THE EVOLUTION OF SATELLITES. 119 



more slowly until tbo tide solidified, aud thenceforward and to the 

 present day she has shown the same face to the earth. Helmholtz 

 was, I believe, among the lirst in modern times to suggest this as the 

 explanation of the fact that the moon always shows us the same face.^ 

 Our theory, then, receives a striking confirmation from the moon; for, 

 having ceased to rotate relatively to us, she has actually advanced to 

 that condition which may be foreseen as tbe fate of the earth. 



Thus far I have referred in only one passage to the influence of solar 

 tides, but these are of considerable importance, being large enough to 

 cause the conspicuous phenomena of spring and neap tides. N^ow, 

 while the moon is retarding the earth's rotation, the sun is doing so 

 also. But these solar tides react only on the earth's motion around the 

 sun, leaving the moon's motion around the earth unaffected. It might 

 perhaps be expected that parallel changes in the earth's orbit would 

 have proceeded step by step, and that the earth might be traced to an 

 origin close to the sun. But the smallness of the earth's mass com- 

 pared with that of the sun here prohibits the application of the theory 

 of tidal friction, and it is improbable that our year is now longer, from 

 this cause at any rate, by more than a few seconds than it was at the 

 very birth of the solar system. 



Although the solar tides can have had no perceptible influence upon 

 the earth's movement in its orbit, they will have affected the rotation 

 of the earth to a considerable extent. Let us imagine ourselves trans- 

 ported to the indefinite future, when the moon and the earth shall be 

 revolving together in fifty-five of our days. The lunar tide in the 

 earth will then be unchanging, just as the earth tide in the moon is 

 now fixed; but the earth will be rotating with reference to the sun, 

 and, if there are unfrozen oceans, its rotation will still be subject to 

 retardation in consequence of the solar tidal friction. The day will 

 then become longer than the month, which for a very long time will 

 continue to occupy about fifty-five of our present days. It is known 

 that there are neither oceans nor atmosphere on the moon; but if 

 there were, she would have been subject to solar tidal friction, and 

 would have undergone a parallel series of changes. 



Up to recent times it might have been asserted i)lausibly that the 

 absence of any such mode of motion in the solar system afforded a 

 reason for rejecting the actual etficiency of tidal friction in celestial 

 evolution. But in 1877 Prof Asaph Hall discovered in the system of 

 the planet Mars a case of the kind of motion which we have reason to 

 foresee as the future fate of the earth and the moon; for he found two 

 satellites, one of which has a month shorter than the planet's day. 



In his paper on the discovery of these satellites Professor Hall gives 



' Kaut, in the middle of the last century, drew attention to the importance of 

 tidal friction in celestial dynamics; bnt as he did not clothe his argument in mathe- 

 matical form, he was unable to deduce most of the results which are explained in 

 this paper. 



