PREDICTIONS OF C CULT ATIONS. 31 



For obtaining the time 



it will be well to tabulate the values of 



(^^ sin jE-d) 



^' y sec cp - [9.4027] cos {H-d) 

 for every half hour of (S"- (^) as far as the greatest semidiurnal arc computed for 

 the latitude of the station with a declination of 30°; and for all values of jp', using two 

 decimal figures, from 0.50 to 0.60. 



It will also be found advantageous to have tabulated values of 

 u = Q' cos $' sin (h — d) 

 u' = T cos $' A cos {h—d) 

 which should be given for every minute (in time) of {h~ d), from 0'^ to 6\ If (h-d) 

 exceeds 6", the argument will be 12* - {h-d) instead oi{h- d). It will be seen by 

 the equations that u will have the same sign as sin {h — d), and that u' will have the 

 same sign as cos {h — d). 

 In the equation 



V = r sin <p' cos D — b sin D 



the term r sin <p' cos D may be tabulated for every tenth minute of declination, from 

 0° to 30°. 



The practical application of the preceding formulae will be seen by the following 

 calculations for an occultation of the star h^ Sagittarii, March 31st, 1853, as it will 

 appear at San Diego, California; in north latitude 32° 45' = cp, and west longitude 

 from Washington 2* 40™ 29'= d. The data for the computation are given on page 9, 

 and, with the latitude and longitude of the place, are as follows : — 



March 31st, 1853. h^ /Sagittarii 



^ -f- 32° 45' H -¥■ I 03 12 J>' ■+■ 0.5800 



d -*- 2 40.5 dt H- 2 40 29 q — 0.0395 



cC 19 51. 1 H—d — I 37 17 logsinD — 9.6265 



d —d 17 10.6 F + 0.7558 logcos-D -+- 9.9571 



Calculation of the time T— <?,and reduction of the elements of computation. 



». 

 logy H- 9.763 (0 — 0.9^ 



logsec^ H- 0.075 (Reduced to hours and minutes) (<) — o 54 o 



logy sec t= log(i) -H 9-838 Sid. equiv. for (0 (ft) — o 54 9 



log const 9.403 E—d — I 37 17 



logaoBiH—d) -1- 9.960 E—d +{!>)= Ti — d — 2 31 26 



log [9.403] cos (5^- (^)=: log(2) -I- 9-363 ^ ^-^ '7 i°-6 



(2) -t- .231 c/ — c^+(0= T—d 16 16.6 



(i) -t- .689 (<)y = — 0.9X0-5800= p — 0.5220 



(i)-(2)= (3) -t- .458 -0.9X0.0395= (O9' -0.0355 



iog(3) + 9.661 y -H 0.7558 



logsin(fi^-ci) - 9-615 y-^i!)4 1 -*- °-7203 



log!!£C|=i)_ log.(0 - 9-9J4 



