Regular Reflexion of Light by Gas Molecules. 93 



both planes, we get as the multiplier of dydz in the final 

 integral 



\0 2 r- : \c{x 2 +y 2 ) + lkQ{r-^x 2 + y 2 )A-v- 2 x}co^{v{r-x)+y}\ X 



= v 2 [0 2 r-'%l 2 + if •) +lAO- 2 Z{cos (1/ .r-Z + 7) + cos (v . r +l + y)} 



+ ^ACV- 3 (Z 2 + v 2 ){cos(u.r"-^I + 7) — cos(u.r + / + 7)}]. 



Since Z is arbitrary, let it be so chosen that vl is a multiple 

 of 2tt ; I may then be omitted from the arguments of the 

 cosines, and dropping also the constant factor Cv 2 l, we have 

 for the quantity whose surface-integral must vanish 



Cr-%l 2 + if) + Ar- 2 cos (i/r+7). 



39. If q' : = y 2 + z 2 , the above expression must be multiplied 

 by 2irgdq, that is by 2irrdr, and integrated from r = l to 

 y=ao , the result being equated to zero. Thus 



Ci r~*(l 2 +y 2 )dr + A j r _1 (cosi;rco3 7— sin wsin7)^r=0. 



. . . (48) 



In the first integral, for any given value of r, y 2 may be 

 replaced by its average value ±<f = ±(r 2 — I 2 ). The first term 

 in (48) is therefore 



iC 



Wr~*-r 



=#cz 



The second term in (48) may be dealt with in two portions, 

 each of which, by successive integration by parts, is trans- 

 formed into a series of descending powers of vl. Remem- 

 bering that vl may be chosen as large as we please, and that 

 it has already been designated a multiple of 2tt, we readily 

 obtain for the second integral the value — Au" 1 Z~ 1 sin 7. 

 Hence finally C=fAu~ 1 sin 7, and (42) becomes 



[Type I.] a' = 0, 0, ~ A slnycos( 2 Jt-vr-y); . . (49) 



corresponding to the primary disturbance (45). 



40. By way of example, two types of electromagnetic 

 vibrators are considered in this paper ; type I., whatever 

 its orientation, when excited by plane-polarized waves is 

 capable of vibrating symmetrically with respect to an axis 

 parallel to the electric vector in those waves. Such a 

 vibrator, placed at the origin and excited by primary waves 

 (45), emits the secondary disturbance (49) in which the 



