m of light across
the vast space between Jupiter and the earth. When the eclipse has
commenced, the little orb is no longer luminous, but there is,
nevertheless, a long stream of light on its way, and until all this has
poured into our telescopes we still see the satellite shining as before.
If we could calculate the moment when the eclipse really took place, and
if we could observe the moment at which the eclipse is seen, the
difference between the two gives the time which the light occupies on
the journey. This can be found with some accuracy; and, as we already
know the velocity of light, we can ascertain the distance of Jupiter
from the earth; and hence deduce the scale of the solar system. It must,
however, be remarked that at both extremities of the process there are
characteristic sources of uncertainty. The occurrence of the eclipse is
not an instantaneous phenomenon. The satellite is large enough to
require an appreciable time in crossing the boundary which defines the
shadow, so that the observation of an eclipse cannot be sufficiently
precise to form the basis of an important and accurate measurement.[23]
Still greater difficulties accompany the attempt to define the true
moment of the occurrence of the eclipse as it would be seen by an
observer in the vicinity of the satellite. For this we should require a
far more perfect theory of the movements of Jupiter's satellites than is
at present attainable. This method of finding the sun's distance holds
out no prospect of a result accurate to the one-thousandth part of its
amount, and we may discard it, inasmuch as the other methods available
seem to admit of much higher accuracy.

The four chief satellites of Jupiter have special interest for the
mathematician, who finds in them a most striking instance of the
universality of the law of gravitation. These bodies are, of course,
mainly controlled in their movements by the attraction of the great
planet; but they also attract each other, and certain curious
consequences are the result.

The mean motion of the first satellite in each day about the centre of
Jupiter is 203 deg..4890. That of the second is 101 deg..3748, and that of the
third is 50 deg..3177. These quantities are so related that the following
law will be found to be observed:

The mean motion of the first satellite added to twice the mean motion of
the third is exactly equal to three times the mean motion of the second.

There is another law of an