(236.) The principles have been definitively fixed by Galileo and his successors, down to Newton, on a basis of sound induction; and as they are perfectly general, and apply to every case, they are competent, as we have already before observed, to the solution of every problem that can occur in the deductive processes, by which phenomena are to be explained, or effects calculated. Hence, they include every question that can arise respecting the motions and rest of the smallest particles of matter, as well as of the largest masses. But the mode of reasoning from these general principles differs materially, whether we consider them as applied to masses of matter of a sensible size, or to those excessively minute, and perhaps indivisible, molecules of which such masses are composed. The investigations which relate to the latter subject are extremely intricate, as they necessarily involve the consideration of the hypotheses we may form respecting the intimate constitution of the several sorts of bodies above enumerated. (237.) On the other hand, those which respect the equilibrium and motions of sensible masses of matter are happily capable of being so managed as to render unnecessary the adoption of any particular hypothesis of structure. Thus, in reasoning respecting the application of forces to a solid mass, we suppose its parts indissolubly and unalterably connected; it matters not by what tie, provided this condition be satisfied, that one point of it cannot be moved without setting all the rest in motion, so that the relative situation of the parts one among another be not changed. This is the abstract notion of a solid which the mechanician employs in his reasonings. And their conclusions will apply to natural bodies, of course, only so far as they conform to such a definition. In strictness of speaking, however, there are no bodies which absolutely conform to it. No substance is known whose parts are absolutely incapable of yielding one among another; but the amount by which they do yield is so excessively small as to be demonstrably incapable, in most cases, of having any influence on the results: and in those where it has such influence, an especial investigation of its amount can always be made. This gives rise to two subdivisions of the application of mechanical reasonings to solid masses. Those which refer to the action of forces on flexible or elastic, and on inflexible or rigid, bodies, comprehending under the latter all such whose resistance to flexure or fracture is so very great as to permit our adoption of the language and ideas of the extreme case without fear of material error.