utility. These rejected contrivances have found their way, in many cases, into the mills of our manufacturers; and we now find them busily effecting purposes, far different from any which their inventor dreamed of, in the spinning-frames of Manchester.*

Another department of mechanical art, which has been enriched by this invention, has been that of tools. The great variety of new forms which it was necessary to produce, created the necessity of contriving and constructing a vast number of novel and most valuable tools, by which, with the aid of the lathe, and that alone, the required forms could be given to the different parts of the machinery with all the requisite accuracy.

6

The idea of calculation by mechanism is not new. Arithmetical instruments, such as the calculating boards of the ancients, on which they made their computations by the aid of countersthe Abacus, an instrument for computing by the aid of balls sliding upon parallel rods-the method of calculation invented by Baron Napier, called by him Rhabdology, and since called Napier's bones-the Swan Pan of the Chinese-and other similar contrivances, among which more particularly may be mentioned the Sliding Rule, of so much use in practical calculations to modern engineers, will occur to every reader: these may more properly be called arithmetical instruments, partaking more or less of a mechanical character. But the earliest piece of mechanism to which the name of a calculating machine' can fairly be given, appears to have been a machine invented by the celebrated Pascal. This philosopher and mathematician, at a very early age, being engaged with his father, who held an official situation in Upper Normandy, the duties of which required frequent numerical calculations, contrived a piece of mechanism to facilitate the performance of them. This mechanism consisted of a series of wheels, carrying cylindrical barrels, on which were engraved the ten arithmetical characters, in a manner not very dissimilar to that already described. The wheel which expressed each order of units was so connected with the wheel which expressed the superior order, that when the former passed from 9 to 0, the latter was necessarily advanced one figure; and thus the process of carrying was executed by mechanism: when one number was to be added to another by this machine, the addition

* An eminent and wealthy retired manufacturer at Manchester assured us, that on the occasion of a visit to London, when he was favoured with a view of the calculating machinery, he found in it mechanical contrivances, which he subsequently introduced with the greatest advantage into his own spinning-machinery.

of each figure to the other was performed by the hand; when it was required to add more than two numbers, the additions were performed in the same manner successively; the second was added to the first, the third to their sum, and so on.

Subtraction was reduced to addition by the method of arithmetical complements; multiplication was performed by a succession of additions; and division by a succession of subtractions. In all cases, however, the operations were executed from wheel to wheel by the hand.*

This mechanism, which was invented about the year 1650, does not appear ever to have been brought into any practical use; and seems to have speedily found its appropriate place in a museum of curiosities. It was capable of performing only particular arithmetical operations, and these subject to all the chances of error in manipulation; attended also with little more expedition (if so much), as would be attained by the pen of an expert

computer.

This attempt of Pascal was followed by various others, with very little improvement, and with no additional success. Polenus, a learned and ingenious Italian, invented a machine by which multiplication was performed, but which does not appear to have afforded any material facilities, nor any more security against error than the common process of the pen. A similar attempt was made by Sir Samuel Moreland, who is described as having transferred to wheel-work the figures of Napier's bones, and as having made some additions to the machine of Pascal.†

Grillet, a French mechanician, made a like attempt with as little success. Another contrivance for mechanical calculation was made by Saunderson. Mechanical contrivances for performing particular arithmetical processes were also made about a century ago by Delepréne and Boitissendeau; but they were merely modifications of Pascal's, without varying or extending its objects. But one of the most remarkable attempts of this kind which has been made since that of Pascal, was a machine invented by Leibnitz, of which we are not aware that any detailed or intelligible description was ever published. Leibnitz described its mode of operation, and its results, in the Berlin Miscellany, but he appears to have declined any description of

* See a description of this machine by Diderot, in the Encyc. Method.; also in the works of Pascal, tom. iv., p. 7; Paris, 1819.

† Equidem Morelandus in Anglia, tubæ stentoriæ author, Rhabdologiam ex baculis in cylindrulos transtulit, et additiones auxiliares peragit in adjuncta machina additionum Pascaliana.

Tom. i., p. 317.

6

its details. In a letter addressed by him to Bernoulli, in answer to a request of the latter that he would afford a description of the machinery, he says, Descriptionem ejus dare accuratam res non facilis foret. De effectu ex eo judicaveris quod ad multiplicandum numerum sex figurarum, e. g. rotam quamdam tantum sexies gyrari necesse est, nulla alia opera mentis, • nullis additionibus intervenientibus; quo facto, integrum absolutumque productum oculis objicietur.' * He goes on to say that the process of division is performed independently of a succession of subtractions, such as that used by Pascal.

It appears that this machine was one of an extremely complicated nature, which would be attended with considerable expense of construction, and only fit to be used in cases where numerous and expensive calculations were necessary. Leibnitz observes to his correspondent, who required whether it might not be brought into common use, Non est facta pro his qui olera aut 'pisculos vendunt, sed pro observatoriis aut cameris computorum, aut aliis, qui sumptus facile ferunt et multo calculo egent.' Nevertheless, it does not appear that this contrivance, of which the inventor states that he caused two models to be made, was ever applied to any useful purpose; nor indeed do the mechanical details of the invention appear ever to have been published.

Even had the mechanism of these machines performed all which their inventors expected from them, they would have been still altogether inapplicable for the purposes to which it is proposed that the calculating machinery of Mr Babbage shall be applied. They were all constructed with a view to perform particular arithmetical operations, and in all of them the accuracy of the result depended more or less upon manipulation. The principle of the calculating machinery of Mr Babbage is perfectly general in its nature, not depending on any particular arithmetical operation, and is equally applicable to numerical tables of every kind. This distinguishing characteristic was well expressed by Mr Colebrooke in his address to the Astronomical Society on this invention. The principle which essentially distinguishes Mr Babbage's invention from all these is, that it proposes to calculate a series of numbers following any law, by the aid of 'differences, and that by setting a few figures at the outset, a

*Com. Epist. tom. i., p. 289.

† Sed machinam esse sumptuosam et multarum rotarum instar horologii Huygenius aliquoties admonuit ut absolvi curarem; quod non sine magno sumptu tædioque factum est, dum varie mihi cum opificibus fuit conflictandum.Com. Epist.

long series of numbers is readily produced by a mechanical operation. The method of differences in a very wide sense is 'the mathematical principle of the contrivance. A machine to add a number of arbitrary figures together is no economy of time or trouble, since each individual figure must be placed in 'the machine; but it is otherwise when those figures follow some law. The insertion of a few at first determines the magnitude of the next, and those of the succeeding. It is this constant repetition of similar operations which renders the computation of tables a fit subject for the application of machinery. Mr Babbage's invention puts an engine in the place of the computer; the question is set to the instrument, or the instrument is set to the question, and by simply giving it motion the 'solution is wrought, and a string of answers is exhibited.' But perhaps the greatest of its advantages is, that it prints what it calculates; and this completely precludes the possibility of error in those numerical results which pass into the hands of the public. The usefulness of the instrument,' says Mr Colebrooke, is thus more than doubled; for it not only saves time and trouble in transcribing results into a tabular form, and setting types for the printing of the table, but it likewise accomplishes the yet more important object of ensuring accuracy, obviating numerous sources of error through the careless hands of transcribers and compositors.'

Some solicitude will doubtless be felt respecting the present state of the calculating machinery, and the probable period of its completion. In the beginning of the year 1829, Government directed the Royal Society to institute such enquiries as would enable them to report upon the state to which it had then arrived; and also whether the progress made in its construction confirmed them in the opinion which they had formerly expressed, that it would ultimately prove adequate to the important object which it was intended to attain. The Royal Society, in accordance with these directions, appointed a Committee to make the necessary enquiry, and report. This Committee consisted of Mr Davies Gilbert, then President, the Secretaries, Sir John Herschel, Mr Francis Baily, Mr Brunel, engineer, Mr Donkin, engineer, Mr G. Rennie, engineer, Mr Barton, comptroller of the Mint, and Mr Warburton, M.P. The voluminous drawings, the various tools, and the portion of the machinery then executed, underwent a close and elaborate examination by this Committee, who reported upon it to the Society.

They stated in their report, that they declined the consideration of the principle on which the practicability of the machinery

depends, and of the public utility of the object which it proposes to attain; because they considered the former fully admitted, and the latter obvious to all who consider the immense advantage of accurate numerical tables in all matters of calculation, especially in those which relate to astronomy and navigation, and the great variety and extent of those which it is professedly the object of the machinery to calculate and print with perfect accuracy ;—that absolute accuracy being one of the prominent pretensions of the undertaking, they had directed their attention especially to this point, by careful examination of the drawings and of the work already executed, and by repeated conferences with Mr Babbage on the subject;-that the result of their enquiry was, that such precautions appeared to have been taken in every part of the contrivance, and so fully aware was the inventor of every circumstance which might by possibility produce error, that they had no hesitation in stating their belief that these precautions were effectual, and that whatever the machine would do, it would do truly.

They further stated, that the progress which Mr Babbage had then made, considering the very great difficulties to be overcome in an undertaking of so novel a kind, fully equalled any expectations that could reasonably have been formed; and that although several years had elapsed since the commencement of the undertaking, yet when the necessity of constructing plans, sections, elevations, and working drawings of every part; of constructing, and in many cases inventing, tools and machinery of great expense and complexity, necessary to form with the requisite precision parts of the apparatus differing from any which had previously been introduced in ordinary mechanical works; of making many trials to ascertain the value of each proposed contrivance; of altering, improving, and simplifying the drawings; -that, considering all these matters, the Committee, instead of feeling surprise at the time which the work has occupied, felt more disposed to wonder at the possibility of accomplishing so much.

The Committee expressed their confident opinion of the adequacy of the machinery to work under all the friction and strain to which it can be exposed; of its durability, strength, solidity, and equilibrium; of the prevention of, or compensation for, wear by friction; of the accuracy of the various adjustments; and of the judgment and discretion displayed by the inventor, in his determination to admit into the mechanism nothing but the very best and most finished workmanship; as a contrary course would have been false economy, and might have led to the loss of the whole capital expended on it.

Finally, considering all that had come before them, and