Coefficient of End- Correction. 143 



Then 



— I P v (» sin fa V ^T~ 7r ) +' Q'C 1 ') cos (*— ~^J~~ 7r ) J \ * 



Substitute the values of 



( A — j) and sin ( A '-f)' 



cos 



then we have 



1 ( eosy [P,PiX + Q,QiX] -sin"!" [P r Q,\-P 1 <iX] } , 

 or J44^cos V J(P 1 P, + Q 1 Q v )+ S m 1 'J(P 1 Q,-Q 1 P^ 



1T4-QQ 1 " V - 2a) I "V-W~ 42 > 

 r^+Vi^-J- 2!(2x) 2 4!(2.r/ 



PQ _Q P -* 2 - 12 fl- ^- 12 >^- y } + 



If we stop at the terms last written and if x>ki >r3 , 84 

 the error will be less than 1 in 3000. 



Putting v = 2/3 we obtain the approximate relations 



^2J a a/a (k r ) lr_, 1 5V3^i_ , 5^_1___1^J_"1 



rK / J 2 (k r ) ll- r K r J r&r O r fC r & r «r J 



= •02809, 



= •015080, 

 and '-^ =-010261. 

 Now /(w)=A+B(l-« s )+C(l-«r s )-" 



= 1 — 2A- r ar Jo(^rW) • 



