Improved Trigonometrical Calculating and Measuring Instrument.
Year: 1895

page_text: Date of Application, 16th Apr., 1895-Accepted, 29th June, 1895
COMPLETE SPECIFICATION.
Improved Trigonometrical Calculating and Measuring Instrument.
I ADOLPHE LAURENT LACOSTE, of Front Street, Natchitoches in the Parish
of Natchitoches and State of Louisiana, United States of America, Civil and
Mining Engineer do hereby declare the nature of this invention 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 calculating and measuring instruments, and it has for
its object to provide an instrument which is comparatively simple and durable in
construction, easily manipulated, and more especially designed to enable surveyors
and others to readily obtain without the use of tables, the sine or cosine corre-
sponding to a given distance and to a given angle. The said device also forms a
mechanical traverse table, giving for any angle and any distance the projections of
said distance corresponding to said angle, and also forms a mechanical table of
natural sines and cosines.
The invention consists of certain parts and details and combinations of the same,
as will be hereinafter described and then pointed out in the claims.
Reference is to be had to the accompanying drawings forming a part of this
Specification, in which similar letters of reference indicate corresponding parts in
all the figures.
Figure 1 is a plan view of the improved instrument with graduations from 0°
to 45° ;
Figure 2 is a sectional side elevation of the same on the line 2-2 of
Figure 1;
Figure 3 is a cross section of the same on the line 3-3 of Figure 1 ;
Figure 4 is a similar view of the same on the line 4-4 of Figure 1 ;
Figures 5 to 25 are diagrammatic views illustrating the use of the
instrument;
Figure 26 is a plan view of a modification arranged for directly giving sines and
cosines for angles from 0° to 360°;
Figure 27 is an inverted plan view of the same;
Figure 28 is a sectional side elevation of the same on the line 28-28 of
Figure 26;
Figure 29 is a cross section of the same on the line 29-29 of Figure 26;
and
Figure 30 is a similar view of the same on the line 30-30 of Figure 26.
Referring to Figures 1 to 4, the improved trigonometrical instrument is provided
with a suitable base board or other support A, on which are pivoted at B³ and C'
the two parallel arms B and C respectively, pivotally connected with each other by
a link D so that the two arms B and C, when swinging at their pivots, remain at
all times parallel. On the free end of the arm C is arranged a vernier E indicating
on a graduation F supported on the base A and arranged on the segment of a
circle, as plainly illustrated in Figure 1. The graduation Findicates degrees and
subdivisions.
The arms B and C are formed with longitudinal slots B and C respectively, in
which are fitted to slide blocks G and H respectively, of which the block G is
pivotally connected with the apex of a square or two membered arm 1, having its
leg ¹ pivotally connected with a vernier H', forming part of the slide block H
moving in the slot C2 of the arm C. The vernier H', indicates on a graduation C

page_text: arranged on the arm Caparallel, with the slot C. The other slotted leg I³ of the
square or arm I is provided with a sliding block J engaging a longitudinally
extending slot A' formed in an over-hanging board A' which forms part of the
base board A.
$
The slot in the leg, I extends at right angles, to the slot A and the block J
carries a vernier K formed with a graduation K¹ indicating on a graduation L
arranged alongside the slot A', on the top face of the over-hanging board A'.
A block N similar to the block J is fitted to slide in the slot of the leg 1' of the
arm,l, the said block N. also,engaging a transversely-extending, slot,A formed in
the over-hanging board A. The block N is connected with a vernier O arranged
on, top of the board A and formed with a graduation O' indicating on
graduation P arranged on the upper-surface of the over-hanging board A parallel
with the slot A: The graduation P indicates the.sines and the graduation L
indicates. the cosines for angles less than-45°, but for- angles included between 45°
and 90° the said graduation P will give the cosines and the graduation L the
sines. It is understood that the verniers, and Kindicates the respective sine or
cosine for the given angle and distance. To the above-mentioned verniers, can be
attached, if desirable, a clamp, and tangent movement screw; also if required a
reading lens or glass...
In order to conveniently move, the several, parts, I provide the link D, with a
handle D', adapted to be taken hold of, by the operator so as to impart a swinging
movement, to the arms B, and C. The handle D' is formed with an extension,D
pivotally connected with an arm Q fulcrumed at Q on the base board: A 'and
arranged parallel to the arm B, as will be readily understood by reference to
Figures 1 and 8. The length of the extension D is equal to the distance between
the pivots B and Q. The handle D may be provided. with clamp, and tangent
movement screw if desired.
On the base board A are arranged the stops A and A° for the arms B and C, so
that, when the latter rest on the said stops, the vernier. E.ou the arm C indicates
zero on the graduation F and the two arms B and C are in alignment with teach
other. When the device is in this position, the square or right angled arm I can
be readily adjusted forward and backward on the arms B and C, whereby, the
verniers H and K are shifted to indicate at different points in the graduations C¹³
and L, and the distance may be read either on graduation C³ or. L. When the
arm I has been adjusted to the desired point and the operator shifts the handle D'
iuward, then the arms B and C swing at their pivots and parallel to each other.
whereby the square or right, angled arm I is carried along, and the two verniers K
and O move in their slots A' and A' to indicate the corresponding, sine and cosine
for the angle indicated by the vernier, E on the graduation F. The length or
distance is given by the vernier H' on the graduation C. When the arms. B and C)
are in alignment with each other, the verniers H' and K should indicate the same
values or numbers on graduations C and L. (test.of, accuracy, of instrument) :
consequently graduation C3 and its vernier H₁ could be suppressed and distance
read on graduation L if the instrument is to-be used only as a mechanical table of
sines, and cosipes, or as a traverse table. The graduation Cand.its, vernier H
are, however, necessary when using the instrument, for solving geometrical
problems.
The zero point of the graduation C³ is at the pivot C of the arm C; the zero
point of graduation L is in a line extending through the pivots B' and Q, and the
zero point of the graduation P is in a line extending, through the pivots B and C³.
The graduation F reads from 0 to 45° upward, and from 45% to 90°. downward,
with 5° more or less above the 45°, and 5° more or less below 0, as will be readily
understood by reference to, Figure 1.
The connection between the sliding blocks and the respective vernier is by means
of a bolt, as will be readily understood by reference to Figures 2, 3 and 4, so that
the sliding, block and vernier move, together, but permit the part connected there-
with to turn whenever movement is given to the several parts constituting the

page_text: device. The square 'or right angled arm I may be arranged in four positions as
indicated in Figures 9, 10, 11 and 12, with the 'result always the same, provided the
graduations of sines and cosines on graduations P and L are placed in the right
position. "The square with extended branch, arm or leg may also be arranged in
following positions, indicated in Figures 13 to 20 inclusive, with result always the
same provided the graduations P'and L of sines and cosines are placed in the right
position. The parallel 'notion of the arms B and C is secured by means of the
link D, extension D' and arm'Q of Figure 1. or the triangular link'D D' and arm Q
of Figure 25; or the arms B and C, link D and arm Qof Figure 27.
In using the instrument the parts are first moved into the position shown in
Figure 5, so that the arms D and C, are in alignment with each other; and then
the operator loosens the bolts on the sliding blocks G and 'H, so as to permit of
shifting the squaré I 'to 'the right or to 'the left until the vernier 'H' indicates a
desired distance, say a, on the graduation C, the distance reading from zero,
corresponding to the pivot C, to the desired numeral. As previously mentioned,
the distance a can also be read on the graduation L.
E
Now, when the operator pushes the handle D', or turns the arm Q of Figure 27,
the several parts will move until the vernier E finally indicates on the graduation F
a'desired angle, says, as 'plainly shown in Figure 9. The vernier K now indicates
on the graduation La'distance n or the cosine corresponding to the distance a and
angle &, provided the angle is less than 450, and the said vernier will also indicate
the distance n; or sine corresponding to the distance a and angles, provided angle
is greater than 45°. On the graduation' P, the vernier O indicates at the same
time the distance m, or the sine corresponding to distance a and angle &, provided
angle & is greater than 45°. On the graduation P, the vernier O indicates at the
same time 'the distance mi, or 'the' sine corresponding to distance a and angle ε,
provided angle is less than 45°, and "the said vernier also gives distance m or
cosine corresponding to "distance' a' and angle &, provided angle & is greater
than 45°.
""
= a;
It is understood that the same operation is gone through for any variation in
the distance a and angle e. "Now, if the vernier O be clamped in position on the
over-hanging board Aat the given distance m indicated on graduation P, and the
screws on blocks G, H and J. are loosened, then 'the square I can be shifted right
or left, and if then the vernier K is brought to a distance n on the scale L, then
the arm C will turn and vernier E will indicate angle . Also the vernier H' will slide.
in the groove Cof the arm C and stop'at a 'distance equal to a at the time the vernier E
stops on angles. Now; let 'the distance Between the pivot C' and vernier H':
angle = ε; sin ε = m ;" and "cos = n. When sin (m) and cos ε (n) are given,
the instrument will at once indicate the distance a and the angle .by operating as
explained above. "When" sin (m) and angle are given the instrument will
indicate cos (n) and the distance a. "When sin (m) and distance a are given,
the measuring instrument will indicate cos E (") and angle &. When cos (n) and
angles are given, sin (m) and the distance a are indicated by the instrument, and
when cos (n) and distance are given, Bin (m) and angle e are at once read on
the instrument. In other words; any, two-elements of a right angled plane triangle
being known or given, the instrument indicates the other elements. Consequently
all cases of right angled plane triangles can be readily solved with the device.
E
E
The instrument will also indicate the chord of an are when the angle & and the
distance a are given. As the chord or subtense of an arc is twice the sine of
oue-half the angle given, consequently the side of an inscribed polygon is found
when the distance (radius) a'anit corresponding angle & are given. The instrument,
'sin &
by a simple division will also give the tangent, as tant= and the cotangent
COS E
⚫ BID Є
COS E
as cot =
By subtraction we find versed sine 'a cosine,= 'distance
(radius) - cosine.
It will also be further understood, without going into details, that the instrument.

page_text: will permit of solving quite a. number of other geometrical problems. For
instance, it will permit of solving any plane triangle when two sides and their
included angle are given; also when two angles and included side are given.
As illustrated in Figure 6, the instrument is arranged in connection with
a sighting device, which may be a transit or compass, said device being so
arranged that the line of sight of the compass or optical axis or line of
collimation of telescope of transit corresponds exactly with line from pivot C¹
to zero of vernier E, the centre of limb of compass or transit corresponding
exactly to centre of pivot and line of sight of compass or optical axis of
telescope following all motions of arm C. The sight R of the compass or the
telescope of the transit is made to always follow the motion of the arm C, so that
the projection of a certain line making the angle with; the true north line, will
be readily read on the scales of the graduations P and L of sines and cosines
as the survey progresses.
E
The instrument above described with compass or transit attached and with the
graduation F of only 45° will answer the purpose only for angles less than 45°, it,
however, being understood that the instrument with graduation from 0° to 45° only
without compass or transit attached will answer all purposes for office work. It is
also understood any instrument giving sines and cosines from 0° to 45° will also
give sines and cosines for angles from 45° to 90°, and from 0° to 360°. In order
to avoid the change of graduation L from scale of cosines to that of sines when
the angle is included between 45° and 90°, then by having the graduation of limb F
extended to 90° (see Figure 6), instead of 45°, the graduation I will always
remain the scale of cosines, and the same is true as regards the graduation P of
sines with a graduation of 0° to 90° for limb F.
In surveying, when using the magnetic needle, the angles read are never greater
than 90°; therefore, the instrument with graduation of limb F from 0° to 90° will
directly give sines and cosines without change of scales. The instrument can also
be used independent of the magnetic needle in localities where local attraction is
manifested, and this is very desirable at times when careful surveys are required.
The graduation F in this case should then be used instead of the graduation of the
compass of transit for reading the angles. Instead of complete compass or
transit, compass sights or a telescope only may be attached at the pivot Cand
made to follow the motion of the arm C and the angles read directly on the
graduation F. Such a combination, made in the size of a pocket instrument will
very useful to find directly the distance from one point to an inaccessible point,
or during war times, for instance, the distance between two armies, or the distance
to a fortress, etc., to enable artillery to be pointed with accuracy.
be
By reference to Figure 8, it will be noticed that the arin Q is parallel to and
equal in length to the arm B, and the distance between the pivots B' and Q¹
corresponds to the length of the extension D. By pushing or drawing on the
handle D', the arm D and its extension I), so that the arms B and C and the
arm Qmove in unison and always parallel one to the other, the verniers K and
always follow the motion of the square or right angled arm at the time the
arms B and C are swung, as will be readily understood by reference to Figure 7,
the vernier indicating increasing length on the upward movement of the arms B
and C, while at the same time the vernier K indicates decreasing length, and when
the said arms B and C swing downward the vernier K indicates increasing length
and the vernier O decreasing length.
The instrument shown in Figures 26 to 30 is arranged for giving directly sines
and cosines for angles from 0° to 360°, and for this purpose the graduation of the
limb F is from 0° to 360°, and the urins B and C are arranged to make a whole
revolution on their pivots B' and C with the square I of Figures 26 and 25
following their motions and giving sines and cosines on two fixed scales L and P
standing at right angles one to the other.
The square and scales may be arranged in the four positions indicated. in
Figures 9, 10, 11 and 12, or if the arm of the square is extended the scales and

page_text: square can be arranged in. eight positions indicated in Figures 13 to 20'inclusive,
the rosult being always the same... For the instrument showing on its limb. Fa
graduation from 0 to 360° the same main parts are used as for the one having: a
graduation from 0° to-45°, but the parts are differently arranged as indicated in
Figure 25.
The arms B, C, revolve around their two pivots B and C and are- always
parallel in their motion, the arm C having a vernier reading. on the graduated
limb F. The arms B and C, are maintained parallel in their motion by the
connection of link D and arm Q, or by link D extension D' of Figure 25, or
link D and arm Q of Figure 27, and the verniers K and O indicated the sines
and cosines..
In order to permit a complete swinging around of the arms B and C, I extend
their pivots through the base board or support A to the under side thereof, and
secure on the lower ends of the pivots the arms B and C respectively, pivotally
connected with each other by a triangular link D³, same connection as the link D
and extension D' of Figure 25, also pivotally connected with an auxiliary arm Q
fulcrumed at Q on the under side of the base board, as plainly shown in
Figures 27 and 29. The arms B and C, are adapted to indicate on circular
graduations F, F³, respectively formed or secured on the under side of the base
board A, and as the said arms stand in perfect alignment with the arms B and C
respectively, they indicate the same degrees as the said arms B and C do on their
circular graduations F and F' respectively, see Figures 26 and 27 respectively.
One only of the four graduations F and is necessary, and it can occupy either
of the four positions alluded to. As shown in Figure 26, the arm C is provided
at each end with a vernier E.
The improved measuring and calculating instrument with any graduation of
limb F from 0° to 360° may have attached to it a compass or transit, or a telescope
or sight of any kind, to be fixed either at pivot C₁ or pivot B', and with the line
of sight following all motions of the arms B and C.
Having now particularly described and ascertained the nature of my said inven-
tion, and in what manner the same is to be performed, I declare that what, I
claim is,-
1. An instrument of the class described, comprising pivoted moving arm, a
square or right angled arm pivotally connected with the said arm, and guides for
keeping the members of the square parallel to their initial position during the
movement of the said pivoted arm, substantially as described.
2. An instrument for the purpose described, comprising two pivoted parallel
arms, a square whose respective members are pivotally connected to the said arms,
slides having movement longitudinally of the members of the square, and stationary
guideways for the slides, said guideways extending transversely of the members of
the square, substantially as described.
3. A measuring instrument of the class described, comprising two pivoted
parallel moving arms, a link for connecting the said arms for simultaneous move-
ment, and a square or right angled arm held adjustable on the said parallel arms
and moving with the same, substantially as shown and described.
4. A measuring instrument of the class described, comprising two pivoted
parallel moving arms, a link for connecting the said arms for simultaneous. move-
ment, a square or right angled arm held adjustable on the said parallel arms and
moving with the same, and verniers actuated by the legs of the said square and
indicating ou fixed graduations arranged at right angles to each other, substantially
as shown and described.
5. A measuring instrument of the class described, comprising two pivoted
parallel moving arms, a link for connecting the said arms for simultaneous move-
ment, a vernier held on one of the said arms and indicating on a fixed graduation
indicating degrees and subdivisions, the arm carrying the vernier and also provided
with a distance graduation, a square or right angled arm held adjustably on the

page_text: said parallel arms, a vernier held on one end of the said square and indicating on
the said distance graduation of the corresponding arm, and two movable verniers
controlled from the legs of the said square and indicating on fixed distance
graduations arranged at right angles to each other, substantially as shown and
described.
6. A measuring instrument of the class described, comprising two pivoted
parallel moving arms, a link for connecting the said arms for simultaneous move-
ment, a vernier held on one of the said arms and indicating on a fixed graduation
indicating degrees and subdivisions, the arm carrying the vernier being also
provided with a distance graduation, a square or right angled arm held adjustably
on the said parallel arms, a vernier held on one end of the said square and
indicating on the said distance graduation of the corresponding arm, two movable
verniers controlled from the legs of the said square and indicating on fixed distance
graduations arranged at right angles to each other, and intermediate mechanism
for connecting the said movable verniers with the legs of the said square,
substantially as shown and described.
7. A measuring instrument of the class described, comprising two pivoted
parallel moving arms, a link for connecting the said arms for simultaneous move-
ment, a vernier held on one of the said arms and indicating on a fixed graduation
indicating degrees and subdivisions, the arm carrying the vernier being also
provided with a distance graduation, a square or right angled arm held adjustably
on the said parallel arms, a vernier held on one end. of the said square and
indicating on the said distance graduation of the corresponding arm, two movable
verniers controlled from the legs of the said square and indicating on fixed distance
graduations arranged at right angles to each other, and a handle held on the said
link for actuating the latter and the arms and square, substantially as shown and
described.
8. A measuring instrument of the class described, comprising two pivoted
parallel moving arms, a link for connecting the said arms for simultaneous move-
ment, a vernier held on one of the said arms and indicating on a fixed graduation
indicating degrees and subdivisions, the arm carrying the vernier being also
provided with a distance graduation, a square or right angled arm held adjustably
on the said parallel arms, a vernier held on one end of the said square and
indicating on the said distance graduation of the corresponding arm, two movable
verniers controlled from the legs of the said square and indicating on fixed distance
graduations arranged at right angles to each other, and fixed stops for the said
arms, to cause the first named vernier to indicate on zero on the degree graduation,
substantially as shown and described.
9. An instrument of the class described, comprising a pivoted moving arm, a
sighting device secured on the said arm to move therewith, a square pivotally
connected with the said arm, and guides for keeping the members of the square
parallel to their initial position during the movement of the said pivoted arm,
substantially as described.
10. An instrument of the class described, comprising a pivoted moving arm, a
two-membered arm pivotally connected to the said moving arm, and guides for
keeping the members of the two-membered arm parallel to their initial position
during the movement of the said pivoted arin, substantially as described.
Datad this 10th 1.
CA 1005
A. M. & WM. CLARK,
53 Chancery Lane, London, Chartered Patent Agents.