PREDICTION OF OCCULTATIONS. 19 



very close to the star, wlien log cos ^ will result very near 0. In these cases, a re- 

 calculation should be made according to the method which follows, using 



t = ——cos{M—N'), 

 n 



which may give log mmi{M — N) less than log k, when the star will be occulted. 

 On the other hand, it may happen that in these cases of very near approach, a first 

 determination may give a cos ^ less than 1, which a re-calculation will show to be 

 impossible. The angle ^ is then to be considered = 0° when mnm{M — N) is positive, 

 and we shall have Q = 270° — N. When mmi{M — N) is negative, ^ — 180°, or 

 Q = 270° — iV-i- 180°. We shall also have, at the time of nearest approach, 



star's distance from moon's limb = 57' y.\niwi{M — N) — 2725), nearly, 



the error in this computed distance increasing with the distance. 



By Angle from North Point, is to be understood the arc included between the star, 

 when in contact, and the point where the limb is intersected by an arc of a great circle 

 passing from the moon's centre to the North Pole ; and by Angle from Vertex, the arc 

 between the star at contact, and the point where the limb is intersected by an arc of 

 a great circle passing from the moon's centre to the zenith. These angles are reckoned 

 from the North point and from the vertex, towards the right hand round the circum- 

 ference of the moon's disc, as seen with an inverting telescope. For direct vision, add 

 180° to the angles given by the equations. It is usual to compute these angles for 

 both phases of an occultation ; but for an immersion, they are of no importance, unless 

 when daylight is present or where the star is so small as to be seen with some dif- 

 ficulty. Where several stars of a close group are occulted at nearly the same lime, 

 the angles are useful for the purpose of identifying a particular star. For an emersion, 

 one of the angles, at least, is indispensable. With a telescope equatorially mounted 

 and furnished with a position-micrometer, the angle from North point only will be 

 required. The angle from vertex may also be dispensed with where the observer is 

 tolerably familiar with the positions of the more prominent spots on the lunar disc. 



The results obtained by the above equations are only approximate, yet the com- 

 puted times of immersion and emersion will generally be within one or two minutes 

 of the truth. The error increases with the star's distance from the apparent path of 

 the moon's centre, and is greater where the interval of time, t, is large, than where it 

 is small. In some cases, it may amount to several minutes. For an immersion, this 

 error is not of much consequence, but for an emersion, especially of a small star, the 

 time should be determined with greater precision. For this purpose, «' and «/ must be 



computed with 



H' = E:+d + tx4.5V'2 



2sin(^x45r.2) 

 log^ = ^^^ 



