GENERALIZED COORDINATES 321 



nature, the probability that our provisional conceptions are near to 

 the truth is strengthened. If, on the contrary, the results obtained 

 are not found to agree with what is observed in nature, the pro- 

 visional conceptions from which these results have been deduced 

 must be either modified or withdrawn. 



Different sets of conceptions as to the structure of the matter 

 dealt with will lead to different branches of mathematical physics. 

 As in stances of such branches of mathematical physics may be 

 mentioned the theory of elastic solids which is based upon certain 

 provisional conceptions as to the behavior of the particles of 

 which solid bodies are composed, and the kinetic theory of gases 

 which is based upon certain provisional conceptions as to the 

 behavior of the particles of a gas. The tracing out of the conse- 

 quences of different sets of provisional conceptions as to the struc- 

 ture of matter cannot, however, be regarded as coming within the 

 scope of a book such as the present one. 



261. There is, however, an alternative way of proceeding. We 

 have taken Newton's laws of motion as the material supplied by 

 experimental science for theoretical science to work upon. The^, 

 truth of these laws as applied to the ultimate particles of the 

 material universe is by no means certain, because we cannot obtain 

 the ultimate particles to experiment upon. Suppose, however, that 

 we examine whether any further progress can be made in the 

 study of mechanics without introducing any hypothesis beyond 

 the single one (admittedly uncertain) that Newton's laws apply to 

 the ultimate particles. If we can make progress in this direction, 

 the results obtained will of course apply to all further extensions 

 of mechanics, whether or not additional hypotheses are introduced 

 as to the nature and arrangement of the ultimate particles. 



262. The standpoint from which we are regarding the matter 

 can, perhaps, be explained by an analogy, first suggested by Pro- 

 fessor Clerk Maxwell. Suppose that we have a complicated ma- 

 chine in a closed room, and that the only connection between 

 this machine and the outer world is by means of a number of 

 ropes which hang through holes in the floor into the room beneath. 



