Matter and Force in Theoretical Physic$. 463 



tities, it is only required to substitute this expression for V in 

 the foregoing equation, the second term of which will then 

 become 



(S. [n* sin q(z-Kat+ 0)]) . 





This expression, which gives the means of drawing the inference 

 which has been the main object of the preceding reasoning, is 

 clearly equivalent to 



ttt-X, [rcsin 2 ^— Kat + d)], 



together with periodic terms having as much positive as negative 

 value. These being omitted, the part which does not change 

 sign is the quantity I have called AS at the end of the article in 

 the May Number. Hence if the axes pi the vibrations be sup- 

 posed to diverge from a centre, the above argument proves that, 

 since each number (n) that passes through a given area varies 

 inversely as the square of the distance, the quantity AS varies 

 according to the same law. The conclusion that the motion of 

 translation of a small sphere acted upon by a series of undula- 

 tions diverging from a centre varies inversely as the square of the 

 distance, may thence be drawn as in the article cited. 



Having now, in a series of articles (to which the foregoing dis- 

 cussion may be regarded as an addendum), maintained and eluci- 

 dated the mathematical reasoning which I have employed to 

 prove the propositions in hydrodynamics that are applied in my 

 general Theory of Physics, I proceed to the main object of this 

 communication, which is to assert again and defend the princi- 

 ples of that theory. Its fundamental hypotheses, which have 

 been frequently stated in this Journal, and are repeated here for 

 the sake of convenience, are these which follow. All matter 

 consists of very minute atoms having no other properties than 

 constancy of form, constancy of magnitude, and an intrinsic 

 inertia which is always the same for matter of the same magni- 

 tude. All atoms are supposed to be spherical. No other kind 

 of force is recognized than that of pressure. The resistance of 

 the atoms, when pressed, to all change of form and magnitude 

 constitutes a physical force which may be called atomic reaction. 

 All other physical force has its origin in the pressure of a uni- 

 versally diffused elastic fluid medium called the aether, which per- 

 vades all space, and fills those portions of space in the interiors 

 of visible and tangible substances that are not occupied by their 

 proper atoms. The sether undisturbed has the same density and 

 elastic force throughout its extent, but is susceptible of varia- 

 tions of density. The variations of its density are accompanied 



