SKCT, IV. ECLIPSES OP THE SATELLITES. 29 



times that of the second ; and that the mean longitude 

 of the first satellite, minus three times that of the 

 second, plus twice that of the third, is always equal to 

 two right angles. It is proved by theory, that if these 

 relations had only been approximate when the satellites 

 were first launched into space, their mutual attractions 

 would have established and maintained them, notwith- 

 standing the secular inequalities to which they are 

 liable. They extend to the synodic motions (N. 92) of 

 the satellites ; consequently they affect then* eclipses, 

 and have a very great influence on their whole theory. 

 The satellites move so nearly in the plane of Jupiter's 

 equator, which has a very small inclination to his orbit, 

 that the first three are eclipsed at each revolution by 

 the shadow of the planet, which is much larger than 

 the shadow of the moon : the fourth satellite is not 

 eclipsed so frequently as the others. The eclipses 

 take place close to the disc of Jupiter when he is near 

 opposition (N. 93); but at times his shadow is so pro- 

 jected with regard to the earth, that the third and 

 fourth satellites vanish and reappear on the same side 

 of the disc (N. 94). These eclipses are in all respects 

 similar to those of the moon : but, occasionally, the 

 satellites eclipse Jupiter, sometimes passing like obscure 

 spots across his surface, resembling annular eclipses of 

 the sun, and sometimes like a bright spot traversing one 

 of his dark belts. Before opposition, the shadow of the 

 satelb'te, like a round black spot, precedes its passage 

 over the disc of the planet ; and after opposition, the 

 shadow follows the satellite. 



In consequence of the relations already mentioned in 

 the mean motions and mean longitudes of the first three 

 satellites, they never can be all eclipsed at the same 

 time. For when the second and third are in one direc- 

 tion, the first is in the opposite direction ; consequently, 

 when the first is eclipsed, the other two must be be- 

 tween the sun and Jupiter. The instant of the begin- 

 ning or end of an eclipse of a satellite marks the same 

 instant of absolute time to all the inhabitants of the 

 earth; therefore, the time of these eclipses observed 

 by a traveler, when compared with the time of the 

 eclipse computed for Greenwich, or any other fixed 

 c2 



