e law to which the mean motions of
the same satellites of Jupiter are subject:

If we add to the mean motion of the first satellite twice the mean
motion of the third, the sum is exactly equal to three times the mean
motion of the second.[38]

This numerical coincidence, which is perfectly accurate, would be one of
the most mysterious phenomena in the system of the universe if Laplace
had not proved that the law need only have been approximate at the
origin, and that the mutual action of the satellites has sufficed to
render it rigorous.

The illustrious geometer, who always pursued his researches to their
most remote ramifications, arrived at the following result: The action
of Jupiter regulates the movements of rotation of the satellites so
that, without taking into account the secular perturbations, the time of
rotation of the first satellite plus twice the time of rotation of the
third, forms a sum which is constantly equal to three times the time of
rotation of the second.

Influenced by a deference, a modesty, a timidity, without any plausible
motive, our artists in the last century surrendered to the English the
exclusive privilege of constructing instruments of astronomy. Thus, let
us frankly acknowledge the fact, at the time when Herschel was
prosecuting his beautiful observations on the other side of the Channel,
there existed in France no instruments adapted for developing them; we
had not even the means of verifying them. Fortunately for the scientific
honour of our country, mathematical analysis is also a powerful
instrument. Laplace gave ample proof of this on a memorable occasion
when from the retirement of his chamber he predicted, he minutely
announced, what the excellent astronomer of Windsor would see with the
largest telescopes which were ever constructed by the hand of man.

When Galileo, in the beginning of the year 1610, directed towards Saturn
a telescope of very low power which he had just executed with his own
hands, he perceived that the planet was not an ordinary globe, without
however being able to ascertain its real form. The expression
_tri-corporate_, by which the illustrious Florentine designated the
appearance of the planet, implied even a totally erroneous idea of its
structure. Our countryman Roberval entertained much sounder views on the
subject, but from not having instituted a detailed comparison between
his hypothesis and the results of observation, he abandoned to Huyghens