434 Dr. T. J. Fa. Bromwich on the 



(ii.) n = 3. 



Here we have to take the formulae * 



-eP g = s, if s>0; -^ s = 0, if *<0. 

 P P 



Then the result is 



0<r<l, * i -5^ I {(r+3i)-3(r+Z)-r-(3*-r) 



^^ + 3(Z-r)}; 



ZO<3Z, *,= [ j^ip'{(r + 3Z)-.3(r+0 + 3(f-0 



-(3Z-r)}. 



Summing up, we see that 



* 3 =8rf' ° <r< ' 



or 



& 



3Z 



, l<r<Zl 



3 ~167rrZ s 



agreeing with (61) of: Lord Rayleigh's paper. 



(iii.) w=4. 



fc 



1 1 



4 64?rrZ 4 p ! 

 Here the standard formulae are 



M(* r -«- fr )(* l -«-' 1 ) 4 - 



(1-3) 



■i«*"=£, if s >0; \eP s = 0, if s<0. 



p l 2 p 



Hence we obtain the results 



0<r<2Z, ^ =M - -{(r + 4Z) 2 -4(r + 20 2 + 6r 2 



1Z&7rn _(4/-r) 2 + 4(2Z-r) 2 }; 



2Z<r<4/, 4 =-^i^{(^ + 4Z) 2 -4(r + 2Z) 2 + 6r 2 



1Jb7rW _ 4 (r-2Z) 2 -(4Z-r) 2 }. 



* Bromwich, Proc. L. M. S. 1. c. p. 425. 



