XVI 



Therefore, 



THE THEORY OF THE LONG INEQUALITY 

 dK b a 2 / . ,., aV*> . ffibtf^ 



aa 4 \ da fla' ! / 



, , dK i 



log a 2 — — = 1-1781943, 

 da 



jy 



logfl ! -i= 1-7467763 -, 

 da 



logo*— - 5 = 1-3004887, 

 da 



dK% 



log a 2 — — = 1-4203660 - 

 da 



log a» -— = 1-8313179, 

 aa 



. dA" fi 



log a 2 = 1-4584086 -. 



6 rfa 



15. The following logarithms will be required. 



log cos v = 1-9907711 -, 



log cos -ar' = T-8322198, 



logCOS2-ar = T-9620142, 



log cos 2-ar' = 2-8832664 -, 



log cos (-ar + -ar') = T-9113136 -, 



log cos 2 n' = 1-8181742, 



log cos (2-sr - -ar') = T-5 168508, 



log cos (2-ar - -ar) = T-4453671, 



log cos (211' — -zjt) = T-9020604 -, 



log cos (2D' - -ar') = T-0228363 — , 



log cos 3w = T-9110959 -, 



log cos 3-ar' = T-8939967 -, 



log cos (2^ + sr') = T-9621480, 



logcos(2sr' + ts) = T-1113349 -, 



log cos (2L1' + sr) = T-6901009 -, 



log cos (2lT + -ar') = T-9998162, 



log e = 2-6691250, log e = 3-9404896, 



log e 2 = 33382500, log ee = 4-6096146, log e' 2 = 5-8809792, 



log e 3 = 4-0073750, log eV = 5-2787396, log ee" = 6*5501042, 



loge' 3 = 7-8214688, log sin 7 = 2-4198955, log sin 2 ^7 = 4-2378065 



loge sin 2 !^ = 6-9069315, loge' sin 2 !^ = 6-1782961, 



