368 Lord Rayleigh on the Dispersal of 



"Extracting the factor (k l2 — k 2 ), we may conveniently 

 write (9) 



+=-**gr&{tt)*" L co *° ur~ 



Be 1 



in which 



-^- cos 20], . . (10) 



n kV + Pc 2 Fc 2 on 



cos 6 ^ 3- cos 2& 



lb o 



-3 KG fCC k C „ _ /-1 1 \ 



= cos# — t-COS^. . . (11) 



lb 4: 



" In the direction cos# = 0, the secondary light is thus not 

 only of" high order in Jcc, but is also of the second order in 

 (k' — h). For the direction in which the secondary light 

 vanishes to the next approximation, we have 



%Tr-e=ie(k'V-kV) = k ^ 1 ± 1 A. . . (12) 



This ... is true it kc, k'c be small enough, whatever may be 

 the relation of k' and k. For the cylinder, as for the sphere, 

 the direction is such that the primary light would be bent 

 through an angle greater titan a right angle. . . . "" 



" If we suppose the cylinder to be extremely small, we 

 may confine ourselves to the leading terms in (6) and (9).. 

 Let us compare the intensities of the secondary lights emitted 

 in the two cases along — } i. e. directly backwards. From 

 (6) 



fcfi{Jc ,2 c 2 -k 2 c 2 ), 

 while from (9) 



Tjr oc -Pc 2 (k' 2 -k 2 )/(k' 2 + k 2 ). 



The opposition of sign is apparent only, and relates to the 

 different methods of measurement adopted in the two cases. 

 In (6) the primary and secondary disturbances are repre- 

 sented by /t/K, but in (9) by the magnetic function c. • . . . " 



It may be remarked that Ignatowskr's equation agrees 

 with (5) for this case, and that his corresponding equation 

 (11) for the second case also agrees with (8) after correction 

 of some misprints. His function Q corresponds with my ^> 

 at least when we observe that the introduction of a constant 

 multiplier, even if a function of ???, does not influence the 

 final result. 



In proceeding to numerical calculations we must choose a 

 refractive index. I take for this index 1*5, as in similar 



