Improvements in and connected with Lineal Measures.
Year: 1892

page_text: Date of Application, 21st Sept., 1892
Complete Specification Left, 10th May, 1893-Accepted, 21st Sept., 1893
PROVISIONAL SPECIFICATION.
Improvements in and connected with Lineal Measures.
CHARLES MANNERS, Junior, F.I.C. 10 Moss Street, Paisley, North Britain,
Analytical and Consulting Chemist, do hereby declare the nature of this invention
to be as follows:-
The application or adhibition of numbers (so called index numbers) to all kinds
of lineal measuring apparatus such as rules, tapes, chains, etc., to facilitate the
computation of square and cubical quantities, when such index numbers are
employed in conjunction with a table or tables of index numbers, and their corre-
sponding quantities.
The index numbers, such as shall be employed, shall be printed or otherwise
marked upon the measuring line, and in the case of measuring lines already
graduated and printed upon, such index numbers shall be printed or otherwise
marked upon the back or such other portion of such measuring lines as shall be
found convenient. The distances at which such index numbers shall be printed
apart from one another shall be in accordance with the index numbers employed.
All dimensions, as will be evident, will be denoted by such index numbers,
instead of by those usually employed, namely, feet and inches.
If it be required, say, to find the number of cubic yards of digging work done,
and the index numbers corresponding to the length, breadth, and depth are taken,
the three right band figures of the sum of the index numbers will be found, on
reference to the tables, to represent the cubical dimensions of the digging work
done.
1
CHAS. MANNERS, JR.
COMPLETE SPECIFICATION.
Improvements in and connected with Lineal Measures.
CHARLES MANNERS, Junior, F.I.C. 10, Moss Street, Paisley, N.B. Analytical
and Consulting Chemist, do hereby declare the nature of my invention for
IMPROVEMENTS IN AND CONNECTED WITH LINEAL MEASURES and in what
manner the same is to be performed, to be particularly described and ascer-
tained in and by the following statement :-
The object of the invention is to facilitate the computation of square and
cubical quantities by the adhibition of numbers (hereinafter described as index
numbers) to all kinds of lineal measuring apparatus such as rules, tapes, chains etc.,
and to be used in conjunction with tables such as shall have quantities corresponding
to such index numbers.
The index numbers employed shall be printed or otherwise adhibited upon the
back or such other portion of the measuring apparatus as shall be found convenient,
and at such distances from one another as shall be found most useful.
The unit of measurement adopted is the inch so that each inch on the measuring
line shall have an index number corresponding to it. (See illustration.)
In computing cubic capacities three dimensions are taken, which dimensions if
multiplied together give a product, the contents, in terms of the standard employed.
If the dimensions be taken in feet the product is cubic feet; if in metres the
product is cubic metres. But, if measurements be taken in feet and the contents
require to be expressed in cubic yards, then the product in feet requires to be
divided by 27. It is found that this standard of measure, the cubic yard, is much

page_text: employed in the expression of large works. The index figures employed upon the
measuring apparatus are such that the sum of the index numbers corresponding to
the three dimensions will be equivalent to the cubic contents of the body in cubic
yards.
The index numbers employed upon the tape are found in the following
way Let a, b, and c be the three dimensions of a body in inches the cubic
contents of which require to be expressed in cubic yards. The equation may be
represented thus..
And since the denominator in each is constant, the dimensions a, b, and c, require
to be modified by that figure, that is, divided by 3√✓16656. This is accomplished
by finding the common logarithm of each dimension, and from each such logarithm
subtracting the common logarithm of the denominator 346656. The equation now
becomes log. a
log. 346656 + log. — log. 3✓ 16656 + log. c -
-
log. .
-
-
log. 346656
Son fan
(leaving out in every case the characteristic), and that from each is subtracted the
common logarithm of 346656 viz. 22298 then we shall have three distinct numbers
the sum of which will be the common logarithm for a number which will express
the number of cubic yards in the body measured.
The index number for each inch on the measuring line will therefore be the
common logarithm for that number, minus the common logarithm for 346656, at
all times leaving out of account the characteristic. The index number for the first
inch on the measuring line will therefore be 00000 minus 22298 = 77702; for the
second inch 30103 minus 22298 = 07805 and so on for every other inch reckoning
from the first. (See illustration.)
It will be found convenient to employ only three figures at the most as an index
number so that for the first inch the index number will be 777 and for the
second 078 or simply 78. The decimal point is not employed there being no
characteristic preceding. (See illustration.)
The use of the contrivance will be best described by an example.
The cubical measurement in yards is required say of a piece of digging work
measuring 15' 2" x 10' 6" x 4' 9". The index numbers on the measuring line
corresponding to these dimensions are read off' instead of the measurements in feet
and inches, and the sum found thus :-

page_text: It often happens that the cubical contents require to be expressed in terms other
than cubic yards, such, for example, as in the measurement of ships' cargoes
where 40 cubic feet of space are allowed for each ton. Now the tables of cubic
yards can be used to express tons if to the three dimensions be added 830. For
the original equation upon which the tape was constructed differs from this one
Therefore by this difference between the logarithms of these numbers viz. 82933
or shortly 830 must the sum of the three dimensions be modified in order that the
table of cubic yards express tons.
Say for example it is required to find how many tons in a space measuring
20' x 12' x 16'. The index numbers for these dimensions are respectively 157, 935,
and 60, and if to these is added 830 the sum 1,982 is obtained which will be the
index number of the number of tons viz. 96 tons.
It will, however, prove in many cases more convenient to supply tables from
which the contents can be found by the addition simply of the index numbers taken
from the tape. In this particular case each index number in the tables increased
by 170 will be equivalent to the same number of tons as it was previously equal to
cubic yards, because the common logarithm of any given number of cubic yards
will differ from the common logarithm of the same number of tons as the common
logarithm of 46656 differs from the common logarithm of 69120 that is 17. Thus
or snortty 170.
Such other modifications can be carried out on similar principles if necessary.
In using the measuring line for square measurement only two dimensions are
taken. In order that the tables of cubic yards may express square yards it is
necessary to supply a constant increment viz. 33 which is added to the sum of
the index numbers of the two dimensions. For we have the equation
2
b
1
ah
Therefore each index number on the line should be increased for such measure-
ments by 16668. But in the equation there are two dimensions, therefore to the
sum of the index numbers of the two dimensions twice 16668 or 33336 or shortly
334 will require to be added in order that the tables may express square yards.

page_text: a
b
ab
12 12 144
and the logarithm of the square root of 144 differs from the log. of the cube root
of 46656 by 14380: But we have here two dimensions also therefore twice 14380
that is 28760 or roughly 288 will require to be added to the sum of the index
numbers of the two dimensions in order that the tables may express square feet.
For example Required the superficial area of a floor measuring 9' x 8' in square
yards. The index numbers for such measurements are 810 and 759 and to the
sum of these is added 334 giving the index number 903: = 8 square yards. 1
Again: Required the area of the same in square feet. To the sum of the index
numbers is added 288 which gives the index number 857 = 72 square feet.
was formerly expressed as cubic yards is now expressed as square yards or feet.
It is evident that this process of computation is capable of being applied to
almost any standard of measurement, and that it lends itself easily to all such 1
modifications.
What
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 :
All kinds of lineal measuring apparatus on which are imprinted or otherwise
adhibited such index numbers as have been described within, with or without such
other units of length such as metres, feet, or any multiple or sub-multiple of such
units imprinted or adhibited thereon, for the purposes of facilitating the computation
of square and cubical quantities such as have been herein described, and for all
such other similar purposes as have not been specially mentioned, employing in 2
conjunction with such measuring apparatus such tables as shall have index numbers
with corresponding quantities, it being of no importance how, or upon what part
of the measuring apparatus such index numbers are adhibited.
Dated this 9th day of May 1893.
CHAS, MANNERS, JR.