30: .PREDICTIONS OF OC CULTATIONS. 



For obtaining the time 



T-d=^ -d+ {t), 



it will be well to tabulate the values of 



sin [H— d) 



(t) 



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



for every half hour of {E— d) as far as the greatest semidiurnal arc computed for 

 the latitude of the station with a declination of 30°. 



It will also be found advantageous to have tabulated values of 

 ti = T cos <p' sin (h — d) 

 u' = r cos $' A cos {h — d) 

 which should be given for every minute (in time) oi {li — d), from 0* to 6*. If (A — (?) 

 exceeds 6*, the argument will be 12* — {Ji — d) instead of (7i — J). It will be seen by 

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

 same sign as cos {h — dy 

 In the equation 



V = r shi <p' cos D — b sm D 



the term r sin $' cos Z> may be tabulated for every tenth minute of declination, from 

 0° to 30°. 



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

 the requisite calculation for an occultation of 6 Libras, which will take place on the 

 15th of January, 1852, as it will appear at San Diego, California; in north latitude 

 32° 45' = (p, and west longitude from "Washington 2'' 40™ 29' = d. With the quantities 

 corresponding to this star and date, on page 5, we have the following data : 



January 15<7i, 1852. lAhrtB. 



3"= — o 13 46 $ = -f- 32° 45' 



d = -^ z up 21) T =■ -^ 0.5727 



S—d = — 2 54 15 y = -I- 0.5622 



logcosZ) = -t- 9.9822 4 =■ — 0.1659 



Calculation of the time T—d and reduction of the elements. 



logy -)- 9.750 (rt 



log sec $ -H 0.075 (Reduced to hours and minutes) (0 



logp'sec^^ log(i) +9.825 Sid. equiv. of (0 (J) 



log const 9403 U—d 



logcos(jff— (^) -)- 9.860 H—d-^(ji)= h — d 



log[9-4°3]cos(5'— rf)— log (2) + 9.263 d—d 



(2) -4- .183 cf—d-k-if) T—d 



(i) -1- .668 (<)/ = — 1.4 X -5622= p 



(0-(2)= (3) + 485 -14X-.1659 (t)q' 



log(3) -+- 9-686 Y 



\ogsm{H—d) - 9.838 r+(Os' q 



log^^5i|=l)^ log(0 -0.152 



d 



= 19 51 .1 



d 



= -4- 2 40.5 



d -r-d 



= 17 10.6 



log sin D 



= — 9-4479 



— 14 



I 



24 



I 



24 14 



2 



54 15 



4 



18 29 



7 



lo- 6 



1 



46-6 





.7871 





-2323 





■'i7^7 





.8050 



