( 11'^ ) 



of the star, after tlie moon's parallax, calculated for the point where 

 the occultation took place, has been added to it with a contrary 

 sign, be denoted by 1 ; let the geocenti'ic radins of the moon (as 

 it was used for this calculation) be =: R, the iiorizontal parallax = 77 

 and the ditference in declination between the reduced place of the 

 star and the moon's centre = v, then we have 



and hence 



15 "'"'^ ^^"-''"^ 



R^ — v^ 



but as R= nk 



we have d R=z lid k 



IRn ^^ IR' dk 



hence o 1 = o k = . — . 



7^' — v' R' — v' k 



The reduction to be added to the star's R. A. to get that of the 

 apparent moon's centre is =f: I -f- II, wiiere the 2^ term is indepen- 

 dent of k and the upper sign of the first is to be used for disap- 

 pearances, the lower for reappeai"ances. 



If the hourly motion of the moon in R. A. is A«, the correction 



=F I +n 



of the Greenwich mean time of an occultation is V 3600^ 



and the correction of the eastern longitude derived from it : 



^ ~^ X360(>. Now as the assumed value of k was 0,272525 

 A« 



we have dk = + 0,000115 : 



0.000115 T7^^ 



and ö E. L. = ± 3600 X 



r= zt [0,1814] 



0.272525 {R' — v')Aa 

 IR-" 



{R^ — v^) A H ' 



where the value in square brackets is a logarithm, and the loga- 

 rithms of the other factors may be derived from the former cal- 

 culation. The + sign is to be used for disappearances, the — sign 

 for reappearances. 



In this way I have found the corrections given in table II and 

 thus obtained corrected values for the longitude. I think it best to 

 use indistinctly the results from disappearances and reappearances. 



