THE SATELLITES OF JUPITER.

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their occurrence, by the comparison of which with local timethe longitude may he immediately deduced. More exact methods(the eclipses not being of a sufficiently instantaneous character)are, however, necessary when much precision in the longitudeis desired.

To conclude our discussion of these four far-distant Moons,we may remind our readers of the proof which we gave, in Lec-ture III., pp. 58-61, that the Moon ’s orbit is always concave tothe Sun ; and we may mention that we have been asked morethan once, during the delivery of this course of lectures, whetherthis is also the case with the orbits of Jupiter’s Satellites. Itis easy to see that it is otherwise. In the case of our ownMoon we showed that the Earth would draw it when new about;(yths of an inch in a second of time out of a straight line,towards itself, and away from the Sun , while we found that theSun would draw both the Earth aud the Moon through nearlyayths of an inch per second in the opposite direction; the resultbeing that the Moon is at such a time drawn not quite T bth ofan inch in a second away from the Earth , while it travels incompany with it through a distance of about 94,500 feet aroundthe Sun. The Moon’s orbit is therefore concave to the Sun when the Moon is new; and when it is full, since both theEarth and the Sun pull it in the same direction, towards thelatter, the concavity is still more marked.

But if we consider the outermost Satellite of Jupiter whenit is in the position of new moon, we find, that Jupiter ’s powerover it is sufficient to draw it about x ydis of an inch towardsitself in a second, while the Sun would only draw it aboutAths of an inch in the opposite direction. At that time,therefore, the orbit must be concave to Jupiter , and convex tothe Sun. And the power of Jupiter over the three innerSatellites being greater still, their orbits will, when theyare new moons, be still more convex to the Sun than that ofthe 4th.

Let us investigate this statement a little further; and, tobegin with, let us notice that the orbital velocity of Jupiter round the Sun, of which the Satellites partake in addition totheir own velocities round the planet, is rather less than 29,000