92 Tables of the Decimal Parts of a Day and an Hour. 



{cos 8, sin (a 2 J II cos <p sin ( 2 a 3 ) } 9 

 + {cos 8 sin 8 2 cos ( 2 aj) sin 8 t cos 8 2 



~ II (cos p sin 8 2 cos (a 2 3 ) sin f cos 8 2 } 2 = A 9 



Let co be the inclination of the moon's orbit to the equator, 

 v the right ascension of its intersection with the equator; then 

 the equation to her orbit is 



x sin co sin v y sin co cos v + z cos co = 

 The equation to a plane passing through the star and the 

 centre of the moon and perpendicular to this plane is 



( x #,) (cos co cos 8 2 sin a 2 -f- sin 8 2 sin co cos v) 

 -f (y i/,) (sin co sin v sin 8 2 cos 8 2 cos 2 cos co) 

 (z zj (sin co cos 8 2 cos ( 2 v) =0, 



and putting R cos <$> cos 3 for ,r, JR cos <p sin 3 for z/, and 

 jR sin p for z, 



n { cos <p sin S 2 sin co cos (v 3 ) + cos $ cos 5 2 cos co sin ( 2 3 ) , . 

 sin $ cos 2 sin cos (a 2 -v)} 



cos 8, sin 8 2 sin co cos (v a,) cos Sj cos S 2 cos co sin ( 2 a,) 



-f sin 8, cos 8 2 sin co cos (a 2 v) = 0, 



the geographical longitude east of the point corresponding 

 to 3 = 3 the sidereal time at the place from which longi- 

 tudes are reckoned. 



Equation (1) may be considered as the equation of a cone 

 having its apex at the earth's centre, the variables being <p 

 and 3 . This determines the points on the earth's surface 

 for which the star is occulted at any instant; the intersection 

 of this cone with the plane, Equation (2), determines the points 

 at which the star is just occulted or appears to graze the edge 

 of the moon. The mathematical solution here given compre- 

 hends also those points on the opposite hemisphere of the 

 earth to the moon, which are intersected by the cylinder and 

 plane, and which must obviously be excluded. 



XVI. Tables of the Decimal Parts of a Day and an Hour. 

 By A CORRESPONDENT. 



To the Editors of the Philosophical Magazine and Annals. 



Gentlemen, 



A S I see that in a former Number of your Journal you 

 -*^- have commenced a publication of correct Tables requisite 

 in practical astronomy, I forward two of the same nature, in 

 the hope that other correspondents may be induced, like my- 

 self, to follow so useful an example. 

 December 10, 1830. 



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