* English translation by Brian Stone, Australia 2007

PATENT   N° 8282
of 25 April 1849

Description of the Arithmometer,
calculating machine invented and perfected  by Charles Xavier Thomas (de Colmar),
 domiciled in Paris, Rue du Helder, 13

Preliminary considerations
  

This machine, by the use of which all arithmetic operations may be easily and promptly carried out, is the perfected form of the one presented by Mr Thomas (de Colmar) in 1822 to the Société d’Encouragement pour l’Industrie Nationale, for which he had obtained a patent in November 1820 (See N° CCXXI of November 1822, Bulletin of the Société d’Encouragement pour l’Industrie Nationale).

It was in 1818 that Mr Thomas began trials of this invention which is the first of its kind.

Pascal had invented a mere adding machine which was of no practical use. One hundred years later, Mr Lépine presented an adding machine which was improved but still lacked real usefulness. Thus for more than 200 years many have busied themselves seeking the way to expedite arithmetic operations with calculating machines ; not one has succeeded before Mr Thomas (de Colmar).

His arithmometer is an entirely new invention ; it is no simple machine for addition only, but rather a mechanical multiplier with which the most complicated problems can be solved.

The four fundamental arithmetic operations are carried out with astonishing speed and precision.
The rules of three, and the extraction of square and cube roots, are performed as if by magic.

This machine, in comparison with those which have appeared previously, is like a person well skilled in arithmetic alongside a man who can only count on his fingers.

Mr Thomas' first machine embodied the discovery of the secret of multiplying a number of Figures by one [digit?] ; The machine with which we are now concerned is the developed and perfected version of that original ; it is the fruit of thirty years of daytime and evening work [or, of travail always on the point of success]. What has been impossible for centuries is today completed by Mr Thomas ; the success and the utility are beyond dispute.
More than fifty thousand francs have been spent by the inventor on the numerous prototypes which he has had constructed.
Mr Thomas is no artisan ; he has had to rely on workmen to whom he had to explain his ideas, but after two or three years of work, a fresh start would become necessary : the component parts were badly made, and so the mechanism did not work smoothly.

At last Mr Thomas found a young man, Mr Piolaine, the son of a clockmaker of Neuilly, who was put in charge of first equipping Mr Thomas' workshop, and then fabricating, under his eye, a machine according to a new system. Soon the young man became bored with this work and went to England. During this time, Mr Thomas had had a larger-sized arithmometer constructed, but a number of parts had not been completed by the technician : the machine was inoperable.

Persevering still, at his own expense he brought back Mr Piolaine from England, and instructed him firstly to put this arithmometer into working order ; so he assembled all the component parts, remade many of them, and the task was completed in July 1848. This machine functioned perfectly. 

Immediately after this, the building of a new machine was begun according to a simpler system. However the young man contracted a long-lasting illness to which he succumbed in 1848, without finishing either the machine which he had started upon prior to his departure for England, or the one he had begun after the successful completion of the large machine.

 Several technicians are at work to complete under the supervision of Mr Thomas the two machines commenced before the death of Mr Piolaine, and some other less important examples will shortly be manufactured ; these will provide the means for demonstrating new and significant improvements.
The large machine has been complete for ten months, but it is only today that Monsieur Thomas is claiming his patent. He had believed he could finalize his numerous improvement initiatives before worrying about patents, but an article which appeared in several newspapers showed him that others were also busy on calculating machines ; he realized that it would be prudent to put on record the date of these improvements and the additions which he had made to his arithmometer.

Description
  

The large-scale machine has twice the [linear] dimensions of the one which will be available to the public ; hence it occupies eight times the volume of the latter.

Here we shall give the dimensions of the small machine.

Between two brass plates 18cm by 5cm, connected together by four 9cm spacer pillars, are brought together the multiplicand, the multiplier and their joint motion.

This enclosure has a brass front plate in which are machined as many slots as there are digits in the multiplicand, plus one for the multiplier.
In these slots there are sliding knobs[, one] for indicating the [number of significant] Figures in the multiplicand and [one for each of] the digits of the multiplier.

On a separate plate 28cm by 24cm are mounted several dial wheels, each one bearing the ten Figures from 0 to 9, which indicate, through small window holes cut in the plate, the product values which are obtained. This plate can lift and slide lengthwise in the enclosure along a steel rod which serves as a hinge for it, such that the row of ten dial wheels is displaced, rendering them successively independent of the motion of the mechanism.

Under each dial wheel is fixed a wheel with ten teeth, and the dial carries a point or short projecting arm which releases a ratchet when the dial moves from the 9 to the 0 position or from 0 to 9 (See Fig.1 & Fig.2).

 Inside are (Figure 2) cylinders, slotted with 20 teeth, of which eleven are cut along the full length, while the remaining nine are shortened by one-ninth parts, in staircase form representing multiplicand digit values from 1 to 9  (see Figure 5 which shows one of the cylinders, each 7cm long). A tenth movable tooth is placed following these 9 teeth, as explained below.

 The teeth on the cylinders can engage in a small wheel with ten teeth carried by a fork attached to the indicating knob. The small wheel slides along a square arbor and can be carried along to the multiplicand digit value. That position causes it to be engaged by the section of the teeth whose number is equal to the Figure indicated by the knob. When the cylinder has completed one turn, it will have rotated the small wheel through the number of teeth which that Figure indicates, the dial making the Figure visible. A ratchet lifted by the cylinder teeth accompanies the small wheels. When they are no longer engaged with the teeth of the cylinder, the ratchet falls and holds them in place. 

To the left of these cylinders is another cylinder of spiral shape (see Figure 7). A longitudinal slot cut in it allows an arm moved by a knob to adjust the number of rotations through which the cylinders must turn together to represent one of the digits of the multiplier.

Thus when the multiplier knob is at N° 9, the multiplicand, of up to ten digits, will be multiplied by 9.

All the cylinders of the multiplicand, together with that of the multiplier, mesh with a set of gear wheels, one having a handle attached, in such a way that every rotation of the handle turns all the cylinders together by one rotation (this gearing arrangement is shown in Figure 3).

This same movement can be obtained by means of a [bearing] shaft fastened along the plate, holding gears on edge [bevel gears?] in mesh with those of the cylinders. This is a much better mechanism, but more costly. 

On the cylinders other than the first and last there is a gearing system to implement the carries. A movable tooth, running the full length of the cylinder, replaces the tenth tooth. It is recessed in the cylinder (Fig. 6) and only projects at the level of the other teeth to engage the pinion when [it is necessary] to produce a carry (Fig. 6).

To achieve this, a coil spring along the cylinder arbor, as seen in Figure 6, pushes  the tooth out against two inclined planes ; an[other] inclined plane fixed on the [mechanism mounting] plate compresses the spring by pushing the tooth back at each turn of the cylinder ; a small lever which communicates with the dial at the right holds the spring compressed while there is no carry evident, but when the dial passes from 9 to 0 or from 0 to 9, the little pin or arm on the dial releases the ratchet, and the spring presses [out] the tooth of the digit at the left, so that when the [new] digit [value] is produced, the carry is added.

 Here we must explain why a total of eleven teeth are cut in the cylinders ; this gap is essential for the carry operation ; every cylinder must be able to receive the carry after producing its [new] value. In order for this to occur, the carries must be made successively, one after the other : thus the tens must be produced before the hundreds, those [carries] of the hundreds before those of the thousands and so on. That is why the cylinders must be positioned so as to engage with the wheels of the multiplicand Figure one after the other. A two-tooth [rotational] difference must be left between every [pair of] cylinder[s] ; that is, the second cylinder will have a gap [delay] of 2 teeth, the third 4 teeth, the fifth [sic: fourth?] 6 teeth, the sixth [sic] 8 teeth, etc.
Each cylinder must have two teeth cut off [omitted] for each multiplicand digit which the machine is built to accommodate, plus one for the carry, which implies eleven teeth for a five-digit machine. 

Subtractions and divisions being the inverse operations to additions and multiplications, to do these operations there has been added behind the arbors which communicate the movement to the dials, and [also] on the same arbors, a double system of gearing by means of which the dials can be made to turn from right to left and from left to right (Figure 5).

The square arbors of the gear wheels which engage with the cylinders are extended beyond the enclosure, to just below the dials ; a tube on which are fixed two 10-tooth crown wheels [bevel gears], facing each other, is fitted on to the arbors such that it can engage one or the other crown wheel with the gear which controls the dials.
It will readily be imagined that engagement of one of them turns the dial to the left and the other to the right. A straight-sided bar which engages with grooves machined in the tubes causes them to move backward or forward together to change the engagement with the dials. This movement is operated by a knob fitted with a pointer ; by turning the knob, the dials are prepared for multiplication or division at will. (This knob is shown on Figures 1 & 2). It is located at the top of the multiplier slot.

How the Arithmometer is used  

The machine is so laid out [?lit. by its position, posture] that it imitates perfectly the 4 operations of arithmetic, and the movements of its mechanism seem to act out [lit. paint] all the reasoning that is required to arrive at the result.

Addition

The user should move the knobs to the required Figures, along the slots, and move that of the multiplier, farthest to the left, to 1. Then the handle is turned through one complete turn until the hand is restrained [by the stop], and the dials now show the Figures selected by the knobs.

If this operation is performed twice, two equal numbers will have been added, and the dials will immediately show the total, for example :

35,695 + 35,695 = 71,390

This total will be seen to appear in the small windows.

If it is desired to add another different number, the knobs should be moved to indicate the Figures of that number, the multiplier should be reset to 1, and a turn of the handle adds that third number to the two others, giving the result in the windows, and so on for every number which one desires to add.

Multiplication

For example  : 35,695 x 2 = 71,390

Proceed as for addition, with the difference that instead of setting the multiplier knob twice to 1, it should be set to 2, and the handle should be rotated twice. It will be understood that the same applies if the same number is to be multiplied by any other digit, it is only necessary to set the knob to that multiplier digit.
If the required multiplication is  25 x 25, proceed as though with pen and paper, first multiplying by the units digit 25 x 5, which will give 125, then lifting the dial plate and moving it one notch from left to right, so as not to affect the units further. The 5 will be disengaged, and so the first [more significant] digit will be active ; set the multiplier knob to the second digit, that is, set the tens to 2. By turning the handle, the tens product is added to the first total giving 625, the product of 25 x 25, and so on for the the hundreds, thousands and tens of thousands.

If the requirement is to multiply multiple digits by multiple digits, the machine as built can multiply five digits by five digits ; a version will be constructed to multiply ten digits by ten digits, which will give 20 digits in the product.

Subraction 

Proceed exactly as for addition ; the sole change is to turn the pointer to the subtraction side. This causes the dials to rotate in the reverse direction.

Division 

Turn the pointer to the division or subtraction side, which are the same thing.

For example  : to divide 625 by 25. 

Lift the dial cover plate for access to turn the dial knobs, and set in them the number 625, or alternatively achieve this with a turn of the handle, as would be done in setting up an addition.

So the dividend 625 is displayed in the windows, and the divisor 25 is set by the multiplicand knobs.

Move back the dial plate to put the 5 out of range, and turn the handle until the number to be divided is smaller than the divisor. The multiplier knob will have shown how many times the divisor was contained in the dividend, and the dials will show the number which remains to be divided.

Move the dial plate one notch to the right, and proceed as for the tens, it will have been found that in the tens, 25 was contained twice in 62, and that there remained 125.
On the dials, the second time, it will have been found that 25 was contained 5 times in 125, and that only zeros remained [the remainder was zero].

A more detailed instruction book will show all the advantages which can be realized with this machine for large calculations of arithmetic and algebra.

The reader will be astonished to see how easily even the largest problems can be solved.

Signed in two copies at Paris on the 23 April 1849

Thomas

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Table of diagrams : 

* Transcribed from original patent manuscript by Valéry Monnier, France 2006.
* English translation by Brian Stone, Australia 2007