18 THE TIDAL PROBLEM. 



problems respecting the influence of the tides on the earth's rotation are 

 essentially the same, whatever the genesis of the moon, and so these further 

 problems may well be deferred until it is seen where and how the various 

 genetic theories come onto common ground and may be treated in a com- 

 mon manner. 



(3) There is nothing in the planetesimal hypothesis that is, in itself, 

 necessarily prohibitive of an origin of the moon by centrifugal separation 

 from the earth-mass, for under it the planetary bodies may have had very 

 high rates of rotation. So also the mass of the planetary nucleus may 

 have been so large and the ingathering of the planetesimals may have 

 been so rapid, by hypothesis, that a molten or even a gaseous condition 

 could have arisen. In the case of the larger planets such a primitive state 

 is quite within the limits of the probabilities. The case of the earth is 

 debatable, but it will be of no service in this discussion to follow the 

 gaseous or molten alternative, as it would be essentially identical with the 

 preceding. 



There are two other possible modes of origin of the moon, in neither of 

 which was the moon-mass ever a part of the earth-mass. In both of these 

 it is supposed that the nebular nuclei of the earth and the moon were 

 separate knots of the parent spiral nebula. In the first case, they are 

 supposed to have been companions in projection from the ancestral sun, 

 and to have revolved about their common center of inertia from the out- 

 set. In the second case, the nuclei are supposed to have been at the outset 

 independent knots having separate orbits about the sun but near one 

 another. The two are supposed to have come into their present relations 

 in the course of the segregation of the parent nebula. Rather grave 

 dynamic difficulties attend this latter view, and it need not be pursued 

 further here, as the rotatory problems under it are not essentially different 

 from those of the first and much more probable alternative. 



In this preferred alternative, the nuclei of the earth and moon, at the 

 instant they left the ancestral sun, are supposed to have been a single mass 

 which was given a forward rotation by the unequal resistances on its oppo- 

 site sides to the expelling impulse, for which there are assignable reasons. 

 Just after leaving the sun, the mass is supposed to have separated as an 

 incident of the expulsion, but the two parts are supposed to have continued 

 to revolve about their common center of inertia essentially as before, i.e., as 

 a rigid body. After separation, however, each was subject to the rotational 

 effects of the accession of planetesimals, and when their rotations came to 

 differ from their revolution about the mutual center of inertia they were 

 subject to tidal reaction. The extent to which such differences of rotation 

 arose is an essential part of the problem under this hypothesis. 



There were many possible alternatives, theoretically speaking, as to 

 the relative sizes of these nuclei and the distances to which they separated 

 under the initial impulse, but there were limitations to these. If the com- 

 bined masses of the two nuclei were one-eighth of the combined mass of 

 the present earth and moon, the moon could not have been more than 

 460,000 miles from the earth, but as this is farther than it is at present the 



