242 Prof. Thomson on the Forces experienced by inductively 



called, " the resultant magnetic force at P ;" and let R/ denote 

 the same with reference to P. Then, if a small sphere of any 

 kind of non-crystalline homogeneous matter, naturally un- 

 magnetic, but susceptible of magnetization by influence, be 

 placed at P, it will experience a force of which the component 

 along PF is 



1 R' 2 -R 2 

 ^ 2 a ' 



where <r denotes the volume of the sphere, and jw, a coefficient 



depending on the nature of the substance. This coefficient, ^ 



3 

 has a value a little less than — for soft iron, and it has very 



47T 



small positive values for all ferromagnetic substances con- 

 taining little or no iron. 



2. If it be true, as I think it must be, that the forces experi- 

 enced by diamagnetic substances are occasioned by the influ- 

 encing magnet magnetizing them inductively*, and acting 

 upon them when so magnetized, according to the established 

 laws of the mutual action of two magnets, the preceding re- 

 sult will hold for all non-crystalline matter; and to apply it 

 to a diamagnetic substance it will be only necessary to give p 

 a negative value. 



3. To interpret this result, we may remark, that, by the ele- 

 mentary principles of the differential calculus as applied to the 

 variation of a quantity depending on the position of a point in 



R' 2 _R 2 



space, it may be shown that the fraction is greater 



when the point P' is chosen in a certain determinate direction 

 from P than in any other; that it is of equal absolute value, 

 but negative, if P' be chosen in the opposite direction ; and 



dinally, magnetized, and if, when an end of one is placed at a unit (an 

 inch, for example) of distance from an end of the other, the mutual force 

 between these ends is unity ; the magnetic strength of each is unity. The 

 force R, defined in the text, is of course equal and opposite to the force 

 that a " unit south pole " would experience if placed at P. 



* This most natural explanation of the phenomena which he had dis- 

 covered is suggested by Faraday in his original paper on the subject, and 

 it is confirmed by the researches of subsequent experimenters, especially 

 those of Reich and Weber, who have- 1 made experiments to show that a 

 diamagnetic substance, under the influence of two magnets, will act upon 

 one in virtue of the magnetization which it experiences from the other. 

 The extreme feebleness of the polarity induced in diamagnetic substances 

 is proved by Faraday in a series of experiments forming the subject of his 

 last communication to the Royal Society; in which an attempt is made, 

 by very delicate means, to test the induced current in a helix due to mag- 

 netization or demagnetization of a diamagnetic substance which it sur- 

 rounds, but only negative results are obtained. 



