186 MR. GEORGE W. WALKER ON THE INITIAL ACCELERATED 



wave-length which depends on the closeness of m'fm to 2. "Unless ra'/m is very 

 nearly 2, it will be in the ultra-violet. 



With the present estimates it appears that in general the radiation in the visible 

 spectrum from a single negative particle is but 10 uoo^ n ^ ^ ne ra( liation from a single 

 positive particle, and if m'/m is very nearly 2, the fraction will be still smaller. 



We have thus proved important optical differences between positively and 

 negatively charged particles. The results appear to have some application in the 

 theory of excited luminosity, but as experimental knowledge of this subject is 

 making rapid progress, this does not appear a suitable occasion on which to discuss 

 a possible application of the results of this section. 



12. Slow Rotation of a Charged Sphere. -The linear motion of a charged sphere 

 is, as we have seen, attended by a disturbance in the surrounding aether. This 

 disturbance gives a reaction on a moving sphere which is a single force. The 

 fundamental forms which we found it necessary to assume are sometimes spoken of 

 as disturbances of the first type. They might with propriety be called disturbances 

 of electric type. 



The skew-symmetry of the equations for the ;ether suggests that we should inter- 

 change the expressions for electric and magnetic force with the requisite change of 

 sign. The disturbances represented by such forms are spoken of as of the second 

 type, and might be called of magnetic type. 



It at once appears that disturbances of this second or magnetic type give a 

 reaction on a charged sphere which is not a single force, but is a couple tending to 

 rotate the sphere. We thus have the means of investigating the problem of an 

 accelerated motion of rotation of the sphere, similar in general character to the 

 method developed for dealing with accelerated linear motion. This problem, which 

 appears to have attracted some attention (LoiiENTZ, ' Enc. d. Math. Wiss.,' Vol. V., 

 2, Part 1, pp. 182-194, and others) in modern electron theory, is of considerable 

 importance in general electrodynamics, and clearly falls within the scope of the 

 present essay. 



Taking, therefore, the case of a uniformly charged sphere, and assuming a 

 disturbance of the second type depending on a first order zonal harmonic, the state 

 of the aether outside the sphere is given by 



(X, Y, Z) = fa y t Z ) + (o, z, -y) (r x " + x '), 

 (a, ft y) = (-1, 0, 0) ( r y + r x ' + X ) + , *y, a*) W + 3V + 3 X ). 



We may first observe that if the sphere is a perfect conductor, we require that the 

 tangential component of electric force should vanish when r = a. 



Hence 



Ct-a = 0. 



