24 



THE SIMULTANEOUS DISAPPEARANCE OF JUPI- 

 TEE'S FOUR MOONS, WITH SOME NOTES UPON 

 THE LAWS THAT GOVERN THEIR MOTIONS. 



By F. Abbott, F. R. A. S. 



The four satellites, wliicli accompany the planet Jupiter, are 

 known to disappear when they enter into the planet's shadow, 

 causing eclipses much more frequent than, but in other respects 

 quite analogous with those of the moon. Galileo, who first 

 contemplated those phenomena, at once inferred that observa- 

 tions of this kind might be rendered subservient to the 

 promotion of geographical science. It only required that the 

 course of these satellites should be reduced into tables of 

 sufiicient exactness to rectify a multitude of errors in the 

 determination of longitude. 



The system, composed of Jupiter and his four satellites, is 

 a world in itself that mirrors to us those rapid revolutions 

 which are constantly taking place in the general system of the 

 universe. The study, therefore, of the inequalities of these 

 satellites becomes to astronomical knowledge of the utmost 

 importance. 



The three first satellites of Jupiter, as well as the planet 

 itself, are subjected to the mutual action of two very remark- 

 able laws, not less simple or constant than those of Kepler. 

 There is a reciprocal dependence between their movements 

 and their position, so that the place of two of them being 

 known, that of the third is readily determined. 



All the satellites except the fourth are eclipsed at every 

 revolution. Their orbits are ellipses slightly eccentric, they 

 describe equal areas in equal times, and the cubes of their 

 mean distances are in proportion to the square of their periodic 

 times, the mean sidei^al revolution of the first is half the time 

 of that of the second ; the second half that of the third ; the 

 mean longitude of the first, minus three times that of the 

 second, plus twice that of the third, is always equal to 180°. 

 Or the angular velocity of the first, added to twice that of the 

 third, is equal to three times the angular velocity of the second; 

 it is not difiicult therefore to prove that if from the mean 

 longitude of the first, added to twice that of the third, there 

 be subtracted three times the mean longitude of the second, 

 the remainder will be a constant angle which is found to be 

 180°. So that when the first satellite is eclipsed, the other 

 two will always be between Jupiter and the sun, and vice vei^sd. 



