786 CALCULATING THE OCCULTATION OF STARS BY THE MOON. 



of time becomes i= -. — ^ — . As this is troublesome to 



X - IDC 



work out, and as CM is always small, I ha\'e found an approximation 

 sufficient : this is, t (displacement of ' central occultation) = 



~ — (2 H* — 100 y') and the jn'oper signs + or - of a and y' 



must be observed. For example, in the </ Piscium case a was 



-0-04 and y = + -2, hence t^ H = + 2 mmutes. 



•57- -2 



The time of mid-occultation is (G T <5 +2 hours +- + /), and 

 in the above case was therefore 6.54 p.m. when all corrections 

 are applied, giving 6.14 and 7.34 as the corrected times of immersion 

 " and emersion . 



B. To find the true value of AB or T in the formula on 



page 785, we have the complete formula T - ^^ \/"i - k- cos'-' 6, 



k being a h- rV- Alternatively, this may be stated as 



T =^-, ;r- sin fcos"^ — A cos OV, and in this form can be worked 



.V - i6c 



out on the slide-rule in a minute, using the sin scale on the back, 



marked S., mentally subtracting the angle obtained by using 



'tt a cos H from 90° and taking the sin of the latter angle : Thus 



if A is - 0-04, V A cos H is -14, op}wsite to which is 8°. 



T is .-. ^^ ;r-5i;i82° = 7Q minutes. By the square-root formula 



.r -i6c '^ ' 



33 cos ft" , , ^., ... . ^, .^ 



= ^ -p- V I -(-14)- which gives the same result. 



X - IOC 



It ma}- be useful if I give a table showing the values of this 

 correcting- factor for T, viz. s/ 1 - ( V a cos B)- or sin \cos ' V a cos ^]°. 

 For this purpose cos H will be assumed constant = -95, and 

 the table serves b}' comparison to ehminate arithmetical errors 

 when cos H is taken into account. 



Table for Correcting-Factor to Dur.a.tion of Occultation. 



When A is ± o 10 or less, factor lies between i and o ■ 94 



,, A is ± 0-136 (half moon's radius), factor is 0-88 



,, A is ± o-i6 . . 



,, A is ± 0-20 . . 



„ A is ± 0-23 . . 



„ A is ± 0-25 . . 



,, A is ± o -26 . . 



,, A is ± 0-27 . . 



,, A is ± 0-28 . . 



,, A is ± 0-29 . . 



Applying the approximate value for cos ^, and calling this 



factor F we have finally T = '^■-' \ 2^ ) giving the duration 



x' - i6c 

 of the occultation in minutes. 



*H=hour angle to the nearest hour. 



