DlAMAGNETIC CONSTANTS OF BlSMUTH AND CALC-SPAR 189 



magnetic field. Let the field be symmetrical around an horizontal axis, 

 and also with reference to a plane perpendicular to that axis at the 

 centre. If the bar is very long with reference to its section and a 

 plane can be passed through it and the axis we must have Z = 0, and 

 the equation becomes 



Let the axis of X coincide with the long axis of the bar, as this will 

 in the end lead to the most simple result, seeing that we have to inte- 

 grate along the length of the bar. 



Let r be the length along the bar from the centre to any point, and 

 let 6 be the angle made by the bar with the axis of symmetry : then 



1 dV 



j>- v _ 



~~dr ~ 



also let the section of the bar be 



a = dy dz 



and let the axis of the bar pass through the origin from which we have 

 developed the potential in terms of spherical harmonics. We can then 

 write as before 



where Q t , Q ltl , etc., are zonal spherical harmonics with reference to 

 the angle 6, 



from which we have the following: 



X* = A'Q* + SA*,^ + 25^-#f + QA^Q.Q^ 



^Q&i* + MA ltt A,Q M QS + etc., 



* + ZA.A^Q'ff^ 

 '&i* + ZA^A^&r* + etc.} sin-*, 



The moment of the force tending to increase 6 is 



dE 

 ~W 



whence we may write, 



*i * + *,) + B ((^ - kj '* + h) C (Tc, - 2 ) ' \, 



