Thcovij of Refraction in Gases. 475 



The curves required for the discussion are shown in the 

 diao-rams (PI. XIX.), in which the abscissa? represent values 



AVe may first note that E/(.i') is infinite for .i' = 0, but since 

 Lta:loo-^ is zero, the function E(,i') is finite for cc = 0. It is 



x=0 



also finite for all positive values of /r, converging to 1 when 

 In the function 



F^ e {H' E; 



CO 



c=?) 



which is drawn for -^ =5, it will be observed that the infinity 

 (o- 



at/> = n is of extraordinary sharpness, and for larger A^alues 

 of :=rx the sharpness would be still more marked. We have 

 already pointed out that -^^ niust be a large number. Thus 

 yLt^ — 1 is adequately represented numerically by 



o (a^ \m-^ 77Z2 / ( V ^ / J 



except in the immediate vicinity of the point j9 = 12. Just at 

 this point we should get negative values for fju', or in other 

 words absorption must occur. 



We may now justify the selection of the principal value 

 of the integral. In any physical problem the denominators 

 are prevented from vanishing by frictional terms in the 

 equations of motion. In this case radiation produces the 

 result. Thus, instead of the integral 



'C5 

 X 



dx 



we should get 



x-f ' 



[w-2J^f + li' 



dx 



where h is a small quantity depending on radiation. By 

 Lorentz/s method we find that 



'6 \h(i JH2/ ^'o' 



