Bowditch on correcting the apparent distance of the Moon kc. 5t 



MS 



(LA 



2°) + (no' — SA) + (59' 42" — LiM) + (SA 4- AB) 



-f (L M 



LK)-f-(18" + BM — BK)-f-BC + (MS — MC) Because the icvm^ 



2° -I- 60' + 59' 42 



rf 



+ 1 8", 



SA + SA, 



LM + LM, 



LA + AB 



LK 



BK, BM+ BC — MC, wbich occur in this expression 



mutually destroy each olhcr, leavm^ the identical ofj^uations MS 



MS. 



Now AB 



SA . cos A, neglecting the third power of 



SA. 



Hence S A + AB = SA . (1 + cos. A) = 3 . SA . cos. -f A^ and if 



Ave put ZL 



90 



m 



f 



ZA 



1)0 



3 



} 



LA 



2S 



d+s + m, 



S 



■ji 



d 



s 



s 



g, we shall have, by 



the noted theorem for finding an angle of a spherical triangle when 

 the three sides are given, namely 



COS. 4- A 



sm 



I (LA + ZA + ZL) . sin | (LA + ZA 



ZL) 



sin. ZA. sill. IjA 



CQg.f.sin. «;■ 



cus. s. hin. d 



hence SA + AB = — — X 



1 



COS. s sin. d. cosec ^. sec. J 



or by 



using propor- 



tional logarithms Prop. log. (SA + AB) = Prop, lo 

 log. sin. d + log. cosec. g 4 log. sec. /. 



2. SA 



COS. s 



+ 



To simplify this calculation, 1 have computed and published 

 the " Practical Navigator" the tables, numbered XTII (or 

 XVIII), in which by a single entry may be found the quantity 



in 



eo'-SA, and the Prop, lo 





2, SA 



COS. s 



, and then by the preceding formu- 



*w 



la the quantity SA + AB, called the ^r^ correction, is to be 



found. 



In a similar manner we have LM 



S. LM. sin, 4^ L 



LK 



LM 



LM. cos. L 



o T \yf '^'"- ^ (Z'^ + L\^Z L).sin.i(ZA4-ZL 



LA) 



2LM. 



sin. Zli . sin. LiA 



sin. ST. COS. S 



^ 



and by using Proportional logarithms, we shall get 



Prop.log.(LM— LK)=Prop log. 



2.LM 



COS. m 



+ log. sin. d+log. cosec. ^4- log. sec. S. 



This is also simplified by a Table numbered XIX, containing 



^ 



F- 



V 



■» 



