292 PROCEEDINGS OF THE AMERICAN ACADEMY 



5r= 0.01365 



+ 0.00097 COS. 2{w — ^) 



+ 0.00023 COS. 3 (it— I?) 



-f 0.00008 COS. 4 (]j[ — ]g) 



-j- 0.00003 COS. 5 (]i[ — f) f 



+ 0.00001 COS. 6 (]j[ — f ) 



+ O.OOOOl COS. 7 (lit — ]^) 



-f 0.00275 COS. (l2 — ]g) 



-f 0.00003 COS. 2 {\i—j§) 



4- 0.00497 COS. (^ — ]^) 

 + A COS. C^, —6) -\- B. 



" In these equations, k^ h, qp, 6, A, and £ are determined by the 

 following formulse : — 



k COS. q, = 1.87 COS. (¥ — ]^ +306 5 13) 

 + 0.22 COS. [2 ( It — f ) 4- 171 28] 

 4- ^•'^6 COS. [3(^ — :^)-f 5] 

 + 0.35 COS. [4 (\r — ii) + 221 30] 

 + 0.13 COS. 5{w — '^) 

 -1-0.07 COS. 6(^ — ]^) 

 + 0.03 COS. [7 (it — f ) + 348] 

 -j- 0.01 COS. [8 (it — :^) -j- 348] 

 + 0.44 COS. (>2 — f 4-242 47) 

 + 0.55 COS. [2 (l2 — f ) + 271 3] 

 4- ^-44 COS. (^ — f + 208 18) 

 4- 0.82 COS. [2 {Jl —-^)\. 348 9] 



k sin. (p = 1.87 sin. ( If — :^ +306 5 13) 



+ 0.22 sin. [2 (it — f ) + 171 28] 



4- l-''0 sin. [3 (\i — :^) + 178 45] 



+ 0.32 sin. [4 ( ¥ — |;) + 180] 



+ 0.11 sin. [5 (it — :^) + 180] 



4- 0.05 sin. [6 ( II — f ) 4- 180] 



4- 0.03 sin. [7(^ — f ) 4- 168] 



+ 0.01 sin. [8 (n — :^) 4- 168] 

 4-0.5isin. (>2 — f 4- 77 0) 



4- 0.55 sin. [2 ( l2 _ f ) 4- 268 55] 



+ 0.46 sin. [:^ — f + 64 0] 



+ 0.82 sin. [2 (:^ — f) 4- 348 9] 



