Action of a Galvanic Coil on an external small Magnet. 183 



small needle from which, by the intervention of certain arbitrary 

 hypotheses, Gauss inferred the law of the inverse square in mag- 

 netic action. For this purpose it will be convenient to refer to 

 the detailed exhibition of Gauss's argument given in the Astro- 

 nomer RoyaPs ' Treatise on Magnetism ' (Macmillan and Co., 

 187Q). I have already discussed this question on hydrodyna- 

 mical principles in a " Note on the Hydrodynamical Theory of 

 Magnetism " contained in the Philosophical Magazine for July 

 1869, to which I beg to refer for details of the mathematical 

 reasoning relating to the physical conditions of magnetic force. 

 I propose to "reproduce here only so much of that discussion as 

 may be required for understanding the subsequent theory of the 

 action of the galvanic coil on a small magnet, which is the ulti- 

 mate object of the present communication. 



7. In the article just referred to it is assumed that in a mag- 

 netized bar there is a small and regular increment of atomic 

 density from end to end, like that which must be produced by 

 the action of gravity from the top to the bottom of a solid or 

 fluid mass resting on a horizontal plane. In a " New Discus- 

 sion of the Hydrodynamical Theory of Magnetism/' contained 

 in the Philosophical Magazine for June 1872, 1 have proved (in 

 arts. 4-9) that if any body in which such gradation of density 

 exists be traversed either by a steady setherial stream, or by a 

 uniform series of undulations of the aether, a secondary steady 

 stream will be produced by impulses continually given to the 

 fluid in the direction from the rarer to the denser parts of the 

 body, this being the direction of the contraction of channel 

 by the occupation of space by the atoms. The application of 

 this result forms an essential part of the hydrodynamical the- 

 ories of electric and magnetic attractions and repulsions which 

 I have proposed and discussed in several previous communica- 

 tions. In the case of a magnet, the gradation of atomic density, 

 when once induced, subsists independently of the action of an 

 external body, and is consequently maintained by the intrinsic 

 molecular forces of the magnet itself. Accordingly I have as- 

 sumed that whereas in general the molecular attractions acting 

 on a given atom in equilibrium counteract each other, as do 

 also the molecular repulsions, in the case of a magnetized steel 

 bar the equilibrium of the atom results from an equality between 

 the molecular attraction towards the denser end and the mole- 

 cular repulsion towards the rarer end. This, in short, is con- 

 sidered to be the distinctive property of a substance suscep- 

 tible of being magnetized. Steel possesses this property in an 

 eminent degree, and can be permanently' magnetized. Soft 

 iron admits only of temporary magnetization. 



8. The magnetic state of a substance being thus defined, 



