622 THE PRINCIPLES OF SCIENCE. [CHAP 



On this principle Stevimis beautifully demonstrated that 

 weights resting on two inclined planes and balancing each 

 other must be proportional to the lengths of the planes be- 

 tween their apex and a horizontal plane. He imagined a 

 uniform endless chain to be hung over the planes, and to 

 hang below in a symmetrical festoon. If the chain were 

 ever to move by gravity, there would be the same reason 

 for its moving on for ever, and thus producing a perpetual 

 motion. As this is absurd, the portions of the chain 

 lying on the planes, and equal in length to the planes, 

 must balance each other. On similar grounds we may 

 disprove the existence of any self-moving machine ; for if 

 it could once alter its own state of motion or rest, in how- 

 ever small a degree, there is no reason why it should not 

 do the like time after time ad infinitum. Newton's proof 

 of his third law of .motion, in the case of gravity, is of 

 this character. For he remarks that if two gravitating 

 bodies do not exert exactly equal forces in opposite direc- 

 tions, the one exerting the strongest pull will Garry both 

 away, and the two bodies will move off into space together 

 with velocity increasing ad infinitum. But though the 

 argument might seem sufficiently convincing, Newton in his 

 characteristic way made an experiment with a loadstone 

 and iron floated upon the surface of water. 1 In recent 

 years the very foundation of the principle of conservation 

 of energy has been placed on the assumption that it is 

 impossible by any combination of natural bodies to pro- 

 duce force continually from nothing. 2 The principle admits 

 of application in various subtle forms. 



Lucretius attempted to prove, by a most ingenious argu- 

 ment of this kind, that matter must be indestructible. 

 For if a finite quantity, however small, were to fall out 

 of existence in any finite time, an equal quantity might 

 be supposed to lapse in every equal interval of time, so 

 that in the infinity of past time the universe must have 

 ceased to exist. 3 But the argument, however ingenious, 

 seems to fail at several points. If past time be infinite, 

 why may not matter have been created infinite also ? It 

 would be most reasonable, again, to suppose the matter 



1 Principia, bk. i. Law iii. Corollary 6. 



* Helmholtz, Taylor's Scientific Memoirs (1853), vol. vL p. 1 18. 



3 Lucretiv.s, bk. i. lines 232 264. 



