PREDICTION OF OOCULTATIONS. 21 



With « and log a, taken from this table, with t as argument, (« with the same sign 

 as t,) we have 



m' := r cos cp' A. cos H' 



v' = rcos<p'?^sinDsmJB'' 



Then, with these values of u' and v', compute iV, n, ^, and t, by means of 



wsiniV = y — u' 

 ncosJV^=: q' — t/ 



, msm(M — JV) 



cos<4/ = ^^ 



k 



t = Gos(M—N)^ 



n n 



using the iff and m obtained by the 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 



M = rcos<|>'sin(J5r-f- 6?-i- i( X 902'4) 



V = rsm (p' cos D — r cos <p' cos {II -t- d -^ t x 902'4) 



and we should have 



(p + tp' — uY -*-{q + tq'—vf = F = 0-0743 



but if msinM, mcosM, log^^siniV, and logwcosiV, have been correctly computed, we 

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

 culations for the time of contact : 



(m sin iHf -+- t n sin iV)^ -i- [m cos if h- tn cos NY = F = 0.0743 



For an example of the practical application of the preceding formulae, we will make 

 the requisite calculations for an occultation of |' Librae on the 20th of February, 1851, 

 as it will appear at Halifax, Nova Scotia; in north latitude 44° 39'. 3 = $, and longi- 

 tude from Washington 13° 27'.0 = 0'' 5 3™. 8 ^=cl. We have the given star and date 

 on page 9 ; and taking out the corresponding quantities T, H, etc., we have the data 

 for computation, as follows : — 



