An Apparatus for Demonstrating the Elementary Principles of Geometry.
Year: 1898

page_text: Date of Application, 1st Apr., 1898
Complete Specification Left, 24th Dec., 1893-Accepted, 11th Feb., 1899
PROVISIONAL SPECIFICATION.
An Apparatus for Demonstrating the Elementary Principles of
Geometry.
I, WILLIAM BARRODALE, 302, Hagley Road, Birmingham, Government
Certificated Schoolmaster, do hereby declare the nature of this invention to be as
follows:-
The construction of an apparatus for the purpose of demonstrating the elementary
This
principles of geometry, particularly the nature and value of angles.
apparatus consists of a board, sheet of metal or cardboard having two or more con-
centric circles marked or printed upon it, the circumferences being divided into
degrees or multiples of degrees. There is also marked or printed on the said beard,
metal, or card a horizontal line running through the centre of the circles, and
also a vertical line running through one end of the horizontal line, or two vertical
lines, one at each end of the horizontal line. These lines are divided into equal
divisions, as half or quarter inches. At the centre of the circle a pivot is fixed
about which two or more rods of wood or metal revolve so as to form various
angles. These rods are capable of being lengthened in one or both directions by
means of telescopic joints, or hinges, or by one rods being screwed into another.
By this means, the meaning and nature of angles, their various properties and
their relations when forming triangles, and also some of the uses of geometry may
be practically demonstrated.
1
011 Jarch 1898
WILLIAM BARRODALE
COMPLETE SPECIFICATION.
An Apparatus for Demonstrating the Elementary Principles of
Geometry.
I, WILLIAM BARRODALE, 302, Hagley Road, Birmingham, Government
Certificated Schoolmaster, do hereby declare the nature of this invention and in
what manner the same is to be performed, to be particularly described and ascer-
tained in and by the following statement:-
This apparatus is intended for demonstrating to children the elementary
principles of geometry and for affording illustrations of these principles in a con-
crete form; particularly, for showing the nature and value of angles, their various
It consists of a plate, made of wood, metal,
properties and relations.
on
other suitable substance, which is printed, engraved,
cardboard,
or

page_text: or delineated two or more concentric circles having their circumferences
divided into degrees or other equal divisions. At the centre of the
said circles, I fix an axis or short spindle to which are attached two or more
straight pointers or arms, made of wood or metal, which may be turned about the
said axis in either direction. Two, at least, of these arms are capable of extension
in one or both directions. For this purpose each arm is composed of parts fitted
together by means of telescopic joints, or by one part being screwed into another.
For the purpose of giving practical illustrations of the uses of geometry, as for
example, in finding the height of a distant object, also print, engrave, or delineate
on the plate (1) a horizontal line running through the centre of the said concentric
circles and terminating either beyond the circumference of the largest circle or
otherwise, and (2) a vertical line running through one end of the horizontal line
or two vertical lines one at each end of the horizontal line. I divide the horizontal
line into a number of equal divisions, and along the vertical line I set off a
number of distances, each equal to one of these divisions, measuring from the
point where the vertical line meets the horizontal line.
I will now explain the accompanying drawing, which is a representation of one
form of this apparatus. Three circles, having a common centre G, have their
circumferences divided into parts, each measuring five degrees. GHN and GKL
are two arms or pointers which may be turned about an axis at G, and moved
independently of one another. Each is capable of extension in the manner above
described. In the arm GHN, for example, the part HN slides within the
part GH. The dotted portion represents the part HN drawn out. On the other
side of the axis these arms are shown extended by screwing a straight rod into
each. A third arm GM is shown as a single bar revolving round the axis G.
When the arms GHN, GKL do not extend to the middle circle, the angle formed
by them may be measured by the smallest circle. By extending the arms to the
middle circle, the angle may be again measured, and by further extension, as
shown by the dotted parts, the angle may be a third time measured, in this case
by the outermost circle; and it is seen that although the arms have been con-
siderably lengthened, the angle still remains of the same size, thus affording a
practical illustration of the truth that the size of an angle is independent of the
length of its arms.
When either of the arms GHN, GKL move through a certain distance, as
five degrees, it is seen that the continuation of the arm on the other side of the
centre G moves through the same number of degrees, thus affording a practical
illustration of the equality of vertically opposite angles. The horizontal line AB
is divided into twenty equal divisions on each side of the centre G, and the
divisions on the vertical lines are of the same size as these. The lines AG, AC,
together with the arm GM, form a right-angled triangle, the perpendicular vary-
ing in length according as G M is raised or lowered. This portion of the apparatus
is useful for showing how the height of a distant object may be ascertained. The
arm GM is raised or lowered until the eye looking along its length can just see
the top of the object whose height is to be found. Then the number of divisions
on AC intercepted between the arm and the horizontal line bears the same ratio
to the twenty divisions on AG, as the height of the object bears to the distance
of the object from the centre G.
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
The construction of all or any of the following parts in any apparatus for
illustrating the elementary principles of geometry, namely:-
(1) Two or more straight arms or pointers fixed to one axis or spindle round
which they may be turned in either direction; each arm being made up of parts,
consisting of rods or tubes, or of both rods and tubes, which are fitted together.
by means of telescopic joints or by one part being screwed into another; by which.

page_text: means the said arms may be extended or lengthened in one or both directions, the
said arms being used to represent the arms of an angle.
(2) A plate or board showing two or more concentric circles each divided into
degrees or other equal divisions, and having an axis or spindle fixed at the centre
of the said concentric circles to which are attached arms or pointers used to
represent the arms of an angle.
(3) A plate or board showing a horizontal line divided into a certain number of
equal divisions, having at one end a vertical line marked with divisions, each
equal to one of the divisions on the divided horizontal line, and having fixed
at the other end of the said horizontal line, an axis or spindle to which is attached
a straight arm or pointer, the said lines and arm being used for the purpose above
described.
Dated this Twenty-second day of December 1898.
WILLIAM BARRODALE.