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XXIV. On the Hydro dynamical Theory of Attractive and Repul- 

 sive Forces. By Professor Challis, M.A., LL.D., F.R.S.'^ 



AT the commencement of the " New Discussion of the Hy- 

 drodynamical Theory of Magnetism'"' contained in the 

 Number of the Philosophical Magazine for June, I have enun- 

 ciated the following principles : — (1) That all the active forces 

 in nature are different modes of pressure under diflferent circum- 

 stances of a universal elastic aether, which may be mathematically 

 treated as a continuous substance pressing always proportionally 

 to its density. (2) That all visible and tangible bodies consist 

 of inert spherical atoms of constant magnitudes, held, when un- 

 disturbed, in positions of equilibrium by attractive and repulsive 

 forces, acting according to laws which are referable both to the 

 active pressure of the aether and the passive resistance of the atoms 

 to such pressure due to the constancy of their form and magni- 

 tude. In conformity with these principles the aether at rest is 

 assumed in that theory to be everywhere of the same density ; 

 and I have, besides, supposed the atoms to be so small that even 

 in dense bodies the space they occupy is very small compared 

 with the intervening spaces. 



These physical principles (which are applied in the above-cited 

 article in the theoretical explanation of a large number of facts 

 both of galvanism and magnetism) will be seen to be partly hy- 

 pothetical and partly iyiferential. All that relates to the qualities 

 of the aether and the atoms is hypothetical ; but what is asserted 

 respecting the dependence of the laws of the physical forces on 

 modes of pressure of the aether must rest on deductions by ma- 

 thematical reasoning from the hypotheses, and can be established 

 by nothing but such reasoning. To account by this deductive 

 process for the modus operandi of forces to which facts of obser- 

 vation are attributed, has been the object of various articles which 

 from time to time I have communicated to the Philosophical 

 Magazine. After giving reconsideration to these theories, and 

 in particular the Hydrodynamical Theory of Magnetism in the 

 June Number, it occurred to me that they might be much elu- 

 cidated by separately exhibiting the principles and processes of 

 the mathematical reasoning which connects the different forces 

 with hydrodynamical pressure; and accordingly to do this is the 

 purpose of the present communication. It is to be understood 

 that the following discussion has reference to reasoning founded 

 on hypotheses, irrespectively of their being true or false, and 

 that I do not ask any one to accept the hypotheses, but only to 

 give consideration to the mathematical reasoning by which the 

 consequences that result from them are ascertained. It may, 

 * Communicated bv the Author. 



