LONGITUDE. 



The formula is as follows : 



Let 



I a / cof. i{d + a + h) cof. ^{J ^ {" + />) cof- A cof. H 



cof. i ( A + H ) cof. VcoL'6 



Then fin. i D = cof. J (A + H) cof. N. 

 In which A = true altitude of J) 



a = apparent altitude of ]) 



H = true altitude of 



h = apparent altitude of 



d = obferved or apparent diftance © ]> 



D = true diftance required. 



fin. N. 



Apparent diftance © (f 

 Apparent a'titude © 

 Apparent altitude d 



Sum 



Half fum 

 Diftance half fum 

 Correfted altitude © 

 Correfted altitude ([ 



Sum 



Half fum 



86' lo' 19" 

 32 34 47 

 39 3 4 



157 43 10 



73 54 5 



7 16 14 



(■32 a 2? 



1.39 47 18 



72 20 43 

 36 10 21.5 



Example I. — Borda's Method. 



Com. ar. log. cof. 

 Com, ar. log. cof. 



log. cof. 

 log. cof. 

 log. cof. 

 log. cof. 



0.0743564 

 0.1098114 



9.2844366 

 99964940 



99257)39 

 9.8855952 



Sum 

 Half fum 



Log cof. N 



39.2764375 



log.Tof. ('9:9070039} ^'^- 9-73I2H8, which is the log. fm. N.' 

 \ 9.9256221 



Sum log. fin. of the 9.8326260 



Half diftance 

 True diftance 



42'' 51 '29" 

 85 42 58 



When Callet's Logarithms are ufed, much labour may be avoided, by taking the neareft multiple to 10" in the 

 apparent diftance and making an equal alteration in the refult. In the above example, the diftance for calculation might 

 be 86 10' 20"; and then one fecond ftiould be dedudled from the refult, which would have been 8c" 42' 59". 



Example II. — According to the method given by Dr. Mafl<elyne in the Preface to Taylor's Logarithms. Let the 

 apparent altitude of the moon's centre be 39 3' 4'', that of the fun 32" 34' 47" ; their apparent diftance 86^ 10' 19", and 

 the moon's horizontal parallax 58' 28". Required the true diftance of the fun and moon. 



J 's horizontal parallax ... o' 58' 28" Log. fine . - - 8.23061 



Ji 's apparent altitude - - . 39 3 4 Log. cofine - - 9.89019 



J 's parallax in altitude 



D 's refraftion from Table I. • - 



Correftion of moon's altitude 

 B 's apparent altitude ... 



D 's true altitude - • - 



©'s apparent altitude ... 

 Difference of refraftion and parallax 



©'s true altitude • . . 



i) 's true altitude - - - 



Difference of true altitudes of © and D 



©'s apparent altitude ... 

 ]) 's apparent altitude ... 



Difference of apparent altitudes of © and J) 

 Apparent diftance .... 



o 45 24 

 — I 10 



Log. fine 



8.12080 



Sum 

 Vol. XXI. 



92 38 36 



Yy 



Difference 



