An improved Gyimutical Di
Year: 1895

page_text: Date of Application, 23rd Feb., 1895
Complete Specification Left, 23rd Nov., 1895-Accepted, 4th Jan., 1896
An improved Gyimutical Di
I, JAMES EAGLES, of 55 Edith Grove, Chelsea, London in the County of
Middlesex, National Scholar do hereby declare the nature of this invention to be
as follows
This invention relates to slide rules in which the logarithmic scale is arranged
on a cylinder of wood or other material, and consists essentially of the.
following:
11
A cylinder of wood, or celluloid, or other suitable material on which is marked,
or printed, a graduated logarithmic scale in the form of a continuous spiral or other
convenient arrangement, which scale may also be marked or printed on paper
or other suitable material and then fastened to the cylinder in any well-known
manner.
Each complete turn of the scale is marked and at each end of it there is another
scale of decimal parts, concentric with the cylinder, for reading off fractions of a
turn of the logarithmic scale, and thus by the proper numbering of the complete
turns and graduation of the concentric scales, the logarithm of any number on the
logarithmic scale can, with the aid of the index tube to be hereafter described, be
determined, within the limits of the instrument..
An index tube which is made of a transparent substance such as transparent
celluloid, or glass, or other suitable material. It is made an accurate sliding fit
over the cylinder before described and carries three indices or index points, one of
which is moveable, and the other two fixed but one or both adjustable if found
necessary. The moveable index may also be of transparent celluloid or any
other suitable material and it is made an accurate sliding fit over the index tube.'
Instead of, er in addition to the concentric scales on the cylinder before
described, there may be a concentric scale on the moveable index and suitable
markings on the index tube in order to read off fractions of a turn of the
logarithmic scale.
By suitably arranging the parts of the instrument, and the markings on the
cylinder, and on the index tube and moveable index, all the ordinary arithmetical
operations which slide rules are used for may be performed.
The cylinder before described may be made hollow to contain other cylinders
or tubes on which tables of constants and other data may be printed or marked.
Dated this Twenty-first day of February 1895.
1, JAMES EAGLES, of 55 Edith Grove, Chelsea, in the County of Middlesex,
National Scholar, 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 cylindrical slide rule, which consists of a

page_text: logarithmic scale arranged on a cylinder of wood or other suitable material and
enclosed in a movable transparent tube of celluloid or other suitable transparent
Diaterial.
And in order that my invention may be thoroughly understood, I now proceed
to describe the accompanying drawing thereof, reference being had to letters and
figures marked thereon.
Fig. 1, is a plan of the end of the instrument.
Fig. 2, is an elevation of the movable tube and collar.
Fig. 3, is an elevation of the movable tube, collar and cylindrical graduated slide
complete.
Fig. 4, is an elevation of the cylindrical graduated slide.
My invention is constructed with a logarithmic scale a printed or cut on a
cylinder b made of wood or other suitable material. This said scale a is marked
or printed preferably in the form of a continuous spiral, but any other convenient
arrangement may be used, which said scale a may also be marked or printed on
paper and then fastened to the cylinder & in any well-known manner.
Each complete turn of the scale a is marked by a straight line or scale h h which
is marked on the cylinder b from end to end of the scale a as shewn in Fig. 4, the
divisions of this scale being formed by the turns of the scale a and numbered
from the beginning of said scale a as shewn.
The scale a makes a whole number of turus on the cylinder b.
At each end of the scale a there may be on the cylinder b and concentric
with it, a scale e divided into 100 divisious, for the purpose of reading off
fractions of a turn of the scale a. It is however preferable to have a concentric
scale at one or both ends of the index tube d to be hereafter described as at st in
Fig. 2, the said concentric scales being then numbered the opposite way round
to scale a.
An index tube d which is made of transparent material such as transparent
celluloid, or glass or other suitable substance, transparent celluloid being prefer-
able, the transparency of the substance used permitting the scale a to be visible
through it.
This index tube d is made an accurate but easy sliding fit as in Fig. 3 over the
cylinder before described and carries three index points e k and f, the one
marked being on a movable collar 9 to be hereafter described, the other
two e and are fixed at a distance apart equal to the distance between the
beginning and end of scale a so that when e is at the beginning, is at the end of
said scale a. The index ek though always fixed when the instrument is being
used, may be made adjustable if necessary, by being made in the form of pointers
on collars (not shewn) made a tight fit on the index tube d. It is in my opinion
preferable to have them permanently fixed in the form of simple marks on the
index tube d. The said index tube d is made rather shorter than the cylinder b
for convenience in handling the instrument. At one or both ends of the said
index tube d are the concentric scales s tas before described, and the said concentric
scales are exactly alike and their zeros in a line with the index points ek as shewn
in Fig. 2.
The collar may be made of any suitable material such as metal, wood or
glass, but preferably of transparent celluloid, the index point f heing simply a
mark on the said collar g as shewn in Figs. 2 and 3.
This collar g is made an accurate easy sliding fit over the index table d as before
described.
The cylinder 6 before described may be made hollow to contain other cylinders
or tubes on which tables of constants or other data may be fastened printed or
marked.
The advantage of having a transparent index tube, is that the instrument
is reduced in bulk for the same length of scale and hence rendered more portable.
By suitably arranging the parts of the instrument and the markings on the
cylinder and on the index tube d and movable index f, all the ordinary

page_text: arithmetical operations for which slide rules are used may be performed within the
limits of the instrument.
To multiply, find the number on the logarithmic scale a which represents the
multiplier and set either of the index points e k to it, then slide the index point f
over the index tube d until it is at that end of scale a visible between e and k,
next move the cylinder 6 until the index point f is over the number on the scale a
that represents the multiplicand, and the product may then be read off at that
index e or k which is now on the scale a. From the construction of the instrument
it is obvious that the index points ek can never both point to a number on the
scale a.
The index point f must not in any operation be moved outside the space
between e and k.
To perform division find the number on the scale a that represents the dividend
and if it be less than the divisor set it to the index e, if it be greater than the
divisor set it to the index k, then set the index f to that number on the scale a
which represents the divisor, next move the cylinder b until the index f is at one
end of the scale a, when the quotient will appear at that index e or k which is then
over the scale a.
To find the logarithm of any number set the zero of scale s on index tube d to
the number on scale a whose logarithm is required and read off on scale hh the
number of whole turns and on scale s the decimal parts of a turn of scale a,
between the beginning of scale a and the number whose logarithm is required,
then multiply the number and parts of a turn thus obtained by a constant which
depends on the length of scale a and which is marked on scale a or otherwise
supplied with the instrument. The product is the mantissa of the required
logarithms, and the characteristic is obtained by inspection in the usual well known
manner.
Since logarithms of numbers can be found by the instrument the roots and powers
of numbers can be found as if by means of a table of logarithms in the usual well
known manner.
Another method of performing involution and evolution is as follows:-
Find on the scale a the number whose power or root is required, place it to the
zero of the scale s on the index tube d, and read off the number of whole turns on
scale h h and fraction of a turn on scale s, between the beginning of scale a and the
number whose power or root is required and if the number whose power or root is
required be in units, multiply the reading so obtained by the index of the power or
root required to obtain a new reading and adjust the index tube d so that the zero
of scales will make this new reading on scales h and s. The number on the
scale a now appearing at the zero of scale s will be the required power or root. If
the number whose power or root is required is in tens, the the whole number of
turns made by scale a must be added to the reading obtained from scales h h and s
before multiplying or dividing by the index of the required power or root. If
the number is in hundreds twice the whole number of turns of scale a must be
added and so on.
If after multiplying or dividing by the index of the required power or root, the
product or quotient is greater than the whole number of turns of scale a the said
product or quotient must be diminished by multiples of the whole number of turns
of scale a until the remainder is less than the whole number of turns of said scale a
and this remainder is the reading to which the index tube must then be adjusted as
above explained.
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. In cylindrical slide rules, a transparent index tube d with index points e k,
substantially as herein described.
2. In cylindrical slide rules, a transparent index tube d with suitable index points

page_text: and scales in combination with the movable collar g, substantially as herein described
and according to the accompanying drawing.
3. In cylindrical slide rules, the combination of the various parts described
in this Specification to form the instrument, substantially as described and for
the purpose specified.
Dated this 23rd day of November 1895.
J. P. BAYLY,
18 Fulham Place, W., Agent for the Applicant.