1849 Patent 
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Description of the Arithmometer,
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. 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. 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 largersized 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 longlasting 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.
Description The largescale 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. 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 oneninth 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). 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 twotooth [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. 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 10tooth 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.
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 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. 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.

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