#=(. 



Light and the Theory of a Quasi-labile Ether. 135 



quired to maintain the vibrations in an element of volume 

 in the other theory. 



To fix our ideas in regard to the signification of W and 0, 

 we may consider the case of isotropic media, in which these 

 operators reduce to ordinary algebraic quantities, simple or 

 complex. Kow the curl of any vector necessarily satisfies the 

 solenoidal condition (the so-called ' equation of continuity '), 

 therefore by (6) W& and (§ will be solenoidal. So also will % 

 and 0% in the electrical theory. Now for solenoidal vectors 



_ , Cv (Jj Cv . . 



-curl curl = _+_ + _, (15) 



so that the equations (6) and (10) reduce to 

 - ( d 2 d 2 <f\ 



d' cT d' \'^ 



S + W + W n (17) 



For a simple train of waves, the displacement, in either the- 

 ory, may be represented by a constant multiplied by 



e i(gt+ax-+by + cz) (18) 



Our equations then reduce again to 



g 2 ¥(Z = {a 2 + b 2 + c 2 )(£, (19) 



tf%=(a 2 -\-b 2 + c 2 )<% (20) 



Hence, 



W- 1 =$=-^ v (21) 



a 2 + b 2 + c 2 ■ v ; 



The last member of this equation, when real, evidently ex- 

 presses the square of the velocity of light. If we set 



*=*£&**, (22) 



J 



k denoting the velocity of light in vacuo, we have 



n?=k*W=Jc*$-\ (23) 



When n 2 is positive, which is the case of perfectly traus- 

 parent bodies, the positive root of n 2 is called the index of 

 refraction of the medium. In the most general case, it would 

 be appropriate to call n — or perhaps that root of n 2 of which 

 the real part is positive — the (complex) index of refraction, 

 although the terminology is hardly settled in this respect. A 

 negative value of n 2 would represent a body from which light 

 would be totally reflected at all angles of incidence. No such 

 cases have been observed. Yalues of n 2 in which the coefiS- 



