All have occasional experience of the fact that a person pushed on one side beyond a certain degree loses his balance and falls. It is observed that a stone flung, or an arrow shot, does not proceed in a straight line, but comes to the earth after pursuing a course which deviates more and more from its original course. When trying to break a stick across the knee, it is found that success is easier if the stick is seized at considerable distances from the knee on each side than if seized close to the knee. Daily use of a spear draws attention to the truth that by thrusting its point under a stone and depressing the shaft, the stone may be raised the more readily the further away the hand is toward the end. Here, then, are sundry experiences, eventually grouped into empirical generalizations, which serve to guide conduct in certain simple cases. How does mechanical science evolve from these experiences? To reach a formula expressing the powers of the lever, it supposes a lever which does not, like the stick, admit of being bent, but is absolutely rigid, and it supposes a fulcrum not having a broad surface, like that of one ordinarily used, but a fulcrum without breadth, and it supposes that the weight to be raised bears on a definite point, instead of bearing over a considerable portion of the lever. Similarly with the leaning body, which, passing a certain inclination, overbalances. Before the truth respecting the relations of center of gravity and base can be formulated, it must be assumed that the surface on which the body stands is unyielding, that the edge of the body itself is unyielding, and that its mass, while made to lean more and more, does not change its form--conditions not fulfilled in the cases commonly observed. And so, too, is it with the projectile: determination of its course by deduction from mechanical laws, primarily ignores all deviations caused by its shape and by the resistance of the air. The science of rational mechanics is a science which consists of such ideal truths, and can come into existence only by thus dealing with ideal cases. It remains impossible so long as attention is restricted to concrete cases presenting all the complications of friction, plasticity and so forth.