An Improved Calculating Apparatus.
Year: 1898

page_text: Date of Application, 24th Dea., 1898-Accepted, 2nd Dec., 1899
An Improved Calculating Apparatus.
I, ARPAD HORVATH, of 16, Akaziengasse, Budapest, in the Kingdom of Hungary,
Royal Chief Engineer, 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 :-
This invention relates to a new or improved system or means of calculating and
comprises a system of calculating rods or bars by means of which multiplication and
division may be speedily and almost mechanically effected. The manipulation of
these calculating bars is far simpler than is the case with calculating machines as
hitherto constructed and may be readily mastered.
The invention is illustrated in the accompanying drawings in which :—
Fig. 1 shows the eleven bars constituting the system.
Figs 2 to 6 illustrate various examples of the use of the said bare.
Fig. 7 represents a pattern or method which enables the figures required to be more
readily found.
Fig. 8 is a plan view of the calculating bais, and
Fig. 918 a perspective view of the frame of a pattern.
The bars may be made of wood metal or other suitable material in the form of long
rectangular prisms.
The system of bars consists of an index bar A and of ten or more calculating
bars B. One side of the index bar A is divided into ten squares (as illustrated) the
topmost of which forms what is termed the head whilst each of the remaining nine
squares is marked in order with one of the numerals 1 to 9 running from top to
bottom.
The calculating bars B are divided into ten squares upon each of their four sides.
At the bend of each side is marked one of the numerals from 0 to 9 (see Figs 7 and 8)
whilst in the remaining divisions the product of the head figure and of the numerals
of the series 1 to 9 is marked see Fig 1.
Each of the divisions on squares is divided by means of a diagonal line into two
triangles in which the "unit" of the product 18 arranged below the diagonal and the
above it (Fig 1). In addition to this the triangular spaces below the diagonal
are or may be coloured (red for example) in order to facilitate the finding of the
requied figures.
ten
In the topmost division there are also marked in addition to the head figure
to the right and left and above it smaller figures indicating the head figures of the
remaining sides of the bar.
In order to effect any operation of multiplication those bas are selected the head
numbers of which correspond with one of the factors These bars B are laid beside
the index bar A in the order of the figures of the factor and the figures of the other
factor are found upon the index bai.
Upon a level with the figures so found the squares of the calculating bars form
separate horizontal columns which contain the whole of the elements of the product
sought. These elements are then added together in accordance with the value
represented by their position in order to obtain the required product,

page_text: This operation is illustrated in Fig. 2 by means of two simple examples. In the
upper example (3 x 647) a number consisting of one figure is to be multiplied by
a number containing several figures. The one figure factor (3) is found upon the
index bai and the calculating bars having the head fignres 6, 4 and 7 which consti-
tute the number 047 are laid beside the index bar in the older named.
In the horizontal columns which are on a level with the index figure 3 are to he
found the numbers 18, 12 and 21 forming elements of the required product. If
these elements are added together in a manner corresponding to the value of the
position of the respective head figures in the number 647 (that is to say the "ten "
of 21 to the unit of 12 and the "ten" of 12 to the unit of 18) the product 1941 18
obtained.
The example illustrated in the lower portion of Fig. 2 represents the operation of
multiplying 67 x 647 in which case the elements 36, 24, 42, 42, 28 and 49 are found
in the horizontal columns opposite the index figures 6 and 7. The addition of these
elements in a manner corresponding to then place value is represented in Fig 3;
the figures in question being replaced by identical letters provided with various
indices The number haring the lowest place value is designated by the letter a
which in the present case represents the unit and always stands in the last or outer-
most coloured triangle of the topmost or undermost row. The sum of the numbers
designated by b¹ 2 and 3 gives the tens, the sum of the numbers designated by cl cc3
and e' the hundreds, the sum of the numbers designated by dd² and d³ the thou-
sands and the number designated by the ten thousands,
From this figure the rule may readily be deduced in accordance with which the
elements must be added together; that is to say the numbers which stand in the
oblique ron formed by the diagonals belong one to the other or in other words have
to be added together (as if at ranged in a vertical column) and the place value of these
rows increases from the right to the left hand. This rule is of general application
also in the case where the figures of the first factor do not constitute any connected
portion of the series 1, 2, 3, 4, 5, 6, 7, 8, 9; that is to say when the horizontal
columns of the elements do not stand directly one under the other but when other
columns not connected therewith come between them or when the figures in the
factor form a connected but uniformly falling teries of numerals. In this latter
case however the horizontal columns of the elements must be first arranged in the
order in which the figures in the factor run Concrete examples of such cases are
shown in Figs. 5, 6 aud 8. In Fig. 5 the multiplication of 32 and of 870 by a
number containing three figures is represented. If the horizontal columns of the
elements are arranged in an order corresponding with the factors 32 and 876 that is
to say if the actual order is reversed (23 and 678) and the oblique rows bounded by
the diagonals formed the following results are obtained. In the case of the multiph-
cation by 32 a is the unit, +61 + b tens, c + c² + c² + c³ hundreds, d + d + d²
thousands and ten thousands whilst in the multiplication of 876 by a number con-
taining three figures g is the unit, h+h² + h the tens, i+² + 1² + i³ + i³ the
hundreds, h¹ + h² + k³ + k the thousands, ++ the tens of thousands and
m the hundreds of thousands.
In Fig. 6 the multiplication of 258 by a number containing three figures is repre-
sented. When the horizontal columns opposite the indices 2, 5 and 8 are arranged
directly one under the other the following rows are formed a, b + b¹ + b², c + a² +
c² + c + c, d + d' + d² + d + d', ƒ + ƒ¹ + ƒ² and g.
In Fig. 8 the multiplication of a number containing four figures by 97531 iR
represented that 18 to say by a number in which the figures run in an order opposite
to that of the natural numerical order and thus form a constantly decreasing arith-
metical senes. Assuming the horizontal column arranged in a line with the index 9
to be arranged above and below in accordance with the order of the columns 7, 5, 3
and 1 the figures of the oblique rows are obtained as shown in Fig. 8 by identical
letteung.
Finally by means of Fig 4 the case is represented in which one of the factors
(such for example as 4 4 4) consists of several identical figures; in this instance the

page_text: result is obtained by the addition of three identical columns. In the foregoing case
the following result is obtained (see the horizontal column opposite the index 4)
unit, a+b+ 61 tens, a + b + b² + 0 + c hundreds, b + b² + c + c¹² + d + di
thousands, c+ c² + d + d + + e tens of thousands, d + d² + e + e² + ƒ + ƒ¹
hundreds of thousands, e + e + £ + ƒ¹ + g¹ millions ƒ +/+g' tens of millions
and gl hundreds of millions.
In order to check this rule the multiplication 222 x 836517 may be effected by it.
From the above examples it will be seen that according as the figures of one of
the factors assume a different position upon the index bar (either in reversed
numerical order separated one froin the other by one or more numbers in reversed
numerical order and separated and so forth) the connected numbers must be sought
by various but regular transitions. For the purpose of gaining experience in these
transitions various forms or patterns may be employed which are cut out in different
places in such a manner that only the figures required that is to say the numbers
forming an oblique row are visible. Different patterns of course correspond to
different transitions. A pattern of this kind is represented in Fig. 7 which is suit-
able for effecting the multiplication 97531 × 123456789 which represents tens of
millions. The various groups of numbers are rendered visible by the step-wise dis-
In order to render the manipulation
placement of the pattern in a lateral direction.
of the pattern more easy the bars as shown in Figs. 7 and 8 are laid between two
parallel rails C over which the pattern may be laterally displaced.
In Fig. 8 the rails are arranged in a box D thereby enabling the whole device to
be conveniently carried or stored.
In order to be able to adjust the patterns to the various columns in the direction
of their height also they are arranged in frames in such a manner that they may
be slid up and down. Fig 9 is a perspective view of such a frame. The frame E
itself is capable of being displaced along the rails C whilst the pattern may be dis-
placed in the direction of its height beneath the members El E of the frame. As
already stated however the use of these patterns is soon rendered unnecessary by
practice so much the more that the colouring (red or otherwise) of the triangular spaces
beneath the diagonals enables the oblique rows to be readily located and affords a
resting point for the eye when looking for connected numbers.
The following is an explanation of the method of multiplication of the numbers
635498 and 374285.
When a form or pattern is employed such as is hereinbefore described the rods
are arranged in the order of the second of the above numbers, the pattern is moved
from the right towards the left from rod to rod over the horizontal columns up to
the eight and nine which are the units and ten's ciphers respectively of the first
number.
3- = 0.
The unit's cipher of the product is first obtained
A movement of the pattern a step to the left will give: 4 + 4+ 5
cipher 1 hundred's cipher).
1
A further similar movement of the pattern will give 6 +6 +2 + 4 =
hundred's cipher 1 thousand's cipher).
(9
=
== 1 =
-
=
1).
1
And the next movement will give: -2+1+8 + 7
carried
19. (ten thousand's cipher to be carried
The next movement will give -6 + 3 + 6 +
thousand's cipher to be carried 1).
=
The next movement will give :-4 + 5 + 3 + 3
number to be carried
16 (number to be carried
= 1
1
The next movement will give :-2 +7 +6
carried
H
=
16 (ten million's cipher to be carried
==
13 (3
-
ten's
18 + 1 = 19
= 18 number to be
16+1
= 17 (hundred
15 hundred thousand +
=
=
1).
=
=
15 million number to be
1).
The next and final movement will give :-2 = 2 + number to be carried
= 1 3 = ten million's cipher.
F
The numbers obtained as above indicated are written in order and the product
of 98 × 37-4285 will be found to be 36,679,930.

page_text: - The products for the remaining figures are then obtained in the same marner]
and written one under another thus -
30
-
The products for the remaining figures are then obtained in the same marner |
and written one under another thus
Product of 374200 × 80
Product of 974285 x 5400
Product of 374285 × 030000
1
=
30,079,930
2,021,189,000
235.799.550.000

page_text: In division the rods are arranged to represent the divisor.
To find the quotient of 5628391+562389 the rods are arranged to represent the
number
362389.
5628391562389 = 10.008003.
"
"
"
"
"
1888000+
"
8 × 562,380 = 1687167
200833 (0)÷562389 &c.
Division is effected in the common manuer and only constituent products obtamed
on the new instrument.
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 18
1. A system of calculating bans consisting of an index bar A upon which the
figures 1 to 9 are inscribed in squares in uumerical order in combination and acting
in conjunction with calculating bars B in the squares or divisions of which the
multiples of the numbers marked at the head of the respective bars are marked in
suchwise as to cause those numbers to lie in a horizontal row which form the product
of the index number multiplied by the numbers at the head of the bars upon placing
the calculating bars side by side substantially as and for the purposes hereinbefore
set forth.
2. In the system of calculating bars claimed in Claim 1 dividing the squales or
divisions of the calculating bars B into two triangular parts in which the units are
arranged in the lower tiangular portions (coloured red or otherwise) whilst the tens
mie aranged in the upper triangle for the purpose of facilitating search for the
numbers required substantially as and for the purposes herein before set forth.
3 In the system of calculating bars claimed above the employment of patterns dis-
placeable over the bars which patterns are provided with apertures corresponding with
the irregular arrangement of the numbers to be added together in such a manner
that only the numbers required are visible substantially as and for the purposes here-
inbefore set forth
4. The combination of devices forming new or improved means of calculating con-
structed and arranged to act substantially as and for the purposes hereinbefore
described and illustrated in the drawings hereunto annexed.
Dated that day of December 1900
A. HORVATH,
Per W. II. Beck,'
Agent.