Apparatus for use in Teaching Arithmetic.
Year: 1890

page_text: Date of Application, 11th Apr., 1890-Accepted, 17th May, 1890
COMPLETE SPECIFICATION:
Apparatus for use in Teaching Arithmetic.
I, GOTTFRIED GEORG BETTENHAUSER, resident of 1 Kleine Sandkaul Street of;
Cologne on the Rhine, in the Province of the Rhine, in the German Empire,-
Merchant, do hereby declare the nature of this invention and in what manner the
same is to be performed, to be particularly described and ascertained is and by the.
following statement :-
My invention serves for calculating with numbers of two or more degrees, it does!
not serve for the first instruction in arithmetic with the cardinal numbers 1 to 10.
The counting board is longitudinally devided into: several columns, alternatively
filled with the numbers 1, 10, 100, and is provided with slides moveable about
these columns, in such a manner, that the respective positions of the several slides
answer to respective numbers and that the descending of the slides represents an
addition, while the rising represents a subtraction of numbers.
This counting-board is illustrated in the accompanying drawing, in which similar
letters denote similar parts throughout the different figures:
Fig. 1 is an elevation of the counting board, and
Fig. 2 is a vertical section from the left to the right trough the line A B of
Fig. 1.
The board B, surrounded by the frame A, is longitudinally divided into seven.
columns, about which the slides S. S1 S2 can move down and up between the
guiding bars m or-the first and the last of them-between a guiding bar, m and
a part of the frame. The vertical columns are laterally crossed by ten lines in
such a manner, that each column is provided with ten squares. The lower part of
the board is covered with a slate supplied with a network of vertical and lateral
lines. The longitudinal columns of the upper part are filled with the numbers 1,
10 and 100. The first, fourth and seventh row-counted from the right to the
left show the numbers 1, the second and fifth the number 10, and the third and
sixth show the number 100, all squares of the same column being filled with the
same number. The upper ends of the slides S S¹ S² . . . carry the buttons b,.
seized by the child, which is employing the counting-board, when moving the slides
upwards and downwards. Immediately below the buttons of the slides S, S1, S2, S³
as well as at the heads of the corresponding columns of the slate, there are placed the
denominations: million, thousand, thousand, thousand.
As above mentioned, the counting board serves for adding and subtracting numbers
of two or more degrees.
The first column, that is to say the row covered by the slide So, represents the
units, the following column represents the tens etc. unto the seventh column repre-
senting the millions.
In the first position which is always to be arranged before the beginning of the
calculation, all slides are completely drawn upwards, thus covering all numbers of
the different columns. This position of the slides answers to the number 0. Each
other position represents a certain number, which can be gotten by adding the
uncovered numbers of the different rows, by writing the sums into the corresponding
squares of the slate and by reading these figures from the left to the right. That
position shown in the drawing Fig. 1, represents the number 10549710. Adding of
numbers is answered to by drawing down the slides and subtracting by moving them.
upwards.
:

page_text: In order to explain more clearly, how to employ my counting-board, T relate to
the following instances:
Problem 60+.30.
The child draws down the second slide (counted from the right to the left) until
six squares are uncovered. This position of the slide represents the first number 60, 5
as slide has six times passed the number 10. Now the child continues with drawing
down the same slide until three further squares are uncovered. After having counted
the squares passed by the slide on its descending, the child will write the gotten
number 9 at the head of the second vertical column of the slate (also counted from
the right to the left). As the first slide has remained in its primar position, all squares
of the first row are covered and the child will therefore write the number 0 at the
head of the first vertical column of the slate. Thus the number 90 will appear as the.
sum of 60 and 30.
Problem 53 + 26:
By drawing down the second and the first slide-the former 5 squares and the 2
latter 2 squares the number 53 will appear, and by removing upwards the same
slides the second 2 squares and the first 6 squares-the number 26 is added and the
sum 79 will result.
Problem 87
-
27:
After having represented the number 87 by drawing down the second and the first 2
slide, both slides are to be removed upwards as far as the number 27 requires.
The problems 200 + 300 and 800-300 are solved by drawing the third slide down
and up, the problems 610 + 50, 730 20 by moving the second and the third
slide, the problems 423 + 30, 768 601 by moving the first, second and third
slide etc.
The above mentioned problems are called problems without transformation. The
problems with transformation are a little more difficult.
For instance: 360 + 40:
The third and the second slide are to be applied. When moving down the second
slide the child will uncover all ten squares of the second column, and now it must be a
very exactly explained to the child that in the second column 10 x 10 = 100 makes
up with the 300 in the third column 400 together.
Another problem with transformation : 500
70.
The third slide show 500. The subtracting of 70 does not go, therefore the child'
must exchange 1 hundred of the third column by moving upwards the third slide
about 1 square and by uncovering all squares of the second column. Now the child
will remove the second slide upwards about 7 squares and thus get'the number 430.
Of course the counting-board can be supplied with more than seven columns in
such a manner that numbers of more than seven degrees can be indicated by the
position of the slides, but the counting board with seven columns will be sufficient for
the use in schools.
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 :
A counting board, longitudinally devided into several columns, alternatively filled'

page_text: with the numbers 1, 10, 100, and provided with slides moveable about these columns,
in such a manner,
that the respective positions of the several slides answer to respective
numbers and that the descending of the slides represents an addition, while the rising
represents a subtraction of numbers, for the purpose as described.
Dated this 10th day of April 1890
RAYNER & CASSELL,
37, Chancery Lane, London, Agents for the Applicant.