80 THE TIDAL PROBLEM. 



It is quite evident from Darwin's discussions that he accepts, as a general 

 basis for reasoning on the problems of cosmogony, the Laplacian nebular 

 hypothesis with its implication of a one-time fluid earth; indeed, in 2, 

 p. 536, line 3, and in 4, p. 530, first paragraph, he explicitly states that 

 he adopts this hypothesis in its main outlines. It is obvious that this 

 point of view might tend to give one a confidence, perhaps without his 

 realizing fully the postulates upon which it was based, that, even if the 

 spherical harmonic analysis should not be strictly applicable to a hetero- 

 geneous earth whose liquid parts are broken up by continental masses, 

 it still would be sensibly correct when applied to a fluid body such as the 

 earth was supposed, according to this theory, to have been in the past. 

 It is now known that there are very grave, and I believe fatal, objections 

 to the Laplacian ring theory. At any rate, one would not now make it a 

 postulate in a discussion involving so many and such serious complexities 

 as arise in the theory of tidal evolution, or allow it seriously to influence 

 his conclusion as to what is the most probable of the various possible 

 hypotheses. Darwin examined with great thoroughness the character of 

 the results for various conditions of viscosity and semi-elasticity, and onl}'' 

 where he undertook to say what seemed to him the most probable of vari- 

 ous possible series of events was he influenced, possibly, by his preconcep- 

 tions as to the early condition of the earth. To illustrate the delicacy of 

 the discussion we shall enumerate a few of his conclusions together with the 

 hypotheses upon which they were based. 



In 3, Part IV, and in its summary, pp. 871-876, Darwin discussed 

 the inclination of the moon's orbit and the obliquity of the ecliptic. Con- 

 sidering first the hypothesis of small viscosity and tracing back the system 

 until the day and month were equal, he found that, if this hypothesis is 

 true, the lunar orbit and the earth's equator must initially have had con- 

 siderable mutual inclination. "If this were necessarily the case, it would 

 be difficult to believe that the moon is a portion of the primeval planet 

 detached by rapid rotation, or by other causes." (3, p. 873.) Then taking 

 up the hypothesis of large viscosity and supposing that it was "large 

 enough," he found, tracing the system back, that when the day and month 

 were of equal length, then the lunar orbit was sensibly in the plane of the 

 earth's equator, which was inclined 11° or 12° to the plane of the ecliptic. 

 His final conclusion from this discussion (pp. 875-876) was that it will be 

 most nearly correct to suppose that the earth in the earliest times, though 

 plastic, possessed a high degree of stiffiiess, and that now the greater part if 

 not the whole of tidal friction is due to oceanic tides, and not to bodily tides, 

 for in this way the theory of the fission of the parent mass into two bodies 

 and the present inclination can be best reconciled. 



In 3, Parts V and VI, the effects of tidal friction upon the eccentricity 

 of the lunar orbit were considered. The equations were integrated on the 

 hypothesis of small viscosity, and it was found that in past times the 

 eccentricity was much smaller than at present, nearly vanishing when the 

 day and month were equal. If it had been assumed that the viscosity was 

 very large, the eccentricity of the lunar orbit would have been the gi*eater 

 the farther back the system was traced. Since a large original eccentricity 



