even with this evidence before him. A second declaration was obtained from the priest, and the bishop refused to go further. The sympathies of the community were evidently against the youthful zealots; and finally Pascal's father, convinced that enough had been done to vindicate the truth, successfully interposed as mediator.1

Pascal's health about this period appears to have undergone a change for the worse. He suffered from excessive headache and great internal heat and pain. A singular characteristic of his malady was his inability to swallow water unless it was heated, and even then only drop by drop. He was the subject, also, of a remarkable paralytic seizure thus described by his niece :

"He fell," she says, " into a very extraordinary state, as the result of his great application to his scientific studies; for the senses (les esprits) having mounted strongly to the brain, he became in a manner paralysed from the waist downwards. His legs and feet grew cold as marble; and they were obliged every day to put on socks soaked in brandy in order to try and restore heat in his feet. At the same time the physician interdicted him from all study."2

3

M. Lélut explains at length this attack of Pascal's as a well-known form of dynamical paralysis, of a similar nature with hypochondria and hysteria, proceeding from a disordered state of the nervous affections, the result

1 Cousin, app. 392.

2 Faugère, Lettres, Opuscules, &c., p. 452. It is difficult to make out the exact chronological sequence of some of the facts mentioned by Pascal's sister and niece. But a special accession of ill-health, according to both, seems to have followed his conversion at Rouen, and to have been amongst the causes of his removal to Paris in 1647. 3 Pp. 134-137.

of overwork acting upon a delicate organisation. The result is temporary, as distinguished from the paralysis arising from organic lesion, but indicates a highly susceptible constitution, the ready prey of melancholy and imaginative exaggeration, to which, in M. Lélut's opinion, Pascal was more or less liable during the remaining years of his life.

25

CHAPTER II.

PASCAL'S SCIENTIFIC DISCOVERIES.

PASCAL'S Scientific studies may be said to have begun with the remarkable incident of his youth already related, when he elaborated for himself, in a solitary chamber without books, thirty-two propositions of the first book of Euclid. On the other hand, these studies may be said to have extended to his closing years, when (in 1658 and 1659) he reverted to the abstruser mathematics, and made the cycloid a subject of special thought. But his scientific labours were in the main concentrated in the eight or ten years of his life which followed the removal of the family to Rouen. It will be convenient, therefore, to notice these labours and discoveries in a single chapter here, which will, at the same time, carry on the main history of his life during these years. All that can be expected from the present writer is a slight sketch of this part of the subject, which indeed is all that would be interesting to the general 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." 1 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,

2

It bears the date of

Pour les Coniques,' still survives. 1640, and occupies only six pages. 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 con

duct 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,

1 Jacqueline Pascal, p. 73.

2 Euvres de Blaise Pascal, t. 4. Paris, 1819.

ARITHMETICAL MACHINE.

27

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 condi