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The case then corresponds to that of the "Station of Venus" and 

 it is a very ancient problem to compute its epochs. 



Let be 7' and r' the radii vectores of two satellites ; 6 and 6' the 

 corresponding amplitudes, then for the occultation : 



r sin ^ = r' sin 6' . 



The condition of an equal change of longitude leads to : 



^dS , ^, d& 

 r cos 6 — = r cos 6 — . 

 dt dt 



Now, if T and T' represent the sidereal periods, we have, neglecting 

 the apparent movement of Jupiter : 



dO dd' _l 1 _ 1 ^ 1 



It ' ~dt~'T ' Y'~?l^ ' /V^' 



consequently : 



r~V2 cos 6 = r'~V2 cos 6\ 



from which : 



The equality of the hourly changes of the two elongations of 

 course only lasts for an instant ; very soon inequality sets in and 

 the two satellites begin to separate. Meanwhile it may be long ere 

 such becomes perceptible at the telescope, only, in a case like the 

 present, the satellites do not pass each other, but after the conjunction 

 they have the same position the one to the other as before. 



As an example take a conjunction of I and II under the circum- 



