TENDENCIES OF MODERN PHYSICS 45 



known as elasticity ; they must have a propensity which 

 makes them build geometrical crystals: in fact they 

 must be arbitrarily and occultly endowed with all the 

 attributes of ponderable matter which they were created 

 to explain. This sub-atom has many more duties to 

 perform, but sufficient have been given to show that 

 either it is excessively complex in essence or is en- 

 dowed with complex forces; so far, this is our arbitrary 

 resting point in the matter of subdivision, but it is 

 merely a temporary makeshift. But there is a still 

 more cogent reason for this philosophical objection 

 than the empirical ones given. The equally funda- 

 mental concepts of space and time are invariably con- 

 sidered as continuous or infinitely divisible functions, 

 and this theoretical difference assigned to matter, in- 

 troduces inevitable trouble in mathematical analysis. 

 The science of mechanics, in its theoretical aspect, may 

 be defined as the attempt to apply the laws of geometry 

 to real bodies, and while there is always an insurmount- 

 able break in thought between the laws of the imag- 

 inary bodies discussed in geometry and the concrete 

 ones of mechanics, we can, by the assumption of the 

 continuity and indefinite divisibility of matter, approxi- 

 mate as closely as we wish to the rigorous laws of 

 geometry. The geometrical point and line are re- 

 spectively abstract bodies of no, and of one, dimension ; 

 in experimental mechanics, they are both real bodies of 

 three dimensions, the point is the atom and the line 



