3%0 Aativnomical and Nautical Cu/ lections. 



translation. For my own part, I think that the substitution of 

 F'(x,u) in an argument inferred from reasoning on ¥{x + u), as 

 well as the exchange of x for u and u for x, when u only had 

 before been supposed evanescent, requires something more of 

 illustration than the learned and accomplished author has here 

 thought it necessary to bestow on it, though I am not at all dis- 

 posed to deny the general validity of his reasoning, or the truth 



of his conclusions. 



Believe me, dear Sir, 



Yours, very sincerely, 

 Lo7idon, 19 Mai/, 1823. * * ♦. 



iv. An easy Method of computing ihe Time of Conjunction in 

 Right Ascension from an observed Occultation. 



I. Observe, if possible, the difference of apparent altitudes at 

 the time of immersion, or emersion ; if not, compute it either 

 by finding the altitudes separately, or from the differences of 

 declination, and right ascension, allowing for the change of de- 

 clination between the conjunction in right ascension at Green- 

 wich, and the time of immersion, by reckoning ; and reducing 

 the difference of declination in the ratio of the radius to the 

 cosine of the parallactic angle (Pj Z), and that of right ascen- 

 sion in the ratio of the radius to the cosine of the same angle. 

 (See Astr. Coll. No. III.) 



II. The true distance at the time of immersion may be found, 

 as in the correction of a lunar observation, by the method in the 

 Appendix to the Requisite Tables, observing that the Reserved 

 Logarithm will become simply log. (cos. P' — sin. A' sin. P), P 

 being the horizontal parallax, P' the parallax in altitude, and 

 A' the apparent altitude. This multiplier, however, may be 

 altogether omitted without inconvenience, and the triangles may 

 be treated as plane instead of spherical, the square of the true 

 distance being equal to the sum of the squares of the semi- 

 diameter and of the difference of true altitudes, lessened by the 

 square of the difference of apparent altitudes. 



III. The square of the true distance being thus obtained, the 

 distance of the star from the orbit may be found by reducing 

 the difference of declinations at its conjunction in right as- 



