352 Lord Rayleigh on Light dispersed from 



In like mariner i£ the condition to be satisfied at the surface 

 of the cylinder is 



£ + ?-* • ^ 



we get, using C , Cj &c. in place of B , B x &c, 



C =-J '(kc) + I) '(kc), 



C n =-2i»J n f (kc)+Dn'(kc), .... (12) 



the dashes denoting differentiation. 



The next step is to introduce approximations depending 

 upon the smallness of kc. In addition to (4) we have 



+ (7+lo g J){|-...}-| + ..'. J (13) 



B,(z) = -l-l + ..., (14) 



and so on. Also 



ty(*)=j + !-!(y+logJ)' . . . . (15) 

 Di'(z) = j 2 + i(v+|+logf), • . . (16) 



».'(*)= ^. : 07) 



Using these, we find 



-Bj- 1 = 7 + log(i^c) +lP6- 2 (l + 3 5 2^ 2 ) • • • (18) 



-zB 1 =Pc 2 {l + pV( 7 -|+log(i^))} . . . (19) 



B 2 =-P 4 c 4 (20) 



Bef erring to (8) we see that when kc is small the pre- 

 dominant term is the symmetrical one dependent on B . 

 Retaining only this term, we have as the expression for the 

 secondary waves 



^ = Y+ log(i^'c) \2ikr) 2 > ' ' ' ( 21 ) 



as in the papers referred to. Relatively to this, the term in 

 cos 6 is of order Pc 2 , and that in cos 26 of order & 4 c 4 . 



