f energy, one
of which is due to its separation from the earth, and the other to the
speed of its motion. Though these are distinct, they are connected
together by a link which it is important for us to comprehend. The
speed with which the moon revolves around the earth is connected with
the moon's distance from the earth. The moon might, for instance,
revolve in a larger circle than that which it actually pursues; but
if it did so, the speed of its motion would have to be appropriately
lessened. The orbit of the moon might have a much smaller radius than
it has at present, provided that the speed was sufficiently increased
to compensate for the increased attraction which the earth would
exercise at the lessened distance. Indeed, I am here only stating what
every one is familiar with under the form of Kepler's Law, that the
square of the periodic time is in proportion to the cube of the mean
distance. To each distance of the moon therefore belongs an
appropriate speed. The energy due to the moon's position and the
energy due to its motion are therefore connected together. One of
these quantities cannot be altered without the other undergoing
change. If the moon's orbit were increased there would be a gain of
energy due to the enlarged distance, and a loss of energy due to the
diminished speed. These would not, however, exactly compensate. On the
whole, we may represent the total energy of the moon as a single
quantity, which increases when the distance of the moon from the earth
increases, and lessens when the distance from the earth to the moon
lessens. For simplicity we may speak of this as moon-energy.

But the most important constituent of the store of energy in the
earth-moon system is that contributed by the earth itself. I do not
now speak of the energy due to the velocity of the earth in its orbit
round the sun. The moon indeed participates in this equally with the
earth, but it does not affect those mutual actions between the earth
and moon with which we are at present concerned. We are, in fact,
discussing the action of that piece of machinery the earth-moon
system; and its action is not affected by the circumstance that the
entire machine is being bodily transported around the sun in a great
annual voyage. This has little more to do with the action of our
present argument than has the fact that a man is walking about to do
with the motions of the works of the watch in his pocket. We shall,
however, have to a