teration
of the energy of the system may be expressed by multiplying the
relative rotation by the change in the earth's angular velocity._ This
result will explain many points to us in the theory, but just at
present I am only going to make a single inference from it.

I must advert for a moment to the familiar conception of a maximum or
a minimum. If a magnitude be increasing, that is, gradually growing
greater and greater, it has obviously not attained a maximum so long
as the growth is in progress. Nor if the object be actually decreasing
can it be said to be at a maximum either; for then it was greater a
second ago than it is now, and therefore it cannot be at a maximum at
present. We may illustrate this by the familiar example of a stone
thrown up into the air; at first it gradually rises, being higher at
each instant than it was previously, until a culminating point is
reached, when just for a moment the stone is poised at the summit of
its path ere it commences its return to earth again. In this case the
maximum point is obtained when the stone, having ceased to ascend, and
not having yet commenced to descend, is momentarily at rest.

The same principles apply to the determination of a minimum. As long
as the magnitude is declining the minimum has not been reached; it is
only when the decline has ceased, and an increase is on the point of
setting in, that the minimum can be said to be touched.

The earth-moon system contains at any moment a certain store of
energy, and to every conceivable condition of the earth-moon system a
certain quantity of energy is appropriate. It is instructive for us to
study the different positions in which the earth and the moon might
lie, and to examine the different quantities of energy which the
system will contain in each of those varied positions. It is however
to be understood that the different cases all presuppose the same
total moment of momentum.

Among the different cases that can be imagined, those will be of
special interest in which the total quantity of energy in the system
is a maximum or a minimum. We must for this purpose suppose the system
gradually to run through all conceivable changes, with the earth and
moon as near as possible, and as far as possible, and in all
intermediate positions; we must also attribute to the earth every
variety in the velocity of its rotation which is compatible with the
preservation of the moment of momentum. Beginning then with the