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.
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]
Stevinus, now, easily derives from this principle the laws of equilibrium on the inclined plane and numerous other fruitful consequences.