262 Prof. G. F. FitzGerald on the 



up and down along the equator are very close to one another 

 and consequently the force is concentrated ; while this same 

 force which is concentrated within a wave-length has the whole 

 hemisphere to return in, and so the longitudinal concentration 

 is quite small, and that is what is represented by the small 

 value of the longitudinal component at any point. The total 

 quantity of longitudinal component must be, on the whole, 

 equal to the transverse component at the equator. 



II. In the case of several simple oscillators oriented in dif- 

 ferent directions the resultant vector potential can be repre- 

 sented by 



A = U CQS lP*~9 r ) | y s ' mpt ~^ r 

 r r 



where U and V are vectors at right angles to one another. 

 The effect is the same as if two opposite electrons were 

 moving on opposite sides in an elliptic orbit whose plane was 

 that of U and V and whose axes were these two lines. 



It is interesting to observe that this case, coupled with a 

 slow rotation of the ellipse which would be produced by 

 almost any small disturbing force in its plane, has been 

 shown by Dr. Stoney to be a sufficient cause for the double 

 lines in spectra which are so common and which are familiar 

 to everyone in the double sodium line. 



If the directions of U and V be taken as those of x and ?/, 

 and z be taken perpendicular to the plane of this ellipse, we 

 may take 



F , r , «»(^-y) , G = o sin (p f -<r\ H =o, 



and we get a sort of corkscrew wave with a longitudinal 

 component which can be represented by 



sin<f> ,_ 

 o-=-^{Lcos(^- r + Z)}; 



where <f> is the angle between r and z, and L and I are func- 

 tions of F , G , r, 0, and q. 



This component vanishes along the axis perpendicular to 

 the plane of the ellipse, and is a maximum in this plane. If 

 F =G , this simplifies to 



0"= — j*- {2qs'm(pt — qr — 0)-+ ,-cosQtrt — qi — 0)}. 

 This case is rather interesting, as being the form of magnetic 



