THE EVOLUTION OF SATELLITES. Ill 



tion of tbe tide, whether it consists in the swaying of molten lava or of 

 an ocean, must be stopping the rotation of the planet, or at any rate 

 stopping the motion of the system in some way. 



It is the friction upon its bearings which brings a fly wheel to rest; 

 but as the earth has no bearings, it is not easy to see how the friction 

 of the tidal wave, whether corporeal or oceanic, can tend to stop its 

 rate of rotation. The result must clearly be brought about, in some 

 way, by the interaction between the moon and the earth. Action and 

 reaction must be equal and opposite, and if we are correct in supposing 

 that the friction of the tides is stopping the earth's rotation, there must 

 be a reaction upon the moon tending to hurry her onward. To give a 

 homely illustration of the effects of reaction, I may recall to mind how 

 a man riding a high bicycle, on applying the brake too suddenly, was 

 shot over the handles. The desired action was to stop the front wheel, 

 but this could not be done without a reaction on the rider, which some- 

 times led to unpleasant consequences. 



The general conclusion as to the action and reaction due to tidal 

 friction is of so vague a character that it is desirable to consider in 



detail how they operate. The circle / ^ -^^^ 



in the figure is supposed to represent / y'^^ ^"^v 



the undisturbed shape of the planet, / , f \\ 



which rotates in the direction of the \— "'^^^\\ — ,,-- ' \^_,;^— — -7 'j 



curved arrow. A portion of the orbit \ ^^<r^^^^i.^^-%^'^ )/ 



of the satellite is indicated by part of \^^^^ ^=^;^-___-;:?^ 



a larger circle, and the direction of its \\ 

 motion is shown by an arrow. I will ^ 



first suppose that the water lying on the planet, or the molten rock of 

 which it is formed, is a perfect lubricant, devoid of friction; and that at 

 the moment represented in the figure the satellite is at M'. The fluid 

 will then be distorted by the tidal force until it assumes the egg-like 

 shape marked by the ellipse, projecting on both sides beyond the circle. 

 When there is no friction, the long axis of the Q.gg is always directed 

 straight toward the satellite M', and the fluid maintains a continuous 

 rhythmical movement, so that as the planet rotates and the satellite 

 revolves, it always preserves the same shape and attitude toward the 

 satellite. 



But when, as in reality, the fluid is subject to friction, it gets belated 

 in its rhythmical rise and fall, and the protuberance is carried onward 

 by the rotation of the planet beyond its proper place. In order to 

 make the same figure serve for this condition of affairs, I set the satel- 

 lite backward to M; for this amounts to just the same thing, and is less 

 confusing than redrawing the protuberance in its more advanced posi- 

 tion. The planet then constantly maintains this shape and attitude 

 with regard to the satellite, and the interaction between the two will 

 be the same as though the planet were solid, but continually altering 

 its shape. 



