386 Remarks on M. Mossotti's Theory of Molecular Action. 



three equations represent the total actions (respectively par- 

 allel to the axes of co-ordinates) exerted by all the molecules 

 of the system but one, upon that one. Consequently the 

 other six terms must refer to the action of the aether upon the 

 molecule under consideration. Accordingly the second terms 

 express the attraction (according to the assumed law of the in- 

 verse square of the distance) exerted by the whole body of 

 aether upon the molecule in question. But this, according to 

 the hypothesis, comprises the whole action of the aether upon 

 the molecule. What then do the first terms represent? 

 They represent the components parallel to the axes of the 

 total pressure exerted by the aether over the surface of the 

 molecule. Hence it appears that the idea of fluid pressure 

 enters into the formation of our equations. But, on the 

 molecular hypothesis of the constitution of bodies, what is 

 fluid pressure but a form of molecular action ? Hence the 

 first terms of our equations, as well as the second, refer to 

 molecular action between the aether and the material particles. 

 We are thus reduced to the following alternative : — either the 

 molecular action expressed in the first terms is included in 

 that expressed in the second, in which case the first terms 

 are superfluous, and the equations are incorrect ; or, beside 

 the forces given in the hypothesis, we must take into account 

 certain other forces, whose nature is wholly unknown, namely, 

 those by which the pressure on the molecules is produced. 

 As the object of the hypothesis from which we set out is to 

 explain the nature of molecular action, it is clear that we are 

 not at liberty to introduce the agency of unknown molecular 

 forces. Thus the only conclusion we can adopt is that M. 

 Mossotti's second system of equations is not in accordance 

 with his hypothesis, and that the latter does nofeadmit of be- 

 ing modified so as to produce an agreement. Let us now 

 examine the first system of equations, those, namely, which 

 refer to the equilibrium of the aether. They are, in reality, 

 only the ordinary equations of fluid equilibrium, which are 

 generally put in the following form : — 



^ = pX^ = P Y^ = pZ (3.) 



ax ' ay dz 



where p is what M. Mossotti denotes by s ; pis equivalent to 

 his g, and X, Y, Z, are the forces impressed upon the fluid. 

 If we consider with some degree of attention the signification 

 of these equations, we shall find that they express the conditions 

 of the equilibrium of an element of the fluid, taken as a con- 

 tinuous mass. The circumstances under which we are justi- 

 fied in considering a congeries of molecules as a continuous 



