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.19
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,20 but he appears to have declined any description of 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.'21 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.22 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 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