72 



MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 



If we designate the preceding series by 



{%) a£l = 22 b (i,i',c) cos [(i — *'/') e — *'(#' — Mff)} + ^2 b (i,i',s) sin [(i — i'/i) e — i'(g'— jug)] 



ar ( Wj = 22 c { - i,i '^ cos K i - i 'v) e - *'(.'/' - I'd)] + 22 c (i,i',s) sin [[i - i'jn) e - i'(g' - fig)] 



at ( -£ )=22d (i,i',e) cos [{i - i'/i) s - i'(g' - fig)] + 22 d (i,i',s) sin [(t - i'/i) e - i'(g> - fig)] 



F, G, H, T, V, and V were first computed by the formulas x 



G (i,i\ I) = A_, b (i + l,i', 9 + A b (i,i>, 9 + A, b [i - IV', 9 + A 2 b (i - 2,i>, 9 



+ G_, c (i + 1,1', 9 + Co c (i,i>, 9 + O, c (i - i,v, 9 + C\ c (i - v, 9 

 H (i,i', 9 = A_, 6 (» - 1,/', 9 + A b (/,«', :) + A, b (i + l,t' f 9 + A 2 b (i + 2,i>, l) 

 - C_, c (i - l,i', 9 - Co c (i,i>, 9 _ C x c (i + l,i>, 9 - Cs c (i+2,i>, «J 

 F(i,i>, l) = -i [G(i+l,i', 9 + H(i - 1,/,' 9] - b (i,i>, 9 

 U (i,i', 9 = F_, d (i + l,i', 9 + N d (/,/', 9 + JVi d (i - l,i', 9 + JV a <Z (< - 2,*', 9 

 F(v', 9 = - JV_, ri (i - 1,/', 9 - #o ^ (v', J) - »i '? C + M'i S) - ^ rf (i + 2,i', ;) 

 T (<,*', 9 = - TJ (i + l,i', 9 - v (• - 1,*', 9 



where 



A_,: 



A, = 



2 (MIS -'</; 



2 cos z <p 



4-e 2 



A 2 =-., 



2cos 2 ^ 

 e 



= + 0. 010086 

 = - 0. 215178 

 = + 2. 030257 



C_! = A_, = + O. 010086 



00= A = — 0. 071726 



-2 + e 2 



Oi = 



= -1.010086 



JCOS i cp' 



— 0. 071726 



' 2cos 2 <p' 

 G 2 = -A> =+0.071726 



