GENERALIZATION. 277 



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. Even 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 carry both 

 itself and the other away, and will move with constantly 

 increasing velocity ad infinitum. But though the argu- 

 ment might seem sufficiently convincing, Newton in his 

 characteristic way made an experiment with a loadstone 

 and iron floated upon the surface of water f . 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 whatever of natural bodies 

 to produce force continually from nothing . The principle 

 admits of frequent 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 definite 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 h . But the argument, however ingenious, 



f * Principia/ bk. I. Law iii. Corollary 6. 



Helmholtz, Taylor's ' Scientific Memoirs' (1853), vol. vi. p. 118. 



fa ' Lucretius/ bk. I. lines 232-264. 



