How did we acquire this idea? What are the sources from which we have drawn it? This question is not only of interest in itself, but also for the important reason above touched upon. The opinions which are held concerning the foundations of the law of energy still diverge very widely from one another. Many trace the principle to the impossibility of a perpetual motion, which they regard either as sufficiently proved by experience, or as self-evident. In the province of pure mechanics the impossibility of a perpetual motion, or the continuous production of _work_ without some _permanent_ alteration, is easily demonstrated. Accordingly, if we start from the theory that all physical processes are purely _mechanical_ processes, motions of molecules and atoms, we embrace also, by this _mechanical_ conception of physics, the impossibility of a perpetual motion in the _whole_ physical domain. At present this view probably counts the most adherents. Other inquirers, however, are for accepting only a purely _experimental_ establishment of the law of energy. It will appear, from the discussion to follow, that _all_ the factors mentioned have co-operated in the development of the view in question; but that in addition to them a logical and purely formal factor, hitherto little considered, has also played a very important part. I. THE PRINCIPLE OF THE EXCLUDED PERPETUAL MOTION. The law of energy in its modern form is not identical with the principle of the excluded perpetual motion, but it is very closely related to it. The latter principle, however, is by no means new, for in the province of mechanics it has controlled for centuries the thoughts and investigations of the greatest thinkers. Let us convince ourselves of this by the study of a few historical examples. [Illustration: Fig. 41.] S. Stevinus, in his famous work _Hypomnemata mathematica_, Tom. IV, _De statica_, (Leyden, 1605, p. 34), treats of the equilibrium of bodies on inclined planes. Over a triangular prism _ABC_, one side of which, _AC_, is horizontal, an endless cord or chain is slung, to which at equal distances apart fourteen balls of equal weight are attached, as represented in cross-section in Figure 41. Since we can imagine the lower symmetrical part of the cord _ABC_ taken away, Stevinus concludes that the four balls on _AB_ hold in equilibrium the two balls on _BC_. For if the equilibrium were for a moment disturbed, it could never subsist: the cord would keep moving round forever in the same direction,--we should have a perpetual motion. He says: "But if this took place, our row or ring of balls would come once more into their original position, and from the same cause the eight globes to the left would again be heavier than the six to the right, and therefore those eight would sink a second time and these six rise, and all the globes would keep up, of themselves, _a continuous and unending motion, which is false_."[41]