84 THE PRINCIPLES OF. SCIENCE. 



of matter ; for were an exceedingly minute fraction of 

 existing matter to vanish in any experiment, say one 

 part in ten millions, we could never detect the loss. 



Successive Approximations to Natural Conditions. 



When we examine the history of scientific problems, we 

 find that one man or one generation is usually able to 

 make but a single step at a time. A problem is always 

 solved for the first time by making some bold hypothetical 

 simplification, upon which the next investigator makes 

 hypothetical modifications approaching more nearly to the 

 truth. Errors are successively pointed out in previous 

 solutions, until at last there might seem little more to be 

 desired. Careful examination, however, will show that an 

 indefinite series of minor inaccuracies remain to be cor- 

 rected and explained, were our powers of reasoning suffi- 

 ciently great, and the purpose adequate in importance. 



Newton's successful solution of the problem of the 

 planetary movements entirely depended at first upon a 

 great but hypothetical simplification. The law of gravity 

 only applies directly to two infinitely small particles, so 

 that when we deal with vast globes like the earth, Jupiter, 

 or the sun, we have an immense aggregate of separate 

 attractions to deal with, and the law of the aggregate 

 need not coincide with the law of the elementary particles. 

 But Newton, by a great effort of mathematical reasoning, 

 was able to show that two homogeneous spheres of 

 matter act as if the whole of their masses were concen- 

 trated at the centres ; in short, that such spheres are 

 aggregates which manifest the simple law of gravity or 

 are centrobaric bodies (vol. i. p. 423). He was then able 

 with comparative ease to calculate the motions of the 

 planets on the hypothesis of their being spheres, and to 

 show that the results roughly agreed with observation. 



