An Improved Trigonometer.
Year: 1889

page_text: Date of Application, 9th Apr., 1889 sit wat mens ha'
Complete Specification Left, 13th Dec., 1889-'Accepted, "5th "Apr."," 1890****
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AUY STUNAL DEMOLT CALIVA
An Improved Trigonometer.
I, ROWLAND BROTHERHOOD, of Cambria House, Chepstow, in the County of
Monmouth, Civil Engineer, do hereby declare the nature of this invention to be as
follows:-
My invention relates to an improved trigonometer for the use of engineers and
surveyors; and its object is to enable the user to find radii, tangents, angles, chords,
half chords, versines, distances and altitudes, and to solve other and similar pro-
blems without it being necessary to have recourse to arithmetical calculations,
the usual arithmetical calculations being replaced by certain adjustments of the
instrument which forms the subject of my present invention, and these having been
effected, the solution of the problem can be forthwith read off.
In carrying my invention into effect. I provide a rigid frame, which is preferably.
of an oblong shape. A central bar, hereinafter called the base bar, extends from one
end to the other. Across one end of the frame I fix a plate, and set out a pro-
tractor thereupon, the centre of which is on the base line. i.e., the graduated edge of
the base bar, and its prolongation. On this centre are pivoted by their ends a pair
of bars of any convenient length (hereinafter called tangent bars), and each tangent
bar has fixed to its pivotted end a short arm carrying a vernier. Provision is
made for the fixation of the tangent bars at any point by suitable locking devices,
e.g., grooves and set screws. A. T-square is adapted to slide by its head upon each
tangent bar at right angles therewith, the blades working the one over the other.
and each one upon the opposite tangent bar. These blades are hereinafter called
radial bars.
Across the frame there is a bar. hereinafter called a chord bar, adapted to slide up
and down the frame. A connection between this chord bar and the radial bars may
be made by a stud-and-groove or other equivalent device adapted to make the chord
and radial bars move together. A second T-square is adapted to slide by its head
upon either of the tangent bars and at right angles therewith.
Sights for taking angles are fitted to the ends of the tangent and base bars, and
to, the centre of the instrument.
The tangent, radial, and chord bars are graduated with any convenient scale. The
scales on the tangent bars have their zerves in the centre of the protractor; those
on the radial bars in the tangent points, i... their intersections with the scales on
the tangent bars. The scale of the chord bar is double, having its zero at the inter-
section of its scale with that on the base bar. the scale on the latter being the
base line. The second T-square is graduated in the same way as to its zero as the
radial bars. The protractor has its zeroes where the base line intersects it, and also
at the ends of a diameter bisecting the base line.
A suitable stand with levelling devices is used to support the instrument or it
may be used in conjunction with an ordinary theodolite. In this case, the theodolite
is mounted upon a pillar working in a ball-and-socket joint in the top of the stand,
and the trigonometer is fixed upon the pillar, the axis of the latter passing up through
the centre of the theodolite.
The following are some of the uses of my improved trigonometer.
Let it be required to take the apex angle of a curve, the length of the tangents
being given. Fit the sights and loosen the set screw in the vernier anus. Move the
chord bar forward or back as required until you have the angle. Tighten the set
screws, then, bring the chord bar (which will carry with it the radial bars) opposite
the length of tangent given from the apex, and read off the radius, which is exactly.
where the inside edges of the radial bars pass over the inside edge of the base line.

page_text: The difference between this point and that where the chord bar cuis the base line, gives
the cosine, and the difference between this and the radius gives the versine. The
T-square will cut the centre of the curve at the same distance from the tangent bars
as that given for the versine
To obtain the distance of any required object. From a fixed point set off at
right angles to the object a base line, and say 100 yards off. On this line fix the
instrument, so that its base line will be at right angles to the line measured off, and
consequently parallel to the original base, or object line. If the object is to the left
of the base line, take the angle with the left tangent bar. Fix the vernier arms and
bring the chord bar forward or backwards until the 100 cuts the edge of the tangent
bar. Then read off the distance in yards, which will be found where the chord and
base bar cross.
For taking altitudes, the above operation is similarly gone through to get at the
distance of the object, and the angle obtained either with a box sextant or otherwise.
Then bring the chord bar to the distance obtained, and read off the height on the
chord bar to the left. With this instrument, the angle and base being given, the
hypothen use and perpendicular can be read off. If the angle and perpendicular are
given, then the base and hypothenuse can be read off. If the angle and hpyothenuse
be given, then the base and perpendicular can be read off; and, likewise, should the
perpendicular and base be given the angle and hypothen use can be read off, and
So on.
The scales on the instrument can be taken as feet, links, yards, chains, metres,
miles, and so on.
PHILLIPS & LEIGH,
Agents for the Applicant.
COMPLETE SPECIFICATION.
An Improved Trigonometer.
I, ROWLAND BROTHERHOOD, of Cambria House, Chepstow, in the County of
Monmouth. Civil Engineer, do hereby declare the nature of this invention, aud in
what manner the same is to be performed, to be particularly described in and by the
following statement :—
-
My invention relates to an improved trigonometer for the use of engineers,
surveyors, and others: and its object is to enable the user to find radii, tangents,
angles, chords, half chords, versines, cosines, distances, altitudes, and to solve other
and similar problems without it being necessary to have recourse to arithmetical
calculations; the usual arithmetical calculations being replaced by certain adjustments
of the instrument which forms the subject of my present invention, and these having
been effected, the solution of the problem can be forthwith read off.
In order that my invention, and the means by which the same is to be carried into
practical effect, may be thoroughly understood. I will now describe them in detail.
referring in so doing to the accompanying drawings which are to be taken as part of
this specification and read therewith.
Fig. 1 is a plan of the trigonometer without the theodolite.
Fig. 2 is a side elevation of the theodolite. trigonometer, and top of the stand.
Fig. 3 is an elevation of the sight to be used under certain circumstances instead of
the theodolite.
Figs. 4, 5 and 6 are diagrams illustrating some of the uses and capabilities of my
invention.
Referring to Figs. 1. 2 and 3, A is a rigid frame of any suitable shape in plan. It
is shewn as made of metal of an angle section. B is a bar the graduated edge b of
which forms the centre line. The prolongation of it passes through the centre, k, of
the trigonometer, and the two form the base line of the instrument.
C is a plate upon the frame. It is sufficiently large to carry a protractor D set
out upon it. The centre of the protractor and zero on the base line 3 coincide. b¹ is

page_text: second base line intersecting the former line 3 at right, angles and at its zero. The
protractor is therefore divided into four, quarters, each intersection of its circumference
by the lines 3, 6, being both at zero and a 90°.
About the centre of the protractor and the zero on the base, line being, the
point L, pivot a pair of bars.E, E, of any convenient length. These; bars are
hereinafter called tangent bars. Both have scales on their adjacent edges, which
scales have a common zero in the point above mentioned. F, F are two vernier
arms fixed, respectively, to the inner ends of the tangent bars E, E. The scales f, fl
on the outer ends of the, arms move over the protractor scale. It must be observed
that a line drawn from the point to zero on either vernier scale is at right angles
with the scale on its respective tangent bur, so that the reading of the latter,ou..i
quarter of the protractor will be the same as that of the vernier upon its quarter.
Due provision is made for the fixation of the tangent bars at any angle, with, the
base line 3. The fixing device. illustrated consists of a semicircular groove Grand
set screws g. g; but any other suitable one may be adopted.
to 10
..its
Each tangent bar is provided with a. graduated T-square. H, H', adapted to alide
along their respective bars by their heads as shewn in Fig. 1, and to work over
each other. They are hereinafter referred to as radial.bars. Their blades are always
at right angles with their respective tangent bars, the connection between bladefand
head being a rigid one. The zero of the scale. on each radial bar coincides with the
tangent point, viz. the junctions of the edge of that bar with the scale, on the
respective tangent bar.
is a double headed T-square adapted to slide up and down the frame,.aud., over
the tangent and radial bars. Its heads i, i, engage with the frame, sofas, to act as
guides to the extent of keeping it always truly at right angles with the base, line 3.
It is graduated with a duplicate scale, there being a common zero, coincident with
the base line, from which the two scales run right and left. terminating, with the
heads. It is hereinafter referred to as the chord bar. Any suitable connection.may
be made between the chord bar and the radial bars, so that the motion of the former
upon the frame A may produce a corresponding motion on the part of the radial
bars along the tangent bars.
6
Jis a graduated T-square adapted to slide, by its head, upon either of the tangent
bars, at right angles therewith. It is graduated with a scale having its zero coincident
with the scale on the tangent bar.
All the scales herein before referred to are identical, that is, they
unit.
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have, a common
f
A sight, , for taking angles is fixed on the outer end of each tangent bar at
the ends of the base line. b, and of the transverse hase line. ; and also at the centre
of the protractor.
inting
Mis a four-legged, or other convenient type of, stand. A pillar, », connected to
the stand by a ball-and-socket, or other equivalent, joint. m, springs from the top, of
the stand. m is the eye from which the plumb line is suspended. n' is a plate fixed
upon the pillar at right angles to its axis: and serves as a table upon which the
frame can be rotated and fixed by suitable fixing devices, .., a fixing screw.n
The axis of the pillar. n. passes up through the centre, k, of the trigonometer
m², m³ are two levels parallel, the former with the base line . and the latter with
the transverse base line W.
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m
mare levelling screws.
O is an ordinary theodolite having a vernier for the purpose of measuring off
horizontal angles upon the protractor. When it is used in conjunction with the
trigonometer, it is fixed upon the pillar, a, or rather upon a vertical continuation of
it, so that both theodolite and continuation can be removed, and the removable
sight used. This substitution of the sight O' for the theodolite is convenient for
short distance work.
14
The following illustrations are given to shew the capabilities of my invention....
Referring to Fig. 4. let it be required to find the apex angle of a curve prepara-
tory to setting the latter out. == are two portions of a line of railway which

page_text: TREAT EQ
i.
1.-
It is uftended to join by 'a curve,, and to which curve the said portions are tangential.
tend the two tangents until they intersect at which is the apex of the are of
curve, 2. Fix the trigonometer with its centre over the apex y, taking care that
its baseline exactly bisects the angle, his bisection is obviously important,
fór if it be at all incorrectly performed; the subsequent operations will be valueless,
because their indications will be altogether misleading. The surveyor then takes his
stand behind the instrument, the base line scale reading away from him in the
direction ofthe centre. c, of the curve, as well as of that, of the circle of which
the said curve is an are. The angley is taken by sighting the terminals.
along the tangent. bars E. E. and either line is measured in the usual way. The
tangent bars now represent, on the trigonometer, the two lines
assume that
the length of either of these lines lias been found to be 278 yards; and, therefore.
slide the radial bärs 'H, H', along the tangent bars until their scales cut the latter
at 278, the tangent points-see Fig. 1. The intersection of the scales of the radial
bars, or of either with the base line, b, will define the position of the centre r of the
circle of which the curve is a part; and its distance from the centre of the
instruineift.iz. 320 yards, "is indicated by the same intersection. The radiusz
of the circle is 160 yards to be read off upon either radial bar. To obtain the position
of the centre of the curve. iz.. the point i, deduct the length of a radius from the
hypothen use y by sliding the T-square J on its tangent bar until the distance
between it and the tangent point, 278 on the scale of the tangent bar E, is equal to
the half chord as the latter reads on the chord bar. The distance of this point w from
the centre of the trigonometer is shewn to be 160 yards. Or, when the triangle
formed by the two tangent bars and the chord bar is an equilateral one slide the said
square opits tangent bar infil its scale cuts the opposite tangent point, and where it
also cuts the base line is the centre, . 160 yards from the apex. It is obvious that
all the parts, or elements, of the angle may be read off on the trigonometer as
adjusted.The angle: y = is one of 600, each angle being 30°, or one half.
The chord is 189 x 2 278 yards, read off from the chord bar; the cosine re,
80 yards the versed sine, 80 yards; the chord of half the are . 160 yards;
and the hypothenuse. ay. 320 yards.
1
Twill be observed that in using my improved trigonometer, its area represents,
butoninuch reduced and therefore quite portable and easily manipulated scale, the
area of ground included within the survey. All the lines of the latter are represented
on the frigonometer by the several scales thereof; and the terminal points of the said
lines, by the intersections effected on the instrument. The curve has been traced
on Fig to facilitate comparison of it with Fig. 4.
Fig is a diagram illustrating the applicability of my improved trigonometer to
ascertaining the distance of an inaccessible object from a given station point.
"
Det be the given object; and 2. the given point: it is required to measure the
line
The trigonometer is placed with its centre k over the station point. and adjusted
so that the base line would, if continued, intersect the point. The transverse
baseline is then produced in either direction-to the right hand in the diagram-
for any convenient distance. This produces a second station point y. "The method of
setting it the line is too simple to require detailed explanation here. The
trigonometer is next fixed truly over the said point : the base line coinciding
with the line and the base line 7, with the line q g' both the latter being, of
Course parallel with the line p p. The next step is to set out the hypothenuse q ).
This done by one of the tangent bars, in this case the left-hand one, E, because the
object is now to the left hand of the surveyor. The tangent bar is set so as to
sight the object p along the graduated edge: and this having been done, it is self
evident that a line at once parallel with the line and intersecting the object p
will bisect the line gg' at the point which is as far from the second station point q
as the object from the point p', inasmuch as the two triangles pg. y ? are
both right angle triangles having a common hypothenuse. The line parallel with the
line is represented on the trigonometer by the chord bar I. This is adjusted

page_text: until it intersects the tangent bar, and the intersection by the chord bar of the base
liue will give the distance y ' = p² p.
The distances ascertained by the trigonometer,
and also the sizes of the angles of the two triangles, are marked on the diagram, for
the purpose of comparing it with Fig. 1.
Fig. is a diagram illustrating the applicability of my improved trigonometer to
ascertaining inaccessible altitudes. In the two previous examples the work was all
done in one plane, that of the trigonometer; but in solving the present problem, work
has to be done in two planes, first with the theodolite, and afterwards with the
trigonometer.
Lets be the required altitude; and t, the given station point. The distance, &s,
is first ascertained, in the way described with reference to Fig. 5. The angle, str, is
next taken, and laid down on the trigonometer by adjusting either tangent bar. The
intersection of the tangent and the chord bars will correspond with the point r, and
give the altitudes to be read off the chord bar.
With my improved trigonometer, if the angle and base of any right angle triangle
be given and laid down thereupon, the perpendicular and hypothenuse may be read
off. If the angle and perpendicular are laid down, the base and hypothenuse can be
read off. If the angle and hypothenuse are laid down, the base and perpendicular
can be read off. If the perpendicular and base are laid down, the angle and
hypothenuse can be read off, and so on.
As the scales are all uniform, they can be read as feel, links, yards, chains, metres,
miles, or any other measure, as circumstances may require.
In the dimensions given above. fractions have been omitted. A calculation of the
elements of any of the right angle triangles of the figures will shew this. Whole
numbers are used as sufficiently accurate for the purpose of explaining the nature and
method of my invention.
I wish to draw attention to the necessity of having two fangent and radial bars. If
there be only one of each, there is no check upon the readings of the instrument, but
the use of two sets supplies a check which will at once show if any inaccuracy has
crept in.
Having now particularly described and ascertained the nature of my said
invention, and in what manner the same is to be performed, I declare that what
I claim is,
1. The combination of protractor, base line, tangent bar, radial bar, and chord bar,
as set forth.
2. The combination of protractor, base line, a pair of tangent bars, and a pair of
radial bars, as set forth.
3. The combination of protractor, base line, a pair of tangent bars, two radial bars,
and a chord bar, as set forth.
4. The combination of tangent bar, base line, chord bar, and T-square adapted to
bisect either or both base line or chord bar, as set forth.
Dated this 13th day of December 1889.
PHILLIPS & LEIGH,
22, Southampton Buildings. Chancery Lane, W.C.,
Agents for the Applicant.