Improvements in and relating to Slide Rules.
Year: 1894

page_text: Date of Application, 18th Dec., 1894
Complete Specification. Left, 9th Oct., 1895-Accepted, 23rd Nov.,
1895
Improvements in and relating to Slide Rules.
I, GEORGE GOUTHWAITE ScurFIELD, of 15 Nelson Street, Sunderland in the
County of Durham, Engineer, do hereby declare the nature of this invention to
be as follows:-
This invention has reference to improvements in and relating to slide rules and
is intended to produce a more compact as well as a novel arrangement of slide rule
as hereinafter foreshadowed.
The device may consist of a pair or system of discs of steel or other suitable
material pivotted together and fitted with a marker.
On the outer ring or circumference there may be a scale of equal divisions
representing logarithmic numbers and on the inner rings or circumferential lines
there may be decreasing scales representing the numbers themselves the distance
from the No. 1 to any other number being proportional to the mantissa of the
logarithm of that number.
Thus in multiplication the number 1 on the revolving or movable or inner scale
may be placed opposite the number to be multiplied on the second scale; opposite
the multiplier on the inner scale the answer may be read on the second or middle
scale; or for division. the reverse plan may be. adopted by placing divisor under
the number to be divided and then reading the answer on the second scale opposite
No. 1 on inner scale.
The logarithmic scale may be used to ascertain the logarithm of any required
number to several places of decimals.
By using a circular form a longer scale may be embraced in a very small space
and as in ordinary slide rules there is a No. 1 at each end of the scale opposite
which the result can be read, confusion and mistakes are apt to follow whereas in
my case there being only one No. 1 no such mistakes can occur.
The centrally pivotted marker serves for marking the position of the last result
in the case of a series of multiplications or divisions one after another and is also
capable of registering the value of the characteristic if desired.
To readily ascertain the characteristic on the marker or in an equivalent position
I 'secure a toothed wheel or equivalent device suitably held in position by a spring
pawl detent or stopper arrangement.
Whenever the marker passes the No. 1 a stop on the circumference of the disc
gears with the wheel-teeth and turns it so as to add or deduct one to or from the
previous characteristic depending on the direction in which the marker is moved the
wheel being graduated from a middle point of zero in both directions representing
plus and minus characteristics.
For multiplication the marker may be moved clock-wise and for division the
reverse way, the wheel having first been adjusted to the required characteristic of
the number to be multiplied or divided and similarly the characteristic of the
multiplier or divisor must be added or subtracted to or from this as the case
may be.
The advantage of the characteristic being given as well as the figures of which
the number is composed will be apparent to every one acquainted with the nature
of a logarithm because it at once tells you the position of the decimal point in your
answer and in addition to the scales above mentioned there may be another scale of

page_text: logarithmic sines and tangents which can either be placed ion the same disc as the
inner scale or on another disc: on the other side of the big scale as found
convenient.
Deted this 17th day of December 1894.
A. CRAWHALL CHAPMAN,
3 St. Nicholas Buildings, Newcastle-on-Tyne, Patent" Agent.
Improvements in and relating to Slide Rules.
I, GEORGE GOUTHWAITE SCURFIELD of 15 Nelson Street, Sunderland in the
County of Durham, Engineer, do hereby declare the nature of this invention an.
in what manner the same is to be performed, to be particularly described ani
ascertained in and by the following statement :-
This invention has reference to slide rules for facilitating calculations and is
designed to produce a more compact as well as a novel arrangement of slide rule.
The device consists of a pair or series of rotary discs of steel, brass or other
suitable material pivoted together all their diameters decreasing from that of the
central disc to such extent as may be required to give room for the marking of the
necessary scales hereinafter referred to upon each disc circularly above the periphery
of the next outer disc and the edges are bevelled off to facilitate reading the
various scales.
This device is fitted with a radial marker which consists of a bifurcated lever or
stirrup mounted at its open end upon the centre pin, the bifurcation -being of such
length and width as to ride over all the discs employed and admit of the centering
of an index wheel and fixed gear stop or paul hereinafter described.
On the outer disc is cut a circumferential scale of equal divisions representing
logarithmic numbers and on the inner discs or circumferential lines are marked
decreasing scales representing the numbers themselves the distance from the No. 1
to any other number being proportional to the mantissa. of the logarithm of that
number.
Thus in multiplication the No. 1 on the revolving or movable or inner scale is to
be placed opposite the number to be multiplied on the second scale; opposite the
multiplier on the inner scale the answer may be read on the second or middle scale;
for division the reverse plan is to be adopted, viz., by placing the divisor under the
number to be divided and then reading the answer on the second scale opposite
No. 1.on.the inner scale.
The logarithmic scale is provided to ascertain the logarithm of any required
number to several places of decimals.
By using a circular form a longer scale can be embraced in a very small space
and as in ordinary slide rules there is a No. 1 at each end of the soale: opposite
which the result can be read confusion and mistakes are apt to follow whereas in
my case there being only one No. 1 no such mistakes can occur.
The centrally pivoted radial marker serves for marking the position of the Inst
result in the case of a series of multiplications or divisions one after another and is
also capable of registering the value of the characteristic if desired.
To readily ascertain the characteristic on the marker or in an equivalent position
.I centre in the marker a toothed wheel suitably held in position by a spring paul or
detent or stopper arrangement.
'
Whenever the marker passes the No. 1 a stop on the circumference of the disc
.gears with the wheel teeth and turns same so as to add or deduct one to or from
the previous characteristic depending on the direction in which the marker is moved
the wheel being graduated from a middle point of zero in both directions representing
plus and minus characteristics.

page_text: For multiplication the marker is to be moved clockwise and for division the
reverse way the wheel having first been adjusted to the required characteristic of the
umber to be multiplied or divided and similarly the characteristic of the multiplier
For divisor must be added or subtracted to or from this as the case may be.
The advantage of the characteristic being given as well as the figures of which
the number is composed will be apparent to every one acquainted with the nature
of a logarithm because it at once indicates the position of the decimal point in the
answer and in addition to the scales above mentioned there is or may be another
scale of logarithmic sines and tangents which can either be placed on the same disc
as the inner scale or on another disc on the other side of the big scale as found
convenient.
i
I will explain my invention in reference to the accompanying drawings in which
Figures 1 and 2 are front and back elevations respectively, Figure 3 is a transverse
section on line ay in Figure 1 and Figures 4 and 5 are front and back elevations
(the side of the marker being removed in each view) of the characteristic
registering device and in the following description like marks of reference
designate like parts.
The rule illustrated consists of three discs 1, 2, 3, a large one 2 in the centre and
a smaller one 1 and 3 on either side of it, a radial marker M, a toothed index
wheel W, peripheral gear stop S¹, sight holes S³ and other parts hereinafter
explained.
Taking Figure 1, representing the front side, first; there are three scales on this
side graduated as on the ordinary straight rule two of the scales (A the logarithmic
sele on the outside and B a numerical scale) being marked on the large disc 2
while C (which is identical with B) is marked on the small disc 1.
In use, supposing the logarithm of any number to be required, I set the radial
marker M at that number on the scale B and read the logarithm which it registers
upoir the scale A; for instance in the position shown in Figure 1 the marker M
stands at 168 on the scale B whilst it registers 2252 as the logarithm on the
sunle.A.
:
In multiplication I proceed as follows:-1 place the No. 1 on scale C under the
number to be multiplied on scale B and opposite the multiplier on scale C the answer
is read on scale. B. For instance, take 6 x 28, set the rule as in Figure 1 putting
the lion scale C under the 6 on scale B and opposite 28 on scale C the product read
on scale B is 168.
.
In division, place the divisor on scale C under the dividend on scale B and
opposite the 1 on scale C the answer is found on scale B. For example 168 + 28,
ret the rule as in Figure 1 putting 28 on scale C under 168 on scale B and opposite
the on scale C, on scale B the answer 6 is found.
Referring now to the means for registering characteristics of logarithmic numbers
I employ the small index wheel W. centered in the radial marker M and adapted to
be operated by a small stop S¹ formed on the periphery of the large disc 2 so that
whenever the marker M passes over the end of the scale in either direction the
wheel W is turned round just one tooth by the stop S'. This wheel W. is marked
on the front side as in Figure 4 and on the back as in Figure 5 the figures being
arranged and running as plainly shown in these figures. S is the small spring
detent controlling the wheel and allowing it to be rotated in either direction. by the
stop S but only one tooth at a time. At the bottom of the wheel small holes SS
are formed through the radial marker M which enable the number registered by
the wheel to be read on either side.
By this wheel and stop device the characteristic of any required answer is
registered so that when the figures of which the number is composed are ascertained
by inspection on the scale B the scale on the wheel indicates the characteristic and
consequently the position of. the dècimal point. This is very useful in a long
caleflation, the position of the decimal point being the most puzzling thing in the
use of the ordinary slide rule although course in a case where the approximate
result is known beforehand there is no need to set the index wheel. When it is

page_text: used the marker M should be set at the first number in the expression to be
multiplied out and the wheel W should be set at the characteristic of that number
then for every succeeding multiplication or division the characteristic of every
multiplier or divisor must be added to or subtracted from the one already registered
care being taken that in multiplying the marker he moved in the direction shown in 5
the drawings, namely, clockwise when looking at the front of the discs, Figure 1,
and anticlockwise when using the disc at the back, Figure 2, (which is for
trigonometrical ratios) and in case of division in the reverse directions in each case
respectively.
A simpler method of using my improved rule is as follows:-Having set the marker Mt
at the first term in the expression set the wheel W at once at the algebraic sum of
the characteristics of the top line less the algebraic sum of the characteristics
of the bottom line, then proceed simply to multiply and divide being careful to
move the marker in the direction above mentioned. As an example I will take the
following onluulation
The sum of the characteristics of the top line
sum of all figures lying to left
of the decimal in the top line (number of terms in top line + number of ciphers
next the decimal in the fractional terms) = 7 - (5 + 0)
=
-
-
-
2.
The sum of the characteristics of the bottom line is obtained the same way 2
and 7 (4+1)=2 also.
Then top bottom = 2 20 and the index wheel must be set at zero before
beginning to multiply or divide in this case. At the end of the operations the
index will be found to have moved to 1 showing that the figures which read 319
stand for 31.9.
2
Referring now to the back of the rule, the disc 3, as shown in Figure 2, is used
for trigonometrical calculations and has five scales, marked 5, 6, 7, 8 and 9.
Opposite each of these respectively is stamped upon the marker M the number
and sign of the characteristic of the sine or tangent required. The third or middle
scale 7 refers to both sines and tangents of very small angles up to about 34'-0" and 3
the two outer scales 5 and 6 refer to sines of angles between about 34'-0" and 90°
The two inner rings 8 and 9 refer to tangents of angles from about 3+'-0" to 45°.
The letters S and T stamped on the marker serve as a guide to the sine and
tangent scales.
The arrow indicates the beginning of these scales and supposing for example the 3
sine of 15° be required the arrow is to be set opposite a mark on the plain surface
of the large disc 2 as shown in Figure 2 corresponding with the beginning of the
scales A and B on its front side then set the inarker at 15° on the outer or sine
scale the answer will be read on the scale B on the front side of the rule. The
figures being 2588 and the characteristic stamped on the marker being 1 the sine 4
required will be 2588.
-
It will be observed that the marker on this side apparently turns in the opposite
direction in multiplication or division but this is merely due to the fact that it is at
the back of the scale B on which all the answers are to be read.
It will readily be seen from the above that in the case of a sine or tangent 4
occurring in any expression all that is required is to read the characteristic and
alter the index wheel accordingly and when the multiplication is required by that
sine or tangent reference is to be made to the back of the disc and the arrow set at
the position registered by the marker M which is then to be moved round
to 15°, 20° or whatever the angle may be whose sine or tangent is being dealt 5
with.
In division, after altering the index wheel the number of the angle is to be set at
the place registered by the marker and the latter moved round clockwise to the
arrow indicating the beginning of the scales.
The scale 7 on the disc 3 need not necessarily be provided as the information 5

page_text: given by it seldom occurs in practical work and such information if required may
be obtained from the other scales.
Instead of composing the rule of discs arranged in tiers precisely as herein
described and illustrated in the drawings I may equivalently recess them one within
the other the scales being arranged as described.
Roots are obtained in the ordinary way, that is, divide the logarithm of the
number whose root is required by 2, 3 or 5 etc. according to whether ✓ ✓ or ✓³.
etc. is required but care must be taken always to prefix the right characteristic
before dividing.
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. A rotary slide rule for the purposes of mechanical calculation consisting of a
pair or series of rotary discs each disc having any required scale or scales marked
circularly upon its surface, and all being pivoted together and provided with a
radial marker, the parts being arranged or adapted to operate substantially in the
manner and for the purposes hereinbefore described.
2. The combination with a rotary slide rule such as above claimed of the means.
for registering the characteristic of any required logarithmic number consisting of
the toothed wheel W centered in the marker M and the peripheral stop ST all
substantially as herein set forth.
3. A rotary slide rule constructed, arranged and adapted for use as a whole
substantially as herein described and illustrated in the drawings.
Dated this 8th day of October 1895.
A. CRAWHALL CHAPMAN,
3 St. Nicholas Buildings, Newcastle-on-Tyne, Patent Agent.