16 



AN ACCOUNT OF THE 



The following quantities have been interpolated from the computed places in 

 the American Ephemeris for the Greenwich meridian: — 



a = the moon's right ascension. 



h = the moon's declination. 



7t = the moon's equ. hor. parallax. 



a' = the sun's right ascension. 



S' = the sun's declination. 



7t' = the sun's mean equ. hor. parallax : 



8".5776. (Encke.) 



If a and h represent the right ascension and declination of the sun's centre, as 

 seen from that of the moon, and g the distance of sun and moon's centres expressed 

 in parts of the equatorial radius of the earth, we have : — 



sin n' cos h , ,-. 



r,(a— a)- 



a = a 



d = h' 



A' sin 7t cos h' 

 sin n' 



9- 



A' sin n 

 sin n' 



{h-h'). 



1 — 



A' sin n 



and we obtain the following values : — 



231'- 

 

 1 



165 43 35.26 



165 45 46.38 



165 47 57.50 



165 50 8.48 



29.99 

 35.97 

 41.93 



47.88 



9.9989500 



— 496 



— 91 



— 86 



If we refer the moon's centre to a rectangular system of co-ordinates, whose 

 origin is at the centre of the earth, the right ascension and declination of the 

 axis z being equal to a and d, and the axis x being contained in the plaine of the 

 equator, and its right ascension equal to 90 + a, we have : — 



cos 8 sin (a — a) 



X- 



Sinn 



y 



sin {8 — d) cos i {a — a)"+ cos (S + d) sin h (of — of 



sin 71 



cos (S — d) cos i (a — ay — cos {8 + d) sin i (a — af 



sin n 

 ■which equations furnish the following computed values for oc, y, and 



