46 THE LIMITATIONS OF SCIENCE 



a succession of them. Theoretical mechanics is thus 

 the link between geometry and physics, for while it 

 deals with concrete bodies of real size, we eliminate 

 by the abstractive method all the variations which re- 

 sult from the finite size of bodies and then discuss them 

 as if they were theoretically simple bodies of no size. 

 That is, we divide a body into infinitesimal portions 

 and consider its effect as being due to the arithmetical 

 sum cf the effects of these parts. An example will 

 make this clearer; the attraction between two spheres, 

 which is one of the fundamental problems of physics, 

 can be solved rigorously only by the application of the 

 principle of centers of inertia, that the attractive force 

 of a sphere is the same as if its entire mass were con- 

 centrated at its mathematical center. As soon as we 

 apply this law of attraction to real spheres, even of 

 sub-atomic size, we introduce an appreciable error, 

 since the attractive force then produces strains and a 

 deformation of shape which reacts to change the force; 

 this error becomes negligible only when we consider 

 matter to be continuous and the sphere to be made up 

 of an indefinitely large number of indefinitely small 

 particles. We are thus brought to this dilemma; ex- 

 perimentally, matter is discontinuous and theoretically, 

 it is continuous, hypothesis might be called the hope- 

 less effort to reconcile these irreconcilables. 



Professor Larmor tries to avoid this pitfall, which 

 has caught the originators of atomic theories, and at- 



