1903.] Electric Waves round a Conducting Obstacle. 63 



Now it may be shown that 

 - 



* w -,: o 



and hence that 



as long as z > n + J and z - (n + J) is of higher order than *l ; also fr< ni 

 the relation 



it follows that 



*, = ^ -( + *) - y + < + 1) sin" ?* , 



subject to the same limitations. Further, when z - (n + J) is of a lower 

 order than s*, 



where R nt R' 7l , . . . denote the values of R u (*), R' t (^). . . . when 

 z = n + J. When TI + > z, writing 



as long as n -f J > z and n + J - is of a higher order than & ; also 



and when w -f \ - z is of a lower order than 2*, 



r= - 



