CERTAIN IMPROVEMENTS IN CALCULATING MACHINES
Year: 1847

page_text: TO ALL TO WHOM THESE PRESENTS SHALL COME, I, JEAN JAYET,
of the City of Paris, in the Republic of France, Gentleman, send greeting.
WHEREAS Her present most Excellent Majesty Queen Victoria, by Her
Royal Letters Patent under the Great Seal of the United Kingdom of Great
Britain and Ireland, bearing date at Westminster, the Twenty-eighth day of
October, One thousand eight hundred and forty-seven, in the eleventh year
of Her reign, did,, for Herself. Her heirs and successors, give and grant unto
me. the said Jean Jayet, my executors, administrators, and assigns. Her
especial licence, full.power, sole privilege and authority, that I, the said
Jean Jayet, my executors, administrators, and assigns, or such others as I.
the said Jean Jayet, my executors, administrators, or assigns, should, at any
time agree with, and no others, from time to time and at all times during the
term of years therein expressed, should and lawfully might make, use, exer-
cise, and vend, within England, Wales, and the Town. of Berwick-upon-Tweed.
my Invention of "CERTAIN IMPROVEMENTS IN CALCULATING MACHINES;" in which
said Letters Patent is contained a proviso that I. the said Jean Jayet, shall
cause a particular description of the nature of my said Invention. and in
what manner the same is to be performed, by an instrument in writing
under my hand and seal, to be inrolled in Her said Majesty's High Court of
Chancery within six calendar months next and immediately after the date of
the said in part recited Letters Patent, as in and by the same, reference being
thereunto had, will more fully and at large appear.
NOW KNOW YE, that in compliance with the said proviso,.I. the said
Jean Jayet, hereby declare that the nature of the said invention, and in what

page_text: manner the same is to be performed, are fully described in and by the present
Specification thereof, reference being had to the Drawings hereunto annexed,
that is to say :-
Figure 1. Sheet I., is a plan on a working scale of a calculating machine.
constructed according to my Invention. A rectangular plate, about eleven
inches long and six inches broad, supports at its corners four strong iron
standards, which are bound together at top by two flat iron bars A. B. A', B'.
to which are screwed the bridges or cross pieces C. D. E. F. G. H. I. K. L.
M. N, O, P, Q. R. S. and T. X. Figure 4. Sheet II., is a longitudinal
elevation of one of these cross pieces, each of which, with the exception of the
last, T. X, is furnished with two bearings. A and B, for the support of the
axles of the toothed cylinders I, I, II, II, III, III, IV, IV, V. V¹, as
well also as for the two end cylinders T and U, which are not toothed,
and which I call governing or check cylinders ("brideurs genereaux), on
account of their being used to check or hold stationary the stops 1, 2, 31. 4¹
&c., on which they act. These toothed cylinders are all of the same
diameter, and arranged in two parallel series, each series being composed of
five cylinders exclusive of its governing or check cylinder, and the axles of
all the cylinders of each series are on the same right line as if they were
a prolongation of one another. The circumference of each of the cylinders,
though calculated for forty-four teeth or for any other number that might be
desired, is only furnished with seventeen teeth, which are in pairs of equal
length (as seen in the first pair of cylinders 1, 1). and the pairs increase
gradually and in equal proportion in length from the two "nine teeth" or
eighth pair, which are the shortest, to the "first," which is the longest. I
say the "first," and not the two "first," because in fact it has no consecutive
tooth of a corresponding length. A rebate is formed on either side of each
tooth, and projects a little way beyond it. That part of the cylinder on which
there are no teeth retains its plain periphery to beyond the two onter
teeth for the space marked A, B, A, C. Figure 1. Sheet II. The inter-
vening portion of the circumference of the cylinder from C to B is cut down
throughout its entire length. as shewn in the Drawings. The cylinders
HI, II, II, III, IV, IV, V, V', represented at rest, and shewing the
sunken portion, do not allow any of the teeth which are placed upon the
opposite side to be seen. Although what I have just described is applicable
to all the cylinders without exception, it is necessary to state that toothed
wheels A, A, A, Figure 1, Sheet II., are keyed on to the axles of the
right-hand series between each of the toothed cylinders I, II, III, IV¹, V¹,
and work into pinions c¹, c', c', c', c', having six teeth each, and keyed

page_text: on to the horizontal axle V1, V, Figure 1, Sheet I., which is placed
longitudinally between the two series of toothed cylinders. Each of the
toothed wheels A', A", A, although calculated to carry forty-four teeth, is
furnished, however, only with thirty-eight, as shewn at Figure 2, Sheet 2,
the part A, B, being stripped, and taking the place of six teeth. The motion
which these pinions c¹, c', c', c¹, c', receive from the toothed wheels A', A",
A, &c., is communicated to the check cylinders by the intervention of the
pinion X, which is keyed on the longitudinal axle V, V, and gears simul-
taneously into toothed wheels fixed on the axles of the check cylinders T, U,
which are thus caused to make one revolution for every revolution of the
toothed cylinder, that is to say, of the toothed wheel A', A", A.
D', Figures 2 and 7, Sheet 2, is a steel stop of about the same size as the
pinion c¹, against which it is fixed, and has three cavities on its circumference,
which coincide exactly with and act upon the plates O, O', which are fixed
upon the wheel A', A", A", at the commencement and termination of the
range of teeth. A groove, D, E, F, Figure 1, Sheet 2, is cut in the front end
of each of the toothed cylinders of the right-hand series, and ends in two
bevilled terminations D and F, the space between which corresponds to that
left between the two plates O, O', Figure 2, Sheet 2. The elbow piece of
The
arm L, L, which is made fast to a rod F¹, I', takes into this groove.
rod F, 1, is supported by suitable bearings, one only of which, M', is shewn
in the Drawing. This rod, which I call cliquet general" (common catch),
because it is common to all the cylinders of the right-hand series, carries at its
furthest extremity, which projects beyond the cross piece M', an arm G', 1',
differing in length and form from the five others L', L", &c. The arm G', 1',
causes the piece S¹ to catch in the slots of the circular plate N', P', which is
made fast at right angles to the end of the central horizontal rod V, VI,
thereby arrests its further rotation.
**
and
Figure 2, Sheet 1, represents a calculating machine constructed upon a
smaller scale, that is to say, its numerical operations are limited to calculations
The only difference
which do not extend to beyond six places of figures.
between the two machines is, that in the smallest one the cylinder is caused
to do the duty of two, for it may be considered as the first or larger machine
deprived of its left-hand portion, namely, the cylinders I, II, III, IV, V,
The
and the apparatuses and cheek cylinder T, which are dependent thereon.
differences which appear in the Drawings are, therefore, mere modifications
of parts which may be exchanged and applied to either machine.
I shall proceed to describe the mode of working this machine, in order that
the action of the several parts thereof before referred to may be the better

page_text: understood. Suppose the toothed cylinder
of the right-hand series (shewin
in the Drawings as in motion) to be at rest, like the others, the pinion C
being opposite the vacant space, that is to say, the portion without teeth of
the wheel A', A", A, the arm L'. L", would then take into the space
between the two bevilled terminations D, F, of the groove D, E, F, Figure 1,
Sheet 2, while the arm G', 1', would hold firmly the circular plate N¹, P'. All
being thus arranged, if either of the toothed cylinders be now made to rotate,
the nearest, 1', for instance, the elbow piece of the arm L, L", entering into the
bevilled terminations of the groove D, E, F, will be thereby lifted up, and
will communicate its ascending movement to the arm G, I, which will
consequently liberate the catch S', from the slot in the circular plate N¹, P
and allow the central and horizontal axle V, VI, to revolve, such rotary
motion being communicated from the cylinder by means of the toothed
wheel A, A, A, and pinion C¹. This movement is continued until the
cylinder (about to finish one revolution) brings the vacant space of its
wheel A', A", A", opposite to the pinion C', and presents at the same time
to the elbow piece of the arm L', L", the bevil of the groove, which will
consequently cause the arm G. 1. to force the catch S' into the slot of the
circular plate N', P', and to arrest its further movement, and at the same
time that of the two check cylinders, until a fresh revolution of this or any
other cylinder, for the motion of each cylinder is so far independant of that
of the others as to render their simultaneous rotation impossible. It will be
seen that the object of the plates O, O'. on which the stop D' acts, is to ensure
the regearing of the pinion into the wheel A', A", A", as well as the
entry of the catch S' into the slots of the circular plate N', P¹. The steel
axles marked 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, are arranged at equal distances on two
circumferences described with the same radius, and having for their respec-
tive centres the points A and B. Figure 4, Sheet 2, which are the centres of
the cylinders, so that the cylinders and circumferences are concentric. These
axles extend the whole length of the machine, and are supported (in order
to prevent their giving) in bearings drilled in bridges or curved cross pieces
made of copper D, C, G, H, I, K, L, M, &c.. Figures 4 and 17, Sheet 2,
which are supported upon the iron cross pieces designated by the same letters
in Figure 1. Sheet 1. Each of these axles carries five pinions (bearing exact
resemblance to the pinion C', Figure 1, Sheet 2), which are furnished with six
teeth intended to gear into the teeth of the cylinders. The axles are semi-
circular in form (one of which is shewn in section Figure 13, Sheet 2), in
order to prevent the pinions turning independently of them, but without
interfering in the slightest with the longitudinal movement, which should be

page_text: as free as possible, so as to allow them to gear into any couple of teeth from
0 to 9. These pinions are so adjusted as to touch that portion of the periphery
of the cylinder which is without cogs (but which is not cut away), and by the
consequent friction be prevented from turning. The rebates between the
cogs shewn upon the cylinder I', Figure 1, Sheet 1, allow the free gearing
of the teeth of the pinions into the teeth of the cylinders. Besides these five
pinions, each of the axles has a catch 11, 2, 3, 4, 5', &c., Figure 1, Sheet 1,
and shewn separately in Figure 7, Sheet 2, which serves to hold the axle on
which it is fixed whilst it is not held by the cylinder, that is to say, during the
passage of the cut-away portion of the cylinder before it. To effect this the
check cylinders T, U, on which these catches act, have indentations on their
peripheries, the lengths of which act in proportion to the cut-away portions
of the toothed cylinders, so that the axles may be always held by the check
cylinders when they are not by the toothed cylinders, and vice versa. In
order to insure the regearing of the pinions into the toothed cylinders, and
of the stops into the check cylinders, I have sloped the cut-away portion, as
shewn at C and B, Figure One, Sheet 2, and the indentations on the check
cylinders, Figure 1, Sheet 1. It follows that the check cylinders will
always hold stationary the axles when the toothed cylinders are in a state
of repose, that is, have their cut-away portions opposite to their respective
pinions. It will be seen from the preceding observation how the axles
may be made to revolve successively by each cylinder. inasmuch as the
other cylinders being in this state of repose allow their respective pinions
which are carried by the axles to turn freely in the cut-away portions of their
peripheries. The axles 1, 2, 3, 4, &c., are each of them supported at one end
by the cross piece R, S, and terminate at the other in bearings drilled in the
centres of the ends of rods 22, &c., which are fixed to the cross
piece T, X, so as to be in the same right line as and the extension of their
respective axles. These rods are alternately of equal length, and on each of
them is mounted a "canon" (hollow cylinder), intended to carry a stop a, a,
rivetted to it, which is fixed (on the five shortest rods) to that side of the
"canon" (hollow cylinder) which is the farthest from the cross piece T, X,
and in the five longest rods to that which is the nearest to the said cross
piece, in order to prevent any bending of these rods. The stops (one of which
is shewn separately shewn in Figure 8, Sheet 2) are composed of two circular
plates rivetted together, one of them having nine circular indentations on its
circumference, which are equal one to the other, while the other circular plate
is divided into the same number of teeth. The five stops which are mounted
upon the five shortest of the rods carry each of them a steel piniou C,
3

page_text: Figure 9. Sheet 2, and Figure 1, Sheet 1, one of the pivots of which rests
against one of the circular plates, and the other is carried by a bridge or cross
piece fixed on the stop a, a, and partakes of its movement. The position of
the five other stops not allowing of their being used for this purpose, attach
to the end of their "canon" (hollow cylinder) a plate d, especially intended to
carry this pinion C, which should be placed at such a distance from the centre
as to gear easily into the pinion b (which is of double its own diameter) and
into the wheel e, e, which carries the teeth on the inside of its periphery, and
whose diameter is fourfold that of the pinion. The wheel which is carried by
the axle 2 is supposed to be cut through, and the upper half removed to allow
of the gearing of the pinion C into it being clearly shewn. It will be seen
from the arrangement just described that the internally toothed wheel e, e,
whose movement is independent of its axle, may be made to turn by means of
the pinion b, which is invariably fixed upon the same axle, or by the pinion C.
(one of them being stationary,) or by the two together, they being made to
rotate in opposite directions. In this last case the internally toothed wheel e, e,
partakes of the two movements, so that its velocity is equal to the sum of the
velocities transmitted by the pinions C and b, and it communicates its motion
to the axles f, f, by means of gearing wheels h, i, the smaller being to the
larger one in the proportion of six to ten. The wheel his fixed upon the
" canon (hollow cylinder) of the internally toothed wheel e, e, and the wheel i
upon the axle f, f, which carries a little further on the circular plate g, k,
called "bridon," bridling wheel, Figure 8, Sheet 2, Figure 1, Sheet 1, because
of its analogy of operation to that of the check cylinders. This bridling
wheel is so adjusted that a small portion of its circumference coinciding with
the circular indentations of the stop a, a, the rotary motion of the latter shall
be prevented until the tooth catches against the teeth of the circular plate
which constitutes a portion of the stop a, a, & causes one of the points of
the circular indentation with which the bridling wheel is in contact to enter
into a notch cut for that purpose in the bridling wheel immediately behind
the tooth g, and consequently to move one tooth onwards, or to make one
tenth of its entire revolution to one entire revolution of the bridling wheel.
This pass" or action is communication to the axles f, f, of the suc-
ceeding bridling wheel, which is caused to make one tenth of its revolution
by means of suitable gearing e, e, c, b. The size of the bridling wheel should
be so proportioned to that of the stop, that the transmission of the pass or
action before described of any one apparatus to the following should be
completely effected during the one tenth of a revolution of the bridling
wheel. I desire that it may be understood that if these conditions were

page_text: fulfilled this pass or action before referred to would be communicated
almost as instantaneously from the first apparatus to the tenth as to the second.
But as the power is in inverse proportion to the velocity, that is, the size of
the bridling wheel, it has been found impossible to transmit this pass or action
beyond a certain apparatus, which practise and calculation have proved to be
the sixth. so that the addition of an unit to 9. 9. 9. 9. 9, is scarcely possible.
To obviate this difficulty, by increasing the power. I break off the communi-
cation between the third and fourth apparatus, that is, instead of transmitting
this "pass" or action directly by the bridling wheel, as before. I accomplish
it by the intervention of the check cylinders T', U', which are furnished with
two teeth each b¹, b¹, placed in suitable positions on the same line of rotation.
and gearing into a pinion m, which has four teeth. Figure 10, Sheet 2, and
Figure 1. Sheet 1, the teeth of which being diametrically opposed are not
upon the same line of rotation as the two others, so that this pinion works as
though it had two teeth only, and can never make more than one fourth of a
revolution at a time. This motion is communicated to its axle, which is
semicircular in form, and transmits it on to the fourth axle by means of the
pinion p in the wheel q. which replaces the stop of that axle, and causes it to
make one ninth of an entire revolution, which is followed by the "pass" or
action before described, and can only take place when the tooth of the pinion m.
which is perpendicular to the surface of the check cylinder, comes on the same
line, as is afterwards explained. In the case when this condition no longer
exists, which invariably follows the "pass" or action before described, it must be
renewed; that is to say, to cause again this "pass or action. the perpendicular
tooth must again be moved on the line of passing of the teeth of the check
cylinder. This to-and-fro movement is communicated to the perpendicular tooth
by means of the excentric r. keyed on the axle r. s. Figure 101, Sheet 2, and
Figure 1, Sheet 1, which works between the collars 1, u, and thereby causes
the pinion m to move alternately backwards and forwards, motion being commu-
nicated to this excentric by the wheel v, x, and pinion s, which receive motion
from the passing of the tooth g of the bridling wheel k, g, in the nine-toothed stop
a. a. The four-faced stop y. Figure 10, Sheet 2, is fixed at the end of the axle
n, o, and in contact with the check cylinder. to insure the immoveability of this
axle. In order to effect this "pass" or action, an opening z is cut in the check
cylinder of sufficient size to allow of the stop turning therein, and of the axle
partaking of the motion communicated to it. When the "pass or action should
terminate, that is, when the pinion m has neither of its teeth upon the line of
passage of those of the check cylinder, the stop y is prevented from taking into
this opening by the spring catch a', b', the head of which takes into a square
"
"

page_text: notch in the collar w, whence it can be disengaged. But at the instant of the
"pass" or action before described taking place, when it takes into a similar notch
in the circular plate 1, the expanding form of which allows of its being disen-
gaged, and of the turning of the axle. this spring catch will then imme-
diately take into a square notch in the same circular plate 1, whence it cannot
be disengaged until the recurrence of the "pass" or action before described.
It then passes into a similar notch of the opposite collar w. of an expanding
form. to allow of the turning of the axle, and to fall again after this movement
into a square notch in the same collar. The entry of the catch a'. b. in the
square notches of the collars f. u, is caused by projections soldered on to the
interior circumference of the check cylinder on each side of the teeth 1. 1.
which act upon the pin fixed upon the spring catch a, b, after each recurrence
of the pass or action. The transference of the "pass" or action which has
just been described to the seventh apparatus is effected in the same manner
as the preceding. All the difference between the series of apparatus shewn
between the cross pieces C. D. G. H. consists simply in that the motion of
the axles 1, 2, 3. &c.. instead of being transmitted directly to the apparatuses, as
in the first series, is communicated by means of the intermediate wheels c', d.
the first of which, c¹, is fixed upon the axles 1, 2, 3, &c., and the second d³.
which is considerably thicker than the other, upon the axle c', which carries
the wheel e'. These intermediate wheels are intended to raise sufficiently
high the bridling wheels g', k¹, of these apparatuses, to allow their axles f. f.
to pass over the bridling wheels of the first apparatus. so that the numbers
which they carry at the extremity of the axles may be exhibited on the fore
part of the machine. The remaining portions of the machine being exactly
similar, even to the passage of the "nines," which is caused by the upper
check cylinders T, U, on which for this purpose are placed the teeth 1, 1, I
shall not give a detailed description, but desire it may be remarked, that as
their action is in some cases useless, I. in order to give the machine all the
freedom of play of which it is capable, suspend their functions by means of
an apparatus which I will now proceed to describe.
It will be observed that the wheel c¹. the centre bearing of which is round,
Figure 11, Sheet 2, does not partake of the movement of the axles 1, 2, 3, &c.,
inasmuch as one of the three openings with which it is pierced is held fast
by the pin i, Figure 1, Sheet 1, fixed on the circular plate n', and adjusted
in half moon upon the axles 1, 2, 3, &c., by means of a screw. This wheel c
will not cease to follow the movement of the axles 1, 2, 3, &c., inasmuch as
when liberated from the action of the pin i it will be held by the pin k', fixed
upon the cross piece H. G. without however getting out of gear with the

page_text: wheel d', which is made unusually thick for that purpose. In this last position
the working of the machine is stopped, since the axles 1, 2, 3, &c., can move
without communicating any motion to the wheel c. This engagement in and
disengagement from the pins and of the wheel c¹ is communicated to all
the wheels marked c¹ of this apparatus. by means of a sliding T-piece X, Z',
furnished with arms q', the forked ends of which embraces the hollow cylinder
of the wheels c'. This T-piece is supported by and moves to and fro between
two cross pieces R', S'. The to-and-fro motion is sufficientiy great to
produce the desired effect, and is communicated by means of the bar T, U,
which is fixed by the middle, and terminates at one end in a button which
projects outside of the machine. At the end of each of the axles f, f, f, f.
which carry the bridling wheels of the two series of apparatuses, is fixed a
circular plate 1, having marked upon its surface the numerals
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, Figure 12, Sheet 2, which can be exhibited only
one at a time through an opening of sufficient size made in the front plate
of the machine, Sheet 3. The position of each of the circular plates upon its
axle should be such that the action of the catch tooth of the bridling wheel
g, k, upon the stop a, a, may take place during the change from 9 to 0 on
the numeral plate
Longitudinal motion is communicated to the six
toothed pinions which are carried by the semicircularly shaped axles 1, 2, 3, &c.,
by means of the ten ladders L, M, &c., Figure 14, Sheet 2, which are sup-
ported in two bridges I, K, P, Q, placed immediately in front of each end.
pair of cylinders. These bridges, the bases of which rest upon the pieces
cd, Figure 1, Sheet i, are pierced with ten rectangular openings,
in which the ladders have a to-and-fro movement which they communicate to
the six toothed pinions by means of the forked rods A, B, C, D, E, I, H, G, F, &c.,
Figure 14, Sheet 2. On each of the first six ladders (counting from left to
right) are screwed five of these forked rods, while the seventh ladder carries
The
only four of them, the eighth three, the ninth two, and the tenth one.
first forked rod of any ladder governs the pinion which belongs to the first
pair of cylinders, and which is carried by an axle, the numeral order of which
is always the same as that of the ladder referred to; and each of the other
rods of this same ladder, taken in the order of their succession, guides a
pinion carried by an axle, the rank of which advances successively by one,
proceeding from right to left, and gears into a pair of cylinders, the rank of
which increases also by one in going from the front to the back of the machine,
whence it results that the pinions marked 12, 13, 2, 1, 2, 3, 1, 2, 3, 4,
Figure 1, Sheet 1, will be without guide rods, and that they are fixed upon
their axles out of gear, in order to hold them stationary during the time they

page_text: are not so held by the check cylinders. I desire it to be remarked, that the
guide rods of the same ladder should be fixed at such a distance one from the
other that their pinions may all simultaneously gear the same number of
teeth, whatever be the pair of cylinders to which they belong. The projecting
pieces N, P. R, S, of the ladder, Figure 14, Sheet 2, is divided into ten
notches 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, into each of which may be made to take
the head of the spring catches t, u, e, z, which indicates by the Figure to which
it corresponds the number of the pair of teeth that the pinions guided by the rod
of this ladder cause to gear into their respective cylinders. The cylinders I, 1',
II, II, III, III, &c., Figure 1, Sheet 1, (as well as the cylinders I, II,
III, &c., Figure 2, Sheet 1,) invariably carry at the extremity of their axles two
pinions y, z, into which gears the wheel J, J', with, however, this difference, that
in the machine, Figure 1, each of these wheels guides simultaneously two pinions,
while in the one represented, Figure 2, the wheel guides only one. Whatever
may be the arrangement, the wheels J, J, are always caused to rotate by
another, the axle of which 1, 2, 3, &c., carries the handles, Sheet 3, and a
circular plate, as shewn only at Figure 2, fixed to it, and divided into ten
equal portions, to correspond exactly with the concentric dial R, T, U, V, Q. P,
fixed upon the front plate of the machine, and consequently divided into ten
portions 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The needles D, C, B, A, L, M, fixed
upon the handles, and indicated by the same letters, carry each of them a pin
which may be made to take into each of the divisions of the corresponding
circular plates S, X. Each needle indicates by the number of these divisions
it has passed over on the fixed dial the number of revolutions executed by its
corresponding cylinder, because the motive gearings are so calculated that the
cylinder shall make ten revolutions while its motive axle makes only one.
These gearings. however, may be calculated and constructed in other propor-
tions, such as five revolutions of a cylinder to one of its motive axle, as
represented, Figure 1, Sheet 1, Figure 1, Sheet 3, being a view of the front
plate thereof. In this arrangement the fixed dials T, R, V, U, Q. P, S, E, I, 0,
instead of being concentric with the motive axle 1, 2, 3, 4, 5, are placed
immediately above it, while the handle thereof projects beyond the machine.
These axles carry also a circular plate S. X, Figure 20, Sheet 2, on which
acts the spring catch F. F. It is divided into five notches, and carries besides
five pins which act upon the eighteen-teeth wheel M, L. on which acts the s
spring stopy z. One end of the axles of each of these wheels projects.
beyond the machine, and carries a needle L, M, A, B, D. C. &c., on which
runs over the dials R. T. U. V. Q. P, &c., which are divided also into eighteen
portions, and marked 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1. This

page_text: needle moving from 0 at each fresh operation indicates by the corresponding
Figure the number of revolutions executed by its corresponding pair of
cylinders either to the right or to the left. according as the portion of the
dial passed over is to the right or left of 0. At the termination of each
operation the needles are to be brought back to 0 by an arrangement hereafter
to be explained.
Addition. Suppose it is desired to add 258 to 668, I place the ladders in
such a position as that they shall indicate the number 668, that is to say. I
place the third ladder which represents the hundreds so that the head of
its spring catch shall correspond to the notch 6, the second which repre-
sents the tens upon the notch marked 6. and the first which represents the
units upon the notch marked 8. The other ladders marked 0, that is to say.
indicate that the pinions which they guide are out of gear, as shewn at
Figure 1, Sheet 1. When these arrangements are completed, I cause the
first pair of cylinders to make one entire revolution by means of the motive
gearing, and bring the needle of the dial, which represents the units, and
corresponds to this pair of cylinders from 0 to 1. the gearing of the appa-
ratuses being calculated in such a manner as that one third of the revolution
of the axles 1, 2, 3, &c., shall produce a corresponding number on their dials.
It will be easily understood that after the movement I have just effected, the
dial of the third apparatus will have passed from 0 to 6, because, after the
indication of the third ladder the pinion of its first guide rod is carried by the
axle 3. and gears into the sixth couple of teeth of the first pair of cylinders.
and consequently causes it to make two revolutions, that is to say. to gear
twelve teeth, and therefore to shew number 6. It will be understood after
the same manner how the second dial (representing the tens) is brought from
0 to 6; and lastly the first dial, that of the units, from 0 to 8. The other
dials having remained stationary show 0 only, so that the same number 668
will be read off through the openings of the two galleries. To add the second
number 258, I place as before the ladder so as to represent 258, and then
cause the first pair of cylinders to make one entire revolution by means before
described, after which the number 926 will be read off through the open-
ings as the sum of the two numbers. The reason of this number appearing
instead of 258, is that the dials were not brought back to 0 before beginning
the operation. It will be seen that the results which appear in the upper
gallery is not of the slightest use in these operations: I therefore consider it
advisable to throw the apparatuses out of gear, in order that the machine
may work with more facility.
Multiplication. Supposing it is required to multiply 668 by 258, I first

page_text: bring the dials of the two galleries to 0, and then, as in the preceding
operation, place the ladder so as to represent 668, after which I cause
the first pair of cylinders (representing the units) to make eight revolutions
in bringing the needle of its dial from 0 to 8, and there will appear through
the gallery 668 added igether eight times, or multiplied by 8, that is
to say. 5,344. To multiply 668 by 50, I remark, that according to the
disposition of the guide rods of the ladders, the pinions which belong to the
second pair of cylinders should give (seeing the rank occupied by their
respective axles, and the number of teeth they gear, Figure 1, Sheet 1.) the
same number as the pinions of the first pair of cylinders, but thrown back
one rank towards the left, that is, multiplied by 10, since the pinions of the
second pair of cylinders taken in the order of their succession are respectively
carried by axles whose rank increases by one towards the left, whence it
follows that by causing the second pair of cylinder to make five revolutions,
and in bringing the needle of the corresponding dial from 0 to 5,668 multiplied
by 50, and added to 5,344, or 38.744, will be read off through the galleries.
To multiply 668 by 200. I bring as before the needle of the dial representing
the hundreds from 0 to 2, and as the pinions belonging to the third pair of
cylinders represent the number 668 moved two ranks towards the left, the
result will be 668 multiplied by 200. and added to 38,744, and the total
product will then appear as 172,344. If the apparatus of the upper gallery
are not thrown out of gear, the same number 172,344 will be there expressed,
so that before commencing a new multiplication, after having brought back to
O the dials of the lower gallery by means hereafter to be described, the
lower gallery will represent the product of this second multiplication, while the
upper will show this product added to the first, whence it follows that by
means of this gallery the addition of all the products of any number by
another may be obtained when the total does not exceed 10,000,000,000
exclusively, which is the limit of the larger machine.
Subtraction. Supposing it is required to subtract 258 from 364, I place
the ladders so as to represent 364, which I cause to appear through the
gallery, in bringing the needle of the dial representing the units from 0 to 1.
and then place the ladders so as to represent 258, after which I pass the
needle of the same dial from 1 to 0 in a direction the reverse of that used in
addition, and 106 will appear as the difference between these two numbers.
Division. To divide 93,912 by 364, I cause the first number to appear
through the gallery by the means before described, and place the ladders so as
to represent the divisor 364. In order that the operation may be the more
easily understood, we will suppose the quotient 258 to be known. Division

page_text: being only a short method of subtraction, the operation to be performed.
may be said to consist in subtracting from 93.912,200 times 364 plus
50 times 364 plus 8 times 364. To subtract 200,364 or twice 36,400, I
bring the needle of the dial representing the hundreds from 0 to 2 in the
reverse direction used in multiplication, and the remainder, 21,112. will
appear through the gallery. To subtract 50 times 364 or 5 times 3,640,
I pass the needle of the dial representing the tens from to 0 to 5 in the
reverse direction used in multiplication, and the remainder. 2.912. will
then appear, from which I subtract 8 times 364 in bringing the needles of the
units from 0 to 8. After this last subtraction, the gallery will not offer to
view any more numbers, and I therefore conclude that the division has
been exactly completed. The quotient (although known) is indicated
by the figures to which the needles of the dials point. representing units.
tens, and hundreds. If the division has not been exact, the gallery, instead
of showing 0, will shew certain Figures which will represent the remainder.
When the quotient is not known the operation becomes long and difficult.
firstly, for the determination of the highest units of the quotient, that is, of
the dial which represents them, this last being known by the comparison
which should necessarily be made between the divisor and the partial dividend
while successively passing the needle of this dial from division to division until
the gallery shows a partial dividend smaller than the divisor. for it is then
only that the figure to which the needle of this dial corresponds represents
the real figure of the quotient. The same operation is performed upon the
other dials.
Figure 15. Sheet 2, represents a means of surmounting all these difficulties.
and consists of a spring catch A. B. which acts upon the pin R. fixed against
the circular plate k, g, which is adjusted firmly upon the axle f. f, which
carries the left-hand dial, Figure 1. Sheet 1, and represents the highest units
of the machine. The head of the spring catch A, B, which is cut square on
one side and on the other sloping, to admit of its being raised by the pin
when the circular plate k, g, moves in the direction for multiplication, and of
its forming a stop when it moves in the reverse direction for division. The
position of this pin should be such that the point of stopping should take
place when the dial shows 0, so that the passage from 0 to 9 of this dial
cannot take place; but in the case when all the dials of the lower gallery
show 0, it is evident, seeing the position then occupied by the teeth of the
bridling wheels in respect to their stops, that this passing from 0 to 9 will be
impossible for any one of all the dials, since that can only take place in
conjunction with the last and all the intervening dials, whence it results that

page_text: every time the gallery exhibits a partial dividend smaller than the divisor it
is impossible to effect a fresh revolution of the operating cylinder. for if it
were otherwise the remainder of this last subtraction would be less than 0.
that is to say, that the passing from 0 to 9 would be effected, which I have
shown above to be impossible. Wherefore the figure of the quotient is the
one indicated by the needle of the dial when the operation is stayed by the
action of the spring catch A, B, before described. The same operation is
performed with the other dials up to the first, that representing units. The
operations which I have just described ought to demonstrate sufficiently the
necessity after each calculation is effected of bringing back to 0 the dials
which exhibit the results through the lower gallery before commencing a fresh
one; and it is effected instantaneously by means of the crank levers a, b, c,
Figure 1. Sheet 1. and Figure 1, Sheet 2. fixed to the extremities of the
axles f, f, which carry the dials of the lower gallery, and are capable of
being always brought back to the same fixed point by means of the pieces
a, b, c, Figure 16, Sheet 2, which are of the most convenient form for
facilitating this movement. These pieces are attached to a sliding piece
M, N, (made to slide between two bridges,) which when drawn out bring all
the crank levers to their fixed point, and cause the dials carried thereby to
show 0. I desire it may be remarked, however, that these crank levers
being fixed to the axles f, f, which can only move by the ordinary action of
the machine, it is necessary, before drawing the sliding piece M, N, in order
that they may obey the action of the pieces a, b, c, to liberate them by
means of the wheels i (shewn in the left-hand portion of the Figure 1, Sheet 1,
to avoid confusion), which are capable of having a rotary motion imparted to
them independently of their axles, when the pin which each of them carries
is no longer held in one of the ten notches cut in the circumference of the
circular plates . Figure 18. Sheet II.. which are fixed firmly upon the same
axles f. f. This disengagement is effected instantaneously by all the wheels i,
by means of the arms n, Figure 1. Sheet I.. the forked extremities of which
take into a small circular plate adjoining their hollow cylinder, while the other
ends are firmly fixed in the sliding T-piece P", L", which is supported by
two bridges, one only of which is seen Q, R', and in which it has a to-and-fro
movement sufficient to allow of the gearing in and gearing out of the pins
of the wheels i, without, however, permitting them to gear out of the wheels h,
which are made unusually thick for that purpose. This to-and-fro movement
is communicated to the sliding T-piece P, L", by means of a sliding bar
M. O, the extremity of which terminates in a button projecting outside of
the machine, and acting on the first by means of a hidden axle which carries

page_text: at its upper end a pinion gearing into the teeth of the arm R", while at its
lower end it carries a stop with four teeth which the sliding piece M", O",
causes to make one fourth of a revolution by means of the tooth V. After
the passing of this tooth in this stop the wheels i are set at liberty, and the
sliding bar M", O", is allowed to again follow up its motion, dragging with
it the sliding piece M, N, to the end of its course. The sliding bar M", O",
is then pushed back, and the lower gallery shewing 0, a fresh operation may
be commenced. It is evident that the dials of the upper gallery will not have
been affected, because their axles 1, 2, 3, &c., from which they receive motion,
have remained stationary. It is chiefly in consideration of this peculiar
advantage that this mode of bringing back the dials to 0 should be preferred
to the following, when the machine is furnished with two series of apparatus.
The bringing back to 0 of these last, that is to say, of the dials which repre-
sent the addition of the products, taking place but very seldom, it is effected
by simple subtraction, that is, by placing on the ladders the number indicated
by the dials, and subtracting this number from itself, the rest is necessarily 0.
To carry out this operation in the machine, Figure 2, Sheet 1., the following
difference is observed;-Instead of the freedom given to the axle f, f, which
carry the crank levers, being effected by the gearing out of the wheels i,
which in this case are soldered to the axles, it is effected by means of the
stops 1, 2, 3, &c., acting upon the check cylinder, which is caused to make
one half revolution, in order that it may offer to them the cut-away portion
of its circumference. The sliding bar P, O, Figure 2, Sheet I., has a pro-
jection towards one end, which takes into the fork of a rod N, D, made fast
to the common spring catch F, I, whereby it is raised at the first movement
of the sliding bar, and allows the general check cylinder U to partake of the
motion communicated to its axle by means of the stop with four teeth t, which
is fixed to it, and caused to move by the two teeth p, q, carried by the sliding
bar P, O. When this movement is accomplished, the other sliding bar M, N,
which carries the projecting pieces a, b, c, commences to act upon the crank
levers a, b, & to bring them to their fixed point. In pushing back the sliding
bar P, 0, the same movements are executed in a reverse direction, and the
dials being brought back to 0, the machine is ready for working. The
bringing back of the needles of the motive dials, Figure 1, Sheet I., is effected
by the preceding method; that is to say, that the axles on which are fixed
the needles L, M, A, B, Figure 20, Sheet 2, and Figure 1, Sheet III., carry
at their other extremities cranked levers on which act projecting pieces similar
to those carried by the sliding bar M, N, Figure 16, Sheet 11. These pro-