THE SATELLITES OF JUPITER.

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of this relation, when, instead of such approximate numbers,the exact values of the velocities of the three inner Satellitesare used. And it results that, if the three be at any giventime in the same straight line drawn through Jupiter, —as, forinstance, if the 1st be in the position of new moon, and theother two upon the opposite side of the planet (see the firstdiagram in Fig . LXXVI.),—they will again occupy similarrelative positions a very short time before the outermost hasquite completed one entire revolution (see the fifth diagram inFig . LXXVI.)

But, for an approximate explanation of this peculiarity oftheir movements, it will suffice to imagine them to start as wehave'just stated,* and then to suppose that the innermost willgo round exactly four times, and the 2nd twice, while the3rd goes round once; which is what would happen if theirvelocities were precisely as the numbers 1, 2, and 4. Thenthe four remaining diagrams in Fig . LXXVI. will sufficientlyrepresent in succession the relative positions of these threeSatellites when the innermost has gone round once, twice,three times, four times, respectively; and will show, in agree-ment with Laplace’s statement, that all three can never liein the same "direction upon the same side of Jupiter at thesame time.

We must now explain a few additional technical terms con-nected with those phenomena of the Satellites , which stillremain for our discussion.

When a Satellite is seen by an observer upon the Earth toenter the shadow of Jupiter , and thereby to be eclipsed, thecommencement of the eclipse is denominated an immersion, oringress ; its end, when the Satellite exits from the shadow, iscalled an emersion, or egress.

But there is another way in which a Satellite may be hiddenfrom our view. It is when the body of the planet is actuallybetween an observer and the Satellite, which is then said tobe occulted. The beginning and the end of an occultationare respectively termed a disappearance and a reappearance.

* It may be well to remark that the relative positions thus supposed aresuch as they really occupy from time to time.