OccuUations of Stars by the Moon. 413 



cos S 

 .(«— A)= l-5585n —0-0015 

 /.A« = 1-4548 —00015 



.(5-D)= 1-4760 

 /.Ao = 0-9481 B 

 I.Itt = 8-52662 



/. r cos (p'= 9-7850 c = 0-7876 



^.sin(^,'— A) = 9-8S87n6 sin D = 0-0285 

 l.cos{f<.'—A) — 9-8017 



I. a— 9-6737« 

 l.bz= 9-5867 

 /.A = 9-4192 

 / . sin D = 8-8683 



^=—0*6656 M=— 0-4717 ^.wsinM = 9-2876^ 

 <^ =+0-5523 t; =+0-7591 Z. m cos M = 9-31 56« 

 ^' = + 0-5242 m' = +0-1014 l.nsm N = 9-6261 

 9'=— 0-1638 ?/ = — 0-0092 /.?i cos N = 9-18927^ 

 M = 223'^9';/ff» = 9-4525; N =110° 5'; In = 9-6533 



/.^= 0-0171 /.-— =9-7992« /.— =9-7821 



* n n 



/.sin (M— N) = 9-9638 /. cos (M— N) = 9-5931;; /. sin ^// =9-4626 

 yp^m^b^Z' +0-247 + 0-176 



Immersion 7" 4'-3 ; Emersion 7" 25'-4 

 Q . . . . 37°-0 3°-2 



10. The method of calculating which Mr. Encke has fol- 

 lowed in constructing his Epheraeris for 1830, is perhaps as 

 easy as the one here given ; but it requires the previous cal- 

 culation of some tables. The use of such tables not being 

 required for the method here given, it will be easy for ob- 

 servers in other places to calculate every occultation for their 

 horizons if the values of J9, q, p', cf and the hour-angle of the 

 star at the time T, viz. ju.' — A, which I will now denote by /i, 

 are given. 



These data referring to the moon alone remain unchanged 

 in the calculations for other places ; only h is to be changed 

 into A + rf, where the positive d denotes eastern longitude from 

 Berlin. For such a place we have 



a =. r cos ip' sin (li + d) 

 b = 7- cos ^' cos {h + d) 

 u = a; u' = b .\ 



u = c — 6 . sin D, i/ = c . A sin D ; 

 hence m, M, n, N, and lastly, the two values of t^ which will 

 show the mean time at Berlin, at the two moments in which 

 the disappearance and reappearance will happen at the place 

 for which the calculation has been made. This process will like- 

 wise be illustrated by calculating the occultation of 82 Leonis 

 for Alton a. 



We assume as given : 



T = 7..ii'=-0-C'^-56,/=+ 0-52421 



' \<7 = +0-5523, <7'= -0-1638 r' ^"^"^ 



For 



