218 EQUATIONS OF MONOCHEOMATIC LIGHT IN MEDIA 



It is important to observe that the existence of molecular vibrations 

 of ponderable matter, due to the passage of light through the medium, 

 will not affect the reasoning by which this equation has been estab- 

 lished, provided that the nature and intensity of these vibrations in 

 any small part of the medium (as measured by a wave-length) are 

 entirely determined by the electrical forces and motions in that part 

 of the medium. But the equation would not hold in case of molecular 

 vibrations due to magnetic force. Such vibrations would constitute 

 an oscillating magnetization of the medium, which has already been 

 excluded from the discussion. 



The supposition which has sometimes been made,* that electricity 

 possesses a certain mass or inertia, would not at all affect the validity 

 of the equation. 



10. The equation may be reduced to a form in some respects more 

 simple by the use of the so-called imaginary quantities. We shall 

 write i for ^/( 1 ). If we differentiate with respect to the time, and 



47T 2 



[U] Ave > we obtain 



substitute 





Pot [U] ATC - V[<j] Ave - 





If we multiply this equation by t, either alone or in connection with 

 any real factor, and add it to the preceding, we shall obtain an 



equation which will be equivalent to the two of which it is formed. 



f)i 

 Multiplying by ~ and adding, we have 



Pot ([U] Ave - 1 ^ [U] Ave ) - V ([g] Ave - 1 - [g] Ave ) 



Ave 



If we set 



p 



our equation reduces to 



(9) 

 (10) 



01) 



(12) 



In this equation 9 denotes a complex linear vector function, i.e., a 

 vector function of which the X-, Y-, and Z-components are expressed 

 in terms of the X-, Y-, and Z-components of the independent variable 

 by means of coefficients of the form a-\- ib. W is a bi vector of which 



*See Weber, Abhandl. d. K. Sachs. Gesdlach. d. 

 Crelle's Journal, vol. Ixi, p. 55. 



Wiss., vol. vi, pp. 593-597 ; Lorberg, 



