Des Cartes's disciples are of two classes, the "mathematical cultivators of physic," and the "deductive cultivators of philosophy." The first class of disciples are far in advance of their chief, and can only be considered as having received an impulse in a true direction. The second class unhesitatingly accepted his principles, and continued his thinking, although they developed his system in a different manner, and arrived at stronger conclusions than Des Cartes's courage would have supported. Some of the physical speculations of Des Cartes have been much ridiculed by subsequent writers; but many reasons may be urged, not only against that ridicule, but also against the more moderate censure which several able critics have dealt out against the intellectual character of Des Cartes. It should be remembered that the theories of all his predecessors were mere conjectural speculations respecting the places and paths of celestial bodies, etc. Innumerable hypotheses had been formed and found useless; and we ought rather to look to what Des Cartes did accomplish under the many difficulties of his position, in respect to the then, state of scientific knowledge, than to judge harshly of those speculations, which, though attended with no beneficial result to humanity at large, were doubtless well intended by their author. He was the first man who brought optical science under the command of mathematics, by the discovery of the law of refraction of the ordinary ray through diaphanous bodies; and probably there is scarcely a name on record, the bearer of which has given a greater impulse to mathematical and philosophical inquiry than Des Cartes. Although, as a mathematician, he published but little, yet in every subject which he has treated he has opened, not only a new field lor investigation, but also a new road for the investigators to proceed by. His discovery of the simple application of the notation of indices to algebraical powers, has totally remodelled the whole science of algebra. His conception of expressing the fundamental property of curve lines and curve surfaces by equations between the co-ordinates has led to an almost total supersedence of the geometry of the ancients. Contemporary with Galileo, and with a knowledge of the persecution to which that father of physics was being subjected by the Church, we are tempted to express our surprise that Des Cartes did not extend the right hand of fellowship, help, and sympathy to his brother philosopher; but it is, nevertheless, the fact, that either jealous of the fame of Galileo (as some have alleged.) or from a fear of being involved in the same persecutions, Des Cartes abstained from visiting the astronomer, although travelling for some time near his place of abode in Italy. Lewes, in his "Life of Des Cartes," says, "Des Cartes was a great thinker; but having said this we have almost exhausted the praise we can bestow on him as a man. In disposition he was timid to servility.