Improvements in Planimeters.
Year: 1894

page_text: Date of Application, 13th July, 1894
Complete Specification Left, 11th Apr., 1895-Accepted, 6th July, 1895
PROVISIONAL SPECIFICATION.
Improvements in Planimeters.
WILLIAM FORD STANLEY of 4 and 5 Great Turnstile, Holborn in the County
of London Optician and ALFRED AMSLER of the same address, Mathematician
do hereby declare the nature of this invention to be as follows :-
:-
The object of our invention is to provide means for measuring the true areas of
shrunk plans. Hitherto planimeters have only been constructed to measure the
area of any plan or diagram according to its size at the time of measuring and as
many plans or the like are mounted the paper in these instances has shrunk and
perhaps unequally, that is to say more or less horizontally compared with vertically
and consequently the true area is not obtained.
Our invention relates to planimeters with adjustable tracing arm, and to carry
our improvements into effect we construct our planimeter as follows:-
Corresponding to any adjustment of the tracing arm, a short portion of a
continuous scale is provided which allows of reading hundredths and sub-divisions
of hundredths of the length of tracing arm.
The percentage of shrinking of a plan in one direction added to the percentage
of shrinking in the direction at right angles to the former direction gives the
number of divisions of the scale engraved on the tracing arm to which the tracing
arm is to be set.
.
The planimeter adjusted in this way measures the true area on the shrunk
diagram.
Theory-Let A denote the area of a square the side of which has the length a
expressed in any unit.
=
Then Aa Suppose now that square to be shrunk so that one side has the
a, and the other side the length a
length a
-
النس
than
ha
Ad h. AL
-
ẞ. The area A¹ of the shrunk
As is well known, the area P of any diagram measured by means of a planimeter
is equal to Pry, r denoting the length of tracing arm and y the reading of the
roller. The area of the same diagram measured by means of the same planimeter
but with the tracing arm adjusted to the reduced length † (1
a + B would be
T

page_text: Various modifications may be made always preserving the essential features of
our invention which is to construct planimeters with a percentage scale for reducing
the length of the tracing arm at the same rate as the plan or diagram to be
measured has shrunk in two directions at right angles to each other.
Dated this 13th day of July 1894.
H. T. TALLACK,
10 Great Turnstile, Holborn, London, W.C., Agent for Applicants.
Improvements in Planimeters.
WILLIAM FORD STANLEY of 4 and 5 Great Turnstile, Holborn, in the County
of London, Optician, and ALFRED AMSLER of the same address, Mathematician,
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 :-
The object of our invention is to provide means for measuring the true areas of
shrunk plans. Hitherto planimeters have only been constructed to measure the
area of any plan or diagram according to its size at the time of measuring and as
many plans or the like are mounted; the paper in these instances has shrunk and
perhaps unequally, that is to say more or less horizontally compared with vertically
and consequently the true area is not obtained.
Our invention relates to planimeters with adjustable tracing arın, and to carry
our improvements into effect we construct our planimeter as follows:-
Corresponding to any adjustment of the tracing arm, a short portion of a
continuous scale is provided which allows of reading hundredths and subdivisions
of hundredths of the length of tracing arm. The percentage of shrinking of a
plan in one direction added to the percentage of shrinking in the direction at right
angles to the former direction gives the number of division of the scale engraved
on the tracing arin to which the tracing arm is to be set. The planimeter adjusted
in this way measures the true area on the shrunk diagram.
Theory. Let A denote the area of a square the side of which has the length a
expressed in any unit. Then A = a².
Suppose now that square to be shrunk so that one side has the length'.a
other side the length a
-
B.
-
a, the

page_text: As is well known the area P of any diagram measured by means of a planimeter
is equal to Pry, r denoting the length of the tracing arm and y the reading of
the roller. The area of the same diagram measured by means of the same
planimeter but with the tracing arm adjusted to the reduced length r
1
-
a t

page_text: of the roller multiplied by any of the number of acres indicated gives the area in
acres at the scale in connection with that number.
If a net of squares is printed on the map and it has shrunk at different rates in
the horizontal and vertical directions, say for example, at such a rate that the
deficiency in one direction is 1-4 and in the other direction 16 then add the two
deficiencies 14+ 16 = 3.0 and adjust the vernier to 3.0 of the graduations on the
top bar.
It will be obvious that our invention is equally applicable for measuring true
areas of plans which may have stretched or enlarged by using the scale and
vernier for elongating the bar of the planimeter in accordance with the same
theory.
Various modifications may be made always preserving the essential features of
our invention, which is to construct planimeters with a percentage scale for
reducing the length of the tracing arm at the same rate as the plan or diagram to
be measured has shrunk or elongating it at the same rate as the plan or diagram
has stretched in two directions at right angles to each other.
Having now particularly described and ascertained the nature of our said
invention and in what manner the same is to be performed we declare that what
we claim is :-
1. In planimeters the combination of a percentage or other additional scale for
the purpose of enabling the operator to set the tracing arm at a reduced or
extended length corresponding with the amount the diagram or plan has shrunk
or enlarged in two directions at right angles to each other, the area of which is
desired to be measured.
2. The improved planimeter substantially as herein described and illustrated in
the accompanying drawing.
Dated this 11th day of April 1895.
H. T. TALLACK,
10, Great Turnstile, Holborn, London, W.C., Agent for Applicants.