(34T) 



We see at the same time tliat the simultaneous motions A and 

 B will differ in phase by V4 period. This is the reason why cir- 

 cularly polarized light can be omitted in the direction of the lines 

 of force. 



§ 7. The foregoiiiu- reasoning shows that, in the magnetic field, 

 the vibrations of order /, will never be perceptibly modified by 

 the vibrations of different orders. We may therefore continue to 

 consider them by themselves. Now, the meaning of the term Q^ 

 in equation (5) is this, that Q^ lip^ is the work of the electromag- 

 netic forces corresponding to the infinitely small displacement deter- 

 mined by (Jpi^. But the electromagnetic forces are linear functions 

 of the velocities; consequently, Q^ will take the form 



Qu = :^. K 



(Ö) 



The coefficients a are easily calculated. Let the centre of the 

 shell be the origin of coordinates, the axis of z having the direction 

 of the magnetic force //. Then, if r be the distance to the 

 centre, and 



the solid liaimonic of degree //, corresponding to the surface har- 

 monic Yhu, I find 



Ha r 



^1 Ih -. 



or 9y 3s 



3 w,., 3 w,., 3W^ 



3.I.' 3^ ' "ès 



d fo 



■ (7) 



I shall suppose that the axis of j/ points to the place the observer 

 occupies when viewing the phenomena across the lines of force. 



It will sometimes be found convenient to distinguish the funda- 

 mental harmonics by suffixes, indicating the position of their poles. 

 Thus Fi will be the surface harmonic of the first order whose pole 

 is determined by the intersection of the axis of x with the sphere; 

 I'ly the harmonic of the second order, having its poles on the axes 

 of x and ?/, Yxx the zonal harmonic, whose poles coincide on the 

 axis of U-. If these notations be used, the suffix which indicates 

 the order of the harmonic may be omitted. 



