STATICS, a subdivision of mechanics, meaning the part of the science in which equilibrating forges are considered, in opposition to DYNAMICS, in which the effects of forces producing motion are investigated : it is subdivided into the statics of rigid and of find bodies, the latter being called HYDROSTATICS. The general con siderations in MECHANICS, FORCE, PRESSURE, POWER, WEIGHT, &C., and such articles as LEVER, INCLINED PLANE, PULLEY, WHEEL AND AXLE, WEDGE, SCREW, may be consulted ; and also the articles VIRTUAL VELOCITIES, THEORY OF COUPLES, &C.
One foundation of statics was first given by Archimedes, and another by Stevinus,as noticed in MEenesies. The former is the more rigorous, the latter being open to some objections of a serious character. The discoveries of Galileo turned the attention of philoso phers upon dynamical problems, and the very easy connection which exists between the statical and dynamical measure of forces caused the theory of statics to be founded, almost up to the present day, upon dynamical principles. The taste for the purer form of statics has however revived, and we imagine that from henceforward it will be customary to make this science stand by itself.
The two great propositions of statics are that of the LEVER, demon strated in the article on that word, and that of the COMPOSITION of pressures, mentioned, but not demonstrated. Which of these shall be chosen as the foundation of the science, and how the other shall be deduced from it, are two Toints on which every writer on the subject should think much, as the character of his work in the eyes of others will, in a great measure, depend on his treatment of these parts of the subject. The method of Archimedes is, in our opinion, the soundest of all; but we say it without denying the possibility of exhibiting a direct statical proof of the composition of pressures which shall be equally satisfactory. In those which have hitherto been given, there is a want of distinction between the mathematical and physical assumptions : the student leaves off with no very clear perception how far the proposition is one of mathematics, and how far one of physics.
There is a general dislike and distrust of these proofs, which is evidence almost conclusive against them : any one who would improve them should not leave off until he has not only made a better separation of the physical axioms from the rest, but has put it in a form in which such separation is exceedingly obvious. Till this is done, the proofs in question will only stifle opposition, while the proposition of Archimedes forces conviction. If there bo anything likely to be mis understood in the latter, it applies as much to the former in all the cases which we have seen. [SUFFICIENT REAsoN.) Statics, like all other mechanical sciences, is usually placed among mixed 3LATHEMATICS. But the line which separates it from the pure sciences is almost imperceptible, and it would seem more reasonable to invent a third and intermediate distinctive term, than to place statics and electricity under the same name, to distinguish them from geometry. It would be easy to show that all which is common to geometry and statics, and not to electricity, is more extensive, more atriking, and more easily described, than the little which is common to statics and electricity, and not to geometry. In fact, when we say that both statics and electricity are concerned with properties of matter as distinguished from space, we have stated the whole of the common tie by which the two sciences are united : while geometry and statics possess in common almost equal degrees of evidence in their axioms, altogether the name rigour of deduction, and strong analogies in their theorems. Mr. Whowell has contended for the alteration of the loca tion of statics : hut ho carries the idea farther than we can follow him, for (' Mechanical Euclid;) he asserts that the axioms of statics are "self-evidently true," "not to be learnt from without, but from within." We may also refer to the same writer's History of Scientific Ideas,' vol. i., 1858. We shall enter further upon this point in the article SUFFICIENT REASON.