NOVIDIONAL DI DUIFIC,
Year: 1890

page_text: Date of Application, 22nd Apr., 1890
Complete Specification Left, 4th June, 1890-Accepted, 27th Sept., 1890
NOVIDIONAL DI DUIFICATION,
Improvements in Planimeters.
1, JOHN GOODMAN, of Yorkshire College, Leeds, in the County of York,
Professor of Civil & Mechanical Engineering, do hereby declare the nature of
this invention to be as follows:-
My invention has reference to improvements in the instrument known as the
Stang Planimeter" for measuring areas, computing weights &c. As is well known
such an instrument comprises a beam, a point to trace round the boundary of the
area to be measured, and a hatchet to record the area of the figure traced by the
point.
With such an instrument as heretofore made it has been necessary to measure the
distance between two dents or marks made by the hatchet, to multiply that distance
by the length of the instrument, and afterwards to correct the result by a somewhat
tedious calculation which has rendered the instrument practically useless to any but
a mathematician, and even then only applicable for comparatively small areas owing
to the liability to error.
Now according to my invention an instrument of similar construction, but which
I in some cases make with a longitudinal or transverse recording wheel, is provided
with a curved or straight scale such that no calculation whatever is needed and the
instrument is thus also adapted to be used for areas of much greater dimensions than
the instrument as heretofore made.
The method of using my improved instrument when constructed with a hatchet is
as follows:-
A point is chosen at or near the centre of gravity of the area to be measured
(which point I will call the central point) and a line I will call the radial line is drawn
from the said central point to the boundary, the instrument is held vertically with its
point and the hatchet both touching the paper, the point of the instrument being
placed at the before mentioned central point and the hatchet pressed into the paper to
form a dent. The hatchet is then released and the point of the instrument caused to
follow the radial line and the boundary line, ultimately returning to the central point
of the area via the radial line. The hatchet is again pressed into the paper to make
a dent-the space between the two dents is then measured by the scale on the
back of the instrument, which at once shows the number of square inches in the
If the central point does not coincide with the centre of gravity, the process
must be repeated with the instrument turned round through 180°, and the mean of
the two readings taken.
area.
By simple methods the moment of inertia, radius of gyration-modulus of section
with regard to bending or twisting, equations to curves, weights of bodies &c., can be
computed by the instrument.
My improved instrument may be made of ivory, bone or composition or of wire,
sheet-cast- or forged-metal, of any convenient shape or length.
In some cases I make it with one of the legs at right angles to the beam to serve
as a square for drawing lines at right angles to each other.
Dated this 22nd day of April 1890.
W. LLOYD WISE,
Per. F. J. Brougham,
46, Lincoln's Inn Fields, London, W.C., Agent for the Applicant.,

page_text: COMPLETE SPECIFICATION.
Improvements in Planimeters.
I, JOHN GOODMAN, of Yorkshire College, Leeds, in the County of York, Professor
of Civil and Mechanical Engineering, 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 has reference to improvements in the instrument known as the
"Stang Planimeter "for measuring areas, computing weights &c. As is well known
such an instrument comprises a beam, a point to trace round the boundary of the
area to be measured, and a hatchet to record the area of the figure traced by the
point.
With such an instrument as heretofore made it has been necessary to measure the
distance between two dents or marks made by the hatchet, to multiply that distance
by the length of the instrument, and afterwards to correct the result by a somewhat
tedious calculation which has rendered the instrument practically useless to any but
a mathematician, and even then only applicable for comparatively small areas owing
to the liability to error.
Now according to my invention an instrument of similar construction, but which I
in some cases make with a longitudinal or transverse recording wheel, is provided
with a curved or straight scale such that no calculation whatever is needed and the
instrument is thus also adapted to be used for areas of much greater dimensions than
the instrument as heretofore made.
Referring to the accompanying sheet of drawings
Fig. 1 is a side elevation, and
Figs. 2 and 3 are two end elevations of a planimeter according to this invention.
Fig. 4 is a side elevation, and
Fig. 5 an end elevation of a modified form of planimeter with longitudinal
recording wheel in place of the hatchet shewn in Fig. 1.
Fig. 6 represents an irregular plane area, and is given to aid the explanation of
the method of using the instrument.
In Figs. 1 to 3, A is the tracing point, B the hatchet, C the beam on which is
engraved the scale D; or this scale may be engraved on a plate that is secured to the
beam. E, Figs. 4 and 5 is a recording wheel which replaces the hatchet. The
beam C may if desired be provided with any ordinary inch scale as shewn at F.
The method of using my improved instrument when constructed with a hatchet is
as follows:-
A point C is chosen at or near the centre of gravity of the area to be measured
(Fig. 6 for example) (which point I will call the central point) and a line C¹ D' which
I will call the radial line is drawn from the central point to the boundary, the
instrument is held vertically or nearly so with its point and the hatchet both touching
the paper, the point of the instrument being placed at the- before mentioned central
point and the hatchet pressed into the paper at any convenient place to form a dent
at C. The hatchet then released and the point of the instrument caused to traverse
the radial line C D' and the boundary line D E F¹ D₁ in the order of these letters,
ultimately returning to the central point of the area via the radial line. The hatchet
is again pressed into the paper to make a dent at C³, that is to say at the point at
which it comes to rest after the point of the instrument has traversed the radial line
and boundary line of the area to be measured. The area of the irregular figure in
square inches is equal to 2 where is equal to the length in inches of the beam
from the tracing point A to the hatchet point B, and O is the angle CC C
estimated in circular measure. If therefore the length r of the beam be
12 inches, the radius of the curved scale thereon be 12 inches
7, and each
division of the scale be made equal to one degree, then each division will correspond
144 X 3.1416
to
140
=
-
2.5 square inches approximately, and by measuring the distance

page_text: between the two dents at C2 C3 by the scale D, the number of square inches in the
area measured can be at once read off. As will be obvious the scale may be so
divided that each division equals one square inch or a fraction of a square inch, and
instead of using a curved scale which is preferred, a straight one may be used in
which the divisions have been projected from a curved scale obtained as described,
but the divisions of such a scale will not be equal. If the central point does not
coincide with the centre of gravity, the process must be repeated with the instrument
turned round through 180°, and the mean of the two readings taken. To obtain
great accuracy the area can be measured several times in the manner described and
the mean of the areas found taken.
A planimeter according to my invention can be used to obtain the areas of plane
irregular figures for use in computing the moments of inertia, radii of gyration,
modulus of sections with regard to bending or twisting, equations to curves, weights
of bodies &c.
My improved instrument may be made of ivory, bone or composition or of wire,
sheet- cast- or forged-metal, of any convenient shape or length.
In some cases I make it with one of the legs as A at right angles to the beam C
as shewn to serve as a square for drawing lines at right angles to each other.
Having now particularly described and ascertained the nature of the said inven-
tion and in what manner the same is to be performed I declare that what 1
claim is :-
++
1. The combination with a planimeter of the kind herein described, of a scale so
divided that the area of a figure measured in the manner described by the plani-
meter, can be read off directly by the scale without further calculation.
2. My improved planimeter and scale combined, as described with reference to and
shown in Figs. 1 to 3 inclusive or modified. according to Figs. 4 and 5 of the
drawings annexed.
Data
W. Lloyd Wise,
JOHN GOODMAN.
46, Lincoln's Inn Fields, London, W.C., Agent for the Applicant.