Whence, now, is derived this strange part which the principle of virtual motion plays in mechanics? For the present I shall only make this reply. It would be difficult for me to tell the difference of impression which Lagrange's proof of the principle made on me when I first took it up as a student and when I subsequently resumed it after having made historical researches. It first appeared to me insipid, chiefly on account of the pulleys and the cords which did not fit in with the mathematical view, and whose action I would much rather have discovered from the principle itself than have taken for granted. But now that I have studied the history of the science I cannot imagine a more beautiful demonstration. In fact, through all mechanics it is this self-same principle of excluded perpetual motion which accomplishes almost all, which displeased Lagrange, but which he still had to employ, at least tacitly, in his own demonstration. If we give this principle its proper place and setting, the paradox is explained. The principle of excluded perpetual motion is thus no new discovery; it has been the guiding idea, for three hundred years, of all the great inquirers. But the principle cannot properly be _based_ upon mechanical perceptions. For long before the development of mechanics the conviction of its truth existed and even contributed to that development. Its power of conviction, therefore, must have more universal and deeper roots. We shall revert to this point. II. MECHANICAL PHYSICS. It cannot be denied that an unmistakable tendency has prevailed, from Democritus to the present day, to explain _all_ physical events _mechanically_. Not to mention earlier obscure expressions of that tendency we read in Huygens the following:[51] "There can be no doubt that light consists of the _motion_ of a certain substance. For if we examine its production, we find that here on earth it is principally fire and flame which engender it, both of which contain beyond doubt bodies which are in rapid movement, since they dissolve and destroy many other bodies more solid than they: while if we regard its effects, we see that when light is accumulated, say by concave mirrors, it has the property of combustion just as fire has, that is to say, it disunites the parts of bodies, which is assuredly a proof of _motion_, at least in the _true philosophy_, in which the causes of all natural effects are conceived as _mechanical_ causes. Which in my judgment must be accomplished or all hope of ever understanding physics renounced."[52] S. Carnot,[53] in introducing the principle of excluded perpetual motion into the theory of heat, makes the following apology: