Prof. Lorenz on the Theory of Light. 421 



termine the constants more precisely. The coefficient -g is in 

 general any function /(#, y, z) which satisfies the equation 



if p, q, rare arbitrary whole numbers, and oc v j3 lt y x are very 

 small constants. This condition expresses that the body is he- 

 terogeneous in such sort that the heterogeneity eludes observa- 

 tion by a very quickly returning periodicity, and the body thus 

 appears to be homogeneous. 



Such a function can be expressed by the well-known formula 



Ax>V> z \ 



= 2 J|^ 7 ):eos.(fe^ + hi^L, 4fe=0). 



where i, i v i 2 are whole numbers which run through the series 

 of numbers from — cc to + oo , and the integral is taken from 

 — «!, — (3 1} — 7 X to ot v /3 it 7 P Further, dra is put in place of 

 du dft dy, and -zc^ is the value of f^'GT = 8a 1 /3j 7^ 



If the term which contains i=i 1 = i 2 = is separately extracted 

 from this sum, and if moreover the negative values of i are ex- 

 cluded by multiplying the sum by 2 and taking the terms which 

 contain i = at half their value, we get, with the meaning of the 

 sign of summation thus altered, 



*t \ f^ 7 x , nvf^ i- (i{x — a) , h(y—P) , io{z—y)\ 

 AW) =J OT ;/+ 32) -/co. ™(-i_J + UV|_J + A_rZ), 



where /is put for /(a, /3, 7). 



If we now compare this value of the coefficient 



-* =M y, *) 



with the previous one, we have 



1 Cdrz f 



6,COS^=2Q 2 f^/cOSTT^ + M +M 



«* J tar/ \ ai ^ yi / 



4 sin J = -2* 





From the last two equations we may deduce the value of 2e p 2 , 

 and simplify the resulting expression by introducing the product 

 of two equal integrals instead of the square of the definite inte- 

 gral. If the variables of the one integral are then distinguished 



