resent
days. Thus you see the month is growing shorter and shorter the
further we look back, the day is also growing shorter and shorter; but
still I think we can show that there must have been a time when the
month will have been at least as short as the day. For let us take the
most extreme case in which the moon shall have made the closest
possible approximation to the earth. Two globes in contact will have a
distance between their centres which is equal to the sum of their
radii. Take the earth as having a radius of four thousand miles, and
the moon a radius of one thousand miles, the two centres must at their
shortest distance be five thousand miles apart, that is, the moon must
then be at the forty-eighth part of its present distance from the
earth. Now the cube of 48 is 110,592, and the square root of 110,592
is nearly 333, therefore the length of the month will be one-three
hundred and thirty-third part of the duration of the month at present;
in other words, the moon must revolve around the earth in a period of
somewhat about two hours. It seems impossible that the day can ever
have been as brief as this. We have therefore proved that, in the
course of its contracting duration, the moon must have overtaken the
contracting day, and that therefore there must have been a time when
the moon was in the vicinity of the earth, and having a day and month
of equal period. Thus we have shown that the critical condition of
dynamical instability must have occurred in the early period of the
earth-moon history, if the agents then in operation were those which
we now know. The further development of the subject must be postponed
until the next lecture.

LECTURE II.

Starting from that fitting commencement of earth-moon history which
the critical epoch affords, we shall now describe the dynamical
phenomena as the tidal evolution progressed. The moon and the earth
initially moved as a solid body, each bending the same face towards
the other; but as the moon retreated, and as tides began to be raised
on the earth, the length of the day began to increase, as did also the
length of the month. We know, however, that the month increased more
rapidly than the day, so that a time was reached when the month was
twice as long as the day; and still both periods kept on increasing,
but not at equal rates, for in progress of time the month grew so much
more rapidly than the day, that many days had to elapse while the moon
accom