344 Asttonomical and Nautical Collections. 



the square of the difference of the apparent altitudes, the remainder 

 being the square of the true distance. 



Example:— Ihe&emxdi.. .14 54 =894, sq. . 799236 

 Diff. true alt. . 50 41 =3041, 9247681 



Diff. app. alt. . 3 32 =r 212, A. C. 99945056 



Truedist. . . 52.42,6=3162.6 10001973 



III. From the difference of declination at the conjunction, 

 reduced in the ratio of the radius to the sine and cosine of the 

 orbital angle, we obtain the nearest distance of the star from the 

 orbit, and the distance of the nearest point of the orbit from the 

 point of conjunction in right ascension; or, in the Nautical Almanac 

 for 1827, and the succeeding years, we find these arcs already 

 computed. The square of the nearest distance, subtracted from 

 that of the true distance, gives the square of the orbital distance 

 from the point of nearest approach, which converted into time from 

 the moon's hourly motion, and applied to the time of the nearest 

 approach, shows the true time of the immersion for the meridian of 

 Greenwich. 



JElraw/j^e .-—Neai'est distance 50' 31"=3031" sq. 9186961 

 True distance sq. 10001973 



Dist. from n. point 15' 2",8 = 902.8 sq. 815012 



Now the hourly motion being 29' 42', the distance 15' 2",8 

 becomes equivalent to 30"" 24', and the time of nearest approach 

 being 3*" 17™ P, the time of immersion at Greenwich becomes 

 3^ 47m 25% instead of 3" 46" 50^ as supposed ; and the error of 

 observation, or of computation, would be 35' of time. 



Mr. Henderson's Improvement on Dr. Young's Method. 

 When neither of the altitudes has been observed, the computation 

 of that of the moon is liable to considerable uncertainty, as depend- 

 ing upon the supposed longitude by account ; and Mr. Thomas 

 Henderson, of Edinburgh, has remarked, that the method pro- 

 posed by Dr. Young does not exhibit so rapid a tendency to con- 

 verge to the true longitude as would be desirable. He has therefore 



