16 THE TIDAL PROBLEM. 



and might be reversed before it escaped the critical conditions named 

 above. The speed of the earth's rotation and the speed of the lunar tide in 

 this early stage must not be confounded, for the speed of the tide is depend- 

 ent on the difference between the angular rate of the earth's rotation and 

 the angular rate of the moon's revolution. At the instant of separation 

 the two rates were the same, and the tide, if the stationary protuberances 

 caused by the moon can be called a tide at all, would be infinitely slow, 

 and the period of the tide— the time required for the tide to make a circuit 

 of the earth— infinitely great. At the first stage of difference in angular 

 rate, if the earth's rotation was accelerated by contraction more than the 

 solar tides retarded it, the movement of the tide would be infinitesimally 

 slow in the present direction, and the tidal period sub-infinitely long. The 

 movement of the tide over the face of the earth would be accelerated only 

 as the contractional acceleration continued to be superior to the solar 

 tidal retardation reinforced by the lunar retardation. If the rate of loss 

 of heat, which must have declined rapidly as the supposed molten earth 

 crusted over and the crust became thicker, fell below that at which its 

 accelerating value on the rotation of the earth was superior to the retar- 

 dational value of the solar and lunar tides, and the latter then became supe- 

 rior, the time of rotation of the earth might be forced back to coincidence 

 with the revolution of the moon, and the lunar tides temporarily suspended 

 and, a little later, reversed, and the moon brought back to the earth accord- 

 ing to the fundamental postulate of the theory.^ To escape this contin- 

 gency it is necessary to suppose that the contractional influence of the loss 

 of heat continued to be superior to the retardational influence of the solar 

 and lunar tides until the lunar tide, though developed with extreme slow- 

 ness, had extended the moon's revolutionary period so much that when 

 the retardational influence became superior to the contractional influence 

 it was too late for it to reduce the rotation-period of the earth to the revo- 

 lution-period of the moon at that end of the evolutional series. These 

 considerations serve to indicate how delicately poised were the initial condi- 

 tions assumed by the hypothesis and how completely they were dependent 

 on the heat-emission of the earth at the critical stage, which in turn was 

 dependent on the cosmogony that preceded it. 



The argument that the balance of influence must have lain on the side 

 of heat-loss or else the moon would not be where it is at present, would 

 be pertinent if the earth-moon evolution were absolutely shut up to one or 

 the other of the alternatives just considered, but it has no force against a 

 hypothesis which entirely avoids these critical alternatives. 



It is to be noted further that the tidal reactions in the initial stages of 

 the hypothesis of Darwin must apparently have been those of the earth's 

 body, for if the heat had been so far dissipated that the earth was crusted 

 over and the oceans were permitted to mantle the earth, the loss of heat 

 would possibly have been too small to start the evolution in the postulated 

 direction. The atmosphere must then have been of that vast vaporous 



» The correctness of this is dependent on the soundness of the theory that the position 

 of the tides determines their accelerative or retardative character, which wiU be con- 

 sidered later. 



