782 ( AL( ULATING THE OCCULTATION OF STARS V.Y THE MOON. 



It may he noted that when the hour-angle (+ longitude) is 

 small, the value of 7 can be obtained b}' simple proportion from 



the formula: t (minutes) = -40 , '"""' "-^ qy even (for rough 



purposes) assuming r to be | h. 



The first rough criterion for an occultation in the Transvaal 

 may now be stated ; viz. : If the average of the limiting parallels 

 lies between —16 and —38, an occultation is almost certain. 

 The Greenwich hour-angle H is next to be examined and com- 

 pared with the mean time of conjunction, adding 2 hours to the 

 latter to get South x\frican time : this is for the purpose of ascer- 

 taining whether the occultation occurs at night or with the sun 

 still up. Remembering that h is H+longitude (=H-l-ii2 in 

 Johannesburg), we can roughly ascertain the local hour-angle 

 at conjunction by multiplying H from the Almanac by 7/4 and 

 adding to the result 3^ hours. This shows that the only really 

 favourable values of H range between — 5^ hours and +2^ hours, 

 for if H is just outside these limits the moon will be too near the 

 horizon to observe, and if H is much outside these limits the moon 

 will not be in our sky when the occultation occurs, i.e., the occulta- 

 tion, is visible in Australia or South America. Again, the local 

 time of conjunction is approximately (Greenwich mean-time of 

 conjunction + 2 hours + - ) from which it can easily be seen 

 whether the sky will be dark enough to enable the occultation 

 to be seen. Thus if the Greenwich conjunction is at 3 hours, 

 ..nd H_is -f- ih hours, t is about +gS minutes (H-I-112 being large, 

 the |h formula is not applicable here), we find the approximate 

 local conjunction to be at 6.35 p.m., and the moon will be 

 oo-f 112 4-95 minutes, or about 5 hours past the meridian. In 

 ^uch a case the disappearance of the star, which in a central 

 occultation occurs about 40 minutes before conjunction, may 

 not be visible owing to twilight, and there is the possibility that 

 the moon will set before the re-api)earance occurs. This is common- 

 ly the case with occultations at new moon, which constitute the 

 most beautiful form of the phenomenon owing to the visibiUty 

 of the " dark " portion of the moon as it approaches the star. 

 If, on the other hand, the hour-angle H had been — 1| hours in 

 the case just discussed, t would have been -f-15 minutes only, 

 and the local conjunction time would have been 5.15 p.m., so 

 That only the re-appearance (about 40 minutes later) could be 

 observed even in winter and nothing in summer, unless the star 

 were an uncommonh' bright one. 



Before passing on to a discussion of the more accurate criteria 

 lor deciding whether an occultation will come oft or not, I will 

 describe my first rough method of finding the time of immersion 

 (disappearance) and emersion (re-appearance) in the case of an 

 occultation which is known a priori to be a fairly central one : 

 I use the Johannesburg longitude for brevity. 



Immersion.- — Express H in minutes and add 75, paying 

 attention to the sign of H. Take the result and x' to the table 

 for T, and take out t, giving it the same sign as (H + 75). Calling 



