Page:The Solar System - Six Lectures - Lowell.djvu/58

 striving by friction to set it at right angles to the line. The bulge, therefore, acts as a brake upon the Earth's rotation, and must continue so to act until the Earth's rotation and revolution coincide.

Now let us determine the tide-generating force :—

Let $$M$$= mass of the Earth; $$m$$ =mass of the Moon; $$x$$,$$y$$,$$z$$ = be coördinates of the Moon referred to the Earth's centre; $$r$$=its distance; $$\xi,\eta,\zeta$$ = the coördinates of the particle referred to the Earth's centre; $$\rho$$ = its distance.

Then the Earth describes an ellipse round the centre of inertia of the Earth and Moon, and its acceleration is $$\frac $$ toward this centre.

To bring it to rest, we must apply to it an acceleration, $$-\frac $$, of which the accelerations along the coördinates are,—

$$\textstyle -\frac.\frac ,-\frac.\frac ,-\frac.\frac $$ Now

and