AND ON THE REMOTE HISTORY" OP THE EARTH. 
535 
So long as there is any relative motion of the two bodies there must be tidal 
friction, and therefore the moon’s period must continue to approach the day. It would 
be a problem of extreme complication to track the changes in detail to their end, and 
fortunately it is not necessary to do so. 
The principle of conservation of moment of momentum, which has been used 
throughout in tracing the parallel changes in the moon and earth, affords the means of 
leaping at once to the conclusion (Section 18). The equation expressive of that principle 
involves the moon’s orbital angular velocity and the earth’s diurnal rotation as its two 
variables; and it is only necessary to equate one to the other to obtain an equation, 
which will give the desired information. 
As we are now supposed to be transported back to the initial state, I shall hence¬ 
forth speak of time in the ordinary way; there is no longer any convenience in 
speaking of the past as the future, and vice versa. 
The equation above referred to has two solutions, one of which indicates that tidal 
friction has done its work, and the other that it is just about to begin. Of the first I 
shall here say no more, but refer the reader to Section 18. 
The second solution indicates that the moon (considered as an attractive particle) 
moves round the earth as though it were rigidly fixed thereto in 5 hours 36 minutes. 
This is a state of dynamical instability ; for if the month is a little shorter than the day, 
the moon will approach the earth, and ultimately fall into it; but if the day is a little 
shorter than the month, the moon will continually recede from the earth, and pass 
through the series of changes which were traced backwards. 
Since the earth is a cooling and contracting body, it is likely that its rotation would 
increase, and therefore the dynamical equilibrium would be more likely to break down 
in the latter than the former way. 
The continuous solution of the problem is taken up at the point where the moon 
has receded from the earth so far that her period is twice that of the earth’s rotation. 
I have calculated that the heat generated in the interior of the earth in the course 
of the lengthening of the day from 5 hours 36 minutes to 23 hours 56 minutes would 
be sufficient, if applied all at once, to heat the whole earth’s mass about 3000° Fahr., 
supposing the earth to have the specific heat of iron (see Section 16). 
A rough calculation shows that the minimum time in which the moon can have 
passed from the state where it had a period of 5 hours 36 minutes to the present state, 
is 54 million years, and this confirms the previous estimates of time. 
This periodic time of the moon corresponds to an interval of only 6,000 miles 
between the earth’s surface and the moon’s centre. If the earth had been treated as 
heterogeneous, this distance, and with it the common periodic time both of moon and 
earth, would be still further diminished. 
These results point strongly to the conclusion that, if the moon and earth were ever 
molten viscous masses, then they once formed parts of a common mass. 
We are thus led at once to the inquiry as to how and why the planet broke up. 
MDCCCLXXIX. 3 Z 
