24 REPORT—1905. 
the day is now being prolonged more rapidly than the month, the number 
of days in the month was greater in the past than it now is ; and if the 
converse were true, the number of days in the month was less. 
Now it appears from mathematical calculation that the day must now 
be suffering a greater degree of prolongation than the month, and accord- 
ingly in retrospect we look back to a time when there were more days in 
the month than at present. That number was once twenty-nine, in place 
of the present twenty-seven ; but the epoch of twenty-nine days in the 
month is a sort of crisis in the history of moon and earth, for yet earlier 
the day was shortening less rapidly than the month. Hence, earlier than 
the time when there were twenty-nine days in the month, there was a 
time when there was a reversion to the present smaller number of days. 
We thus arrive at the curious conclusion that there is a certain 
number of days to the month, namely twenty-nine, which can never have 
been exceeded, and we find that this crisis was passed through by the 
earth and moon recently ; but, of course, a recent event in such a long 
history may be one which happened some millions of years ago. 
Continuing our retrospect beyond this crisis, both day and month are 
found continuously shortening, and the number of days in the month 
continues to fall. No change in conditions which we need pause to con- 
sider now supervenes, and we may ask at once, what is the initial 
stage to which the gradual transformation points? I say, then, that 
on following the argument to its end the system may be traced back 
to a time when the day and month were identical in length, and were 
both only about four or five of our present hours. The identity of day 
and month means that the moon was always opposite to the same side of 
the earth ; thus at the beginning the earth always presented the same 
face to the moon, just as the moon now always shows the same face to 
us. Moreover, when the month was only some four or five of our present 
hours in length the moon must have been only a few thousand miles from 
the earth’s surface—a great contrast with the present distance of 240,000 
miles. 
It might well be argued from this conclusion alone that the moon 
separated from the earth more or less as a single portion of matter at a 
time immediately antecedent to the initial stage to which she has been * 
traced. But there exists a yet more weighty argument favourable to 
this view, for it appears that the initial stage is one in which the stability 
of the species of motion is tottering, so that the system presents the 
characteristic of a transitional form, which we have seen to denote a 
change of type or species in a previous case, 
In discussing the transformations of a liquid planet we saw the 
tendency of the single mass to divide into two portions, although we 
failed to extend the rigorous argument back to the actual moment of 
separation ; and now we seem to reach a similar crisis from the opposite 
end, when in retrospect we trace back the system to two masses of 
unequal size in close proximity with one another. The argument almost 
