Prof. Encke on the Occultations of Stars by the Moon. 409 



(c), the latter filled with pebbles, clay, and sand, as 

 also is (d) a "brash" connected with (c) ; (e) and (f) 

 are red horses, the former not reaching to the top of 

 the limestone, but the latter opening through it and 

 covered by the diluvium. 

 (g) is the rubbly limestone with its fragments sloping 

 to the east ; (h) sand and pebbles of sandstone and 

 limestone. 



Fig. 2. Shows in a quarry at Brotherton a second layer (#) of 

 limestone rubble above the sand and pebbles (h). 



Fig. 3. Represents some irregular ramified layers of gypsum 

 in red marl at Fairburn. 



LXVIII. On the Calculations requisite for predicting Occulta- 

 tions of Stars by the Moon*. 



r | 1 HE columns which are placed together on pages IV and VI 

 ■** of every month are to facilitate the approximate deter- 

 mination of the moon's daily motion. With regard to the 

 manner of using them for the most frequent and most useful 

 application of them, the prediction of the time at which the 

 moon will occult a heavenly body, I beg here to give some 

 further explanation on the most convenient form of the calcu- 

 lation. 



Let a, &, t, r denote the right ascension, declination, hori- 

 zontal-equatorial parallax and semidiameterof the moon, as 

 viewed from the centre of the earth, a', &', r 1 the corresponding 

 quantities for a point on the surface of the earth whose cor- 

 rected latitude is <p, g being the corresponding semidiameter 

 of the terrestrial spheroid : next let signify the sidereal time, 

 A, D the mean right ascension and declination of a star in the 

 beginning of the year ; A', D' the same for the apparent place 

 of the star at another given time. The rigorous calculation 

 of the time of the beginning and end of the occultation will 

 require the following operations. 



For at least two moments of time t, which are near the re- 

 quired one, the quantities a, 8, 7r, r, are to be deduced from 

 the Ephemeris by interpolation ; and from these the a', &', r 1 are 

 to be calculated. Developing the finite expressions into series, 

 and neglecting the terms of the third order (tt being consi- 

 dered as of the first), which are in most cases insensible, we 

 have the following formulae : 



* From Encke's Astr. Ephem. for 1830, p. 253. 

 New Series. Vol. 4. No. 24. Dec. 1828. 3 G «' = « 



