58 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 



0. 



1. r-l + l, 



II. 2 r - 2 ^ + 2 i, 



III. r + I + I, - 2 ;; 



IV. r — I — I, -\- 2 yji 

 V. ^ — ^, — *J + % 



VI. I + It — ri — rj^ 



VII. 2r + 2|^ — 2;? 



VIII. 21 — 2 n 



IX. 2 r — 2 I + 2 ;;^ 



X. 2 I, - 2 ;;, 



XI. r -^ n + rit 



XII. r — 2| + ^ + ;j^ 



XIII. r -\- 2 1^ — 7} — ri, 



XIV. 2 r — I + 1/ - ?7 + ?7, 

 XV. 2 r — 2 ;; 4- 2 ;?^. 



After extensive reductions I find 



, 9^/^% e2e24-m /--^^i . ^^' ^ 1.4 



[o.] 

 + {- •32^*5.1 - 3|-l7'*5,2} {y' +7/'} jee.cos (r - ^ + y 



+ ^§"^5.1 e^, 7/' COS (r - i - I, + 2^^) + ^|^&5,ie e,yy,cos(i -l,-n + %) 



[IV.] ' [v.] 



9 m, a 



T6^\l^e^yy,C0S ($ + ^, - ;; - ^j 



[VI.] 



