XXIV THE THEORY OF THE LONG INEQUALITY 



26. By means of the values of log a, log a', log n, log ri. log , and log , given 



to ai 



in (Art. 21), we shall find 



$n = - o"-00O007676 sin A - o" -000006470 cos X, 

 $a m + 0-000002324. sin X + 0-000001959 COS X, 

 $ri = + 0"-000005533 sin X + o"-000004780 cos X, 

 $a = - 0-000005140 sin X - 0-000004441 cos X. 



dP 



27. a -jfr = - 2aM u e sin 8 ^7 sin (2T1 - nf) 



- 2aM i2 e 'sin 2 A 7 sin (2ll - -sr'), 



dP( . . 



a = — same with cosines for sines. 



dU. 



dP, _ , dP( _ a 



.-. log a -=£ = 5*38632 -, log a —— - 5'49693 - , 



all oil 



win a dP r m'n a dP( n ». R -, a 



.'. — : — Tl ~ 3FT = + 0-4897, — ^-77 - -r=r - + '6318, 



w sin l sin 7 dll w sm 1 sin 7 dll 



— - = \aM b e cos -ar + l«i1f 8 e'cos ■&' 



sin 7 07 



+ laM u e cos (211 - -ar) + ^ai)f 12 e'cos (211 - tsr')j 



a dPi .. . . 



= same with sines for cosines, 



sin 7 dy 

 a 

 sin 7 dy sin 7 ^7 



.-. log — ■ = 1*1679648, log -^ —■ = 2-3363036 



»»'» 



a dPj „ m'n a dP/ 



= _ 77 ''. 8Q03) -^ ^_ ^L = _ „''.4768, 



w sin l" sin 7 dy w sin l" sin 7 ^7 



a' dQy 1 dP, «' dQ } ' _ 1 a dP/ 



sin y dU.' a sin 7 dfl ' 



""' d d %= + 0"-3500, 



w sin l" sin 7' dll 



a' dQ x 1 a dP, / 1 \ , 



— = - — ; -f I a 1 e 



sin 7' d7' a sin y dy \ 4aV 



a' dQi . . . ■■ 



- y. = same with sines tor cosines, 



to) 



sin 7 d7' 



... log A-, ^ = T-36299, log -A ^' - 2-53314, 



sin 7 d7 sm 7 d7 



a ' _ ^i . _ 55 ». 703 , -^ -A ft' - - 8"-2420, 



.' si-.. *.* Lin 1 Cin *s. l\r\. 



sin l" sin 7' d7' a> sin l" sin y dy 



,', $y = + o"-490 sin X + 0"-632 cos X, 

 3ll = + 77"*890 sin X + ll"-477 cos X, 

 $y' = + o"-350 sin X + 0"-451 cos X, 

 3lT = + 55"-703 sin X + 8"-242 cos X. 



