IMPROVEMENTS IN CALCULATING MACHINES, PART OF WHICH IMPROVEMENTS IS APPLICABLE TO PURPOSES WHERE WHEEL- WORK IS REQUIRED
Year: 1843

page_text: TO ALL TO WHOM THESE PRESENTS SHALL COME, I, DAVID
ISAAC WERTHEIMBER, of West Street, Finsbury Circus, in the County of
Middlesex, Gentleman, send greeting.
WHEREAS Her present most Excellent Majesty Queen Victoria, by Her
Letters Patent under the Great Seal of Great Britain, bearing date at
Westminster, the Twenty-eighth day of January, in the sixth year of Her reign,
did, for Herself, Her heirs and successors, give and grant unto me, the said
David Isaac Wertheimber, Her especial licence, full power, sole privilege and
authority, that I, the said David Isaac Wertheimber, my exors, admors, and
assigns, or such others as I, the said David Isaac Wertheimber, my exors,
adiiors, 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, exercise, and vend, within England, Wales, and the
Town of Berwick-upon-Tweed, the Invention of" IMPROVEMENTS IN CALCULATING
MACHINES, PART OF WHICH IMPROVEMENTS IS APPLICABLE TO PURPOSES WHERE WHEEL-
WORK IS REQUIRED," communicated to me by a certain Foreigner residing
abroad; in which said Letters Patent is contained a proviso that I, the said
David Isaac Wertheimber, shall cause a particular description of the nature of
the said Invention, and in what manner the same is to be performed, 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 apnear.

page_text: NOW KNOW YE, that in compliance with the said proviso, I, the said
David Isaac Wertheimber, do hereby declare that the nature of the said
Invention, and the manner in which the same is to be performed, are fully
described and ascertained in and by the following statement thereof; and as it
is imposible to give a description of these machines without the assistance of a
Drawing, I shall therefore have recourse to one in describing their different
parts, the manner in which these parts are connected with each other, the way
in which they act one upon the other, or separately, as well as in explaining
the principle of the whole mechanism, and in pointing out the different
modifications as to shape which the machines may undergo. The subject of
this description is a mechanism by which all the operations of arithmetic from
numeration to logarithms may be effected by combinations more or less
complicated of the elements. As all arithmetical problems are grounded on
numeration, addition, subtraction, multiplication, and division, I shall only speak
of these elementary machines. The other arithmetical problems are naturally
connected with them, without constituting another Invention.
FIRST ELEMENT, COUNTER.
A wheel of copper, wood, iron, or any other substance having twenty cogs or
teeth (see Figure 1), is fixed by means of two lateral holes a, a, Figure 1, to a
tube furnished with a plate, Figure 2. Under this wheel is fixed a double
excentric or snail cam, Figure 3, which is separated from the wheel by the
thickness of the plate. Under the double excentric or snail cam is fastened the
catch plate, Figure 4; to keep this separate from the double excentric or snail
cam, a collar shaped as in Figure 5 is placed between. All these are fixed upon
a tube by the middle holes b, b, b, and joined together by two screws passing
through their lateral holes a, a, a, a, so as to form a single piece of the whole
as in Figure 6, which is a side view of the apparatus. I then take a small
plate, Figure 7, and insert into the middle hole a steel pin e; this pin will enter
the tube connected with the pieces already described, and will form an axis
round which the wheel, the double excentric or snail cam, and the catch plate,
may freely revolve. These pins are afterwards fixed by means of two screws,
which pass through the lateral holes of the plate to a plate of metal, as
represented in Figure 8.. If another plate be placed above this one, and held
apart from it by small pillars, Figure 9, d, d, d, d, d, the frame of the machine
will be formed. Figure 9 is a side view of the frame with the pins e, e, e,
fastened to the lower plate of the frame. The same Figure shows how the pins
e, e, e, ascend into the interior of the frame, and reach the top of it. On taking
off the upper plate of such a frame I perceive, as in Figure 10, d, d, the wheels

page_text: placed on the axes of their pins, to fix to any given point these wheels, which
are capable of revolving on their axes, two pressing springs, Figure 10, f, f,
which press on the teeth of the wheel and give it twenty fixed points. These
pressing springs are fixed to a stud, Figure 11, the lower part of which is fixed
in the holes of the lower plate of the frame, while to the upper part of the stud
is fastened the extremity of a thin spring. Between each pair of wheels is a
lever, Figure 10, g, g, which, considering it separately, is composed of the
following parts:-A piece of metal nearly right angular, Figure 12, is rounded
off at one end h, and bears on its upper surface a pin i; in the middle of the
right angular piece of metal is a round hole k; the other arm bears a pin / on
its lower surface, but its extremity has the form of a hook m, which hook is
furnished with two pins n, n, and a round hole o; in this hole is a small stud
which bears a small spring. This part resembles on a small scale the pressing
springs, Figure 11, with this difference, that the small spring in miniature is
larger at its extremity, while the springs of the pressing springs are of an equal
strength in their whole length. The two pins of the hook m, m, serve to limit the
action of the small spring; the hole k in the middle of the lever serves to fix it on
a small tube, Figure 13. This Figure presents a side view of the lever; through
the middle of this tube passes a screw pin, Figure 14, which is fixed into the
lower plate, the lower part of which is seen in Figure 8 at r, r, and the upper
part Figure 10, 8, 8; to prevent the lever from revolving freely round its axis
there is another stud with its spring, Figure 15, and Figure 10, t, t, t, which
acts on the lower pin of the lever, Figure 12, 1, and fixes it. After having
described each part separately, I will make known their different functions.
The pin of the lever, Figure 12, is continually in contact with the double
excentric or snail cam. I will suppose that this lever is at the nearest point of
the axis of the wheel; if the motion communicated to the wheel be from right
to left at each tooth put in motion, the pin of the lever in contact with the
excentric or snail cam will recede the tenth from the centre of the axis of the
wheel; at the ninth division of time it will be at its greatest distance, and if the
wheel advances one tooth farther, the lever compressed by its spring meeting no
longer with any resistance from the excentric or snail cam, will again enter into
its notch and resume its first position. The spring of the lever is stretched
during nine divisions of time, at the tenth the tension ceases, and the spring is
brought back. In a gun which is cocked and fired, the spring is stretched
during two divisions of time, and at the third the trigger falls, when the firing
takes place, In the machine that I describe, the spring is stretched during
nine divisions of time, and it is at the tenth only that the opposition of the

page_text: excentric or snail cam ceases, and the spring forces the lever to its position;
thus, when a wheel describes the half of its circumference the lever is naturally
stretched during nine divisions of time, at the tenth it escapes and will push
the following wheel one tenth. It is the ordinary course of calculation, where
in addition the tens are always brought over to the line following. Nothing is
easier than to construct a mechanism in which by the turn of a wheel divided
into ten parts, one ten is brought over on the following wheel, and to produce
a similar transmission on two or three wheels. But as soon as it becomes
necessary to produce this transmission upon a greater number of wheels
representing as many figures, the difficulties increase in proportion to the
number of figures. I have had constructed ten different mechanisms of
transmission; one of them for four figures answered completely, but the one
with five figures worked with more difficulty and overrun itself; others went as
far as six, seven, and eight figures. The greatest possible number of transmissions
that I have been able to produce with safety is with nine figures. The
construction of the machine required much care, and the results still uncertain;
if then a self-acting machine for addition is to be tried it must be in the
following manner :-All the wheels are placed at 9, the machine for instance is
placed at 999,999,999, then one unit must be added to the first on the left, all
the 9 must be changed into 0, the transmission must be produced on all the
wheels at the same time, and the sum of 1,000,000,000 ought to appear; if
this transmission is not effected easily and without error, the machine may be
unhesitatingly thrown aside as bad. In all the machines of our predecessors,
and in the first ten essays, the transmission was produced simultaneously, from
which resulted a resistance proportioned to the number of springs, and which
require great exercise of strength to be surmounted. I will speak only of two of
the first attempts of simultaneous transmission, because they are perfectly
applicable to machines of less than six wheels, and I claim this as part of the
Invention. Figure 16 represents the fragment of a similar machine: a, a, are
the wheels with twenty teeth, on which are engraved twice the series of figures
1, 2, 3, 4, 5, 6, 7, 8, 9, 0. In order to economise the expense of engraving
the engraved numbers can be printed on a band of paper that must be
afterwards pasted on the wheels; b, b, are the axes of the wheels fixed on the
pins; c, c, are the pressing springs destined to fix the wheels; d, d, are the
spring levers which are always placed between two wheels, the form of which
may be varied.
When the first wheel has made its demi-circumference, the
pin e, e, acts on the lever and makes the wheel following advance a tenth, but
as soon as the pin e has passed it is again compressed by the spring f, f, and is

page_text: brought back to its place; Figure 17 represents the most simple mechanism
that can be imagined, here the lever acts at the same time the part of the pressing
springs; but beyond six wheels these systems, as I have already mentioned,
require great exercise of strength, sudden shocks are the result when they are
worked rapidly, and in consequence of the frequent errors, arising from the
wheels overrunning themselves, one or the other of them going more quickly
than is necessary. I have then improved upon the principle of simultaneous
transmission for machines, of which the number of wheels are not beyond five
or six; I employ at present a mechanism which allows of producing a trans-
mission of twenty, thirty, one hundred figures, without exercise of strength, with
the greatest rapidity and complete safety. This transmission reposes on the
principle of succession, and this successive transmission is peculiarly the
Invention. It is effected thus: the wheels with twenty teeth, see Drawings
and descriptions, are placed horizontally on fixed pins in a straight or circular
line on a plate; above each wheel is engraved twice the series of numbers 0 to
9; each wheel is furnished with a pressing spring; above each wheel are fixed
double excentric cams, of which the point nearest the centre corresponds with
the cipher 0. Above these excentric cams are fixed double catch plates (sec
for these objects the Drawings and description; the point of the excentric cams
which corresponds with 0 is gradually removed from the centre, and at the
greatest distance it corresponds with the figure 9; in the intervals between
the wheels is formed a detent lever placed likewise on a pin, and furnished with
with a spring; this detent lever of a right angular form bears on its right
When the
extremity a pin, and on its left extremity a little spring driver.
wheel with teeth is at 0, the detent lever is pressed by its spring, and its right
extremity furnished with the pin is at the point of the cam the nearest to the
centre; as the wheel moves the detent lever slides to the most distant point of
If the wheel advances one unit the
the cam corresponding with the figure 9.
detent lever ceases to be removed from the centre by the cam, it returns
pressed by its spring to the point 0 of the cam, and pushes the next wheel one
unit. The little spring driver placed at the other extremity of the detent lever
is destined to let the second wheel pass without disturbing the first. In this
manner the transmission is easy and always safe, since the operator has only to
conquer the resistance of one single spring; the excentric cam may be replaced
by a pin placed on the lower face of the upper wheel. If a wheel with twenty
teeth is furnished with two similar pins, and they are made to act on the
detent lever, which must then be furnished with only one excentric notch, the
same effect will be obtained as with the excentric cam; the principle remains
the same, the form of the mechanism only is changed.

page_text: As before commencing an operation all the wheels must be placed at 0, it
would be very tiresome work if each wheel was obliged to be placed at 0
successively; the following mechanism produces this operation all at once:-
The lower plate has formed in it several semicircular notches, as may be seen
at Figure 8 and Figure 10, m, m, m. On the upper front of this same plate
is fixed a bar, Figure 9, and Figure 10, n, n, n, screws which go through the
semicircular notches without tightening the bar on the lower plate, so that it
can perform a semicircular movement in the notches, Figures 8, 9, 10, 0, 0, 0,
at equal distances. This bar is provided with pins, Figures 9, 10, p, p, p,
which, when a semicircular motion is given to it, act on the catch plates,
Figure 4, of the wheels, and place at once all the wheels at 9. In this position
all the wheels have their detent levers forced as far as possible, and in adding
a unit to the first wheel on the right, that is to say, in making this wheel go a
twentieth of its circumference, all the wheels are placed at 0 successively, but
so rapidly that the eye can scarcely perceive it. In order to direct the bar in
question in its semicircular movement, there is on the lower front of the lower
plate another bar, provided with a handle at its extremity; when this bar is
disengaged from the hook it becomes moveable, and if it is drawn in a horizontal
line it gives the semicircular movement to the long bar. This mechanism also
may be modified in different manners. The principal point is the new idea of
putting at 0 all the wheels of the machine by two movements.
In this rapid motion the wheels could easily overrun themselves, that is
to say, that the force of the spring might make them go beyond the points
noted 9, which would prevent the object being attained. I have endeavoured
to remedy this inconvenience, and in order to do so I have placed a spring
below each wheel, which renders this accident impossible. Each of these
springs are fixed to a stud, fixed under each wheel to the lower plate. As
soon as the wheel arrives at 9, this spring leans on the catch plate and
prevents the wheel from going farther. The pins of the bar serve at the same
time, when the bar is drawn in, to separate the springs, and to restore its liberty
of motion to the wheel, as may be seen, Figure 10, p, p, p, p.
If a plate is taken and pierced with holes which correspond with the figures
of the wheels placed below, and if all the mechanism that I have described is
covered, the first element of the calculating machine will be produced, which
may be called a counter (see Figure 18 and Figure 10. All that is to be
done is to furnish the first wheel on the right with a lever handle, which makes
it always go a twentieth of its circumference. The form of this lever varies
much, according to the purpose to which such a machine is applied. It is
easier to give an idea of the form of the lever employed by me in the expla

page_text: nation of the machine, by the appearance of the Drawing, Figure 10 A, then
it would be to describe it.
2.
SECOND ELEMENT, ADDITION.
With the exception of the lever destined to put the first wheel in motion,
the interior mechanism differs in no manner from the preceding. Only the
upper plate bears, besides the round openings, the semicircular grooves,
Figure 18, z, z, z, z, z. Through these grooves are perceived the teeth of the
wheels which move under the plate. On the edge of each groove are engraved
in the copper the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, upwards, so that the 0 is
placed at the lower extremity and the 9 at the upper extremity of the half
circle. The first groove on the right corresponds with the units, the second to
the tens, the third to the hundreds, &c. In order to make the teeth which
are perceived through the grooves move, a pointer is used, Figure 19, furnished
with a moveable point. In placing it in the space of the groove marked with
the figure 1, and in pushing it from right to left as far as the lower extremity
of the groove, where an obstacle is met with, then the dial will be advanced one
number. If, on the contrary, the pointer is placed in the groove at No. 9, and
conducted as far as the lower extremity of the semicircular groove, 9 teeth of
the dial will be advanced. This manner of conducting the teeth represents
the rotation of the figures. If an addition is to be made with the machine,
first of all it must be placed at 0, with the aid of the handle and the
bar above named, Figure 9, a, a, Figure 8, a, a. There is nothing to be
done after but to describe the figures on the machine, and the addition
will take place of itself. For instance, if there are to be added together

page_text: The sum of each line is always 9; the upper series in encreasing progression
serves for addition, the lower for subtraction. If 15,467 is to be deducted
from the sum of 26,789, the machine must first be put at 0, and on the second
series of figures must be placed the sum 26,789, and afterwards the sum to be
subtracted, 15,467, must be marked on the series of addition, the product will
be obtained, 11,322.
Until now I have spoken only of a counter addition and subtraction; now
I will give the description of a machine which makes calculations in the
four rules of arithmetic, the decimal fractions, and arithmetical progress.
Figure 20, exterior of the machine, reduced to nearly a third of its natural
size; Figure 21, a side view of the same machine; A, A, handles placed on
the sides; B, B, B, B, exterior circle; C, C, middle moveable part; D, locking
pin; E, handle; F, index; G, conducting handle; H, quotient handle; I, I,
handle to change the positions of the parts for addition or subtraction; K, feet;
L, stopping catch of the lever handle E.
EXTERIOR FIXED CIRCLE.
Nine dials, bearing the Figures 1 to 9 on one semicircle of each dial, and
on the other semicircle, in a contrary direction, the Figures 0 to 9; two hooks
to each dial. These dials of the exterior circle are destined to addition and
subtraction. They are perfectly analagous to those of which I have given a
description, with this only difference, that instead of being placed on a straight
line they are on a curved line. Besides these dials for addition and subtraction,
on the exterior fixed circle are seen small openings for the quotient, through
which are perceived the figures of the dial of the wheel of the quotient,
Figure 22.
DESCRIPTION OF THE MACHINE WITH THE EXTERIOR FIXED CIRCLE TAKEN OFF.
Figure 23 represents a series of wheels for addition and subtraction, the
same as in the machines used simply for addition and subtraction. One of
these wheels are represented on a larger scale at Figure 24, and at the side
view Figure 25; but below will be seen each wheel, Figure 24, b, and Figure
25, b, a cogged wheel divided into twenty parts, and acting upon a pinion,
Figure 23, c. The same Figure represents the locking catch M, which fixes
the middle moveable part. This middle moveable part, Figure 20, C, C, bears

page_text: DEVELOPEMENT WHEELS.
The developing wheel is placed on the lower plate of the middle moveable
part, Figure 27, by pins, Figure 27 and Figure 28. It is composed of three
principal parts, Figure 29. First, lower part or pinion, which acts upon the
central wheel; second, middle part, which has teeth that may be drawn in and
out at will, ; third, upper part, which supports the dial, the figures of which
are visible through the five openings of the upper plate of the middle moveable
part m, and Figure 30, Figure 31 m, Figure 26 m. The lower part offers
nothing remarkable; it is merely a pinion divided into twenty parts. The
middle part is a copper disk, of which the fifth part is furnished with nine
slides or grooves, Figure 32, notched in its thickness. In these slides are nine
moveable bolts, which force outside forms so many teeth, but when inside the
slides leave the edge of the disk perfectly free. If one of these bolts is forced
out of its slide the disk has one tooth; it has two if two bolts are forced, and
nine if all are out of their slides. Each bolt is furnished in the middle with
a pin, Figure 32, on which acts a little inclined plane o, notched in a moveable
plate p, which covers the disk and its slides. It is with the aid of this inclined
plane that the teeth are forced out of the slides and return into them.
short, the upper part of the dial m communicates by a pinion and rack q with
the notched plate, and through the upper plate may be seen how many teeth
are out of their slides. Now imagine the five developement wheels f, f, f, ƒ‚ ƒ‚
Figure 26, placed in a circular line on the lower part of the moveable part.
The great central wheel g has two hundred teeth, which act upon the pinions of
twenty teeth of the lower part of the wheels of developement. Divide the great
wheel in ten equal parts, and it will be easy to understand that, whilst it makes
the tenth part of a turn, the developement wheels make a complete turn on
their axis. Moreover, as these developement wheels have only the fifth of
their circumference furnished with teeth, and are placed in such a manner that
the part with teeth of the second wheel can only come in contact with the
circular line described by the exterior circle which supports the system of
addition wheels and their pinions, when the part with teeth of the first is
removed from it, and so on, it results from this that whilst the great wheel
In

page_text: performs only a tenth of its revolution, the parts with teeth of the develope-
ment wheels make a complete turn. If a machine is to be constructed with
six, eight, or twelve developement wheels, the part with teeth may also
necessarily occupy only the sixth, eighth, or twelfth of the circumference of
the developement wheels. It is not necessary to give the machine a circular
form; it can very well admit of a horizontal form.
Now suppose, by means of the pinions c, Figures 23 and 25, the develope-
ment wheels put in contact with the mechanism of the addition of the exterior
circle, so that the first developement wheel is placed opposite the units, the
second opposite the tens, the third opposite the hundreds, &c. If none of the
five developement wheels have teeth, the great central wheel g, Figure 26, can
be put in motion at will, without producing any change in the wheels destined
to addition. But if each of the developement wheels has a tooth, whilst the
great wheel performs the tenth part of the revolution, the five developement
wheels, each of which has, as I have already said, a tooth, will act by means
of the pinion upon the addition wheels; and if the latter are placed at O, they
will cause it to advance a unit, so that 11,111 appear. In this case eleven
thousand one hundred and eleven will have been multiplied by one. If the
great wheel had performed the two tenths, or the three teeth of its circum-
ference, the five developement wheels would have been multiplied two or three
times, and the products obtained would be 22,222 or 33,333. I will show an
example: If 26,546 are to be multiplied by 272, we will begin by marking
on the five developement wheels of the middle moveable part, Figure 20,
d, d, d, d, d, these figures, 26,546, which will appear through the openings
e, e, e, e, e. The first will have two bolts or teeth, the second six, the third five,
the fourth four, and the fifth six.
In the centre of the moveable part is a handle E, Figure 20, destined to put
in motion the great central wheel g, Figure 26, which gears with the pinions
of the developement wheels, Figures 29 and 31; this handle has in the centre,
Figure 33, a ratchet wheel r, of ten teeth, and fixed on the tube of the great
central wheel with its click s, fixed on itself on the handle, and only allowing
this latter to move from left to right. If it is conducted in the contrary
direction it will no longer move alone, but it then, with the assistance of the
clicks, puts in motion the great central wheel g. The handle is furnished
with an index hand F, which marks on the circular dial, divided into ten parts,
and marked with the figures 0 to 9, how many tenths the central wheel
advances, and consequently how many revolutions the developement wheels
make. It must also be remembered that the moveable part has in its lower
plate several notches k, k, k, Figures 25 and 26, in which is lodged the

page_text: locking catch M, Figure 23. By means of the locking pin D, Figures
20, 23, and 25, this locking catch is depressed, and the mobility of the middle
part no longer meeting with any obstacle, the first developement wheel is placed
on the right opposite the units of the exterior circle.*
.
In order to perform the multiplication given, the index hand F must be
placed on the figure 2 on the dial, and the handle turned until this hand F
arrives at 0, when it will be stopped by the stopping catch L, Figures 20 and
34, the catch i of which, see Figures 35 and 26, prevents the developement
wheels from continuing their rotatory motion. The multiplication will have
been performed by two, and the upper openings of addition will show the sum
of 53,092.
This first result once obtained, the locking pin must be pushed to D, Figure
20, which renders the middle part free, and with the assistance of the con-
ducting handle G, Figure 20, this middle part must be turned from right to
left, so that the units of the sum to be multiplied indicated on the developement
wheels come opposite the tens of the sum 53,092.
The handle must be placed on the figure 7, and turned until it comes to 0,
where it must be stopped again. The multiplicand will thus be multiplied by
70, and the product of this multiplication will be added at the same time to the
product of the multiplication by 2. Thus in the openings of addition the sum
of 1,911,312 will be read. The central plate must be again (by the conducting
handle g) advanced one tenth; the index hand must be put on number 2; and
in proceeding as already stated, the product of the multiplication by 200,
added to the product of the multiplication by 72, will be obtained: thus will
be found in the addition openings the entire product 7,220,512.
The Figures 17 and 18 represent two other systems of developement wheels,
on which the wheels are pushed back in the inside by springs; but I prefer
the developement wheels previously described.
To make a division I must proceed thus:-
Be it required to divide 7,220,512 by 26,546. The divisor 26,546 must be
marked on the developement wheels as in multiplication, and the dividend on
the lower series of figures of the exterior circle wheels destined to subtraction,
are discovered in closing the upper figures of addition by the handle of the
blade, Figure 20, I, I. The middle moveable plate must be placed in such
a manner that the first figure from left to right is placed opposite the first figure
of the dividend. It must then be marked completely the same as in multi-
plication, except that, instead of advancing, the central plate must always
recede one figure from left to right. The result of the operation, that is to
say, the number of times the 26,546 has been subtracted from 7,220,512, will

page_text: be given by the quotient 272, which will be seen in the special openings
a, a, a, a, Figure 20. Previous to commencing the operation of division, the
handle H, Fig. 20, must be moved to division as hereafter described.
In order to shew how many times one number has been subtracted from
another, (that is, to say,) the quotient, there is a particular mechanism in the
machine which remains inactive during all the other operations, and that is
marked only for division. Figure 20, H, represents a handle which conducts an
index hand; when this hand is opposite the 0 the machine is at rest; it works
when the index hand marks division. This handle H puts in motion a lever u,
Figure 27, placed on the lower surface of the lower plate of the middle move-
able part.
When the hand marks division, the lever forces out of the
circumference of the circle, Figure 27, a wheel x, which acts upon a pinion
of the first developement wheel, Figure 31, v, and which has a pin y which
counts on the wheels of the quotient, Figure 36, the number of turns made
by the developement wheels, which constitutes the quotient.
Besides the mechanical methods of multiplications and division that I have
described, I have another, much more simple and less expensive, of which I
subjoin a description. It is always by the aid of the system of successive
transmission, of which I have been the first to apply it to calculating machines,
and which I have described above, that the new method of multiplying and
dividing can be usefully put into execution.
The following is a description of the other improvement:―
To each dial of my adding apparatus a series of wheels must be added;
these wheels, with the assistance of the pinions, form a series of continued
gearings, and their speed increases upwards or diminishes downwards progres-
sively one tenth.
The following is the construction of the new machine :-
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Do. "
Hundreds.
"
Do. "
Tens.
Transmission the same as in the addition apparatus.
It will be easily understood by this position of the wheels, that when the
dial of the 9 of the nine tenths is put out of its place, as the wheel 9 will go

page_text: nine times as quickly as the dial of the units, there will be seen in the openings
of the adding apparatus (in consequence of the transmission of the units) the
sum of 81, or the product of 9 times 9; consequently, if 226 is to be multi-
plied by 2, it must be done thus:-The wheel of two of the series of hundred
must be turned two tenths; the wheel of the 6 of the series of tens turned
also two tenths; in short, the wheel of 6 of the series of units still two tenths,
and the sum of 532 will be found in the openings of the adding apparatus.
I here declare that I reserve to myself the exclusive privilege, not only of
the construction of these new mechanisms, as well as the power of varying
their forms, dimensions, and materials, but also of the application of the
developement wheels, and of the anulling of figures; that is to say, the
different means and methods of putting the machine at 0 at one or two
strokes.
And I also declare that I reserve to myself the exclusive privilege, not only
of the construction of these new machines, as well as the power of varying the
forms, dimensions, and metallic materials, or others of which they are composed,
but also the application of a series of continued gearings of wheel work, which
diminish or increase progressively (in arithmetical progression) the speed by a
tenth.
In witness whereof, I, the said David Isaac Wertheimber, have hereunto
set my hand and seal, this Twenty-eighth day of July, in the year of
our Lord One thousand eight hundred and forty-three.
D. I. (L.s.) WERTHEIMBER.
AND BE IT REMEMBERED, that on the Twenty-eighth day of July, in
the year of our Lord 1843, the aforesaid David Isaac Wertheimber came,
before our said Lady the Queen in Her Chancery, and acknowledged the
Specification aforesaid, and all and every thing therein contained and specified,