in Crystalline and Non-crystalline Substances. 183 



three principal axes are I'espectively 



mn{B-C) n/(C-A) /m(A-B) 

 D ^ D ' D ' 



where D denotes the square root of the sum of the squares of the 

 numerators of these three fractions, or the third factor of the 

 preceding expression. 



10. If the sphere be infinitely small, and if it be put into a 

 imiform or non-uniform field of force, the entire action which it 

 expei'iences, whether directive tendency or tendency to move from 

 one part of the field to another, is defined by the following pro- 

 position : — 



The quantity of mechanical work which is required to bring 

 the body from a position where the intensity of the force is F, 

 and its direction cosines with reference to the three principal in- 

 ductive axes /, m, n, to a position where the intensity of the force 

 is F', and its direction cosines with reference to the three prin- 

 cipal inductive axes in theii- new positions /', //i', n', is equal to 



I a { ( A/'2 + B/«'2 -I- Cn'2) F'2 - (A/2 -J- Bm2 + Cn^) F^ } . 



11. If A3=B = C,this expression becomes simply-o-A(F'^— F^), 



and the proposition is equivalent to the mathematical expression 

 of Faraday^s law regarding the tendency to places of stronger or 

 of weaker force, of ferromagnetic or diamagnetic non-crystalhne 

 substances, on which some remarks are pubhshed in the Philoso- 

 phical Magazine for October 1850. 



12. If, ^dthout moving its centre, the ball be tm-ned so that 

 its three principal axes shall successively be in the direction of 

 the lines of force (the field being non-uniform, but the body in- 

 finitely small), it will in each position experience a force in the 

 line of most rapid variation of the " force of the field ; " but the 

 magnitude of the force will in general differ in the three positions, 

 being proportional to A, B, and C respectively*. If each of these 



* Thus a ball cut out of a crystal of pure calcareous spar which tends to 

 turn with its optic axis peqiemiicular to the lines of force, and which tends 

 as a whole fi-om places of stronger towards places of weaker force, would 

 experience this latter tendency more strongly when the optic axis is perpen- 

 dicular to the lines of force than when it is parallel to them ; since, accord- 

 ing to § H of the text, the crystal must have greatest indu(.'tive cai)acity,or (the 

 language in the text being strictly algebraic when negative quantities are con- 

 cerned) least capacity for diamagnetic induction ])erpen<hcular to the optic 

 axis. I am not aware that this jjarticular conclusion has been verified by any 

 experimenter; but I am informed (Oct. 25, 1860) by Mr. Faraday, that he 

 finds a |)iece of crt'stalline bismuth to experience a different " rei)ulsion " 

 according an it is held with its magneciystallic axis along or ])erj)endicular 

 to the lines of force in a non-uniform field ; the repulsion l)eing less in 

 the former case than in tiie latter, which agices jjcrfectly with the conclu- 

 sions of the text, since, as a ball of bismuth would tend to place its magne- 



