102 PHILIPS TECHNICAL REVIEW VOLUME 24

British Crown Copyright, Science Museum, London

THE CALCULATING MACHINE OF BLAISE PASCAL

The digital electronic computer PASCAL inPhilips Computing Centre has been given this namein honour of the French mathematician and philos-opher Blaise Pascal I), who in 1642, at the age ofeighteen, designed a calculating machine at Rouen.His obj eet with this machine, which became knownas the Pascaline, was to ease the burden on hisfather who, as a tax official, had a great deal offigure work to do. Although in the later years of hisshort life (Pascal died in 1662, almost exactly threehundred years ago) he was mainly concerned withother matters, he nevertheless had more than 50models made of his machine 2), each being an im-provement on the preceding ones. In 1645 he present-ed one to Chancellor Pierre Séguier, through whosegood offices he obtained in 1649 a royal privilegeon his invention; in 1647 he showed one to Des-cartes; in 1652 he finally arrived at a form thatsatisfied him; he sent one machine to Queen Chris-tin a of Sweden, and another he demonstrated per-sonally to a distinguished gathering in Paris -successfully, to judge from the poetic effusion of acontemporary 3).

1) W. Nijenhuis, The PASCAL, a fast digital electronic com-puter for the Philips Computing Centre, Philips tech.Rev. 23, 1-18, 1961/62 (No. 1). -It should be mentionedthat according to some, the name is an acronym derivedfrom Philips Automatic Sequence CALculator.

2) P. Humbert, L'oeuvre scientifique de Blaise Pascal, AlbinMichel, Paris 1947, p. 56.

681.14(091)

One model of the Pascaline dating from 1652has been well preserved and is to be seen at theConservatoire des Arts et Métiers, Paris. The titlephotograph is of a replica in the Science Museumin London. The Paris Conservatoire has threeother machines; all four bear the arms of the Pascalfamily (see fis. 1).

Various mechanical aids to arithmetical work,such as the time-honoured abacus and the grad-uated rods invented by Napier in 1617 (Napier's"bones"), were already in use before Pascal's ma-chine. But Pascal went an essential step further, inthat his machine contained a discontinuous mech-

3) Muse historique, Loret, of 14th April, 1652 (see the bookquoted in footnote 2), page 57).

"Je me rencontrai l'autre jourDedans le petit Luxembourg,Au que! beau lieu que Dieu bënieSe trouva grande compagnie,Tant duchesses que cordons bleus,Pour voir les effets merveilleuxD'un ouvrage d'arithmétique,Autrement de mathématique,Oil, par un talent sans égalUn auteur qn'on nornme Pascal,Fit voir une spéculativeSi claire et si persuasive,Touchant Ie calcul et Ie jet,Qu'on admira Ie grand projet.11 fit encor sur les fontainesDes démonstrations si pleinesD'esprit et de subtilité,Que Pon vit hien, en véri té,Qu'un très beau génie il possèdeEt qu'on le traita d'Archimède."

1962/63, No. 4/5 CALCULATING MACHINE OF BLAISE PASCAL 103

anism - the "sautoir" - for automatically carry-ing over tens, etc., in adding operations (fip,. 2).This is the basis of all digital techniques and thelogical consequence of the digital or positionalsystem of writing numbers.

Pascal's contemporaries were aware of the po-tentialities of his idea. Speaking of the "machinearithmétique" his sister Gilberte expressed itthus 4): "This accomplishment has been regardedas something new in nature, to have reduced to amachine a science that belongs entirely to the mind,and to have found the means of performing all oper-ations with complete certainty, without the needfor reasoning". People felt a kind of uneasiness oramazement about the Pascaline, such as many of

4) Pascal, Pensées et Opuscules, éd. par L. Brunschvicg,Hachette, Paris 1945 (p. 10).

a

b

Fig. 1. One of the four models of Pascal's calculating machinepreserved in the Conservatoire des Arts et Métiers, Paris.This model, like various others, was designed for the additionof money up to 1 million livres. For this purpose six decimalplaces are available, plus a seventh place with 20 units forthe sous and an eighth with 12 units for the deniers. (Thesame division, into pounds, shillings and pence, has persistedin Great Britain up to the present day.) The divisions canclearly be seen, on the removed cover (b), on the eight selectordiscs which serve for setting the digits to an amount tobe added.

It is worth noting that even the earliest calculating machinesdemonstrate in this way that digital compnting is not tiedto the decimal system. The binary system 1) employed inelectronic compnters is just another variant.

us feel today about automation, which seems ca-pable, through the use of electronic computers, oftaking over our whole function of logical thought.Gilberte Pascal, incidentally, went on to say:"This effort tired him very much, not because ofthe brainwork or of the mechanism, which he foundwithout any trouble, but because of the difficultyof making the workers understand all these things".Indeed one may assume that the realization of Pas-cal's invention was seriously hampered by the factthat the schooling and probably the equipment ofthe instrument makers at that time were inade-quate for making such intricate devices with thenecessary precision. No model of the Pascaline seemsto have worked for long without faults, and themanufacture of calculating machines on a commercialscale had to await the perfecting of the mechanismand a general improvement in the standard ofengineering.

Photo Conservatoire des A rts et Métiers, Paris

The machine is operated by inserting a peg in each of theeight selector dials and turning the dial through successivestops. The number thus set, and the result of the additionwhen the next number is set, appear in the sight holes in thecover, below which rotate the figure wheels seen in (a). Thecarry-over of the tens (and the twelves and twenties) isauurmatic,

Subtraction is done by pushing down the bar above the sightholes which carries the eight "register" wheels, thus exposingthe top halves of the sight holes, in which there now appearthe figures in the reverse sequence (the complements respec-tively of 10, 12 or 20). A number is set and subtracted by turn-ing the selector dial in the same direction as for addition. Pas-cal devised this method because his automatic carrying device,the "sautoir", worked only in one direction (see fig. 2).

104 PHILlPS TECHNICAL REVIEW

}Y./I.

Photo Science Museum, London

Fig. 2. Mechanism for automatic carry-over in Pascal's calculating machine.The drawing is reproduced from the Diderot and d'Alembert Encyclopedia,Paris 1752-1777. We have added the letters printed in red, for denotingcomponents. The mechanism (the "sautoir") works roughly as follows. Thedrawing in the middle shows all components for one digit; the selector dialis seen on the cover, at the right, and the figure wheel. or drum is on the left,under the cover. The movement of the dial is transmitted by two pairs of gearwheels (pin wheels) via the shaft A to the figure wheel. The middle pin wheelB on this shaft serves for carrying over the tens. In the top drawing can beseen the pin wheel Bl for one digit and the pin wheel B2 for the next higherdigit. Towards the end of a full revolution of BI the two pins Cl engage thetwo teeth of the doubly-bent lever Dl turning about the spindle A2 and liftthe lever. When Bl has completed a full revolution (i.e. completing a ten)the pins Cl release the teeth of DI' tbe lever drops and a pawl El on the leverpushes the pin-wheel B2 one step further. This is made clear by the bottomdrawing, which shows the components from the other side. The arm of pawlEl hinges on the spindle FI and is lifted by the leaf spring Gp so that whenDl drops, the pawl can engage a pin on B2 whereas during the lifting of Dl(and also when B2 is turned independently) the pins are free to slide off alongthe arm of El' A catch H2 prevents B2 from being dragged in the wrongdirection when Dl is lifted.

VOLUME 24

Some stages in this further develop-ment of calculating machines mayusefully be mentioned. In Britain, in1666, Morland built a calculatingmachine (two examples of which arepreserved in London) which, comparedwith the Pascaline, represented a stepbackwards. The machine worked onthe same principle - the adding offigures by successive rotations of a kindof selector dial through discrete angles -but there was no automatic carryingdevice. In 1672 Leibniz began work inHanover, and later In Paris, on acalculating machine based on a newidea, the "stepped gear", which couldalso perform multiplication and division.He worked on this for many years helpedby various instrument makers. It wasnot until 1694.that his first machine wascompleted, and even then seems neverto have been reliable in operation. Thismachine is still at Hanover, and areplica is in the Deutsches Museum inMunich. In Padua in 1709 Poleni utilizedthe same principle as Leibniz andconceivedmechanism

a novel, highly effectivefor the automatic carry-

over - virtually the same constructionis still used in mechanical countingmechanisms today, such as mileometers,gas and electricity meters, etc. Awoodenmodel of his machine so disappointedPoleni, however, that he destroyed it.A machine built in 1727 by AntoniusBraun fared better. Embodying a devicesimilar to that used by Leibniz andPoleni 5), this machine (jig. 3) was puttogether with great care and precision- Braun was apparently both inventorand craftsman - and gives the im-pression of having worked well althoughit does not appear to have been easy tooperate. After numerous other inter-mediate stages the first calculatingmachine to be manufactured on a com-mercial scale appeared in 1820; thismachine was designed by Charles XavierThomas of Colmar and remained on themarket, with few modifications, foralmost 100 years.5) J. Nagler, Beschreibung der Rechenmaschine

des Antonius Braun, Blätter für Technik-geschichte, No. 22, pp. 81-87, Springer,Vienna 1960.

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Fig. 3. Calculating machine madeby Antonius Braun in 1727. Itwas intended as an aid to surveyingwork, and could add, subtract,multiply and divide. Whether itworked satisfactorily is not known.The photo shows the machine with-out the cylindrical side panel thatprotects the mechanism fromdust. The top plate, with the set-ting levers and figure dials, bearsa Latin inscription in which themaker ("Opticus Et Mathemati-cus") humbly dedicates the instru-ment to the Emperor Charles VI.The instrument can be seen inthe Technisches Museum für In-dustrie und Gewerbe at Vienna 5).

CALCULATING MACHINE OF BLAISE PASCAL 105

Fig. 4. Sketch of W. Schickard's calculating machine, takenfrom his letter to Kepler of 25.2.1624. The text referring tothe machine reads (translated from the Latin): "I shall out-line the arithmetic apparatns in more detail another time;being in haste the following must suffice: aaa are the top endsof vertical cylinders, on which are written the multiplicationsof the figures, and those [multiplications] which are necessarycan be seen through the sliding windows bbb. Fixed on theinside to ddd are gear wheels with 10 teeth, that mesh withone another such that if any wheel on the right turns roundten times, the wheel to the left of it turns round once; or ifthe first-mentioned wheel makes a hundred turns, the third

wheel turns once, etc. To wit, [they all do this]~ D in the same direction, for which purpose an~ ~ identical intermediate wheel It was necessary.

??i: Any gi.ve~ inte~med~ate wheel. s.ets all to .the\V left of It 111 motion, In the requisrte proportion;

but none to the right of it, which called forspecial measures. The number on these wheels is visiblethrough the holes eee in the centre ledge. Finally, the letterse on the bottom ledge denote rotary knobs and the letters fare again holes through which figures used when workingcan he seen."

Photo Teelmisehes Museum, Vicnna

This account of the earliest history of the cal-culating machine cannot be closed without men-tioning that a few years ago Hammer and v.Freytag-Löringhoff 6) discovered a predecessor ofthe Pascaline: the hebraist, astronomer and mathe-matician Wilhelm Schickard at Tübingen had al-ready constructed in 1623, i.e. 20 years before Pascal,a calculating machine with automatic carry-overof tens which could apparently add and subtract(even alternately, which was not possible with thePascaline) and which, moreover, had a device thatfacilitated multiplication and division. In twoletters to Kepler, dated 20.9.1623 and 25.2.1624,Schickard reports and describes his invention(fig. 4), and on the basis of this description and asketch found in the papers Schickard left behind,a reconstruction has been made of the machine.Unlike Pascal however, Schickard evidently didnot arouse the interest of his contemporaries in hismachine. A second, improved model which he haddesigned was destroyed by fire before completion,and probably also because of the war at the timeand his death soon after (he and his whole familydied of the plague in 1635), his invention was im-mediately forgotten.

S. GRADSTEIN *).

6) B. v. Freytag-Löringhoff, Wiederentdeckung und Rekon-struktion der ältesten neuzeitlichen Rechenmaschine, VDI-Nachrichten 14, No. 39, 21st December 1960 (p. 4).

*) Philips Research Laboratories, Eindhoven.