408 Astronomical ctnd Nautical Collections. 



for, if the one be observed and the other computed, their 

 difference may err not only seconds but several minutes, 

 which Vf'iW render any method quite impracticable. 



Since the true time at ship is always required to be accu- 

 rately known in order to take the observation, and since the 

 sun''s right ascension does not depend much on the supposed 

 longitude by account, the start's horary angle and true altitude 

 may be found to great perfection. And if the difference of 

 apparent altitudes can be observed, without measuring either 

 of the altitudes themselves, the method by Dr. Young will 

 be the most simple, as well as the most accurate that can be 

 devised for the purpose. 



Mr. Henderson's method is proposed with much ingenuity 

 and mathematical talent, and may, in many cases, give pretty 

 accurate results. However, it may be shown to be only an 

 approximation, and which diverges from the truth as the 

 observer approaches the perpendicular to the moon's appa- 

 rent path, the moon and star being nearly in the same verti- 

 cal circle. 



The error is occasioned by the effects of parallax being 

 computed from the star's altitude, instead of the apparent 

 altitude of the moon ; and its quantity may vary from to a 

 whole degree of longitude, and perhaps more. 



As an example, suppose the immersion of S^ was observed, 

 Jan. 5th, 1824, in latitude 28° 17 N. at 1'' 31^ 49''. 



Then star s right ascension .... 22'^ T'" 32'' 

 Sun's 19. 2 19 



Diff. of R. A 3 5 13 



Time of observation 1 37 49 



•)^'s horary angle, east of meridian . . 1 27 24 



Hence with these, the star's altitude maybe computed thus: 



Log. vers. 1^ 27™ 24" = 21° 51' =: 8.856358 

 Log. cos. declination . . 8° 39' 17" = 9.995027 

 Log. cos. latitude . . . 28 17 = 9.944786 

 Natural numb. . 062542 Log. 8.796171 



N. S. ... 799285 Mer. alt. 53° 3' 43'' 



N. S. ... 736743 ^'s alt. 47 27 17 



