616 THE PRINCIPLES OF SCIENCE. [CH*P. 



In continuous motion every infinitely small space passed 

 over constitutes a separate constituent fact, and had we 

 perfect powers of observation the smallest finite motion 

 would include an infinity of information, which, by the 

 principles of the inverse method of probabilities, would 

 enable us to infer with certainty to the next infinitely 

 small portion of the path. But when we attempt to infer 

 from one finite portion of a path to another finite portion, 

 inference will be only more or less probable, according to 

 the comparative lengths of the portions and the accuracy 

 of observation ; the longer our experience is, the more 

 probable our inference will be ; the greater the length of 

 time or space over which the inference extends, the less 

 probable. 



This principle of continuity presents itself in nature in 

 a great variety of forms and cases. It is familiarly ex- 

 pressed in the dictum Natura non agit per saltum. As 

 Graham expressed the maxim, there are in nature no abrupt 

 transitions, and the distinctions of class are never absolute. 1 

 There is always some notice some forewarning of every 

 phenomenon, and every change begins by insensible 

 degrees, could we observe it with perfect accuracy. The 

 cannon ball, indeed, is forced from the cannon in an 

 inappreciable portion of time ; the trigger is pulled, the fuze 

 fired, the powder inflamed, the ball expelled, all simul- 

 taneously to our senses. But there is no doubt that time 

 is occupied by every part of the process, and that the ball 

 begins to move at first with infinite slowness. Captain 

 Noble is able to measure by his chronoscope the progress 

 of the shot in a 3OO-pounder gun, and finds that the whole 

 motion within the barrel takes place in something less than 

 one 2OOth part of a second. It is certain that no finite 

 force can produce motion, except in a finite space of time. 

 The amount of momentum communicated to a body is 

 proportional to the accelerating force multiplied -by the time 

 during which it acts uniformly. Thus a slight force pro- 

 duces a great velocity only by long- continued action. In 

 a powerful shock, like that of a railway collision, the stroke 

 cf a hammer on an anvil, or the discharge of a gun, the 



1 Philosophical Transactions, 1861, Chemical and Physical Jle- 

 ttarches, p. 598. 



