38 THE HAMILTON ASSOCIATION, 
the shape represented by the ellipse, and at this moment let the 
Moon be at 4%. But in fact there is friction and the crest of the 
wave or the protuberances of the ellipse is belated and, therefore, 
carried onward by the Earth in her rotation beyond the proper pos- 
ition. To put the figure right and avoid confusion, let the Moon 
be set back to // which 1s the proper relative position when the 
effect of friction and rotation are taken into account. What now is 
the effect of the Moon upon the egg-shaped Earth? Suppose the 
tidal protuberances to be centralized in and represented by two 
masses at C and Cj, respectively. Now it is evident that the attrac- 
tion of JZ on C tends to retard the Earth and the attraction of JZ 
on C;, tends to accelerate it. And as Cis nearer to (/ than C,, it 
must follow that the retarding pull is stronger than the accelerating 
pull. Therefore, it is clear that the first effect of fluid friction is to 
throw the tidal protuberances forward, and the second effect is to 
retard the Earth’s rotation. Action and reaction are equal and in 
opposite directions, and as the Moon pulls the tidal protuberances 
they in turn pull on the Moon and therefore the Moon is carried 
forward in the direction of the arrow. This increasing force will 
force the Moon out to move in a spiral curve at ever increasing dis- 
tances and thus the time of the Moon’s revolution is increased. 
And not only so but the effect of this accelerating force is actually to 
retard the velocity. Thus for both reasons the length of the month 
(the time of the Moon’s revolution round the Earth) is increased. 
The same result has been shown as to the length of the day (time of 
Earth’s revolution round her axis). The result may be presented in 
another form. The attraction of the tidal protuberance intreases 
the Moon’s aerial velocity. | Now in a circle the aerial velocity 
V wo /R. Therefore as Vis increased the Moon’s distance £ is 
gradually increased, and hence also her periodic time or month is 
increased. This is true theoretically, but the investigation of astron- 
omical records since observations have been made does not offer 
much or any corroboration to the rigid mathematical proof—the 
changes for centuries past have been so slow. But it does not fol- 
low that this has always been so. When the Moon and Earth were 
gifted with more juvenility in the remote ages relative changes were 
far more rapid. Let us remember that the tide-generating force 
