again, said, "Yes, my child, I grant your request; write to your father, that he may safely return." [Sidenote: 1639. Ætat. 16.] The duchess followed up the impression by an eulogium on Pascal, and by introducing Blaise; "He is but sixteen," she said, "but he is already a great mathematician." Jaqueline saw that the cardinal was favourably inclined; and with ready tact, added, that she had another request to prefer. "Ask what you will, my child," said the minister, "I can refuse you nothing." She begged that her father, on his return, might be permitted personally to thank the cardinal. This also was granted; and the family reaped the benefit. The cardinal received the exile graciously; and, two years after, named him intendant of Normandy at Rouen. Étienne removed with his family, in consequence, to that city. He filled the situation for seven years, enjoying the highest reputation for integrity and ability. About the same time, his daughter, Gilberte, formed an advantageous marriage with M. Périer, who had distinguished himself in a commission entrusted to him by the government in Normandy, and who afterwards bought the situation of counsellor to the court of aids of Clermont-Ferrand. [Sidenote: 1641. Ætat. 18.] Blaise, meanwhile, was absorbed in scientific pursuits. To the acquisition of Latin and Greek was added the study of logic and physics; every moment of his time was occupied--and even during meals the work of study went on. Charmed with the progress his son made, and his apparent facility in learning, the father was blind to the ill-effects that such constant application had on his health: at the age of eighteen, Pascal began to droop; the indisposition he suffered was slight, and he did not permit it to interfere with his studies; but neglected, and indeed increased, it at last entirely disorganised his fragile being. From that hour he never passed a single day free from pain. Repose, taken at intervals, mitigated his sufferings; but when better he eagerly returned to study--and with study illness recurred. [Sidenote: 1642. Ætat. 19.] His application was of the most arduous and intense description. At the age of nineteen he invented his arithmetical machine, considered one of the most wonderful discoveries yet put into practice. A machine capable of automatic combinations of numbers has always been a desideratum; and Pascal's was sufficiently well arranged to produce exact results--but it was very complex, expensive, and easily put out of order, and therefore of no general utility, though hailed by mathematicians as a most ingenious and successful invention. It cost him intense application, both for the mental combinations required, and the mechanical part of the execution:--his earnest and persevering study, and the great efforts of attention to which he put his brain, increased his ill health so much that he was obliged for a time to suspend his labours.