30 PREDICTION OF OC C ULTATIONS. 



using the J/ and m obtained by tke first computation, and we shall have the time of 

 contact T—d-*- t, generally within a few seconds of the truth. 

 As a check on the accuracy of the work, we might compute 



u = r cos <f>' sin {h — d + p) 

 v = r cos <fi' cos D — r cos cp' cos (^ — cZ + /*) 

 and we should have 



{p + tp' - uy + {q + tq'- vy -=¥ = 0.0741. 



But if m sin M, m cos M, log n sin N, and log n cos N, have been correctly computed, 

 we shall have the following shorter and more convenient check on the subsequent cal- 

 culations for the time of contact : 



(»i sin M+ t n sin Ny -t- (m cos ilf -t- tn cos Ny = Z;' = 0.0741. 



The elements of computation, published in our general list, are given for the instant 

 of the moon's true conjunction with the star in right ascension. It is desirable, how- 

 ever, in computing an occultation for a particular place, to assume a time for the cal- 

 culation near to the time of the nearest approach of the moon's centre to the star, as 

 seen at that place, and to reduce the elements to this assumed time. This time, for 

 which the nearest tenth of an hour will be sufficiently accurate, will not diflfer greatly 

 from the time of apparent conjunction, as affected by parallax, which may be deter- 

 mined approximately by the following equations. Let T — cZ be the time of apparent 

 conjunction ; then 



m,{H-d) 

 ^^ p' sec <P - [9.4027] cos {H~ d) 



T— d = time of true cT — cZ -h (<). 

 The elements corresponding to the time T — d may then be obtained as follows : 



h-d = JE[-d-i- {[*) 

 p=it)p' 



q=Y-^{t)q' 



Where occultations are to be generally observed, as at astronomical stations, either 

 temporary or permanent, the observer will find an advantage in looking over the list 

 and selecting, beforehand, all those which may be visible at his station, by observing 

 if his latitude be included between the limiting parallels for any given occultation, if 

 the time (T—d) be favourable as regards the absence of daylight, and if the star's 

 hour-angle (Ji — d) be not greater than its semidiurnal arc for the given latitude. 



