244 Prof. J. W. Gibbs's Comparison of the Electric Theory 



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

 theory, may be represented by a constant multiplied by 



Our equations then reduce again to 



/^(£=(a2 + &2 + c2)@, (19) 



g^% = (a^ + h^ + c^)^% (20) 



Hence 



^"' = *^= .^Ci- 2 (21) 



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

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



n2=A;2!^!±^!±^^ (22) 



k denoting the velocity of light in vacuo, we have 



n 



= /;2^=F*-' (23) 



When n^ is positive, which is the case of perfectly trans- 

 parent bodies, the positive root of n^ 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^ 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^ would represent a body from which light 

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

 cases have been observed. Values of n^ in which the coeffi- 

 cient of t is negative, indicate media in which light is absorbed. 

 Values in wluch the coefficient of t is positive would represent 

 media in which the opposite phenomenon took place"^. 



It is no part of the object of this paper to go into the 

 details by which we may derive, so far as observable phe- 

 nomena are concerned, Fresnel's law of double refraction for 

 transparent bodies, as well as the more general law of the 

 same character which relates to seolotropic bodies of more or 

 less opacity, and which differs from Fresnel's only in that 

 certain quantities become complex, or Fresnel's laws for the 

 intensities of reflected and refracted light at the boundary of 

 transparent isotropic media with the more general laws for 

 the case of bodies seolotropic or opaque, or both. The principal 

 cases have already been discussed on the new elastic theory 



* But I might have been introduced into the equations in such a way 

 that a positive coejEcient in the value of n^ would indicate absorption, 

 and a negative coefficient the impossible case. 



