reader.

At the age of sixteen Pascal had already acquired a scientific reputation.  He is spoken of by the Duchess d’Aiguillon, in the interview with Richelieu in which she pleaded the cause of the exiled father, as “very

learned in mathematics;” and when his sister presented him after the dramatic representation on that occasion, the Duchess gave him “great commendation for his scientific attainments.” [26a]  When allowed by his father to pursue the natural bent of his genius, he made extraordinary progress.  He was still only twelve years of age, but Euclid’s Elements, as soon as put into his hands, were mastered by him without any explanation.  By-and-by he began to take an active part in the scientific discussions which took place at his father’s house; and his achievement in Conic Sections has been already narrated.

Descartes’s incredulity was not without reason; but there is no room to doubt the fact.  The little treatise, ‘Pour les Coniques,’ still survives.  It bears the date of 1640, and occupies only six pages. [26b]  After a very clear statement of his subject, the writer modestly concludes:—

“We have several other problems and theorems, and several consequences deducible from the preceding; but the mistrust which I have of my slight experience and capacity does not permit me to advance more till my present effort has passed the examination of able men who may oblige me by looking at it.  Afterwards, if they think it has sufficient merit to be continued, we shall endeavour to push our studies as far as God will give the power to conduct them.”

It is interesting to notice the beginning of relations betwixt Descartes and Pascal, considering the jealousy that afterwards arose betwixt them.  There is something of this feeling from the first in the older philosopher,

who was now in the forty-fourth year of his age, and in the full zenith of his great reputation.  He appears to have been greatly fascinated by Pascal’s peculiar powers; but the men were of too marked individuality of character, and too divergent in intellectual sympathy and personal aspiration, to appreciate each other fully.

Pascal’s next achievement was the invention of an arithmetical machine, chiefly prompted by a desire to assist his father in his official duties at Rouen.  He has given us no description of this machine from his own pen.  In the “Avis” addressed to all whose curiosity was excited by it, he excuses himself from this task by the natural remark that such a description would be useless without entering into a number of technical details unintelligible to the general reader; and that an actual inspection of it, combined with a brief vivâ voce explanation, would be far more satisfactory than any lengthened account in writing.  There is an elaborate description, however, of the machine, by Diderot, in the first volume of the ‘Encyclopédie,’ which is reprinted in the collection of Pascal’s scientific works.  Pascal’s main difficulties occurred, not in connection with the invention itself, which he seems to have very soon perfected according to his own conception, but with the construction of the instrument after he had mentally worked it out in all its details.  These difficulties proved so great, and so many imperfect specimens of the instrument were made, that, in order to secure both his reputation and his interest, he acquired in 1649 a special “privilége du Roi,” which confined the manufacture of the machine to himself, and such workmen as he should employ and sanction.  All others, “of whatever quality and

condition,” were prohibited from “making it, or causing it to be made, or selling it.”  But neither these precautions nor the merits of the invention itself, which were admitted by all competent judges, were of avail to make the instrument a practical success.  Many men of mathematical and mechanical genius in different countries have applied themselves to the same task.  The celebrated Leibnitz is said to have constructed a machine excelling Pascal’s in ingenuity and power.  In our own time, Mr Babbage’s wonderful achievement in the same direction attracted wide attention, and has been lavishly eulogised by Sir David Brewster and others:—

“While all previous contrivances,” says Sir David, [28a] “performed only particular arithmetical operations, under a sort of copartnery between the man and the machine, the extraordinary invention of Mr Babbage actually substitutes mechanism in the place of man.  A problem is given to the machine, and it solves it by computing a long series of numbers following some given law.  In this manner it calculates astronomical, logarithmic, and navigation tables, as well as tables of the powers and products of numbers.  It can integrate, too, innumerable equations of finite differences; and, in addition to these functions, it does its work cheaply and quickly; it corrects whatever errors are accidentally committed, and it prints all its calculations.”

Notwithstanding this brilliant picture, the great expense and the complications involved in the construction of such an instrument have seriously interfered with its success.  It is said that Mr Babbage’s machine, much more his marvellous analytic engine, have never yet been properly constructed. [28b]

Pascal fortunately turned his thoughts into a new and more fruitful channel.  We have now to contemplate him as one of an illustrious band associated in a great discovery in physical science.  Before his time considerable progress had been made towards a knowledge of atmospheric pressure.  Galileo and his pupil Torricelli had both been busy with the subject.  To Pascal, however, remains the glory of carrying successfully to a conclusion the suggestion of Torricelli, and of verifying the results which he had indicated.  Here, as in almost all such discoveries, it is found that different minds have been actively pursuing the same or similar lines of thought and observation, and controversy has arisen as to the exact merits of each; but Pascal has himself so candidly explained [29a] how far he was indebted to his great Italian predecessors, and how far he made original experiments of his own, that both his relation to them and his own work stand clearly apparent.

It had been found by the engineers engaged in the construction of fountains for Cosmo dei Medici in Florence that they could not raise water in an ordinary pump more than thirty-two feet above the reservoir.  The water, having reached this height, would rise no higher.  Galileo was appealed to for a solution of the difficulty.