[ 410 ] 



LXIII. On the Calculations requisite for predicting Occulta- 

 tions of Stars hy the Moon. By Professor Bessel. 



[Concluded from p. 342.] 



7. 'T^HE quantities referring to the place of observation, 

 •*- viz. u^ w, w', t/, depend on the height of the pole and 

 the sidereal time at that place. It is unnecessary to calculate 

 g and 4i' separately, as we have 



cos ^ _ ^. „;„Af (1— e'')sinip 



r cos 0' = — 7i — ; • ^.,x ; r sm 4^' 



where e denotes the eccentricity of the meridians of the earth. 

 For Professor Encke's example, we have <?> = 52° 31' 15", and 



the oblateness of the earth = -^p^ » hence 



log . r cos cf>' = 9-78505 

 log . r sin <f)' = 9-89752 

 If we denote by ju.' the sidereal time, corresponding to the 

 mean time T expressed in degrees, &c., the sidereal time cor- 

 responding to T + ^ will be 



,«, = |u,' + i . 54.14.7"'84, 

 and consequently sin (ju, — A) = 

 sin (jx' - A) + 2 . sin [^ . 27073"-92] . cos [jt;^' - A + ^ 27073"-92] 



cos(]u,— A.) = 

 cos [y} -A) -2 sin \t . 27073"-92] . sin [ jot' - A + it . 27073"-92] 



We have, therefore, 

 M = 7' . COS <p' . sin (/x' — A) 



zj = r sin (p' . cos D— r . cos <f>' sin D cos (ju,' — A) 

 „- = , . cos c^' . ^-'°['-^J»73-"9g] ^^^ f^,_ A + ^ . 27073"-92] 



x/ = r. cos^' sinD. 'A^Z2Z312^ sin [^'-A + ^ .27073"-92] 



For facilitating the calculation of m' and t/ there is a Table at 

 the end of this paper which contains the values of 

 log ^-^"[^-^7073-92] ^ j^g ^ 



and if .27073"'92 = x for values of ^ between and 1-5. 



8. I shall now finish the example above adduced. For 

 T = 7'' the sidereal time will be 7'' 54' 7"-264, and therefore 

 ft' = 118° 31' 49"-0 

 ju.' - A = —50 42 17 -6 

 We obtain, therefore, 



u = - 0-47177 ; V = +0-75914 

 and next m sin M = p — u = —0*19355 



m cosM. = q—v = —0-20674 

 M = 223° 6' 46"; log m = 9-45210. 



As 



