294 THE GRAMMAR OF SCIENCE 



their velocities as well as by their position,^ Something 

 of this kind may well occur when we regard the action 

 between corpuscles of gross " matter " without regard to 

 the ether in which we conceive them floating. We 

 cannot assume that the mutual accelerations of prime- 

 atoms, chemical atoms, and molecules depends solely on 

 their relative positions ; it may depend also on their 

 velocities relative to each other, or relative to the ether in 

 which we suppose them to be moving. This remark is of 

 special importance when we try to describe electric and 

 magnetic phenomena by the mutual accelerations of 

 particles at a distance. 



It is usually assumed by physicists, however, that the 

 action between particles at a distance is to be considered 

 as taking place in the line joining them and as depending 

 only on relative position. There have not indeed been 

 wanting scientific writers who have asserted that the whole 

 universe could be described mechanically by aid of a 

 system of particles or points, the mutual accelerations of 

 which depended solely on their mutual distances. But 

 simple as such an hypothesis would be, its propounders 

 have hitherto failed to demonstrate its sufficiency." Never- 

 theless it has played a great part in physical research, 

 and its influence may still be seen in much that is written 

 at the present time about the laws of motion and the con- 

 servation of energy. 



The above discussion puts us in a better position for 



1 The ether being neglected, its unregarded kinetic energy appears as 

 potential energy of the moving bodies, and is generally expressible in terms 

 of the velocities of those bodies. Hence those bodies appear to have a 

 mutual acceleration depending not only on their relative position but on their 

 velocities. 



2 The impulse to this mode of describing the physical universe certainly 

 arose from the Newtonian law of gravitation. It was perhaps pushed as far 

 as it could possibly be of service in the writings of Poisson, Cauchy, and the 

 great French analysts at the beginning of the century. Traces of its persist- 

 ency may be still found in modern writers ; for example, we may cite Clausius 

 — one of the most distinguished of modern German physicists — who considered 

 that all the phenomena of nature can probably be reduced to points mutually 

 accelerating each other in the lines joining them with accelerations which are 

 functions only of their mutual distances {Die mechanische Wtirmctheorie, Bd. 

 i. S. 17). Its insufficiency is evidenced, or apparently evidenced, in its 

 failure to describe completely various elastic body phenomena. 



