Year: 1886

page_text: L, PHILIPPE CLAUDEL of Vecoux; France, Inventor do hereby declare the nature
of this invention to be as follows:-
This application for a patent of invention has for its object an apparatus for
calculating, called "Cadran Calculateur" (dial plate calculator), that permits of
rapidly performing all calculating operations: multiplication, division, raising to
the square, square root, et cetera, and besides gives graphically all the trigono-
metrical lines of the angles.
This apparatus has the advantage over the ordinary calculating instruments of
being more exact and more easily handled; the manner of using also can be learned
in much less time.
It is based, almost exclusively, on the properties of similar triangles, as I will
show further on.
2
In order that the nature of my invention may be clearly understood, I.have
shown my apparatus on the drawings annexed to this Specification.
Figure 1, represents the calculating dial, seen in elevation; and
Figure 2, is a plan view of it.
As will be seen on the drawing, my apparatus consists of a well planed board T
having a metallic are E, and a graduated rule F.
•
On the surface of the board, I have traced a square D, H, I, J, a metre along the
sides, and divided by decimetres, centimetres, millimetres etcetera. On this square
I have also traced around D as centre and with D, H, as radius, the quarter circle
J, H, on which I have inscribed at each point of intersection with the vertical
lines, numbers corresponding to those placed on the line D, H. There still remains
on the square D, H, I, J, a certain number of lines and of optional annotations, for
they relate to the solution of particular problems.
The metallic arc E 'is fixed on the board and at a certain distance from this
board, about 10 to 15 millimetres, at its extremities, by means of two pins band
of two little India rubber washers c; it is moreover sustained in its centre, by a
second metallic arc G. The rule F is likewise fixed to the board by a pin d,
around which it freely turns; the axis of the pin d is exactly at the summit D of
the divided square. This rule works under the metallic arc E; and a small spring r,
exerting pressure against the arc E, holds át constantly against the board, and
keeps it fixed in any one position; the rule may be moved by a small button e.

page_text: Squares and Square roots. The square of a number is no other than this number
multiplied by itself. This operation is therefore easily performed. The position of
the rule on the figure corresponds to that which gives the square of 8.
If I mark on the divided square the point corresponding to the division 8 on the
rule, and subsequently move the rule into the position which gives me the square
of 7, and mark the new point corresponding to the division 7, and if I perform
this operation successively for all the numbers and subsequently join up by a curve
on the divided square all the points thus obtained, this curve will be found to be
the place of the square roots of the numbers. It allows of rapidly finding the
square root of a number, by a reading inverse of that which gives the square. In
fact if I wish to obtain the square root of 64, I move the rule in such way that
it cuts the preceding curve on the vertical of the number 64 of the line D, H.
The number 8 that I then read on the circle J, H, at the intersection of this circle
and the rule, is the root required.
This same root-8 would also be read on the rule F at the point of intersection
with the curve..
It will be seen from the preceding examples, which I could multiply, of what,
importance my apparatus is and with which I can rapidly and very accurately
perform all calculations, not only those which I have just described, but also those
relative to the cubes of numbers and their cube roots, to logarithms, to circum-
ferential calculus, to that of the circle, to divers problems on the speed of bodies.
and spaces passed through, to the tension of fluids, etcetera; all these operations
being moreover based on the employment of the rule F, of the divided square and
of logarithmetic, cubic, and other curves, that are graphically traced in a manner
analagous to that for square root and the construction of which I have indicated
by points.
:
Besides I think it useful to show how I find with my apparatus in a single
operation, all the trigonometrical lines of a given angle. I have marked for this
purpose on the lines H, I, and I, J, all the angles, degree by degree, from 0 degrees
up to 90 degrees.
Supposing now I wish to know the trigonometrical lines of the angle of 37 degrees
for instance, I move the rule F so as to bring it in contact with the division 37
marked on the line H, I; I then read, without any need for calculation, that the
length of the tangent of the angle of 37 degrees is equal to the length H, S, that
is to say to 0,75; that the length of the secant is equal to the length D, S, that is
to say to 1,24; that that of the sine is equal to M, N, that is to say, to 0,60, and
that of the co-sine to D, M, that is to say, to 0,80. When the angle exceeds
45 degrees, I can no longer read the length of the tangent on the line H, I, as
previously; in this case, I read this length on the line h, i, and I take care to
multiply the result by 10.
In the case of the length of the arc of a given angle, 1 obtain this by means of
a special curve.

page_text: I, PHILIPPE CLAUDEL of Vecoux France, Inventor, 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:―
"
1. This application for a patent of invention has for its object an apparatus for
calculating called "Cadran calculateur' (dial-plate calculator) that permits of
rapidly performing all calculating operations: multiplication, division, raising to
the square, square root, et cetera, and besides gives graphically all the trigono-
metrical lines of the angles.
This apparatus has the advantage over the ordinary calculating instruments of
being more exact and more easily handled; the manner of using also can be
learned in much less time.
It is based, almost exclusively, on the properties of similar triangles, as I will
show further on.
In order that the nature of my invention may be clearly understood, I have
shown my apparatus, on the drawings annexed to this specification.
Figure, 1, represents the calculating dial, seen in plan, and
Figure, 2, is a side view of it.
As will be seen on the drawing, my apparatus consists of a well planed board T,
having a metallic arc E, and a graduated rule F.
On the surface of the board, I have traced a square, D, H, I, J, a metre along the
sides, and divided by decimetres, centimetres, millimetres, et cetera. On this
square I have also traced around D as centre and with D, H, as radius, the quarter.
circle J, H, on which I have inscribed at each point of intersection with the
vertical lines, numbers corresponding to those placed on the line D, H. There
still remains on the square D, H, I, J, a certain number of lines and of optional
annotations, for they relate to the solution of particular problems.
The metallic are E is fixed on the board and at a certain distance from this
board, about 10 to 15 millimetres, at its extremities, by means of two, pins b and
of two little India rubber washers c; it is moreover sustained in its centre, by a
second metal stay G. The rule F is likewise fixed to the board by a pin d around
which it freely turns; the axis of the pin d is exactly at one angle D of the
divided square.
This rule works under the metallic arc E, and a small spring r,
exerting pressure against the arc E holds it constantly against the board, and
keeps it fixed in any one position; the rule may be moved by a small button e.
In place of the spring, I may use a screw similar to those in certain mathematical
instruments.
To conclude this description of the apparatus, I will add that the rule is bevelled
off, and divided into decimetres, centimetres, millimetres, et cetera, exactly like
one of the sides of the divided square,

page_text: -
If I mark on the divided square the point corresponding to the division 8 on the
rule, and subsequently move the rule into the position which gives me the square
of seven and mark the new point corresponding to the division 7, and if I perform
this operation successively for all the numbers, and, subsequently join up by a
curve on the divided square all the points thus obtained, this curve will be found
to be the place of the square roots of the numbers. It allows of rapidly finding
the square root of a number, by a reading inverse of that which gives the square.
In fact, if I wish to obtain the square root of 64, I move the rule in such a way
that it cuts the preceding curve on the vertical of the number 64 of the line D. H.
The number 8 that I then read on the circle J, H, at the intersection of this circle
and the rule, is the root required.
This same root 8 would also be read on the rule F at the point of intersection
with the curve.
It will be seen from the preceding examples, which I could multiply, of what
importance my apparatus is, and that with it I can rapidly and very accurately
perform all calculations, not only those which I have just described, but also those
relative to the cubes of numbers and their cube roots, to logarithms, to calculation
of circumferences to that of the circle, to divers problems on the speed of bodies
and spaces passed through, to the tension of fluids et cetera, all these operations
being moreover based on the employment of the rule F, of the divided square and
of logarithmetic, cubic, and other curves that are graphically traced in a manner
analogous to that for square root and the construction of which I have indicated
by points.
:
Besides I think it useful to show how I find with my apparatus in a single
operation, all the trigonometrical lines of a given angle I have marked for this:
purpose on the lines H, I, and I, J, all the angles degree by degree, from 0 degree
up to 90 degrees.
Supposing now I wish to know the trigonometrical lines of the angle of
37 degrees for instance, I move the rule F so as to bring it in contact with the
division 37 marked on the line H. I. I then read without any need for
calculation, that the length of the tangent of the angle of 37 degrees is equal to
the length H. S. that is to say, to 0,75 that the length of the secant is equal to the
length D, S, that is to say, to 1, 24 that of the sine is equal to M, N, that is to
say, to 0,60; and that of the cosine to D, M, that is to say, to 0,80. When the
angle exceeds 45 degrees, I can no longer read the length of the tangent on the
line H, I, as previously; in this case, I read this length on the line 1, i, and
I take care to multiply the result by 10.
In the case of the length of the arc of a given angle, I obtain this by means of a
special curve.
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 employment of a divided square on which is traced a quarter of circle
having for its radius the length of the side of the square as a unit; for its centre,
one of the angles of this square and graduated as before described, this divided
square being traced on paper, cloth, or directly on the board.
2. The employment of a polished metal arc, fixed on the outside of the square
by two pins, maintained at a certain distance from the board by means of two little
India rubber washers, and sustained in its centre by a second metallic arc, with a
view of maintaining the rule in any one of its positions.
3. The employment of a bevelled rule graduated like the sides of the square
moving around an axis placed exactly at one of the angles of the square at the
centre of the preceding quarter circle, this rule having besides a button for moving
".

page_text: it and a spring exerting pressure against the preceding metallic arc and also
maintaining the rule in any one of its positions.
Reserving to myself, also, the employment, in the application of the principles
on which my instrument is founded, of any modifications which experience or its
purpose would suggest.
WP. THOMPSON & Co.,
323, High Holborn, London,
Agents for the Applicant.