THE 



PHILOSOPHICAL MAGAZINE 



AND 



ANNALS OF PHILOSOPHY. 



[NEW SERIES.] 



APRIL 1831. 



XLI. On the Computation of the Moon's Motion in Right 

 Ascension. By FRANCIS BAILY, Esq. F.R.S. fyc. $c.* 



A S the method of determining the longitude of places, by 

 -** means of moon-culminating stars, is daily coming into 

 more general use, I trust the following table will be accept- 

 able to such of your readers as may have occasion to make 

 calculations connected with inquiries of that kind. I have 

 already shown (in my paper on this subject, inserted in the 

 Memoirs of the Royal Astronomical Society, vol. ii. p. 1), that 

 " in order to deduce, from the observations, the correct dif- 

 " ference of meridians between the two places, we require 

 " only one element from the lunar tables, viz. the moon's 

 " horary motion in right ascension ; or, more properly, the 

 " true increase of the moon's right ascension between the two 

 " apparent times of culmination :" and that, for the purpose 

 of determining the correct value of this element, it will be 

 best, when the difference of longitude is very great, to com- 

 pute the right ascension of the moon for the two given times 

 of observation ; using the equation of second, third, and some- 

 times even fourth differences. But it appears that in many 

 cases, of frequent occurrence, where the difference of meri- 

 dians does not exceed three hours, we may adopt a much 

 more concise and easy method for the solution of the pro- 

 blem, by computing accurately the semi-diurnal motion of the 

 moon in right ascension, from an ephemeris, by means of dif- 

 ferences only. 



In No. 33 of Professor Schumacher's Astronomische Nach- 

 richten, M. Bessel has given a series which is applicable to 

 this purpose ; together with a short table of the value of that 



* Communicated by the Author. 

 N. S. Vol. 9. No. 52. April 1831. 2 I series, 



