262 DETERMINATION OF THE liONGITUDE OF SEVERAL 



The Dorpat observations of the moon-culmination that night, give 



15 X A (a) 





— 14-71" 



A(«) 





not stated. 



The mean corrections are, 







15 X A (a) 





— 15-54" 



A (a) 





— 2-30" 



Also by Bessel's formulae, 







(e) — sin (N) COS (5) A a 



+ 



cos (N) A (a) — — 14-83" 



© — — cos(N)cos(^)Aa 



H- 



sin(N)A(^) — -H 3-57" 



whence, 



. 





by imm. — T — — 5'' 



33" 



30-7^ H- 4-720 x {ri) 



by emer. — T — 5 



33 



27-6 — 3-343 x (>?) 



mean, = — 5 



33 



29-2 -i- 0-688 X (>?) 



A result which agrees with the mean of the longitudes by moon- 

 culminations, viz., 5'' 33"" 31-8', more nearly than could have been ex- 

 pected, when we consider the largeness of the co-efficients 6, ^ and n. 

 These results are derived from the assumption that Burckhardt's semi- 

 diameter needs no correction, in which case (ji) would be equal to 0. 

 If, however, we adopt Airy's correction for the results by meridian 

 observations -|- 0-2 sec. in time, whence yi =■ -\- 3-", and apply this 

 correction to the results above, viz. to those for A a and A 5, as well as 

 to >7, we derive, 



by immer. _ T = — 5^ 33" 31^-0 

 by emer. — T = — 5 33 39-7 

 mean, ^ T = — 5 33 35-3 



It does not appear, from experience, that Burckhardt's semidiameter 

 requires an additive correction, for occultations of small stars ; on the 

 contrary, most computers apply a negative correction of — 2-5" to the 

 value of >7 : this applied to the former mean result, would give, 



T = 5" 33" 30'-9, by the occupation ; 

 also, as above, T = 5 33 31-8 by all the moon-culminations. 



