IN PERFECTLY TRANSPARENT MEDIA. 201 



Yet, as in the case of the statical energy, we may substitute the 

 average values of these coefficients for the coefficients themselves in 

 the integral by which we obtain the energy of any considerable space. 

 The kinetic energy due to the irregular part of the flux is thus 

 reduced to a quadratic function of , T], f and diff. coeff. which has 

 constant coefficients for a given medium and light of a given period. 



The function may be divided into three parts, of which the first 

 contains the squares and products of rj, f, the second the products 

 of r], f with their differential coefficients, and the third, which may 

 be neglected, the squares and products of the differential coefficients. 



We may proceed with the reduction precisely as in the case of the 

 statical energy, except that the differentiations with respect to the 



4-7T 2 



time will introduce the constant factor 5-. This will give for 



the first part of the kinetic energy of the irregular flux per unit 

 of volume 



J (11) 



p 



<>' 



, (12) 



where A', B', C', E', F', G' are constant, and <' a quadratic function of 

 L, M, and N, for a given medium and light of a given period. 

 12. Equating the statical and kinetic energies, we have 



s / +s // =r+r / +r // , 



that is, by equations (6), (9), (10), (11), and (12), 



2 + C 7l 2 





92 



~ ( A V + B& + G'yf + E'/3 2 y 2 + F'y 2 a 2 + G' 



Jr 



2 >' 



A-/3ia2)]. (13) 



S 



