wait for the object observed to be on some particular
bearing but at any angle in a very short time he can obtain what he desires-the
accuracy of the results only depending on the accuracy of the observer himself.
Land surveyors or the like with a knowledge of some of the angles and sides
of a triangle or four-sided figure can at once determine the measurements including
the length of the diagonal and area of the figure. Ordinance, naval and other
military forces may use the instrument as a convenient range finder.
Engineers with this instrument will find it unnecessary to construct diagrams
(viz.) triangles of forces etc. The graduated scales on the instrument dispense
with the tedious process of drawing to very fine scales. For example once the
initial load on the piston the length of stroke and the length of connecting rod of
an engine are known the stresses on the guides may be obtained without reference
to either trigonometry or graphic statics. The stress on each and every part of
an ordinary jib crane or derrick may be at once ascertained and the safe working
load definitely fixed.
It is not intended that the following examplify the way in which problems
must be solved-but only to show the method by which they might be for there
are various ways in which an accurate result from the same data can be obtained.
The examples given illustrate but a small proportion of the uses to which the
instrument can be reliably put.
To solve right-angled triangles it is necessary that either one side and one angle
or two sides shall be given, then the remaining admeasurements are at once seen.
The pointer denoting an angle of the triangle and also representing the hypotenuse,
the vertical, and the parallel (used horizontally) or the bar will represent the base
or perpendicular. As in Diagram 1 one angle is 50° and hypotenuse equals 28':
to find the other sides and the angles the pointer D is placed on 50' on the pro-
tractor A (the other angle is its complement namely 40°) and the bar E slid
horizontally until it intersects 28' on the pointer which it does at c on its thus
giving this length of and 21 and it is seen that it intersects the vertical C
at bon 18' which is thus the length of a b.
To solve oblique triangles use the parallel obliquely to form the given angle and
the two pointers or one pointer to measure one side when the vertical will indicate
the remaining sides and angles. The distances required are at the different points of
intersection but care must be taken in reading the distance off the parallel to see
that the whole distance contained between the other two sides is noted that is the
measurements if so on both sides of zero. To measure the angle of the parallel
take it direct from the upper protractor as indicated by the index of the parallel.
Thus in Diagram 11 given the sides a band a c and the angle a find other
angles and the side b c. Place the pointer D at known angle a move the parallel H
obliquely so as to cut the vertical and the pointer at the known lengths of the
sides a c and a respectively then the reading on said parallel contained between
these two intersections is the length of the side b c. The angle made on the pro-
tractor by the parallel at c may be read off and the other angle b equals 180°-
(a+c) as well understood.
"
Course S. 40 E. and distance 25' being given the "difference of latitude" and
departure" is ascertained as in Diagram III. Pointer D is placed at 40° and
the bar E to cut 25' on said pointer when the reading 16' on the bar at this point

page_text: of intersection is the departure and the reading on the vertical C namely 19′ is
the difference of latitude.
Difference of latitude 19' and distance 21' being given the course and departure
is ascertained in Diagram IV. Bar E is placed at 19' on the vertical and the
pointer with 21' to cut said bar then the reading 9' on the bar is the departure
and the angle 25° made by the pointer on the protractor A is the course.
To change departure into difference of longitude proceed as in using the traverse
tables latitude is 36° and departure 100' what is the difference of longitude? As
in Diagram V place pointer D at 360 on protractor A move bar E until the
departure 100' intersects the vertical C (that is the difference of latitude column),
then the corresponding distance 124' on the pointer D is the difference of longitude.
To change difference of longitude into departure is a reverse method. Latitude
is 56° and difference of longitude is 50'-what is the departure? As in Diagram V
pointer D is placed at 560 on protractor A and it is cut at 50' with the bar when
the corresponding number 28' on the vertical C is the departure.
The bearing and distance from each other of two points of land being ascertained
from the chart, and bearing taken of each of them when sighted the ship's distance
off them and also the passing distance etc. is found thus. Apply variation and
deviation to the bearing from the chart and thus turn it into a compass bearing
(as in Diagram VI) take the angle which this bearing makes with the ship's course
and lay the parallel H at this angle by means of the upper protractor F and clamp
it. Let the vertical C represent the ship's course and lay the pointers D' and D²
on protractor A at the two bearings taken of the two objects. Move the bar E
and parallel H until the distance of the objects from each other lies on said parallel
exactly between the two pointers D1 and D2 and the intersection on each pointer
then indicates the distance of the object whose bearing it denotes. Further by
placing the parallel H horizontally and moving it as in Diagram VII until it cuts
first one and then the other pointer at these respective distances of objects just
obtained the distance the ship will pass off each object is found on said parallel
and the distance she has to run to do so is given by the vertical C. Two objects
being abaft the beam it is easiest to consider the ship as sailing along the base
then the vertical represents the beam and the bearings are laid off in the same way
as before and the required results obtained. To ascertain the ship's distance off a
point of land also how far she must run to bring it abeam and the distance it will
be off when abeam or how much the ship has run since it was abeam and at what
distance she passed off it, also whether the ship is making her course is illustrated
in Diagram VIII. The bearing of an object is reckoned as so many degrees or
points on the bow place pointer D¹ to represent these degrees or points on the bow
reckoning them from the base line of the instrument and note the time. After
this bearing has conveniently changed take a second bearing and denote it in the
same way as before by the second pointer D2; again the time is noted and thus
the distance the ship has run since the first bearing may be estimated. Move the
bar E horizontally until the distance travelled is indicated on this bar exactly
between the two pointers D1 and D2 and then the distance on the pointer 11 to the
parallel H is the distance the ship was off the object at the first bearing and the
distance on the pointer D is the distance the ship is off (such object) at time of
second bearing; from the bar E to the second pointer D2 on the vertical C is the
distance to run to bring the object abeam-(the time when it will be passed can
therefore be estimated) and lastly the distance on the vertical C to the bar E is
the passing distance. Leave the instrument with parts in the last described
positions and after the bearing has again changed take a third bearing and note
the distance run by the log. Now move the second pointer 12 to this bearing D³
then if the ship is correctly making her course and distance this pointer marked D³
will cut the bar at a distance less than previously by the same amount as the ship
has run and thus the bar will be unchanged in position and give the same passing
distance as before whilst the reading on the pointer now D3 is the distance off at
the third bearing. Again a fourth bearing can be taken to still further verify

page_text: results and to ascertain whether the ship maintains her course so that at any time
after taking the second bearing by simply taking another bearing all these
important details can be ascertained. When the object is abaft the beam estimate
the bearings as so many degrees or points abaft the vertical C as by pointer now Di
when the distance off the object if indicated by the measurement on said pointer D
and the run since the object was abeam is shown on the bar E and the distance off
of the object when abeam is shown on the vertical C.
Having found at what distance a ship would pass off a point of land to find how
much to alter the course to make her pass at a given distance nearer or further
away. Take note of the bearing and distance of the object a and as in Diagram IX
show by the pointer I and move the bar E horizontally until it cuts the required
passing distance on the vertical C. Move the pointer D³ until it is cut at b by
said bar E at the same distance as a on the pointer D¹. The number of degrees
the pointers vary is the number of degrees to alter the ship's head towards or from
the object and the bar E gives the distance the ship has now to run to bring the
object abeam. It thus follows that whenever the ship's course is altered it can
at once be ascertained at what distance she will then pass off the object by moving
the pointer the same number of degrees as the ship's course has been altered and
moving the parallel to cut the pointer at the same distance as before.
The distance a vessel will pass off a light (the range of which is known) how
far it will travel before the light will be abeam is ascertained as illustrated in
Diagram X. A 21-mile light is seen 3 points on the bow the eye being 40 ft.
high. At this height the range of visibility is extended 7' making the light
visible at 28'. Pointer D is placed on the angle on the bow 3 points and the
bar E to cut it as 28' when the corresponding reading 15 on the bar is the distance
the vessel will pass off the light and the reading 23 on the vertical is the distance
the vessel has to travel before the light is abeam.
A vessel steering S. 40° W. is 15' off a point bearing S. 60° W. The problem of
how far must she travel to bring the point abeam and what will her distance off it
then be is illustrated by Diagram XI. As the point is at an angle of 20° (60° - 40°)
on the bow place the pointer D at this angle on the protractor A and move
the bar until it cuts the 15' on pointer D when the corresponding reading 5'
on said bar E is the distance the ship will pass from the point and the distance 14′
on the vertical C is how far the ship must travel to so pass.
A point of land is 30° on the bow distant S' the problem to find how far must
the ship go before it bears 70° on the bow and then what will be her distance off
is not illustrated but it is solved as follows:-Pointer I) is placed at 30° on pro-
tractor A and the bar at 70° and move it until it cuts the pointer at S-the vertical
gives the distance 5 to run and the bar the distance 4 the point is off. The
course being then altered SO as to bring it two points on the bow
the distance she must travel to bring it abeam and what will be
her passing distance is ascertained by placing pointer D at the two-points on the
protractor A and moving bar E horizontally to cut pointer D at 4 when the
vertical indicates the distance 4 nearly to run and the bar E the passing
distance 2' nearly.
Referring to Diagram XII being at a close in with land the ship ran 27 to
Westward then the point of land 6 is found to bear NNW this point by chart
bears WN from first position a distant 29. To ascertain the course steered
and ship's distance from point 6 is solved by regarding the vertical Cas equalling
WN and 29' on it is the distance of b. Difference between WN and NNW
(5 points) is indicated on the upper protractor F and thus by the parallel H;
move the pointer until 27 on it cuts the parallel on which the read-
ing 19' is the distance of the ship from 6 and the angle made by
the pointer D is the course reckoned from the S it gives S. 531° W for the vertical
being WN the 90° line must be SW.
To find distance of a ship at anchor from the shore as in Diagram XIII two
stations a and b are chosen whose distance from each other is known as 2.

page_text: From a the angle subtended by the ship and b is found to be 641° and from b
the angle subtended by the ship and a is found to be 74°. Let the centre of the
protractor represent a and 21 measured on the vertical be b. With the pointer 1
Juake an angle at a equal to 641°. Place the parallel H at b (i.e. 2 on vertical)
and with it make an angle of 74° on the upper protractor when its intersection
with the pointer indicates the ship's position, giving the distance from a as 3.6
miles and the parallel giving the distance from bas 3.4 miles.
In a ship sailing along a coast a church and a mill c are observed in one the
church being the nearer object; at the same time the angle subtended at the
ship by the church band a tower d on the coast is found to be 250. By chart
the distance from church to tower was 1 from church to mill 0.75 of a mile and
from mill to tower 1.9 of a mile. Now the distance of the ship from church and
tower is found as in Diagram XIV; the centre of the protractor is taken as the
tower then 1.5' along the vertical gives the church b; the parallel H is placed
at an angle of 251° with the horizontal as indicated on upper protractor F and is
moved to 1.5 miles (the church b) when .75' further on it will indicate the mill c
(the distance of which may also be measured by moving the pointer I until it
cuts the parallel at 1.9 the distance from tower d to mill c). Where the base B
is cut by the parallel H is the distance 3.3' of the ship a from the tower d and the
reading 3.5 on the parallel at the same place is the distance of the ship a from
the church . It may be noticed that this example is culled from Norrie's
Epitome of Navigation" but it is to be noted that the requirements of the problem
can be solved by this instrument without the slightest necessity for the data
referring to the mill.
66
The calculation of strains on derricks spans etc. is exemplified in Diagram XV.
It is assumed the topping lift of a boom makes an angle of 25° with the boom on
which is supported a weight of 8 tons and it is required to ascertain the strain
on the topping lift and the thrust on the boom. Let the pointer D represent the
topping lift the bar E represent the weight and the vertical C the thrust on the
boom the pointer being at the required angle (25°) on the protractor A. the bar is
moved until it cuts said pointer D at S' the indication of the weight in tons when
the point of intersection on the vertical C is at 17.2' which indicates the thrust
in tons and on the pointer at 19' the strain on the topping lift in tons.
Oll
Again to find the strain on the main lift when the yard is square and a weight
of 2 tons is hanging at the lift and the lift makes an angle of 220 with the yard
as in Diagram XVI. Place the pointer at 22° move the bar until 2'
on it cuts the pointer. The reading 5 on the pointer is the strain
the lift in tons. Another problem unillustrated supposes the two legs of a span
to support a weight of 12 tons making an angle of 24° with one leg and 34°
with the other and it is required to ascertain the strains upon each leg. Let one
pointer make an angle of 24° with the vertical and the other pointer an angle, on
the opposite slide of 34°. Set the bar to one of the pointers say first at an angle
of 24° and move it so as to intersect the vertical at 12' and the second pointer
when the reading 54' on this second pointer gives the strain in tons on this leg
and the distance 8' on the bar between the two points of intersection give the
strain on the other leg in tons. Or the bar may at once be set to the angle of one
side and thus one pointer only need be used.
Similarly as set forth all parallelograms may be solved and the length of the
diagonal and the area of the figure also determined.
As in example (unillustrated) of calculations of angular strains by engineers
the following will suffice, namely the ascertainment of the pressure on guides
due to angularity of connecting rod. The vertical represents the centre line of
the engine the pointer represents the connecting rod-and the parallel the crank.
Taking the relation of connecting rod and crank as 3 to 1 the scales are so placed
that 3 units are cut off on the pointer and 1 on the bar. Then the initial load
being represented on the vertical the reading between the vertical and the inter-
section of the bar and pointer represents the total load of the guide at its maximum.

page_text: In this manner the pressure at any part of the stroke may be ascertained which
being multiplied by the co-efficient of friction will give the resistance of the
wearing surface to the engines motion. In designing and before indicator cards
can be taken a fairly accurate turning moment diagram may be constructed from
data given by the instrument. By subtracting the frictional resistance of the
guide from the initial load a good idea is obtained of the pressure on crank pin
at different parts of the stroke. In this manner all stresses due to angularity of
the connecting rod may be quite easily seen as compared with complicated
calculations in mathematics.
Having now particularly described and ascertained the nature of our said inven-
tion and in what manner the same is to be performed, we declare that what we
claim is:-
First. An improved instrument for facilitating trigonometrical admeasurements
and other calculations the essential features of which are fixed base and fixed
vertical scales and a fixed protractor on which are radial pointer or pointers and
a sliding bar parallel to said base substantially as herein described and explained.
Second. In an improved instrument for facilitating trigonometrical admeasure-
ments and other calculations of the kind set forth the combination with the sliding
bar of an upper protractor and an indicator adapted to revolve about the centre of
said upper protractor and to carry a scale either directly or upon a parallel to it
substantially as herein described and explained.
Third. The improved instrument for facilitating trigonometrical admeasure-
ments and other calculations constructed and operated substantially as herein
described and explained and as illustrated in the drawing.
Dated this First day of October One thousand eight hundred and ninety-cight.
FRANCIS J. BAYLDON.
A. H. ARMSTRONG.
Haseltine, Lake & Co.,
45, Southampton Buildings, London, W.C.,
Agents for the Applicants.