within which an Occultation is visible* 91 



tion referred to coordinate axes which have their origin at 

 the moon's centre ; the axis z of course coinciding with the 

 line which joins the centres of the moon and the star, and r 

 being the radius of the moon. 



Let #,, y l9 z l9 be the coordinates of the centre of the moon re- 

 ferred to the centre of the earth, the plane xy coinciding with 

 the equator, x^y^ z 2 the coordinates of the star referred to 

 the same axes, and let 



4 = a (*-*,) + b(y- yi ) +c(z-z l ) 

 y = a' (a: - *!) + b> (y-y^ + cf (z - Zl ) 

 z* = at' (x - i-J + W (y - y,} + # (z - z,) 



The equation to the cylinder referred to the axes x 9 y 9 z is 



{(*-*!) +b(y- yi ) +c(z-z l )}* 

 + {(a' (x - *,) + V (y -y,} 4- c' (z - *)}* = r* 



The equation to the plane d if is 



of' (x - xj + V'(y - 3/J + </'(*- z } ) = 0. 



If a, and S t denote the right ascension and declination of 

 the moon, and 2 , 8 2 of the star, since the plane di/ is perpen- 

 dicular to a line joining the centre of the moon and star, it is 

 easy to show that 



a n at COS #2 cos ^2> ^" = Sm a -2 COS ^2 C " = Sm &2 



The following well-known equations of condition obtain 

 between the quantities , b, c 9 a', b', c', ", b", c" : 

 aa' + bb' + c c 1 =0 

 aa" + b b" + c c' f 



-f c 2 = 



Since these equations are more than are necessary to de- 

 termine these quantities, we may suppose one of them as c = 0, 

 and then it is easy to show that 



a = sin 2, b = cos a 2 



a' = cos 2 sin 8 2 , b' = sin 2 sin $ 2 , c' = cos 8 2 , 



and the equation to the cylinder becomes 



{ (x - xj sin 2 - (y - */,) cos 2 } 2 

 + {(x- x,) sin S 2 cos a 2 + (y - j/J sin <* 2 sin S 2 



- (a -,) cos& 2 } 2 =r 9 



If x = U cos $ cos 3 , y = R cos <p sin a 3 , z = K sin c^, 

 ^ being the geographical latitude of a point on the earth's 

 surface, and if /I be the moon's horizontal parallax, A her 

 apparent semidiameter, 



N 2 cos 



