82 THE TIDAL PROBLEM. 



100,000,000 years. Very different results were obtained by assuming that 

 the earth is elastico-viscous. Under this assumption in 700,000,000 years 

 the day will be about as long as at present, the month nearly a day shorter 

 than at present, and the obHquity of the ecUptic about 5° less than it is 

 now. The discussion of the secular acceleration of the moon was closed 

 with these remarks (2, p. 483, last paragraph) : 



The conclusion to be drawn from all these calculations is that, at the present time, 

 the bodily tides in the earth, except perhaps the fortnightly tide, must be exceedingly 

 small in amoimt; that it is utterly uncertain how much of the observed 4" of acceleration 

 of the moon's motion must be referred to the moon itself, and how much to the tidal friction, 

 and accordingly that it is equally uncertain at what rate the day is at present being 

 lengthened. 



Notwithstanding these uncertainties, in the general discussion at the 

 end of the final paper of the series (4, pp. 532-533) Darwin states: 



The previous papers were principally directed to the case of the earth and moon, and 

 it was there found that the primitive condition of those bodies was as follows; The earth 

 was rotating, with a period from two to four hours, about an axis inchned at 11° or 12° to 

 the normal to the ecliptic, and the moon was revolving, nearly in contact with the earth, 

 in a circular orbit coincident with the earth's equator, and with a periodic time only slightly 

 exceeding that of the earth's rotation. 



Then it was proved that lunar and solar tidal friction would reduce the system from 

 this primitive condition down to the state which now exists by causing a retardation of 

 terrestrial rotation, an increase of lunar period, an increase of obliquity of ecliptic, an 

 increase of eccentricity of lunar orbit 



It was also found that the friction of the tides raised by the earth in the moon would 

 explain the present motion of the moon about her axis, both as regards the identity of the 

 axial and orbital revolutions, and as regards the direction of her polar axis. 



Thus the theory that tidal friction has been the ruling power in the evolution of the 

 earth and moon completely coordinates the present motions of the two bodies, and leads 

 us back to an initial state when the moon first had a separate existence as a satellite. 



This initial configuration of the two bodies is such that we are almost compelled to 

 believe that the moon is a portion of the primitive earth detached by rapid rotation or 

 other causes. 



The problem of tidal evolution is an extremely complicated one and 

 the uncertain factors which enter into it are very many. Darwin's treat- 

 ment of it as a mathematical problem was masterly and worthy in every 

 respect of the highest admiration. He was generally very cautious in 

 drawing conclusions with respect to the actual earth-moon system. The 

 danger lies in the ^formidable and protracted analyses coming in between 

 the hypotheses and the conclusions, which might lead one to suppose that 

 results drawn from a particular set of postulates necessarily belong to the 

 earth and moon, particularly if they, in a general way, coincided with his 

 preconceptions of cosmogony. Even though Darwin may have been with- 

 out fault in this respect, it is not certain that less criticrl minds, especially 

 if they were without the illuminating experience of finding by actual com- 

 putation how great changes in the results would be produced by admissible 

 changes in the hypotheses, would not attach undue importance to some 

 particular computation. There is nothing deduced from observations so 

 far made or from Darwin's investigations that would prevent one, if it 

 suited his fancy, from drawing the conclusion that the motions of the earth 

 and moon have been for 100,000,000 years about as they are at present. 



