[ 43 ] 



V. Note on the Hydro dynamical Theory of Magnetism. 

 By Professor Challis, M.A., F.R.S., F.R.A.S* 



IN the Numbers of the Philosophical Magazine for January 

 and February 1861 I proposed a theory of magnetism 

 founded on hydrodynamical principles, which is also reproduced, 

 with modifications and additions, in my work f On the Principles 

 of Mathematics and Physics/ recently published. It has since 

 occurred to me that an objection might be raised against the 

 theory because it does not account for the variation of magnetic 

 action according to the law of the inverse square, which seems to 

 be established by Gauss's process for determining the absolute 

 measure of the intensity of terrestrial magnetism. The purpose 

 of this Note is to meet this objection. 



Whatever may be thought of Gauss's fundamental hypotheses 

 of two fluids acting attractively and repulsively under certain 

 conditions according to the law of the inverse square, and of the 

 dependence of sensible magnetic action on the " separation 9i of 

 these fluids, it is certain from the numerical results he has ob- 

 tained that his investigations must have a real physical basis. 

 A true theory of magnetism ought to be capable of indicating 

 what that basis is, and how far the hypotheses are expressions of 

 facts, or are simply empirical. I proceed to try the hydrodyna- 

 mical theory by this test. 



It will be necessary, first, to state the leading principles of 

 this theory. All visible and tangible substances are supposed 

 to consist of inert spherical atoms of constant form and magni- 

 tude, retained in positions of equilibrium by the resultant actions 

 of the forces which I have named atomic repulsion and mole- 

 cular attraction. The laws of these forces admit of being ma- 

 thematically deduced from the hypothesis of a universal and con- 

 tinuous aether, supposed to press proportionally to its density, 

 and from the combination of its action with the reaction of the 

 atoms due to their constancy of form. The space occupied by 

 atoms is assumed to be very small compared to the intervening- 

 spaces, even for substances of great density. This assumption 

 is justified by an inference from the undulatory theory of light, 

 as is shown in page 410 of the above-mentioned work. 



These hypotheses being understood, we may next consider 

 what will take place when a steady stream of the aether enters 

 into a substance atomically constituted in the manner above 

 stated. For the sake of precision it will be supposed that the 

 body has the form of a cylinder the diameter of which is small 

 compared to the length of the axis, and that the direction of the 

 axis coincides with that of the stream. Then from the hydro- 



* Communicated by the Author. 



