ces
of Jupiter's satellites. Calculation does not yield in precision to
direct observation. In this group of satellites, considered as an
independent system of bodies, Laplace found a series of perturbations
analogous to those which the planets experience. The rapidity of the
revolutions unfolds, in a sufficiently short space of time, changes in
this system which require centuries for their complete development in
the solar system.

Although the satellites exhibit hardly an appreciable diameter even when
viewed in the best telescopes, our illustrious countryman was enabled to
determine their masses. Finally, he discovered certain simple relations
of an extremely remarkable character between the movements of those
bodies, which have been called _the laws of Laplace_. Posterity will not
obliterate this designation; it will acknowledge the propriety of
inscribing in the heavens the name of so great an astronomer beside that
of Kepler.

Let us cite two or three of the laws of Laplace:--

If we add to the mean longitude of the first satellite twice that of the
third, and subtract from the sum three times the mean longitude of the
second, the result will be exactly equal to 180 deg..

Would it not be very extraordinary if the three satellites had been
placed originally at the distances from Jupiter, and in the positions,
with respect to each other, adapted for constantly and rigorously
maintaining the foregoing relation? Laplace has replied to this question
by showing that it is not necessary that this relation should have been
rigorously true at the origin. The mutual action of the satellites would
necessarily have reduced it to its present mathematical condition, if
once the distances and the positions satisfied the law approximately.

This first law is equally true when we employ the synodical elements. It
hence plainly results, that the first three satellites of Jupiter can
never be all eclipsed at the same time. Bearing this in mind, we shall
have no difficulty in apprehending the import of a celebrated
observation of recent times, during which certain astronomers perceived
the planet for a short time without any of his four satellites. This
would not by any means authorize us in supposing the satellites to be
eclipsed. A satellite disappears when it is projected upon the central
part of the luminous disk of Jupiter, and also when it passes behind the
opaque body of the planet.

The following is another very simpl