xxvii.] GENERALISATION. 617 



time is very short, and therefore the accelerating forces 

 brought into play are exceedingly great, but never infinite. 

 In the case of a large gun the powder in exploding is said 

 to exert for a moment a force equivalent to at least 2,800,000 

 horses. 



Our belief in some of the fundamental laws of nature 

 rests upon the principle of continuity. Galileo is held to 

 be the first philosopher who consciously employed this 

 principle in his arguments concerning the nature of motion, 

 and it is certain that we can never by mere experience 

 assure ourselves of the truth even of the first law of motion. 

 A material particle, we are told, when not acted on ly 

 extraneous forces will continue in the same state of rest or 

 motion. This may be true, but as we can find no body 

 which is free from the action of extraneous causes, how are 

 we to prove it? Only by observing that the less the 

 amount of those forces the more nearly is the law found to 

 be true. A ball rolled along rough ground is soon stopped ; 

 along a smooth pavement it continues longer in movement. 

 A delicately suspended pendulum is almost free from 

 friction against its supports, but it is gradually stopped by 

 the resistance of the air ; place it in the vacuous receiver of 

 an air-pump and we find the motion much prolonged. A 

 large planet like Jupiter experiences almost infinitely less 

 friction, in comparison to its vast momentum, than we can 

 produce experimentally, and we find in such a case that 

 there is not the least evidence of the falsity of the law. 

 Experience, then, informs us that we may approximate 

 indefinitely to a uniform motion by sufficiently decreasing 

 the disturbing forces. It is an act of inference which 

 enables us to travel on beyond experience, and assert that, 

 in the total absence of any extraneous force, motion would 

 be absolutely uniform. The state of rest, again, is a 

 limiting case in which motion is infinitely small or zero, 

 to which we may attain, on the principle of continuity, by 

 successively considering cases of slower and slower motion. 

 There are many classes of phenomena, in which, by 

 gradually passing from the apparent to the obscure, we can 

 assure ourselves of the nature of phenomena which would 

 otherwise be a matter of great doubt. Thus we can suf- 

 ficiently prove in the manner of Galileo, that a musical 

 sound consists of rapid uniform pulses, by causing strokes 



