60 N. F. DUPUIS 



This particular occultation was taken because it gives in the construction a 

 convenient diagram for explanations, because it is not a very favorable case vfhere 

 accuracy is expected, and because, being calculated for Greenwich in the Nautical 

 Almanac, we have a ready means of comparing results. 



Such a comparison shows a comj)lete coincidence in the times of beginning and end. 



As a modification of this purely graphic method we may employ a certain amount 

 of calculation — principally by means of tables — to find the values of the displacements 

 Aa, aa', etc., and then through these we may readily find the coordinates of the moon's 

 centre, referred to the star as origin. This method dispenses with a great portion of 

 the graphic construction, the construction being employed only in the last stage of the 

 determination. 



The tables herewith given are logarithmic in character, but on account of their 

 arrangement they are very simple in their working. The arguments for Table I 

 are q>, tf, a, and their complements denoted by qj\ ô\ a'. 



For Table II the arguments are H and tt. The tabular results are for convenience 

 indicated by the same symbols as the arguments. 



Table III enables us to return from the logarithm to the corresponding numbers, and 

 is, in fact, a table of anti-logarithms. 



To illustrate the application of the tables we apply it to the same example as the 

 diagram, the occultation of 54 Arietis, as seen at Greenwich, Oct. 9th, 1881. 



We have then 



ip = 51°-5 (p' = 38°-5 



(î=19°-2 (î'=70°-8 



a = 40°-7, 26°-3, ll°-8 a' = 49°-3, 63°-7, 78°-2 



for the hours 11, 12 and 13 respectively. Also 



TT = 57-b- M = 35-0 



The corresponding tabular numbers from Table I are 



Now 



• J = No. from Table III to (rr + (p' + a — 2000) , 

 A= " " " (TT+ip+ô' — 2000), 



B= " " " {TT + qj'+a'-j-a — GOOO), 



and 



D = A — B. 



These give the following results — 



when 



A = 23-33 15-85 7-32, 



I) = 33-63 31-99 31-05, 



t = 11" 12" 13". 



And these are the values of the displacements Aa, Bb aa', bb', 



at the hours given. 



