14 THE TIDAL PROBLEM. 



the protuberances forward towards positions which, according to the 

 above interpretations, are in some cases more favorable for influence on 

 the earth's rotation and in other cases less favorable, and if a wave is followed 

 through its whole course, it sustains various relations, favorable and unfa- 

 vorable, retardative and accelerative. The sum total of influences is thus 

 seen to be a product of much complexity. It has been held that the retar- 

 dative positions predominate in effectiveness. The case has usually been 

 treated on the assumption of a continuous ocean belting the earth and 

 permitting the tides to follow the tidal forces consecutively about the 

 earth. It will be shown later that this is not the actual case, and that 

 the tides are essentially hmited to individual water-bodies. This further 

 and greatly complicates the case. The problem is still further complicated 

 by the past relations of the moon to the earth, and this claims attention 

 before further considering the efficiency of the tides. 



THE GENESIS OF THE MOON. 



(1) The hypothesis of Laplace in its original form took no account of 

 tidal action. Under it the rotation of the earth, when it had become 

 condensed to a molten globe, was assumed to have had the velocity which 

 at an earher stage was necessary to separate the lunar ring, plus that 

 which was added by subsequent contraction. How this high rate of rota- 

 tion was reduced to the existing rate was not explained. 



(2) The supplementary hypothesis of Sir George Darwin replaces this 

 defect of the Laplacian hypothesis by postulating a centrifugal separation 

 of the moon-mass from the earth-mass after the parent-body had been 

 condensed to a liquid or perhaps even incipient sohd state, and a subse- 

 quent recession of the moon by tidal influence, accompanied by a reduction 

 of the earth's rotation as its dynamic reciprocal. The postulated method 

 of this tidal action has been stated above. The fundamental proposition 

 that tidal friction will tend either to separate the two interacting bodies 

 or to draw them together — according to the precise nature of their rela- 

 tions — is not questioned, as it seems to be solidly founded on the laws of 

 energy, but it is necessary to consider the precise relations of the bodies to 

 determine the character of the action under the preceding mode of inter- 

 pretation, and we shall find occasion to question the mode itself. Darwan's 

 method of starting with what was thought to be a fairly reliable astronom- 

 ical indication of the present value of the earth-moon interaction and of 

 working backward mathematically to the primitive state, or so far as the 

 mathematical process would carry, is beyond praise. But as the present 

 value of the earth-moon interaction is open to serious question and is not 

 now replaceable by an unquestionable value, and as the postulates for the 

 backward tracing are themselves in question, it is necessary to consider 

 the hypothesis on more general lines. The value assignable to the tides in 

 each of the earth's ages depends on the assumptions made regarding the 

 physical states of the earth's interior. If the body of the earth be assumed 

 to be molten, or viscous in such a degree that the body tides are important 

 and are of the Hquid or viscous type, the results will be very different from 



