MECHANICS, GENERAL PHYSICS, &c.
THE discoveries of Galileo, Descartes, and other mathematicians of the seventeenth century, had made known some of the most general and important laws which regu late the phenomena of moving bodies. The inertia, or the tendency of body, when left to itself, to preserve unchanged its condition either of motion or of rest; the effect of an impulse communicated to a body, or of two simultaneous impulses, had been carefully examined, and had led to the discovery of the composition of motion. The law of equilibrium, not in the lever alone, but in all the mechanical powers, had been determined, and the equality of action to re-action, or of the motion lost to the motion acquired,. had not only been established by reasoning, but confirmed by experiment. The fuller elucidation and farther extension of these principles were reserved for the period now treated of.
The developement of truth is often so gradual, that it is impossible to assign the time when certain principles have been first introduced into science. Thus, the prin ciple of Virtual Velocities, as it is termed, which is now recognized as regulating the equilibrium of all machines whatsoever, was perceived to hold in particular cases long before its full extent, or its perfect universality, was understood. Galileo made a great step toward the establishment of this principle when he generalized the pro perty of the lever, and showed, that an equilibrium takes place whenever the sums of the opposite momenta are equal, meaning by momentum the product of the force into the velocity of the point at which it is applied. This was carried farther by Wallis, who appears to have been the first writer who, in his Mechanica, published in 1669, founded an entire system of statics on the principle of Galileo, or the equality of the opposite momenta. The proposition, however, was first enunciated in its full generality, and with perfect by John Bernoulli, in a letter to Varignon, so late as the year 1717. Varignon inserted this letter at the end of the second edition of his Prqjet d'utne Nouvelle Mecanique, which was not published till 1725. The first edition of the same book appeared in 1687, and had the merit of deriving the whole theory of the equilibrium of the mechanical powers, from the single principle of the composition of forces. At first sight, appear in mechanics two indepen dent principles of equilibrium, that of the lever, or of equal and opposite momenta, and that of the composition of forces. To show that these coincide, and that the
one may be deduced from the other, is, therefore, doing a service to science, and this the ingenious author just named accomplished by help of a property of the parallelo gram, which he seems to have been the first who demonstrated.
The Principia Mathematica of Newton, published also in 1687, marks a great era in the history of human knowledge, and had the merit of effecting an almost en tire revolution in mechanics, by giving new powers and a new direction to its researches. In that work the composition of forces was treated independently of the composition of motion, and the equilibrium of the lever was deduced from the former, as well as in the treatise already mentioned. From the equality of action and re-action it was also inferred, that the state of the centre of gravity of any system of bodies, is not changed by the action of those bodies on one' another. This is a great proposition in the mechanics of the universe, and is one of the steps by which that science ascends from the earth to the heavens ; for it proves that the quantity of motion existing in nature, when estimated in any one given direction, continues al ways of the same amount.
But the new applications of mechanical reasoning,—the reduction of questions con cerning force and motion to questions of pure geometry,—and the mensuration of mechanical action by its nascent effects,—are what constitute the great glory of the Principia, considered as a treatise on the theory of motion. A transition was there made from the consideration of forces acting at stated intervals, to that of forces acting continually,—and from forces constant in quantity and direction to those that converge to a point, and vary as any function of the distance from that point; the proportionality of the areas described about the centre of force, to the times of their description ; the equality of the velocities generated in descending through the same distance by whatever route ; the relation between the squares of the velocities pro duced or extinguished, and the sum of the accelerating or retarding forces, comput ed with a reference, not to the time during which, but to the distance over which they have acted. These are a few of the mechanical and dynamical discoveries con tained in the same immortal work ; a fuller account of which belongs to the history of physical astronomy.