204  Mr.  J.  W.  Nicholson  on  the  Diffraction  of 
We  must  therefore  multiply  the  previous  result  by 
y/  /CC7T  Sill  V. 
Thus  along  this  direction,  
/     o    \       e-'i       jexp.^(n-sin-^-V/J-l) 
exp.  —  fc&ci  — 7r  +  sin-1  -  +  \/  -^  — 1 J 
77—  Sill       - 
r 
texp.  —  fcArcl  —  7r  +  sin~ 
fcexp.  —  ikcl  —  7r  +  siii~1-  +  A/  i  ~~1 ) 
7T—  Sill     *- 
i 
+ 
exp.  tfc^ir-  sin"1-  -  \J ^  -l) 
7T —  sin    1- 
1 
(40) 
and  at  a  great  distance, 
ylr=  —  ~     exp.  ckcir  .  : —       ....      (41) 
77  r 
becoming  extremely  great  in  comparison  with  the  effect  at 
the  end  of  the  perpendicular  axis  given  by  (38)  with  6=  5-. 
Along  the  other  side  of  the  axis  of  #,  P;i  (p)  —  ( —  1) n  and 
0  =  7T.     a/t  in  this   case  is  given  by   (19),    which   leads   to 
where, 
t  -  —  Ttt  t        f   ^     /l 9         -.  i  37TA' 
Ij  =e     MU  exp.  t/jc  «j  2\/l-r-za;  cos-1#  +  -~ 
-  a/ ^  -^2  +  .i'  cos"1^'  I  rfar.     .     (42) 
I2  =  eT  fuexp.^c  |*cos-1^-'\/£-*»  +  ^1^  (43) 
where 
IT 
T1  /t'c2t«  £~i~  .        ,  a?         ■  1  1 
U= —  ■-: ^-oTT-iOg 
(-?? 
«t,_l-fe-27r'2-^2  +  t/cc(l-'tr2)i 
