340 AS ESSAY OX THE MATHEMATICAL PRINCIPLES OF PHYSICS. 



of the theory. Let us, however, suppose this purely mathematical difficulty 

 surmounted, and let us admit with Professor Challis that if the wave-length 

 of the undulations is very small compared with the diameter of the atom, the 

 atom will be urged in the direction of wave-propagation, or in other words 

 repeUfd from the origin of the waves. If on the other liand the wave-length 

 is very great compared with the diameter of the atom, the atom will be urged 

 in the direction opposite to that in which the waves travel, that is, it will 

 be atti-acted towards the source of the waves. 



The amount of this attraction or repulsion will depend on the mean f 

 the square of the velocity of the periodic motion of the particles of the aether, 

 and since the amplitude of a diverging wave is inversely as the distance from 

 the centre of divergence, the force will be inversely as the square of this 

 distance, according to Newton's law. 



We must remember, however, that the problem is only imperfectly solved, 

 as we do not know the absolute value of this force, and we have not yet 

 arrived at an explanation of the fact that the attraction of gravitation is in 

 exact proportion to the mass of the attracted body, whatever be its chemical 

 nature. (See p. 36.) 



Admitting these results, and supposing the great ocean of aether to l)e 

 traversed by waves, these waves impinge on the atoms, and are reflected in 

 the form of diverging waves. These, in their turn, beat other atoms, and cause 

 attraction or repulsion, according as their wave-length is great or small. Thus 

 the waves of shortest period perform the office of repelling atom from atom, 

 and rendering their collision for ever impossible. Other waves, somewhat longer, 

 bind the atoms together in molecular groups. Others contribute to the elasticity 

 of bodies of sensible size, while the long waves are the cause of universal 

 gravitation, holding the planets in their courses, and preserving the most ancient 

 heavens in all their freshness and strength. Then besides the waves of aether, 

 our author contemplates its streams, spiral and otherwise, by which he accounts 

 for electric, magnetic, and galvanic phenomena. 



Without pretending to have verified all or any of the calculations on which 

 this theory is based, or to have compared the electric, magnetic, and galvanic phe- 

 nomena, as described in the Essay, with those actually observed, we may venture 

 to make a few remarks upon the theory of action at a distance here put forth. 



The explanation of any action between distant bodies by means of a clearly 

 conceivable process going on in the intervening medium is an achievement of 



