ox OEUTAIX DIFFl.'.VC'rioX I'llEXoMEXA. -U.') 



/ ,.x rf<in (: ii) , 1 l' ros ^ II . . ^^ J°{ii z) cos n z u 



+ 2 - sin (. .) 2^ .._,,.- . |- 



Tlieise two cxj^vssioiis ( (• ) nnd ( /') nrc v(\vva\ to — /v •iinl — Tj 



Tims 7v and L are iiiadt' to dcju'iid oii J°(», r), wliidi can 1)0 

 ('al<adated o\\(\' loi" all ; tlic rest involvini;- siiiiplc aritliiiU'(i<-al and 

 triti'oiK/iiU'trical calculations. 



The ex])rossions ( ^' ) and ( /') above dcdncod for K and Jj ro<|uiro 

 special consideration M'licn ^ is a multiple of -, since both then contain 

 terins of the form ---. 



Let us suppose that | ^^ m - ^^ y. Then the expressions for K 

 and L assume f)llo\vini'" f nans. 



wl lere 



1 I sin zu. ^ _ . . "^\^J [n-^cosin-ii) ^ , . . ^ J {n-)cos{nzu) 



. I -_ \--' sin C II. > —. :,—T, \--ZSUlZUy ;;; t, 7, 



'1 V^ z V -- — n--- ^, c- — n- ~- 



1 ' mrl 



-, ^ '"■C^^nJ''{n■ z)sin(nz ii) ^ ,^ ^ ^nJ°xn -)sin{n-n.) 



— 1 - cos C ?( > X., .,- ., ~ COS iC 11.) > i-.r ^-9~ ., 



j^' _ J. ^ sin (? u) cos (y ii.) — y cos {: u) sin (y u) 

 "?=>' Ç- - r- • 



^ 11 cos z V. . „^ . i-^ 'T in-)cos(7i-n.] ... . -P5 J (/?.-) ros ;*-' 



ij = — i-l :: + 2 C COS C Ii > —, 7, — 7, |--"COSC« > —, —r, — 7, 



2 l_ Ç ^ Z-— n- -- ' ^j Ç-— w- -- 



, -, ... ,r,l7°(72n-) st/i (/i;r?«") , -, . , .^^ J° (nz) sin iiz' 

 + 2z sin':ii)y — ^ — ~, — -^^ \- 2 :: suiji z iny -. 7^—7, 



+ 2 7/J°0//-)T 



