Pascal pursued the subject more systematically, and wrote his Treatise of the Equilibrium of Fluids in 1653; in which he shows that a fluid, enclosed in a vessel, necessarily presses equally in all directions, by imagining two pistons, or sliding plugs, applied at different parts, the surface of one being centuple that of the other: it is clear, as he observes, that the force of one man acting at the first piston, will balance the force of one hundred men acting at the other. "And thus," says he, "it appears that a vessel full of water is a new principle of mechanics, and a new machine which will multiply force to any degree we choose." He also referred the equilibrium of fluids to the "principle of virtual velocities," which regulates the equilibrium of other machines. This, indeed, Galileo had done before him. It followed from this doctrine, that the pressure which is exercised by the lower parts of a fluid arises from the weight of the upper parts.

In all this there was nothing which was not easily assented to: but the extension of these doctrines to the air required an additional effort of mechanical conception. The pressure of the air on all sides of us, and its weight above us, were two truths which had never yet been apprehended with any kind of clearness. Seneca, indeed', talks of the "gravity of the air," and of its power of diffusing itself when condensed, as the causes of wind: but we can hardly

1 Quæst. Nat. v. 5.

consider such propriety of phraseology in him as more than a chance; for we see the value of his philosophy by what he immediately adds: "Do you think that we have forces by which we move ourselves, and that the air is left without any power of moving? when even water has a motion of its own, as we see in the growth of plants." We can hardly attach much value to such a recognition of the gravity and elasticity of the air.

Yet the effects of these causes were so numerous and obvious, that the Aristotelians had been obliged to invent a principle to account for them; namely, "nature's horror of a vacuum." To this principle

The action of a cupair is rarefied by

were referred many familiar phenomena, as suction, breathing, the action of a pair of bellows, its drawing water if immersed in water, its refusing to open when the vent is stopped up. ping instrument, in which the fire; the fact that water is supported when a full inverted bottle is placed in a basin; or when a full tube, open below and closed above, is similarly placed; the running out of the water, in this instance, when the top is opened; the action of a siphon, a syringe, a pump; the adhesion of two polished plates, and other facts, were all explained by the fuga vacui. Indeed, we must contend that the principle was a very good one, inasmuch as it brought together all these facts, which are really of the same kind, and referred them to a common cause. But when urged as an ultimate principle, it was not only

It was

unphilosophical, but imperfect and wrong. unphilosophical, because it introduced the notion of an emotion, horror, as an account of physical facts; it was imperfect, because it was at best only a law of phenomena, not pointing out any physical cause; and it was wrong, because it gave an unlimited extent to the effect. Accordingly, it led to mistakes. Thus Mersenne, in 1644, speaks of a siphon which shall go over a mountain, being ignorant then that the effect of such an instrument was limited to thirty-four feet. A few years later, however, he had detected this mistake; and in his third volume, published in 1647, he puts his siphon in his emendanda, and speaks correctly of the weight of air as supporting the mercury in the tube of Torricelli. It was, indeed, by the limit of this horror of a vacuum to the height of thirty-four feet, that the true principle was suggested. It was found that when attempts were made to raise water higher than this, nature tolerated a vacuum above the water which rose. In 1643, Torricelli tried to produce this vacuum at a smaller height, by using, instead of water, the heavier fluid, quicksilver; an attempt which shows that the true explanation, the balance of the weight of the water by another pressure, had already suggested itself. Indeed, this appears from other evidence. Galileo had already taught that the air has weight; and Baliani, writing to him in 1630, says, "If we were in a vacuum, the weight of the 2 Drinkwater's Galileo, p. 90.

VOL. II.

F

air above our heads would be felt."

Descartes also appears to have some share in this discovery; for, in a letter of the date of 1631, he explains the suspension of mercury in a tube, closed at top, by the pressure of the column of air reaching to the clouds.

Still men's minds wanted confirmation in this view: they found such confirmation, when, in 1647, Pascal showed practically, that if we alter the length of the superincumbent column of air by going to a high place, we alter the weight which it will support. This celebrated experiment was made by Pascal himself on a church steeple in Paris, the column of mercury in the Torricellian tube being used to compare the weights of the air; but he wrote to his brotherin-law, who lived near the high mountain of Puy de Dome in Auvergne, to request him to make the experiment there, where the result would be more decisive. "You see," he says, "that if it happens that the height of the mercury at the top of the hill be less than at the bottom, (which I have many reasons to believe, though all those who have thought about it are of a different opinion,) it will follow that the weight and pressure of the air are the sole cause of this suspension, and not the horror of a vacuum: since it is very certain that there is more air to weigh on it at the bottom than at the top; while we cannot say that nature abhors a vacuum at the foot of a mountain more than on its summit.". M. Perrier, Pascal's correspondent, made the observation as he had desired, and found a difference of

three inches of mercury, "which," he says, "ravished us with admiration and astonishment."

When the least obvious case of the operation of the pressure and weight of fluids had thus been made out, there were no further difficulties in the progress of the theory. When mathematicians began to consider more general cases than those of the action of gravity, there arose differences in the way of stating the appropriate principles: but none of these differences imply any different conception of the fundamental nature of fluid equilibrium.

Sect. 2.-Discovery of the Laws of Motion of Fluids.

THE art of conducting water in pipes, and of directing its motion for various purposes, is very old. When treated systematically, it has been termed Hydraulics: but Hydrodynamics is the general name of the science of the laws of the motions of fluids, under those or other circumstances. The art is as old as the commencement of civilization: the science does not ascend higher than the time of Newton, though attempts on such subjects were made by Galileo and his scholars.

When a fluid spouts from an orifice in a vessel, Castelli saw that the velocity of efflux depends on the depth of the orifice below the surface: but he erroneously judged the velocity to be exactly proportional to the depth. Torricelli found that the fluid, under the inevitable causes of defect which occur in