196  Mr.  J.  W.  Nicholson  on  the  Di fraction  of 
If  n  be  neglected  in  comparison  with  kr,  we  get  the  well- 
known  asymptotic  expansion  of  the  Bessel  function. 
For  the  diffracted  waves  diverging  from  the  sphere,  the 
appropriate  solution  is 
Let  c  be  the  radius  of  the  obstacle.  Since  there  cannot  be 
motion  normal  to  it,  Gn  is  determined  by 
^(An  +  ^J=0  when  r=c;    .     .     .     (14) 
or 
Since 
/       \i  co$(  Icg)c—  ~) 
&-^=  r^A-n.tU* *  (12)> 
and  'd(k'ae)  _  (kV-n.n  +  lji  ,       ,u, 
ZW  he b>"  W' 
we  obtain 
c  -    (gB!1)£.   a  {     CQS(^-D     j/a    r         ^H 
Writing  iu  for  &c;  and  H  for  k2c2—n  .  n  + 1 ,  the  denominator 
becomes 
w 
or 
The  numerator  has  the  value 
8 .00,(^,-^1 
