Improvements in Calculating Machines.
Year: 1886

page_text: Improvements in Calculating Machines.
I, EDWARD SELLING of Würzburg, 11 Siebold Street, in the Kingdom of Bavaria,
Professor of Mathematics 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 :-
Two problems are to be resolved by him who will construct a calculating machine.
The first consists in forming the partial products, that is the products of one digit of
the multiplicand with one digit of the multiplier, the second consists in the carrying
of the tens. Both problems are resolved by me in a completely new manner.
I exhibit the partial products by the motions of points of articulation of a pantograph.
If the first of 10 such points lying in one straight line is fixed and the second makes
the way to along that straight line, the 3rd, 4th, ... 10th make the ways 2 w,
3 1, 9w. Thus, if n is a figure o the multiplicand, and wa figure of the
multiplier, the way made by tho (n + 1)th point represents the partial product n w.
It is not necessary for my machine, but very useful to miss the use of the digits
6, 7, 8, 9, and to restrict oneself to the use of the digits 1 to 5, which may be
employed with the opposite signs. I denote -1, -2, -3, -4, -5 by I, 2, 3, 4, 5
or by the inverted figures I, &, E, F, G, which I also call figures, specially negativo
figures. Thus I use 21 or 21 instead of 19, the undeviginti or XIX in latin.
The whole machine is represented by the view from above in Fig. I and by the
profile from the left hand in Fig. VII. Behind other bars two systems of 11 oblique
parallel bars are visible in the right half part of Fig. I. They are articulated in all
points where they cross one another, namely in the points M., Ma, M, Ma, MT, MT,
M₁, M., M, and two analogous points, not visible, which I call M. and M.. These
bars form a pantograph. The length of the bars and the number of the points of
articulation are much greater than it would be absolutely necessary, in order to
increase the surety of the movements. A second pantograph, congruent to the first,
is visible in the left half part of Fig. I. The points N, N
•
M, N,
N, and the
points N. and N, not visible, are connected with the analogous points My,
MX, M, and the points M, and M. by the bars Mr N., MN,
and the bars M, N, and M. N., not visible. The points M. and N. are fixed on the
plate P, P,
P, the points M, and N are moved simultaneously along the
lines M M and No N by means of a frame, the parts Q₁, Q, of which slide
along the grooves R₁, R., R, engraved in the plate P₁ P₁
The motion of
the frame is effected by the hand by means of the ring V, or V, serving as handle,
and is measured and regulated by the scale U₁ or U,. The appertaining pointers lie
5
5
8°

page_text: Mε, the points N5
M, N, are then
in Fig. I at 2. The ways made by the points M5, M4,
NX,
N, and all the points of the bars M, N5, MN,
proportional to the amount of the sliding motion of the frame Q₁ Q, Q, and pro-
portional, also with respect to the signs, to the appertaining indices 5, 4,
1'
19
.
5.
1
The 12 racks K₁ K₁₁, K, K₁₂, K₁ K, visible in Fig. I, shall correspond
to 12 places of a multiplicand, for which the number 152310412345 is adopted in
Fig. I. Corresponding to the first figure from the right, 5, the rack K, K₁, is
connected by the nail L₁, not visible in Fig. I, with the bar M, N, also not visible.
Corresponding to the second figure, 4, the rack K, K₁, is connected by the nail L,,
visible in Fig. I, with the bar M4 N4, and so forth. Thus the longitudinal motions
of the racks corresponding to the several places of the multiplicand are proportional
to the figures occupying those places and to the common multiplier, by which the
sliding motion of the frame Q₁ Q, Q₁ is determinated. The racks K, K₁₁, K,
K¹ K₁, K, communicate their motions to the toothed wheels H., H., .
in Fig. I, and the turning motions of these wheels produce proportional turning
motions of the respective graduated wheels A,, A,, A18 (Fig. 1), each of which
contains 40 equidistant marks of division, designated by the figures 0, 1, ... 9
repeated four times. Thus the respective partial products are added to the former
readings of these wheels, if it can be arranged that 1 is added to the readings of the
wheel following on the left side as often as one wheel passes from 9 to 0, and 1 is
subtracted on that wheel as often as this wheel passes from 0 to 9. The solution of
this problem of carrying the tens will be explained after some other necessary
romarks.
12
H
The plate P, P... P with the described pantographs, bars and racks can be
turned a little round a geometrical axis parallel to the axis B B and represented in
Fig. VII by the point in the pitching line of the racks K K. For this purpose in
the place of pivots or journals, which would hinder the movements of the pantographs,
segments of tubes, W, (Fig. 1) and W, (Fig. I and VII) are fastened to the plate P₁
P. P. They turn in slots of bearings, not shown in Fig. I and VII, by means
of one of two rings serving as handles near M, and No, the latter of which is shown
in Fig. VII, and which are fastened to the bars partly visible in Fig. I drawing over
the pantographs and tying together the pins at M, and N, with the knobs X, X₁₁ and
XX, fastened on the plate P, P₂ P. By this means the racks K K' can be
brought out of gear with the wheels H. Then the frame Q, Q, Q, can be slidden,
till the pointers of the scales U, U, come to 0 and the pantographs, bars and racks
come into the corresponding original places, while the wheels H and A are not
moved. If the multiplier is a negative figure, for example 2, the pointers must be
brought from 0 to 2 on the scales by sliding the frame while the racks are not in
gear, and must be brought back to 0 while the racks are in gear with the wheels H.
.
For the purpose of employing the next figure of the multiplier, f. i. on the right,
the racks are brought out of gear by turning the plate, then the plate is slidden so far
towards the right, by sliding the axles W₁, W, in their slots, that each rack can
*come into gear with the next of the wheels H, for instance K, K¹, with H₁, K, K',
with H, and so forth.
1
In all calculating machines constructed hitherto the equalness of the resistance is
hindered not only by the discontinuous manner of exhibiting the partial products, but
also by the carriage of the tens effected in a discontinuous manner, except in simple
adding machines, which do not permit the simultaneous addition of two figures. In
my machine also the carriage is made continuous, as the hour-hand of a watch passes
continuously from one hour-mark to the next while the minute-hand runs through
60 minutes. Accordingly the wire D D (Fig. 1), serving as index to all the graduated
wheels, generally does not coincide with marks of division of the graduated wheels A,
but lies between two consecutive marks according to the quantity represented by the
wheel following on the right. Thus the readings of the 15 wheels A in Fig. I give
the number 001046207753300.
The manner by which for instance A, is moved partly by H,, partly by A is

page_text: 2入
λ
Бр
21
represented by Fig. II, being a horizontal section of these wheels along the axis B B
(Fig. 1), common to all the wheels A and H, and by Fig. III, being a vertical
section along the line C C of Fig. II. The wheel H, has also internal teeth and the
wheel A, is connected rigidly with a coaxial toothed wheel G, by means of a coaxial
smooth cylinder serving also as axle for the wheel H,. A toothed wheel F, is in gear
at opposite points with the internal teeth of H, and with G,, the axle E, of F, is
fastened to A,. If G, rests and H, turns, F, rolls upon G,, and the axle E, effects a
turning motion of A, amounting 1% of the turning motion of H,, because the
primitive radii of G,, of F, and of the interior gears of H, are together as are 1:4:9,
viz. the primitive radius of G, being designated by p, a little linear motion A of E,
effects a turning motion of A, amounting and is effected by a turning motion of H,
amounting
If otherwise H, rests and G, turns, a small linear motion A of E, is
effected by a turning motion of G, amounting and being therefore to the corre-
sponding amount of the turning motion of A, as 10 is to 1. If H, and G, turn
simultaneously, the two described turning motions of A, are added. On account of
equilibrium and of avoiding an error of eccentricity a second wheel F¹, with the
axle E, (Fig. II and III) is also used. It is the same with each of the 15 systems of
wheels A, F, F, G, H. Only G, is immovable and A₁, gives a signal by the
spring II (Fig. 1) as often as one of its zeros passes by the wire D D.
Instead of the wheel F, any other Kinematic element capable of a compound
motion can be substituted. For example F, can be an analogous wheel being in gear
at opposite points with G, and with internal teeth applied at A,, or F, can be a solid
system of two coaxial wheels, one of which is in gear with G, the other with another
cog-wheel coaxial and fastened to A,. The axle of F, is fixed in these two
cases to H,.
.
Ρ
The essential feature of my invention is the inserton of a Kinematic element
capable of a compound motion to the purpose of receiving the two distinct motions
of G, (that is of A₁) and of H, (that is of a bar M N connected with H, by a
rack K K or a kinematic substitution of such a rack). All solid or flexible elements,
wheels, racks, screws, levers, chains, cords etc. can be substituted, viz. also straight
translations can be substituted for the turning motions, but then a convenient change
between positive and negative partial products must take place or a restitution
must take place sometimes. The requested patent would be quite illusory unless all
such substitutions are included.
The number of the systems of wheels A, H can be made as great as one likes,
without any essential change. In Fig. I the 15 systems of wheels A, H are accom-
panied by 12 quite similar systems of wheels k, l. If their distance from the
wheels A, H were sufficiently great, and if the appertaining racks, analogous to the
racks K K' were present, the wheels could represent an aggregate of products
having the same multipliers as the products formed by the A, but having other
arbitrary multiplicands, which would be often very useful. In Fig. I only one rack m
is adopted for the wheels and is fixed to the bar M, N, produced for this purpose.
Accordingly the multiplicand is 1, and the wheels will represent the sum of the
multipliers, or one multiplier, if only one product has been formed, or the quotient, if
the multiplicand is a divisor and the aggregate of products is the rest.
All wheels H and I must be held when they are not in gear with any of the
racks K K', or with m, while the other wheels H, are in gear.
For this purpose a
special sort of racks like O₁, 0, 0, 0, 0, is adapted, which have only one tooth and
are fixed to the bar M, No. A series of such racks can bo joined, so that only two of
them, like O, and O, must be fixed on M, No, and the place of the others can be
supplied by a rake, which can neither be visible in Fig. I nor in Fig. VII. A similar
rake a a¹ with teeth like b, b₁,
(Fig. I and VII) serves to hold the wheels /
4
Po
at the left of the rack m after all lateral displacements of the plate P, P, .
and is fixed on the right side to the bar NX, X', or n, and on the left side to
a knob a' fastened to an arm projecting from the plate P, P,
Po

page_text: The
For the utmost surety the teeth o₁, ° 01 and P.
bar qq (Fig. 1 and VII) and stop the wheels H₁,
Piz are fixed to a
H₂, H₁, and
4₁, while
by turning the plate P, P... P, all the racks K K', m, O and the rakes described
just now are brought out of gear. The bar qy is lifted and let down by the bars r₁
and r, (Fig. 1 and VII) fastened to the bars X, M, X', and N, X, X, or n.
bars 1 and slide along the bar qq during the lateral displacements of the
plate P, P P, and the bar 99 is prevented from moving sidewise by two arms
shown in fig. I and partly in Fig. VII and fastened to the immovable supports not
shown. Each of the teeth o₁, 027. 01, can also be lifted separately to the purpose
of setting a dividend immediately in the wheels A instead of having it set in by the
racks. Between the position in which the racks are in gear, and the position in
which the teeth o and p stop the wheels, is a very small interval, in which the plate
must be held while the wheels A and K are brought back to zero in a manner
described below.
•
The multiplier or quotient is also represented by the wheels h₁, h₂, h₁, (Fig. 1),
that consist of graduated wheels, the 44 marks of division of which are designataxd
by 5, 4, 3, 2, 1, 0, 1, 7, E, F, repeated four times, and of cog-wheels solid and
coaxial with them. After each displacement of the plate P, P, . P one of these
cog-wheels can come into gear with a rack fastened to an extraordinary point of
articulation i (Fig. I) of one of the two pantographs. For the purpose of perspicuity
the point is chosen in Fig. I so that its motion is of that of M₁, but it is better to
choose it so that its motion is of that of M₁, as is assumed in Fig. VII. Then the
radius of the toothed parts of the wheels h is to be made greater, but it must not be
so great that the cog-wheels are touched by the racks K K' or O after the lateral
displacements. Also for the wheels & the wire DD serves as index.
There are two reasons why all the wheels A, k and h have the same axle and the
same radius, viz. thus at the same time and by the same manipulation their readings
can be copied and brought back to zero.
A drum of India-rubber covered with paper ccc, shown only in Fig. III and VII,
can be pressed by its axle d upon all these wheels. The line of contact e e, serving as
index and distant 90° from the wire D D, is marked on the paper by marks at the
fixed supports, not shown, of the axlo B B. The impression can be made f. e. coloured
by a paper laid between the drum and the first sheet of paper and giving colour to the
same upon pressure.
The wheels A, k and h can be brought back to zero by the rake fif
which can
be slidden a little parallel to the axle B B and can be turned round this axle. Thus
each of its teeth (Fig. I) could be brought in contact with one of the 4 small pins,
visible partly in Fig. I, at the right side and near the edge of each of these wheels,
and could drive then along. In reality two such rakes are applied, each of which
must be turned by 45°. The first, fif,, is adopted in Fig. I in the position when the
wheels have been brought back to zero and the arms connecting it with the
axle BB lie horizontally, the second is adopted in the position before the wheels aro
brought back to zero, and is therefore not visible except its right end and tho
arms ₁ connecting it with the axle B B. The sliding motion of the rakes,
necessary before coming into action, can also be radial instead of being parallel
to the axle B B. The parts of the rakes destined for the wheels h can also be slidden
separately.
The lower ends of the pivots M to MT, M, to M, and N to NT, N, to N, slide in
the grooves S, S and S, S₂, not absolutely necessary.
The friction can be
diminished by small wheels visible in Fig. VII. The bars T, T, and T', T', (Fig I
and VII), also not necessary, further assure the congruity of the motions of the
two pantographs. The bar YY (Fig. 1 and VII) is fixed on the foundation not
shown and serves to guarantee the correct amount of the lateral displacements of the
plate P₁ P P. The ledges Z₁, Z, (Fig. I and VII) fastened to this plate catch
in notches made in the lower side of the bar Y Y. There are steps in the notches for
the mentioned interval in which neither the racks nor the teeth o, p stop the wheels.
The guides wo, to¹ for the racks are fixed at the plate P₁ P, . P. and visible in Fig. VII.
•

page_text: Fig. IV represents a front view of a rack K K' with a nail L, the profile of which
is shown in Fig. V. The rack consists of a vertical plate, toothed above, and a
horizontal plate furnished with 11 small holes visible in Fig. I. When the pointers
of the scales U lie at o, these 11 holes lie over corresponding holes (also partly
visible in Fig. I) in each of the 11 bars MN, and the pin s of the nail (Fig. IV
and V) is to be put through a hole of the rack into a hole of a bar MN. The
springs u, and u, in Fig. V, represented by u in Fig. IV, shall catch in lateral
grooves of the bar MN and fasten the nail. One or more nails can be put in
and out by the fingers or ordinary pincers. But in case that for instance 12 nails are
to be put in, a plate, not shown, is to be used, which has 11 lines of 12 holes
each, and contains 11. 12 nails in the 11. 12 holes. The distances of the holes in the
two directions are equal to the distances of the holes in the racks K K' and in
the bars MN. If the racks are brought to zero, the 11. 12 holes of the 12 racks and
of the 11 bars are situated like the holes in this plate. Then the nails can be
put from the plate into their proper places by an utensil shown by isometrical pro-
jection in Fig. VI. The pincers v₁, v, can manifestly take hold of the head t
(Fig. IV and V) of a nail, if pressed upon it.
Euch of the 12 rods, shown in
Fig. VI, is furnished at its end with such pincers, and on its upside with the
11 figures 5, 4, 3, 2, 1, 0, 1, 2, E, F, 9 in distances equal to those of the 11 holes in
each rack. The distances of the 12 rods themselves agree with those of the
racks KK. Thus the rods can manifestly be so arranged that, if the pincers of each
of them have taken hold of a nail, these are in the same relative position as the
holes in the racks, brought to zero, into which the nails shall be put. It is
necessary for that purpose that the number seen in the slit of the surface of the utensil
agrees with the number to be set in as multiplicand or divisor. The number, assumed
for it in Fig. VI, 1 c 2 3 10 4 178 +5, is the number inserted in Fig. I as multi-
plicand. The pincers, pressed upon, can take their nails out of the described
plate, then, by a single manipulation, all the nails at the same time are put into
their proper holes in the machine, then, by pushing the utensil a little towards the
right hand, the heads of the nails slide out of the pincers and the nails remain in
their places while the utensil is removed. In the inverse order the nails can be
drawn all at the same time out of the racks and be brought back into the plato
or let in the pincers. An assistant can prepare the numbers in the utensil, and, if
more such utensils are at hand, the arrangement of numbers often used can be
preserved. The mentioned figures on the rods are elevated like the marks and figures
on the wheels A, k, h. Thus some copies of the number seen in the mentioned slit
can be obtained by impressing a small roller of India-rubber covered with some leaves
of white and of coloured paper giving colour upon pressure.
If it is permitted that the machine is made longer, viz. that the axle B B is applied
so far behind that no nail can ever come under the wheels, the head (Fig. IV and V)
of any nail needs not be as thin as supposed in the drawings and all the nails can
be taken by the fingers. Then the 11 holes of each rack are not applied beside
but before the toothed parts of the racks. Then also, in order to copy the numbers,
the nails can be fixed immediately in the place of the pincers to graduated rods
like those of Fig. VI and these rods can go separately along with the racks.
Then also another construction of the machine would be admissible, viz. the move-
ments of the bars M N could be the same if the position of the two pantographs
would be so chosen that the pivots at the 22 points M and N lio horizontally and aro
the ends of the 11 bars M N themselves. These pivots are then at the same time
axles of little wheels rolling in the grooves S, S¹, and S, S',, except the imunovable
pivots at M, and No. Even if the distance between the bar M, N, and the axle B B is
made so small as it is assumed in Fig. I and VII, this construction is possible, if
the length of the bars M N and the lateral distance of the two pantographs, moving
then in vertical planes and in slits of the plate P₁ P,
P is made so great
3 that even after all lateral displacements of the plate P₁ P,
graph remains always at the left of the wheel ₁, and
remains always at the right of h₁. This arrangement, needing
67
"P, the left panto-
the right pantograph
either a greater length

page_text: or a greater breadth of the machine, effects the advantage that correspondent bars
of the two pantographs can be rigidly connected and guarantee thereby their
congruent movement without the sliding frame Q, Q, Q, and without the bars T, T,
and T T',. A lateral view of this arrangement is given in Fig. VIII. Two
rings, Vand V₁ are fixed on two of the bars parallel to the bars M N and connecting
rigidly two corresponding rods of the two pantographs. These rings can serve like
in a pair of scissors. Two fingers can be put in and can effect the movements of the
pantographs. The ends of the bars M, N and M, N, are furnished with wheels y, z
rolling on the plate P, P. The axles W, and W, are here ordinary pins. The
racks K K' lie below the bars M N between the necessary guides immediately upon the
plate P, P. In Fig. VIII also the pitch-lines of the covered cog-wheels H and h,
being in gear with the racks K K', and the rack fixed at i are indicated by dotted
lines, but the hooks connecting each of the racks K K' with one of the bars M N are
not represented.
1
I
On the scales U, and U, (Fig. 1) subdivisions are applied for the purpose that a
fractional value can be used instead of the last figure of the multiplier or quotient.
Then the fractional parts only of those wheels always accord with the readings of the
wheels following on the right, which have been moved only by the carriage. But
the readings of these left wheels are always correct, and, like the hour-hand can also
indicate the minutes, these wheels by themselves can indicate the entire number, if
the accuracy of the movements and of the subdivisions, which can be applied on the
wheels A, would be sufficient.
I add some other figures for illustrating the most obvious substitutions for the
wheels F with the other modifications necessitated by them. The substitutions for
the wheels F, A, H are throughout designated by F, A, H, and if For A consist
of two parts, one receiving, the other translating movement, these are designated
by F and F or A' and A', the axle of A is designated by B, the racks by K K', the
movable plate P P, also the immovable' base and pillars are indicated. By two sorts
of arrows the two sorts of movements communicated to A, are shown, viz. by the
greater arrow the movement corresponding to the partial product immediately
entering, by the smaller the movement corresponding to the carriage from the right.
Fig. IX represents a section_taken on the axis B B for the substitution already
mentioned, the Figures X and XI are vertical sectional views taken on the lines bb
and cc of Fig. IX.
The communication of motion from A², to F¹, and from F2, to A¹, could also be
effected by endless chains, bands, cords, and instead of two endless cords one endless
cord can be employed running over A³, and A', and being itself then the substitution
for F. For this Fig. XII is a front view and Fig. XIII a vertical sectional view
taken on the line a a of Fig. XII. The cord F, runs also over two pulleys E, and E¹,
fixed obliquely at the wheel H,, which receives the motion from the racks K K'.
It would also be possible that the cord F, runs over H, and A',, and the
pulleys E, E, may be fixed at A₁, or may be straightly translated in opposite
directions by two racks R., R', moved by A₁, as it is represented in Fig. XIV. The
radii of A, and A', ought here be as is 1:20. Here the bars K K' instead of being
toothed and coming into gear with the wheels H can be immediately brought into
and out of connection with the cords F by means of pincers applied at the ends K¹ of
these bars. These pincers K' must can be opened and closened all at the same time by
one manipulation. The bars K K' can then immediately slide on the base, and they
could be abandoned themselves, if each cord F is connected by such pincers with one
of the bars M N moving below it.
the
In Fig. XV the movement is communicated from A2, to F1, and from F, to A', by
means of racks C, and C, and the element H,, being the support of F, F, is
straightly translated along guides not represented, if, by turning the plate PP,
connection between H, and a rack K K is established by ledges of H, catching in
notches of K K¹ in the represented manner. The graduations else applied at.
wheels A, solid and coaxial with A' and A³ can be applied hero at the upside of the
racks C

page_text: Also the elements H can be missed and the racks K K¹ can come into gear
immediately with F, in the examples sufficiently explained by the Figures XVI
and XVII.
9°
Fig. XVIII is a front view of another combination in which the element F', is a
tangential screw, A', the appertaining screw-wheel. Fig. XIX is a vertical longi-
tudinal sectional view from the left, taken on the line bb of Fig. XVIII. For
effecting the carriage the bevel-wheel A³, is in gear with the bevel-wheel c, solid and
coaxial with the cylinder d₂, grooved longitudinally, which serves as a cog-wheel and
is in with the cog-wheel F¹,, solid and coxial with the screw F, The bearings
gear
of F, F, are fastened at a frame H,, which can receive straight translations by
notched bars K K¹ like also in Fig. XV. Then the tangential screw F³, operates
like a rack and the teeth of the cog-wheel F₁, slide in furrows of the cylinder d
In Fig. XX a cord F₁, stretched at its ends by weights a, and b,, runs over Å³, H,
and a pulley E. The pins of this pulley are drawn downwards by a
weight c
suspended by a second cord d., running over A', and stretched at its other end by
a weight e. The wheel H, instead of receiving the movement by racks, can also
serve merely to change the direction of the cord F₂, which can also directly receive
the movement like in Fig. XIV.
and are
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:
1.) In a calculating machine the partial products are formed by the motions of
points of articulation of pantographs in this manner that different points correspond
to the different figures of the multiplicand, and the amount of motion of the panto-
graphs corresponds to the figure of the multiplier, wherein the factors can both be
exhibited by the 11 whole numbers - 5 to + 5 instead of the 10 figures 0 to 9.
2.) The carriage of the tens is made continuous and simultaneous with the formation
of the partial products by an intermedial kinematic element capable of a compound
motion, viz. either by a stiff body turning or straightly translated relatively to another
one independently turning itself or straightly translated, or by a cord running over
pulleys independently movable, or by other substitutions.
3.) As it was used hitherto only in adding machines, so the figures of the
aggregates of products in a calculating machine are given by graduations, the motion
of which relating to the index is continuous so that the reading of one graduation
includes the reading of those which follow on the right, like the position of an hour-
hand includes the minutes and seconds.
4.) To form at the same time and by the same manipulation different aggregates of
products having the same multipliers but different multiplicands, specially the sum
of the multipliers.
5.) To bring back to zero all the graduated wheels at the same time and by the
same manipulation by means of one or two rakes, which, turning round the common
axle of the wheels, can be put against pins at the edges of the wheels.
6.) To copy automatically the final or intermedial results, aggregates or remainders,
multipliers or quotients and sums of multipliers, all beside each other on the same
paper.
7.) To copy automatically the readings of rods furnished with figures and employed
for setting in and taking out the nails, whereby the employed multiplicands or divisors
are exhibited.