Earth when the hour angle is-and later when +, therefore to determine the apparent hourly motions at apparent conjunction assume two instants; first the time of true conjunction in right ascension and the 2d + or one hour from the first according to the sign of the hour angle; compute the Parallax in right ascension and declination at these two instants, Then making A the Moon's right ascension at 1st instant. D the Moon's declination at 1st instant. = a the true hourly motion in right ascension. d=the true hourly motion in declination. a the apparent hourly motion in right ascension. -when proceeding to the north and + when to the south. A the difference of declinations at conjunction. A' apparent difference of declinations at apparent conjunction when the Moon is N and-when south of the star. p' the parallax in right ascension at the 1st instant. = p": P= P = at the 2d instant. in declination at the 1st instant. at the 2d instant. t-the time from the true to the apparent conjunction. A+p the apparent right ascension at the 1st instant. A+a+p" 2d instant. aap-p' apparent hourly motion in right ascension similarly. d'=d+ P'—P'=apparent hourly motion in declination: The difference of the apparent right ascensions of the Moon and star at the 1st instant will be p', and t the time of the Moon describing this space will be t=P p' a+p a Now 1st instant..+t(+or-according to the sign of the hour angle)=time of apparent conjunction in right ascension. But in the interval t, the Moon's declination will be altered by (d+P-P') t. Therefore ▲'=▲ + P'' + (d· + P' -P')t=apparent difference of declinations at apparent conjunction in right ascension. Let us now suppose the Moon to be stationary and the star to be relatively in motion. Let N. w. y represeut the Moon's surface; c the centre; a b and be the star's apparent horary motion in right ascension and declination; a e the portion of the orbit described in one hour; cx the difference of apparent declinations at apparent in right ascension, and cn the nearest approach of the centres. Now c n x and x d a being right angles. the angle d a x=90-d x a. the angle da x (which we will call O) being the inclination of the star's apparent orbit to the circle of declination; to compute it, we have And t the time describing x n will be = n sin O Now the time of apparent d in right ascension + t' (+ when A' and d' are of like signs and = when con trary) time of nearest approach, or the middle of the occultation. If y represent the place of Immersion, the time of the star describing n y will be the semi-duration, to determine which we have c y S the Moon's semi-diameter c n = n the nearest approach and by the 47th of the 1st Book of Euclid Vs-n2 n2nys n.s n | h a' cos D: 1 :: s+n.s -u: the semi [duration Time of nearest approach { S+= the time of Emersion. -the time of Immersion. The following example will sufficiently illustrate these observations- I find from the nautical Almanac that on the 9th June w2 Scorpii will be occulted; the following are the ele |