An Improvement in Slide Rules.
Year: 1896

page_text: Date of Application, 13th Feb., 1896
Complete Specification Left, 13th Nov., 1896-Accepted, 6th Feb., 1897
An Improvement in Slide Rules.
ROBERT BELSHAW, of No. 7, Sangora Road, St. John's Hill, London, S.W.
Inland Revenue Officer do hereby declare the nature of this invention to be as
follows:-
The invention consists of an improvement in slide rule, which is intended to be
used for ascertaining the quantity of liquor in a partially filled cask, which is
lying horizontally.
The rule can also be used to determine the quantity of liquor which it would be
necessary to add to the cask, before referred to, in order to fill it completely.
The rule is of the usual rectangular shape, and may be constructed of wood, or
of any other suitable substance. It consists of three rectangular pieces, fitted
closely together; the middle piece may be moved freely between the upper and
lower pieces, which are fixed."
I will refer to the upper piece on one face of the rule as a, and to the middle
and lower pieces on the same face of the rule, as b and c respectively. In the
same manner, I will refer to the pieces on the other face of the rule, as d, e, and f,
respectively, d being the upper, e, the middle, and f, the lower piece.
On the lower edge of part a, an ordinary scale of the logarithms of numbers
is graduated; and the same scale is graduated on the upper and lower edges of b,
and also on the upper and lower edges of e. The part c is graduated on its upper
edge, with a scale of percentages of the capacities of the casks.
Part fis also graduated on its upper edge with a scale of percentages of the
capacities of casks, with this difference, that while c indicates percentages which
amount to, or exceed oue per cent., f indicates percentages which are less than
one per cent.
The part d is graduated with a scale on its lower edge, which scale indicates
mean diameters of casks.
1 will now proceed to describe the method of using the rule, and in the
description, I will use the following terms for the purpose of abbreviation.
1. Bung. By this term is meant the internal perpendicular diameter, as taken
at the bung hole of the cask.
2. Wet inches. By this term is meant the perpendicular depth of liquor in
the cask, as taken at the bung hole of it.
3. Vacuity. By this term is meant the perpendicular depth from the surface of
the liquor to the bung hole of the cask.
Length. By this term is meant the internal length of the cask, as taken from
the centre of one end of it, to the centre of the other end.
Content. By this term is meant the full capacity of the cask.
Unity. By this term is meant the line on the extreme right of the fixed part of
the slide rule, to which the slide is set, or adjusted.
If the cask under.consideration should be more than half full, set the length on e
to unity; look for the content also on e, and read above the content, on d, the
mean diameter of the cask.
Set the mean diameter on 6 to unity. Deduct half the difference between the
bung and the mean diameter from the vacuity, and look for the remainder ou b;
under this remainder, read the percentage of empty space in the cask, on c.

page_text: Set this percentage on slide b to unity, look for the content on a, and under it,
on 6 will be found the quantity which if added to the liquor in the cask would
exactly fill it; if this quantity be deducted from the content, the remainder will
express the quantity of liquor in the cask.
If the cask under consideration should be less than half full, the mean diameter
must be obtained as in the previous iustance.
Then set the mean diameter to unity, deduct half the difference between the
bung and the mean diameter, from the wet inches, and look for the remainder on b;
under this remainder, on c, will be found the percentage of liquor in the cask.
Set this percentage to unity, look for the content on a, and under the content,
on b, will be found the number which will express the quantity of liquor in
the cask.
The mean diameter of a cask may be defined as the diameter of a cylinder,
which is equal both in length and capacity to the cask.
I claim as my invention the scale of mean diameters on part d of the rule, and
the scales of percentages on part c and part f. I also claim, as a whole, the
method of using the rule, which I have already described in detail.
Dated this 18th dox of Marab 1806
An Improvement in Slide Rules.
I, ROBERT BELSHAW, late of 7 Sangora Road, St. John's Hill, London, S. W.,
but now of 12 Holland Terrace, Melody Road, London S.W., Inland Revenue
Officer, do hereby declare the nature of this invention and in what manner
the same is to he performed, to be particularly described and ascertained in and
by the following statement:-
The rule is intended to be used for ascertaining the quantity of liquor in a
partially filled cask which is lying horizontally.
The rule is of the usual rectangular shape, consisting of three pieces of wood
enclosed in a metal frame; they are fitted closely together, and the middle piece on
each side, is capable of sliding freely between the other two pieces.
And in order that my said invention may be particularly described and ascertained
reference is hereby made to the accompanying drawings, in which similar letters of
reference indicate corresponding parts.
Fig. 1 is a diagram of one half of one side of the rule, and Fig. 2 is a similar
view of the other half of the same side of the rule; ¹ being a continuation of the
broken off portion at a.
Fig. 3 is a diagram of one half of the reverse side of the rule, and Fig. 4 is a
similar view of the other half of the reverse side of the rule, y' being a continuation
of the broken off portion at y.
Referring to Figs. 1 and 2; on the lower edge of the fixed part a, an ordinary
scale of the logarithms of numbers is graduated; and the same scale is also
graduated on the upper and lower edges of the front face of the slide referred to
as b, as well as on the upper and lower edges of the back face of the slide, referred
to as e. (Figs. 3 and 4).
The fixed part c is graduated on its upper edge with a scale showing percentages
of the capacity of casks; those which amount to, or exceed one per cent. being
indicated upon it. This scale can be used only when the level of the liquor in
the cask falls between the lines M G and N H in the diagram (Fig 5).
Another scale of percentages of capacity is graduated on the upper edge of the

page_text: fixed part f, (Fig. 4) which indicates those which are less than one per cent. This
scale must be used when the level of the liquor is not lower than the line MG, or
higher than the line N H in the diagram (Fig. ), may also be used for all
percentages which are not marked on the scale on that is, for those which which
are less than one per cent.
On the lower edge of the fixed part d, a scale of mean diameters is graduated,
Figs. 3 and 4.
In explaining the principles on which the rule is constructed, and in describing
the method of using it, the following terms will be used:
"Bung" means the internal perpendicular diameter of the cask, as taken as the
bung hole.
>').
"Wet inches" means the perpendicular depth of the liquor in the cask, as taken
under the bung hole.
"Vacuity" means the perpendicular depth from the bung hole to the surface
of the liquor in the cask.
7x7
"Length" means the internal length of the cask, between the ends, and taken
perpendicularly to the ends.
"Content" means the full capacity of the cask.
Jo
"Ullage" means the difference between the content and the actual quantity of
liquor in the cask.
"Mean diameter" of a cask is defined as the diameter of a cylinder the length
and content of which shall be equal to the length and content respectively of
the cask.
"Unity" means the line on the extreme right of the fixed portion of the rule
to which the slide is "set" or adjusted. This term is also intended to apply to
the line on the extreme left of the fixed portion of the rule, which must be used
for the same purpose, when the slide, if set to the line on the right, does not extend
sufficiently far to the left.
The diagram (Fig. 5) represents a cask A BDC, of which the lipe E F is the
"bung," the line EO the "vacuity," and the line OF the "wet inches The
line IK represents the level of the liquor in the cask, and the length of this line
is equal to the "length" of the cask.
21
As the mean diameter is less than the bung, and greater than the diameter of
either end, it is evident that there is a section of the cask, perpendicular to its
axis, between the bung section and either of the ends, the diameter of which is
equal to the mean diameter. Let. G H, (Fig. 5) be the perpendicular diameter of
such a section, which is divided by the level of the liquor into two parts, GL
and LH. Then it is assumed that whatever may be the ratio between the
lines GL and GH, there is a corresponding ratio between the ullage and the
content; and that whatever may be the ratio between the lines L H and GH,
there is a corresponding ratio between the quantity of liquor contained in the
cask and the content. On the foregoing principle, the construction of the
percentage scales is based. The line GL may be found by deducting half
the difference between the bung and the mean diameter from the vacuity; and the
line LH may be found in a similar manner from the wet inches.
The scale of mean diameters depends on the relations existing between the
diameter of a cylinder in inches, its length in inches, and its solidity in imperial
gallons.
In the following description of the method of using the rule, it must therefore
be understood that linear dimensions, such as bung, vacuity, wet inches, and length,
are taken in inches; and that all measures of capacity, such as content, ullage, and
the like, are expressed in imperial gallons.
If the cask to be measured is less than half full, (1) set the length one to unity;
then over the content on e, the mean diameter will be found on d. (2) Set the
mean diameter on 6 to unity; deduct half the difference between the bung and
meau diameter from the wet inches, then under the remainder on b, the percentage
of the content which is filled will be found on c. (3) Set this percentage on b to

page_text: unity; then under the content on a, the quantity of liquor contained in the cask,
will be found on b.
If the cask is more than half full, the ullage can be obtained by the same
method, by substituting the vacuity for the wet inches; and the difference between
the content and the ullage will show the quantity of liquor contained in the
-cask.
The foregoing method can be adopted only when the level of the liquor in the
cask falls between the lines M G and NH in the diagram (Fig. 5).
If the wet inches should not be greater than half the difference between the
bung and the mean diameter, set the whole difference between the bung and the
mean diameter to unity; then under the wet inches on e, the percentage of liquor
in the cask may be found on f. Set this percentage to unity; then under the
content on a, the quantity of liquor contained in the cask will be found on b.
In the same manner, if the vacuity should not be greater than half the difference
between the bung and the mean diameter, the ullage may be found, by using the
vacuity instead of the wet inches in the foregoing method; the difference between
the content and the ullage will show the quantity of liquor contained in the
-cask.
This method necessitates the use of the scale on f; and the cases in which this
scale may be used have already been referred to.
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 improved slide rule, constructed, divided, arranged, and operating
substantially as and for the purpose hereinbefore described, and illustrated by
the drawings.
2. In measuring apparatus for the purpose aforesaid, the application and use
of the mean diameter of a cask, in calculating the quantity of liquor contained in
it, substantially as described.
Dated 12th November 1800
GEO.
DOWNING,
8 Quality Court, London, W.C., Agent.