success—because the supposed explanation was one, he adds, “entirely consistent with the principles of my philosophy, apart from which he [Pascal], would not have thought of it, his own opinion being quite contrary.” {44} This may or may not be true. Pascal certainly held as long as he could to the old maxim of “Nature’s abhorrence of a vacuum.” “I do not think it allowable,” he says in his letter to M. Périer, “to depart lightly from maxims handed down to us by antiquity, unless compelled by invincible proofs.” But the notions of Descartes on the subject of a vacuum were at least as confused as those originally held by Pascal. {45a} It is absurd, therefore, to suppose that the latter could have been indebted to the principles of the Cartesian philosophy—not to say that this is a very different suggestion from that of the former letter, that Descartes himself had advised the experiment to be made. Evidently the older philosopher wrote under vague and somewhat inflated ideas of the value of his labours and his conversation with Pascal; while the latter, again, absorbed in his own thoughts on the subject, and unconscious that he had received any special impulse from Descartes or his philosophy, naturally made no mention of his name. His silence when Descartes’s accusation was communicated to him indicates the same somewhat lofty reserve and confidence in the independence of his own researches, rather than any contempt. He felt too sure of his position to think of defending himself, or of repelling what he no doubt regarded as not so much a deliberate assault on the value of his own work, as an exaggerated estimate by the other of his share in that work. Pascal’s researches regarding atmospheric pressure conducted him gradually to the examination of the general laws of the equilibrium of fluids. {45b} It had been already determined that the pressure of a fluid on its base is as the product of the base multiplied by the height of the fluid, and that all fluids press equally on all sides of the vessels enclosing them. But it still remained to determine exactly the measure of the pressure, in order to deduce the general conditions of equilibrium. With the view of ascertaining this, Pascal made two unequal apertures in a vessel filled with fluid, and enclosed on all sides. He then applied two pistons to these apertures, pressed by forces proportional to the respective apertures, and the fluid remained _in equilibrio_. “Having established this truth by two methods equally ingenious and satisfactory, he deduced from it the different cases of the equilibrium of fluids, and particularly with solid bodies, compressible and incompressible, when either partly or wholly immersed in them.”