An Improved Trigonometer.
Year: 1889

page_text: Date of Application, 13th Dec., 1889
Complete Specification Left, 18th Mar., 1890-Accepted, 31st May, 1890
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,
surveyors, and others; 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 problems without it being necessary to have recourse to arithmetical
calculations, the usual arithmetical calculations being replaced by certain adjust-
ments of the members of the instrument which forms the subject of my present
invention; and these having been effected, the solution of the problem can
forthwith read off.
be
In carrying the present invention into effect, I provide a plate mounted with a
suitable joint capable of motion in any direction upon the top of a suitable stand,
after the manner of the well known theodolite.
The point on the plate immediately over the centre of the joint is the centre of
the trigonometer, and through this centre are drawn two lines at right angles with
each other. These lines are the base and transverse base lines, respectively; the
former extending from one end of the plate to the other.
About the centre of the plate is set out a protractor divided into four quarters
by the base lines above mentioned. I provide a pair of bars hereinafter called
tangent bars, which are pivotted by their ends about the said centre; and their
inner ends are provided with arnis projecting therefrom at right angles and carrying
verniers to be used upon the protractor.
Each tangent bar has a T-square sliding on it by its head. These T-squares I call
radial bars.
The surface of the trigonometer plate is graduated in both directions. The
tangent and radial bars are graduated to correspond i.e. all the scales on the instru
ment have a common unit to which any denomination can be applied.
The zero of the tangent bars is in the centre of the trigonometer, that of the
radial bars in the scales on the respective tangent bars.
The transverse graduations on the trigonometer plate run right and left from
the base line. The latter and the graduations parallel therewith have their zero
on the transverse base line.
Suitable sights are fitted at the ends of the base lines and on the ends of the
tangent bars. A movable sight is also fixed in the centre of the trigonometer to
be used for short distance work. For long distance work, and work to be done in
the vertical plane, I replace the movable sight by theodolite.
The following description of how the distance a given object is from the station
point is ascertained by my invention will give the reader a clear idea of its principle
and practice.
The trigonometer is set with its centre vertically over the station point. Its plate
will then represent the whole area included in the survey. The transverse base
line is then produced in either direction, and for a definite distance, say, to the
right and for 100 yards. The end of this line is a second station point to which
the trigonometer is moved with its transverse base line coinciding with its pro-
duction. The left hand tangent bar is set so as to sight the object. The transverse
base line on the plate from zero to 100 on the left hand side of the trigonometer
centre is the base of a right angle triangle: the tangent bar last mentioned is its
hypothenuse; and the line parallel with the base line of the trigonometer, and

page_text: which starts from the said 100 on the, transverse base line, is the perpendicular of
the triangle, the apex of which is the intersection of the perpendicular and the
tangent bar. This intersection is the equivalent of the position of the object; and
as the plate and tangent bars are all graduated, every dimension can be read off,
being interpreted in terms of the distance measured off, in this case, yards.
If a distance ascertained as just described be noted on the trigonometer, and the
angle of inclination to the top of the object-e.g., a mountain-ascertained by the
theodolite, be set out thereon by a tangent bar, then will the base of the right angle
triangle be the height of the object.
The apex angle of a curve such as is required in railway work to join two straight
portions of the road is ascertained as follows. The said two straight portions will be
tangential to the circle of which the curve is an are. They are therefore produced
until they intersect; and the trigonometer placed with its centre over the inter-
section, and its central base line exactly bisecting the angle. The tangent bars are
set to sight the terminals of the straight portions, and the distance between the angle
of the station point and one of the terminals is set off upon both tangent bars by
moving the radial bars upon them so that their scales shall intersect the scales on the
tangent bars, where occur the points corresponding to the terminals. The inter-
section of the radial bars will give the position of the centre of the circle, and the
other elements can be read off. The central base line will contain the radius, cosine,
and versed sine, as well as the distance between centre and apex angle. One of the
transverse lines will be a chord of the arc. The apex angle will be found on the
protractor, and the curve might be laid down upon the trigonometer.
Dated this 12th day of December 1889.
PHILLIPS & LEIGH,
Agents for the Applicant.
An Improved Trigonometer.
1. ROWLAND BROTHERHOOD, of Cambria House, Chepstow, in the County of
Monmouth, Civil 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 :-
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 problems
without it being necessary to have recourse to arithmetical calculations, the usual
arithmetical calculations being replaced by certain adjustments of the members of the
instrument which forms the subject of my present invention, and these having been
effected, the solution of the problem cau be forthwith read off.
In carrying the present invention into effect, I provide a plate mounted with a
suitable joint capable of motion in any direction upon the top of a suitable stand after
the manner of the well known theodolite.
The point on the plate immediately over the centre of the joint is the centre of the
trigonometer, and through this centre are drawn two lines at right angles with each
other. These lines are the base and transverse base lines, respectively; the former
extending from the centre of the trigonometer to the end of the trigonometer-plate;
and the latter from side to side.
About the centre of the plate is set out a protractor divided into four quarters by the
base lines above mentioned. I provide a pair of bars. hereinafter called tangent bars,
which are pivotted by their ends about the said centre; and their inner ends are pro-
vided with arus projecting therefrom at right angles and carrying verniers to be used
upon the protractor.
Each tangent bar has a T-square sliding on it by its head. These T-squares I call
radial-bars.
The surface of the trigonometer plate is graduated in both directions. The tangent

page_text: and radial bars are graduated to correspond, 2.e., all the scales on the instrument have
a common unit to which any denomination can be applied.
The zero of the tangent bars, common to both, is in the centre of the trigonometer;
and that of the radial bars in the scales on the respective tangent bars.
The transverse graduations on the trigonometer-plate run right and left from the base
line. The latter, and the graduations parallel therewith, have their zero on the
transverse base line.
Suitable sights are fitted at the end of the base line, and on the ends of the tangent
bars. A movable sight, adapted to be fixed in the centre of the trigonometer, is also
provided; and is intended to be used for short distance work. For long distance work.
and for work to be done in the vertical plane, I replace the moveable sight by a
theodolite.
The follow description of how the distance, a given object is from the station-point.
is ascertained by my invention, will give the reader a clear idea of its principle
and practice.
The trigonometer is set with its centre vertically over the station-point. Its plate
will then represent the whole area included in the survey. The transverse base line
is then produced in either direction, and for a definite distance, say to the right, and
for 100 yards. The end of this line is a second station-point, to which the trigono-
meter is moved with its transverse base line coinciding with its production. The left
hand tangent bar is set so as to sight the object. The transverse base line on the plate
from zero to 100, on the left hand side of the trigonometer-centre, is the base of a
right angle triangle; the tangent bar last mentioned is its hypothenuse; and the line
parallel with the base line of the trigonometer, and which starts from the said 100 on
the transverse base line, is the perpendicular of the triangle, the apex of which is the
intersection of the perpendicular and the tangent bar. This intersection is the
equivalent of the position of the object; and as the plate and tangent bars are all
graduated, every dimension can be read off, being interpreted in terms of the distance
measured off, in this case, yards.
If a distance ascertained as just described be noted on the trigonometer, and the
angle of inclination to the top of the object, e.g., a mountain ascertained by the
theodolite, be set out thereon by a tangent bar, then will the base of the right angle
triangle be the height of the object.
The apex angle of a curve such as is required in railway work to join two straight
portions of the road is ascertained as follows. The said two straight portions will be
tangential to the circle of which the curve is an arc. They are therefore produced
until they intersect; and the trigonometer placed with its centre over the intersection,
and its central base line exactly bisecting the angle. The tangent bars are set to
sight the terminals of the straight portions, and the distance between the angle of the
station point and one of the terminals set off upon both tangent bars by moving the.
radial bars upon them so that their scales shall intersect the scales on the tangent bars
where occur the points corresponding to the terminals. The intersection of the radial
bars will give the position of the centre of the circle, and the other elements can be
read off. The base line will contain the radius, cosine, and versed sine, as well as the
distance between centre and apex angle. The transverse line on the plate which cuts
the two tangent points will be the chord of the are. The apex angle will be found on
the protractor, and the curve may be laid down upon the trigonometer, as hereafter
explained at length.
In order that my present invention, and the means by which it is to be carried into
practical effect. may be thoroughly understood, I will now describe them in detail.
referring in so doingto the accompanying drawingswhich are to be taken as part of this
specification and read therewith.
Fig. 1 is a plan of the trigonometer-plate, with its tangent and radial bars.
Fig. 2 is a side elevation of the same and of the top of the tripod stand.
Figs. 3 to 12 are diagrams illustrating some of the various problems which my
invention is capable of solving, and also the methods of solving them, respectively.
In the specification of a former patent for a similar invention, viz., No. 6084 of 1889,

page_text: I have illustrated and described the construction, and use of a trigonometer having as
one of its principal operative parts a graduated chord bar adapted to slide up and down
the trigonometer-plate and always at right angles with the base line. This present
invention is an improvement upon the said former invention, the improvement con-
sisting principallyin replacing the sliding chord bar bya series of graduated transverse
lines parallel with the transverse base line and, consequently, at right angles with the
base line. Each of the said transverse lines is therefore a chord line.
Referring to Figs. 1 and 2, A is the trigonometer-plate; and a, the centre of the
trigonometer.
Č is a protractor about the centre a. D is the base line; and E, the transverse base
line, the scales of both having their zeroes in the centre of the trigonometer. These
two lines meet at right angles in the said centre, thereby dividing the protractor into
four quadrants. Each intersection of the protractor is at once a zero and a 90°.
F is the left hand; and G, the right hand, tangent bar. Both are movable, but
independently of each other, about the centre, . f, g are two arms at right angles with
the respective tangent bars F, G. They are engraved with scales f¹, g'. Inasmuch as the
arms are at right angles with their respective tangent bars, the readings of a tangent
har and its arm upon their respective quadrants of the protractor will always be
the same.
H is the left hand, and I, the right hand, radial bar. Both are made to slide up and
down their respective tangent bars, F and G, at right angles therewith, and to move
over each other. Each radial bar has its zero at the intersection of its scale with that
on its tangent bar.
, dare lines parallel with the base line D, each one capable of being used as a sub-
sidiary base line, as circumstances may require.
ee are the chord lines. The scales of the chord lines run right and left from the
base line D upon which are their respective zeroes. The subsidiary base lines 7 d. on
the contrary, have their zeroes in the transverse base line E. The scales of the tangent
bars radial bars; base and subsidiary base lines: transverse base, and chord lines,
have a common unit, which is, throughout them all, equally subdivided, so that it can
be read off in any term of length. as may be required, according to the absolute
distances being dealt with. It will be noticed, also, that the said scales are set out on
the metrical system, but it will be readily understood that this is a matter of detail, or
of convenience; and has nothing to do with the principle of my invention, although it
may be regarded as adding to its convenience as a scientific instrument.
is the removable centre sight; &, the sight at the extremity of the base line;
and 7,, the sights at the extremities of the tangent bars. They are all of any
convenient construction.
m, mare two spirit levels, parallel with the base and transverse base lines,
respectively. N is a socket about which the tangent bars are pivotted. It receives
either the centre-sight, or a leg depending from the centre of a theodolite. N¹, N¹
are screw-devices of the well-known type for adjusting and locking the vernier arms
and tangent bars.
The instrument is, or may be, mounted on a substantial tripod stand, upon which it
is movable in any direction. Fig. 2 shews it as mounted upon one of Stanley's three
screw adjustable tripod stands.
With reference to the material and size of the instrument as above described, these
are points which are decided by considerations of portability, convenience, and
durability, takinginto consideration the circumstances under which such an instrument
as a trigonometer is used.
Instead of mounting the trigonometer in the way illustrated, it may be, if preferred,
mounted upon a joint of a construction adapted to allow of the trigonometer-plate
being turned up into the vertical plane. The advantage of being able to turn the
plate into the vertical plane is that then the user will be able to take vertical angles
with the tangent bars. In the following problems, however, this vertical position is
not introduced, inasmuch as its utility, and the circumstances under which it would be
useful, will be apparent to any efficient surveyor,

page_text: THE GESTIived the.construction of the instrument, L will now proceed to describe
some of the, uses to which it can be put..
PROBLEM 1. TO ASCERTAIN THE DISTANCE OF A GIVEN OBJECT FROM A GIVEN
POINT. See Fig. 3.
Leto be the given object; and p, the given point, or station-point. Fix the
trigonometer with its centre a vertically over the station-point, and adjust the plate
until the object is sighted along the base line D. Having done this, set out a line
either to the right or left-in the case illustrated in the figure, it is to the left-taking
care to align it with the transverse base line E, or, in other words, to lay it down at a
right angle with the line po. This can be effected by setting the left hand tangent
bar at a right angle with the base line, and taking a sight along it. The length of
this second line is quite arbitrary, but it is preferable that it be within the scale of the
transverse base line; which is its equivalent on the trigonometer-plate. just as the
line po is represented on the trigonometer-plate by some portion of the base line D.
If however, this cannot be done, then the scale of the survey must be reduced, and the
reading of the instrument afterwards multiplied accordingly. According to the
diagram, this arbitrary distance has been measured off 150 yards. This settles the
unit-value (for this particular survey), of each subdivision on the trigonometer, as one
yard. The end of the line ppl, establishes a second station point, p¹, to which the
trigonometer is transferred and fixed over it, in the same way as it was at first fixed
over the point, the alignment of the transverse base line E with the line being
accurately settled by sighting back to the original station point.
The base line D, as the trigonometer now stands, will (as to some portion of it) be
the equivalent of the line, and be also parallel with the line of sight o, which
latter is now represented on the trigonometer plate, not by the base line D, but by the
subsidiary base line. 150 subdivisions (yards) to the right of it. Next sight the
object o along one of the tangent bars (G for preference), and where it cuts the said
subsidiary base line will be the distance po which is forthwith read off. The reader
will now understand the function, and appreciate the utility, of the divided trigono-
meter plate; for, if it were not for the scales on the plate. the only elements of the
triangle po ascertainable by the instrument would be the base line of the right
angle triangle pop and its angles op p¹ and ppl the remaining elements being
matter for arithmetical calculation. The dotted and broken lines of the figure are
added to it to shew the geometrical elements and complements of the problem; and.
the distances and angles are marked so that the correctness of the solution by my
invention may be verified arithmetically if the reader wish to so verify it.
Instead of, moving the trigonometer from the station point p to the second one p¹:
a theodolite, or any instrument adapted to take angles, may be used at the last
mentioned point for taking the angle po, to which the tangent bar is then set.
This trigonometer used as above. described forms an efficient range-finder. But a
useful modification of the instrument for this special purpose consists of half a
graduated plate. i... one divided along the base line D, and having one tangent bar
pivotted at the outer extremity of the transverse base line E instead of at the centre a.
This modification is used as follows. The object is sighted along the base line D.
and a measured base line is set off corresponding in length to the length of the
transverse base line on the plate (i... from the centre to the axis of the tangent bar).
according to the scale. The object is again sighted, but this time along the tangent.
bar, and where the latter cuts the base line defines the range.
'
PROBLEM 2. TO ASCERTAIN THE ALTITUDE OF A DISTANT OBJECT.-See Fig. 4.
Let oo¹ be the given object; and p, the station point. First, ascertain the distance
po by Problem 1, and read it off along the base line D. I assume it to be 300 yards.
as in the previous problem. Then take the angle op with the theodolite, and
transfer it to one of the quadrants of the protractor, by setting the respective tangent

page_text: bar. The intersections of the bar, or bars, with the chord line which cuts the 300 point
on the base line D will give, on the said chord line, the required altitude. Any
necessary correction for height of trigonometer can then be made.
In working such a problem as the above, it will be seen that I first deal with the
vertical plane to the extent of ascertaining the perpendicular and the apex angle of
the triangle concerned, and then turn that angle down into the horizontal plane to get
at the base.
PROBLEM 3. To ASCERTAIN AND LAY DOWN A CURVE JOINING THE TERMINALS OF
TWO STRAIGHT PORTIONS OF A LINE OF RAILWAY BY FINDING THE APEX ANGLE
OF THE CURVE.--See Fig. 5.
I
Let gq be the two terminals. These are the only data the surveyor has given him.
He first settles the station point p (= the. apex angle) by getting sights of both
terminals along the respective tangent bars taking care that both make equal angles
with the base line D. It is of the first importance that these angles should be equal,
i.c., that the apex angle should be bisected exactly, inasmuch as any inaccuracy at
this stage of the survey will vitiate every subsequent step. The point, p, may also be
found by continuing the lines terminating in q, q', until they intersect each other.
Either tangent line, por pg', is next chained off, or its length ascertained according
to Problem 1. Having ascertained the length of either line. I note it on both tangent
bars, and so transfer to the trigonometer the equivalents of the two tangent points, g q'.
The chord line which cuts these two points is the equivalent of the chord, q q¹. The
intersection of the radial bars, when they are set at the respective equivalents of the
tangent points, or the intersection of the base line D by either radial bar, will give the
centre, e, of the circle of which the curve, yeg', is an are. It will also give a radius
of the curve. The centre point, v, of this curve is the distance from the trigonometer
centre (apex angle p) to the equivalent on the plate of the point e. less the length
of a radius. s is the versed sine; g s or q₁s, the half chord; es, the cosine: and
org, the chord of half the are, all of which distances can be read off the
instrument as it stands, excepting the chord of half the are, which last can be obtained
by transferring the distances to the trigonometer from the centre a along the base
line D, noting the distance s g', or half the cord upon the chord line cutting D in the
equivalent of and setting the tangent bar to cute and q¹.
PROBLEM 4. TO SET OUT THE CURVE OF PROBLEM 3 UPON THE TRIGONOMETER-PLATE,
PREPARATORY TO PEGGING IT OUT ON THE GROUND.-See Fig. 6.
For the purpose of shewing the relation between the figure of this problem and that
of the preceding one, part of the latter figure, viz., the apex angle gpq', and the two
tangent lines and pg', have been introduced in dotted lines. Further, the same
reference letters are used in both figures for corresponding points and lines.
Transfer the angles q¹es and ges of Fig. 5 to the trigonometer, treating the
centre a of the latter as the equivalent of c, and, after noting the length of a radius,
remove the radial bars from the instrument. Transfer the distances s and us, also
thereby noting on the trigonometer the centres of the circle and of the curve,
respectively.
Next, noting the length of a radius on a tangent bar, say the left hand one-set
it to cut the subsidiary base line-say the 5-next on the left of the base line D, with
that distance, thereby producing the point 1; and the distance 1-2 will be the
equivalent of the first ordinate. This process is repeated until the requisite number
has been found. For the sake of convenience and accuracy, equidistant subsidiary base
lines are chosen; and, if there is a fractional remainder in the half chord, it is left
outside the last ordinate. It is not necessary to find ordinates on both sides of the base
line D. If they are found for only one side, that will suffice; as the two sides are
counterparts of each other. As each point in the curve is found, it can be
pegged out,

page_text: PROBLEM 5. TO FIND THE RADIUS OF A CURVE WITHOUT USING A RADIAL BAR. -See
Fig. 7, which is a diagrammatic plan of the trigonometer. The curve is a
reproduction of that of Figs. 5 and 6.
Ascertain the apex angle, and lay off one half of it, ea qor e a q', on the trigono-
meter by either tangent bar. The figure shows both halves as laid off. Ascertain
the length of a tangent line (= a g), and lay it off on the base line D of the trigono-
meter from the centre of the latter, giving a. The half cord linery, so laid off
from the base line to the tangent bar, equals the radius of the curve.
PROBLEM 6. TO FIND THE RANGE OF ANY OBJECT, e.g., A FORT OR A SHIP, FROM A
FIXED STATION, e.g., A FORT OR A MAN-OF-WAR.-See Fig. 8.
Lets be the fixed station point; and o, the object. Plant the trigonometer with
its centre over s; and the base line, D, coincident with the line st. The transverse
base line will then be coincident with the line s u. Set the angle so on the trigono-
meter by adjusting the right tangent bar till it sights the object. At the same time,
a second surveyor, with another trigonometer or any instrument proper for taking
angles, and having its station point at e, takes the angle eo. This second station
point may, of course, be either to the right or the left of s according to the relative
position of o. The distance sc is known--say 100 yards.
The left tangent bar of the first trigonometer, i.e., the one at s, is then set to the
angles which is transferred from . to already found, thereby giving the
-distances st, er, and sď. It may be remarked that the equivalent of a on
the trigonometer will be the subsidiary base line 100 units to the right of the centre a.
As, is common to both triangles and cose and are necessarily
equal
Now the length of seis known (100 yards), and is read or measured off to the
right along the chord line which passes through the equivalent on the trigonometer of
the point, and where it cuts the right tangent bar of the trigonometer planted over s
will be the equivalent of the object 0. The distance so can then be read off the said
bar. The distance sa, =vo, can likewise be read off the left tangent bar.
It will be noticed that this problem to some extent resembles Problem 1. There is.
however, a practical difference between them which is this, that according to
Problem 1. the observer can stand exactly opposite the object, and start with a right
angle. Circumstances will frequently, or rather in naval warfare do generally arise
to prevent the object being sighted from a point at right angles with it. For
instance. (referring to Fig. 8) let the points and be taken as on a man-o'-war's
deck, and the point somewhere over the bows or astern. If it were impossible to
take a distance with the trigonometer without being at right angles with the object,
the vessel would have to change position before the range in question could be taken;
whereas by means of my improved trigonometer, a range can always be taken
irrespectively of the relative position of the object.
PROBLEM 7. TO FIND A KANGE AT SEA, EITHER FROM A FORT, OR A MAN-O'-WAR, ON
TO A MAN-O'-WAR, EITHER STATIONARY OR IN MOTION.-See Fig. 9.
Let F be the fort, or the deck, from which the range is to be found on to 0,
another man-o'-war, either stationary or steaming past.
Two instruments for taking angles. T. T, trigonometers for preference, are aligned
as to their transverse base lines. An observer stands at each. The two observers
are attended by an assistant provided with a portable improved trigonometer (i.c.. one
without the stand or theodolite), or the latter may be in the hands of the gunnery
lieutenant.
.
Both observers sight, say, the mainmast. If either vessel be moving, both observa- ·
tions must be taken simultaneously. The internal angles T T 0 and T T 0) are
forthwith reported to the assistant and transferred to his portable trigonometer, the

page_text: =
centre of which is treated as the equivalent of O, so that the angles T¹ TO
T TO,
TO and TO, respectively, will be laid off on the outer quadrants of
the protractor by the arms of the tangent bars, instead of by the tangent bars on the
quadrants upon the graduated portion of the plate. Where the chord line, of the
length of the measured base line T T', cuts the tangent bars, will be shewn
the distances TO, TO, and the intersection of the base line D and the said chord line
will give the distance f 0-i.c., three distances found without any calculation, from a
pair of observations, and that in spite of both objects being in motion, perhaps at
different speeds.
PROBLEM 8. To FIND THE DISTANCES
RESPECTIVELY SEPARATING TWO OBJECTS,
e.g., TWO MEN-O'-WAR, FROM A GIVEN POINT e.g., A' FORT OK ANOTHER MAN-O'-
WAR; AND ALSO THE DISTANCE SEPARATING THE SAID TWO OBJECTS FROM EACH
OTHER, ANY ONE OR MORE OF THE SAID OBJECTS AND POINT BEING EITHER MOVING
OR STATIONARY.-See Fig. 10.
Lay down a convenient base line ts; and on it mark off the given point P, and at
a measured distance therefrom-say 50 yards-a second point 1". Plant a trigono-
meter with its centre over P, and a second one over P. Any instruments for taking
angles may be used instead of trigonometers, but the latter are preferable.
Q, R are the two given objects. From P take the angles Q P P and R P s, with
the left and right tangent bars, respectively; and repeat the process from the point Pl
which will give the angles Q P₁ and R. P₁ P.
Then, on a portable trigonometer, lay off the angles Q P P and Q P¹t, with the
left and right tangent bars, respectively. Where a chord line of the length P P
(being the equivalent of the line Q1) cuts the two tangent bars, will mark the
equivalent of Q on the trigonometer, and give the distance Q P on the bar.
Next, on the trigonometer at P1, lay off the angle RPs with the right tangent bar,
and the angle R P P with the left. Likewise, where a chord line of the length P Pi
[being the representative of the dotted line (shewn in part on the figure) running to
the right from R] cuts the two tangent bars, will mark the equivalent of R on the
trigonometer, and give the distance R P on the bar.
The equivalent of having been already noted on the portable trigonometer, it
only remains to read off the distance QR along the last mentioned chord line, if the
latter suits. If, as will most probably be the case, it will not, then the distance
is measured by a loose scale u graduated to correspond with the scales of the trigono-
meter.
Or, instead of using a loose scale, the point Q may be transferred to the trigonometer-
centre a, and the point R moved over the trigonometer-plate accordingly, the
angle RQ being carefully preserved. This can be readily done by measuring along
a chord line for the distance Qg', and transferring it to the base line D from a; and
along a base line for the distance R, and transferring it to a chord line from q'.
The two new positions of the points Q. R, having been ascertained, a tangent bar is
made to cut R, which gives the distance Q R.
The portable trigonometer above referred to consists of the trigonometer-plate A
having protractor, and base and transverse base lines, as well as subsidiary base and
transverse lines, tangent and radial bars. It requires neither levels nor sights, and
has not, of course, either theodolite or stand.
It is, preferably, made larger than the surveying trigonometer, so that it can be
graduated more finely; and it may be of lighter material. I have already pointed
out its practical utility in rapidly working out problems from data in the form of
angles only, ascertained by my improved trigonometer, or any other instrument
capable of measuring angles; and I have now to explain a more extended use to which
this adaptation of my invention can be put. It is this. When surveys are being
taken all the work, or a good deal of it at any rate, of ascertaining distances may be
omitted; and the outdoor work is restricted to taking angles. These being noted in the
survey book, the remainder of the work can be done in the office at leisure upon a

page_text: portable trigonometer, and that with the greatest facility and a greater accuracy than
could be achieved in the field, inasmuch as the scales on the portable or office trigono
meter being larger, are more subdivided. Moreover, this trigonometer for office use
may be only half the instrument illustrated in Fig. 1, i.c., it may consist of the plate
divided along the base line D. It will consequently have only one tangent and one
radial bar.
PROBLEM 9. TO ASCERTAIN THE DISTANCE WHICH A MOVING OBJECT, e.g., A STEAMER,
MAKES IN A GIVEN TIME; THE RATE AT WHICH SHE IS STEAMING; AND THE COURSE
SHE IS ON. See Fig. 11.
This problem is very similar to the preceding one. The demonstration of it need
not be diffuse; and will, nevertheless, be easily understood.
Let Vrepresent the first position of the steamer, and V V the course she is on.
Lay down a convenient base line ts, of measured length, in the same way as the
base line ts of Fig. 10.
Take the angles Vts and Vst simultaneously with the trigonometers standing
over and s, respectively, and note the exact time at which these observations, which
ascertain the point V, are made.
So soon as the steamer has reached the end of that portion of her course which
it is desired to measure-say V V-take the angles V₁s and V1st, and note the
exact time at which these latter observations, which ascertain the point V¹, are
made.
Transfer the point V to the trigonometer-centre a, and note the relative position
of the point V on the plate, carefully preserving the angle VVV
The line V Vs
will now be along the base line D on the plate. The right hand tangent bar is
next adjusted to cut the point V1, when the distance V V₁ is read off the bar. A'
comparison of this distance with the time which elapsed between the two obser-
vations will give the rate at which the steamer is sailing, and the course on which
she is sailing is ascertained by laying a compass axially over the trigonometer-centre
with its north pole, preferably, over the base line D.
PROBLEM 10. TO SET OUT A SERIES OF POINTS ALONG AN IMAGINARY LINE, e.g., A
SERIES OF SOUNDING POINTS, OR THE POINTS OF A LINE OF PIERS, OR TO SOLVE
ANALOGOUS PROBLEMS.--See Fig. 12.
Let Y Z be the line upon which the points are to be taken, at distances 20 yards
apart; the nearest one being 130 yards from the shore.
Set out a line at right angles with the line Y Z and cutting the point Y. Measure
off along it right and left from the point Y a pair of distances Y w and Y .r. They
are, for the purpose of this demonstration, assumed to be 100 yards each. A trigono-
meter with a single tangent bar only is placed over each point wand, botli
instruments having their transverse base lines carefully aligned with the base line wa
The base lines D, D, of the trigonometers will then be parallel with the line YZ,
coincident with the lines ww and ¹, respectively, and be the counterparts of Y Z,
while their centres a will be the counterparts of the point Y.
The man at we then selects that subsidiary base line d on his trigonometer-plate, to
the right of the base line D thereon, which is, for him, the counterpart of Y Z, and
the man at z does the like, only he selects his subsidiary base line to the left of his
base line D.
The sounding staff row out in the direction Z, while the men at w and a make
their tangent bars cut the points on their base lines corresponding to a distance of
130 yards from Y. When the sounding staff reach station No. 1, which they do
when say a flag staff at the stern is sighted by both men along their tangent bars
simultaneously, they are stopped by signal, and the sounding is taken. The
angles 1 Y and 1 Y may also be noted.
The tangent bars are then set to cut the respective base lines D at points thereon
corresponding with points 130 + 20 yards from the point Y, and the sounding boat is

page_text: stopped, as before, at the station No. 2, the sounding taken and the angles 2 Y
and 2 Y noted. The process is repeated until all the soundings have been taken.
Notes of the positions and and the series of angles 1 etc. w Y and 1 etc. Y will
always fix the sounding stations.
The boat may be kept on the course Y Z by erecting a flag at Y, and one
before and another behind it, both aligned with Y and Z. The oarsmen, will then
require only the stopping, and no directing signals to be given to them.
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. The combination with a protractor and a pivotted bar, of a plate having a base
line, a transverse base line, and chord lines parallel with the latter set out thereupon,
all graduated to a common scale, as set forth.
.1
2. The combination of protractor and bar pivotted over the centre thereof and
thereby adapted to take angles, with a plate graduated to the same scale in. two
directions at right angles with each other, the graduations in each direction being
respectively parallel with two diameters of the protractor at right angles. with each
other, as set forth.
3. The combination of trigonometer-plate, base line, transverse base line, chord
lines at right angles with the base line, and tangent bar, as set forth.
4. The combination of trigonometer-plate, base line, transverse base line, chord
lines at right angles with the transverse base lines, and taugent bar pirotted at the
outer extremity of the transverse base line, as set forth.
5. The combination of trigonometer-plate graduated in two directions at right
angles with each other, protractor, graduated tangent bar, and joint adapted to allow
of the plate being used in any plane, as set forth.
6. The combination of graduated trigonometer-plate, tangent bar, radial bar, and
protractor, as set forth.
Dd111511
1....
1900