| Mercury | 39 |
Friction now comes in to modify the result. At Effect of frictionF, in consequence of the tide-raising force, the particle is traveling less rapidly than the rest of the Earth. Friction, therefore, urges it on and increases its tangential velocity up to some point P’ , where its speed becomes equal to the mean speed of the earth. After this, its speed being greater than the Earth's, friction retards it, until it again becomes the mean at P. Then friction begins again to accelerate it.
In consequence, the particle is accelerated from Q to P’', retarded from P’ to P, and then accelerated again. From A on, friction thus helps the retarding tangential force, and the Earth causes the particle to turn the corner of the ellipse at E sooner than it otherwise would. The tangential force thus reaches its maximum earlier, and the crest of the tide is thus shifted from E backward to some point P.
On the Earth, in the case of the ocean, we are dealing with superficial tides. In celestial mechanics, it is the substantial tides, or tides of the whole body, with which we are concerned. The latter are immensely the more potent. As the tidal crest lies ahead of the line joining the two bodies, the Sun or the Moon is constantly trying to pull it back into this line, while the Earth is