FURTHER EXPLANATIONS OF THE INSTRUMENT OR APPARATUS AND PRINCIPLES OF ACTION OF SAME
Year: 1885

page_text: '
AVA
and Spherical Trigonometry in General
I, CHARLES PERKS of 56 Fenny Street Higher Broughton Manchester in the
County of Lancaster Timber Merchant do hereby declare the nature of my
invention for SOLVING PROBLEMS IN NAVIGATION ON GREAT CIRCLES AND
SPHERICAL TRIGONOMETRY IN GENERAL to be as follows:-
--
The Instrument consists of an oblong plate, on which are marked the degrees of
the Quadrant in the form of Tangents on one end and one edge-A sliding plate
marked with the sines of the ninety degrees, also two straight lines or edges,
moving independently of each other on the centre of the Quadrant.
The object of this arrangement is the working out of all problems in Spherical
Trigonometry including Navigation on Great Circles (Longitudes, Latitudes,
Distances, Courses, Amplitudes, Azimuths &°) by constructive Trigonometry
without the aid of curved surfaces-The Problem being fixed, and the solution
obtained, by simple inspection.
FURTHER EXPLANATIONS OF THE INSTRUMENT OR APPARATUS AND PRINCIPLES
OF ACTION OF SAME.
The sines, cosines, versed sines, co-versed sines, tangents, co-tangents, secants,
co-secants, &c which are ordinarily used, in the form of representative figures, or
numbers for the purposes of calculating, are in this instrument, represented
by actual sizes, or distances, to any scale chosen, the different parts of the
instrument, being placed so as to give the requisite and relative positions of the
different parts.
The multipliers, and divisors (i.e. sines, secants &c &c) are simply proportionate
distances, marked on the moveable arms, measured from centre, or zero, on which
they, (the arms) move; and form inclined planes, the heights on which, at the said
distances, giving the heights of the sines required, which are to be read on the
moveable plate of sines, opposite the said distance, or multiplier, (sine, secant &c &c)
The part marked 1- or radius on the moveable arm, being set to height of the
sine (on moveable plate) which has to be multiplied.

page_text: Or in case of division the divisor (sine, secant &c &c) to be placed to the height,
(on moveable plate of sines) of the sine which is to be divided, and the answer to
be read on moveable plate, opposite mark 1-
- or radius on moveable arm.
The same applies to the co-tangents, as, in multiplying by co-tangents the
mark 1 or radius on moveable arm is placed to the height of (on moveable plate)
the sine which is to be multiplied, and the answer read on the moveable plate
(opposite the point of the moveable arm) at the horizontal or co-tangential distance
from the centre, or from a line drawn perpendicularly to the centre.
And in dividing by co-tangents, the arm being placed to the height of the sine
which is to be divided, on moveable plate of sines, (at the said horizontal or
co-tangential distance from centre as before mentioned) the answer is read on
moveable plate of sines, opposite mark 1- or radius on moveable arms.
This being an entirely new or novel invention the foregoing technical description
of the working thereof, though, perhaps not intelligable to the general public, will
be thoroughly understood by nautical men, and mathematicians, being entirely
designed for their assistance.
There has never yet been brought forward any invention of a similar kind, of
which I can find any record whatever.

page_text: and Spherical Trigonometry in General.
I CHARLES PERKS of 56 Fenney Street Higher Broughton Manchester in the
County of Lancaster Timber Merchant, do hereby declare the nature of my
invention and in what manner the same is to be performed, to be particularly
described and ascertained in and by the following statement :-
The object is to provide means for ascertaining with facility and ease numbers
bearing relation one to another such as represent the ratios between angular
degrees sines tangents secants and co secants for the purpose of simplifying
the process of working out or obtaining solutions of problems in spherical
triginometry.
For instance my invention may advantageously be used in ascertaining the
distance from one place to another when the latitudes and longitudes of the places
are known or for determining the course to be pursued from day to day to arrive
at a given position in great circle sailing or for the calculation of amplitudes and
azimuths.
In carrying my invention into practice I make use of an instrument consisting
essentially of a base plate a sliding plate and two radial arms graduated in such
manner that by various movements of the parts the desired results may be obtained.
To facilitate accurate readings sliding indicators verniers and magnifying glasses
may be used.
:
To effect the calculations above mentioned and similar calculations the base
plate is graduated with lines and figures representing angular degrees and the
tangential ratios of an angle of 90°. The sliding plate is graduated to represent
the ratio of sines and the radial arms which are pivotted at the centre from whence
the angular degrees radiate are graduated to obtain secant and co-secant ratios.
Figure 1 is a plan and figure 2 an end elevation of an instrument for use in
solving problems in spherical trigonometry.. Under my invention A is the base
plate graduated with angular degrees at B and tangent ratios at C. D is the
sliding plate graduated with sines The said plate slides in a groove in A and is
held in position by springs pressing against the edge of the groove so as to prevent
shake. E F are radial arms pivotted at G. and graduated to represent secants and
co secants in such manner that when a cross line on D is brought to a given figure
on the scale C the corresponding figure on E. or F will intersect the said cross line
on the graduation line marked 90. E¹ F¹ are wires attached to the radial arms to
make reading edges, or such edges may be on the arms themselves. H. sliding
indicator on the arm F.
It will be evident that the base plate A instead of being flat at the top might be
continued in the form of a quadrant.
The drawing illustrates the method of calculating the distance a vessel proceeding
from latitude 23° to latidue 35° with a difference of longitude of 48° would have to
traverse. The radial arms are first placed in the position shown in figure 1 The
reading edge F¹ of the arm F lies on the line 23 of the scale B whilst the reading
edge E of the arm E lies on the line 35 of the said scale B. The sliding plate is
'

page_text: now moved until the line marked I crosses the reading edges of the arms E and F
in such manner that the difference between the lower crossing 37 and upper
crossing 85 gives 48° the difference of longitude. The arm E is now moved out
of the way and the arm F is moved in the position shewn in diagram 3 so that
the reading edge where it crosses the line I is on the line marked 90. The
indicator H. is then slid to the same point of intersection. The radial arm F. is
now again moved back to the position shown in figure 1. or latitude of departure
namely 23° the point where the indicator H. intersects one of the line on d in
this case 42° 46' is the distance from the node or equator as shown on diagram
Fig. 4. The arm fis then placed with the reading edge on latitude of destination
namely 35° when the indicator h gives the distance from node 86°. The difference
between 42° 46' & 86° is the required distance between the places namely 43° 14′
or 2594 miles.
For the course the arm f. is moved until the indicator h is placed on the line
on d representing the complement of the longitude 37° which will in this case
be 53. The course is then read off on the line b on the base plate as shown in
diagram 5.
The secant and co-secant graduations on the radial arms will be of use in many
trignometrical calculations. It would facilitate some operations if the radial arms
were extended beyond the centres to a further graduated plate, but the apparatus
would become so cumbersome that it could not be recommended.
Having now particularly described and ascertained the nature of the said
invention, and in what manner the same is to be performed, I declare that what
I claim is
First. The combination of a base plate a, sliding plate d. radial arms ef, and
graduations for the purpose set forth.
Second. The combination of a base plate a sliding plate d radial arms e f
indicator h and graduations for the purpose set forth.
Third. The graduations b. c and d combined with a base plate a sliding plate
and radial arms substantially as specified for the purpose set forth.
Fourth. The graduations b c d and e with or without f combined with a base
plate, a sliding plate and radial arms substantially in the manner specified for the
purpose set forth.
Doted this 2nd day of June 1886