PRESIDENT’S ADDRESS. 65 
quently, increase the length of the day. The reaction upon 
the moon tends to continually push the moon further from 
the earth, to make its orbit more and more eccentric, and 
te increase the length of the lunar month. Darwin shows 
that the present rate of increase of the day must be mucn 
more rapid than that of the month, and, looking forward 
into time, he estimates that ultimately the day and the 
month will become equal when each is as long as 55 of our 
present days. In other words, the action of the moon upon 
our tides will ultimately cause the earth to continually show 
the same side to the moon, just as the friction of the tides in 
the moon in ages long ago has caused the moon always to’ 
turn the same face towards us. When this stage is reached 
there will then be no tide due to the moon, but the sun 
will still produce tides on the earth. These will tend to still 
further retard the rotation of the earth, so that the day will 
become longer than the month. This will tend to pull the 
moon back again gradually closer and closér to the earth, 
until, possibly at the end of time, it ultimately falls into it. 
Looking backward, and applying the seme reasoning, we 
see that there must have been a time when the moon was 
very much closer to the earth than it is now. These tidal 
actions would chen take effect much more rapidly, for the 
tidal retardation produced by the moon varies as the inverse 
sixth power of the distance. Going further and further 
back in the life history of the moon, we can thus trace it to 
a time when it must have revolved round the earth with 
very great rapidity, and very close to it. From this it is 
a natural step to suppose then that the moon must Have 
been thrown off by the rapidly-revolving earth when in a 
molten liquid condition. The brilliant mathematical in- 
vestigations of Jacobi, Poincaré, and Darwin have shown the 
existence of forms of equilibrium for rotating masses of 
liquid which are not solids of revolution having the axis of 
rotation as the axis of figure. Such a figure becomes un- 
stable at a certain speed, and tends to break up into two 
masses, which may be nearly equal to one another. It 
seems probable then, that the moon was in the beginning of 
time thrown off by the rapidly-revolving earth, and that its 
subsequent career has been principally controled by the 
action of the tidal forces we have been dealing with. In 
our own solar system there is no other planet with a satellite 
so comparable with itself in mass as is the case with the earth 
and moon, and it is probable that only in the case of the 
earth and moon has tidal friction been the main factor in the 
evolution. Our own solar system, with its central con- 
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