LONGITUDE. 



a + h 



M 



(« + A) + M 



(a + i) - M 



A + H 



J + M 



J - M 



True Diftance 



60" 39' 27" 



60 24 54 



,21 421 N.V.S. «-p6i" 1 ,.5,6, NM. 



o 14 33 N.V.S. o.ooooio J 



61 3 22 N.SV.S. 1.483953 = 1.483953 = N- II. 

 ,69 6 57 N.V.S. 1.9820.1 I ^ g j^„iii 



48 17 9 N.V.S. 0.334585 S i >^ 



108 27 45 



5.316681 



4 



1.316681 



If the proportional part for feconds of apparent altitudes be taken from the tables, the analogy with' the above will 



be apparent. 



The following approximate method, by means of the fmall triangles, [Plate XV 11, AJlronomy, Jig. I.) is computed 



without any auxiliary tables, by this formula. ' 



CorreCliun Y — q tof. S — ^ cof. L. 



... , T /cof. i (D -4- a + ^) fin. i (D + a — *) D = apparent diftance. 



And fin. i L = / ( 2-^ ' \ " '- 



>y \ cof. a lin. D 



cof. ^ (D + a + ^) fin. X (D + 3 - a) 



col. b fin. D. 



fin. i S 



=ye 



a =: apparent altitude J . 

 b = apparent altitude ©. 



Let the apparent diftance © » be lo8°42'3"; apparent altitude © 6^27-30"; apparent altitude 2) 54" 12'; 

 refradion - paraUax 7' 43 ' for the © ; and parallax - refraftion 31' 42" for the J) . Requu-ed the true diftance. 



Computation of the angle S at the centre of the Sun. 

 App. dift. e B I0S°42' O" com. ar. log. fin. 0.02355 

 App. alt. 5 6 27 30 com. ar. log. cof. 0.00277 



App. alt. 5 54 120- 



Computation of the angle L at the centre of the Moon. 



... . - 002355 



com. ar. log. cof. 0.23287 



Sum 



Half fum 



Half fum — ap. alt. 



169 21 30 

 84 40 50 

 30 28 50 



log cof. 8.96712 

 log. fin. 9.70522 



8.96712 

 Half fum - app. alt. © 78-13' 10" log fin. 999075 



Sum 18.69866 



Half fum 9.34933 



which is log. fin. | 8 = 12 55' o" 



which is log. fin. | L = 13" 52' 25" 



Sum 19.21429 



Half fum 9.60715 



Ref. 



therefore S ^ 25 50 o log. cof. 9.95430 therefore L = 47 44 5° log. cof. 9.82763 

 par. of© =463" log. 2.66558 Par. - refr. I) = 1902" log. 3.27921 



Carried forward Sum 2.61988 



Carried forward Sum 3.10684 



