Mr maxwell, ON FARADAY'S LINES OF FORCE. 75 



and for internal points 



«i= 12 — -> a?. 



So that in the interior of the sphere the magnetization is entirely in the direction of .v. 

 It is therefore quite independent of the coefficients of resistance in the directions of w and y, 

 which may be changed from k^ into k.^ and ks without disturbing this distribution of magnetism. 

 We may therefore treat the sphere as homogeneous for each of the three components of /, 

 but we must use a different coefficient for each. We find for external points 



, f [k,-k' k^-k' k^-k' \aF\ 



and for internal points 



, / Sk^ , Shi Sks \ 

 Pi= I — —, Ix + — -, my + — -, nx . 



The external effect is the same as that which would have been produced if the small 

 magnet whose moments are 



K^—K «2"" k k^— k 



— — -, lla?y — -, mlar, — -; n/a' 



2*1+ A; 2*2+ ft 2*3+ A; 



had been placed at the origin with their directions coinciding with the axes of <B,y, «. The 

 effect of the original force / in turning the sphere about the axis of x may be found by 

 taking the moments of the components of that force on these equivalent magnets. The 

 moment of the force in the direction of y acting on the third magnet is 



and that of the force in x on the second magnet is 



Kn-^ Hi 



The whole couple about the axis of a? is therefore 



, mnlV. 



mnPa?, 



(2*3 + *')(2*2 + *') 



tending to turn the sphere round from the axis of y towards that of z. Suppose the sphere 

 to be suspended so that the axis of ■» is vertical, and let / be horizontal, then if 9 be the 

 angle which the axis of y makes with the direction oi I, m = cos 0, n = — sin 9, and the 

 expression for the moment becomes 



I . /'^t~r^\'. /Vsin2g 



^ (2&2+^)(2*3+*) 



tending to increase 9. The axis of least resistance therefore sets axially, but with either 

 end indifferently towards the north. 



Since in all bodies, except iron, the values of k are nearly the same as in a vacuum, 



10—2 



