Euler is to be measured by the assistance which he gave to his immediate successors, and here it is well known that he paved the way for the research of others in a more effectual manner than any of his contemporaries. The incessant repetition of his name in later authors is sufficient authority for this assertion. His writings are the first in which the modern analysis is uniformly the instrument of investigation. His predecessors, James and John Bernouilli, had perhaps the largest share in bringing the infinitesimal analysis of Newton and Leibnitz to the state of power required for extensive application. To Euler (besides important extensions) belongs the distinct merit of showing how to apply it to physical investigations, in conjunction with D’Alembert, who ran a splendid and contemporary career of a similar character in this respect. But though it would be perhaps admitted that there are individual results of the latter which exceed anything done by the former, in generality of application, there is no comparison whatsoever between the extent of the labours of the two. Euler was a man of a simple, reserved, and benevolent mind; with a strong sense of devotion, and a decided religious habit, according to the Calvinism of the Established Church of his country. At the court of Frederic, he himself conducted the devotions of his family every evening; a practice which then and there implied much moral courage, and insensibility to ridicule. But he possessed humour, for when he was asked to calculate the horoscope of one of the Russian princes, he quietly suggested that it was the official duty of the astronomer, and imposed the duty upon a colleague, who doubtless did not feel very much flattered by the application. There are few men whom the usual biographical formulæ as to moral character and habits would better fit than Euler, according to every account which has appeared of him. But such praises are no distinction; and it will be more to the purpose to state that the only occasion in which he was betrayed into printing a word which his eulogists have regretted, was in the dispute between Maupertuis and himself against others on the principle known by the name of _least action_, one of the warmest and most angry discussions which ever took place. Perhaps it is to the quiet abstraction of his life that he owed the perpetuity of his tenure of investigation. Many eminent mathematical discoverers have run the brilliant part of their career while comparatively young. Euler “ceased to calculate and to live” at once. But it may be that this was a part of his natural constitution, and a distinct feature of his mind. The nature of his writings rather confirms the latter supposition. There is the same difference between them and those of others, that there is between conversation and oratory. He seems to be moving in his natural element, where others are swimming for their lives.