Geology. 191 



" As a concession to the theory, we may assume that the earth 

 and moon have separated by fission so that their periods of rota- 

 tion and revolution are precisely equal, and then inquire whether 

 the present system could develop from it. If the original orbit 

 were exactly circular the orbit would always remain circular. 

 Since the moon's orbit now has considerable eccentricity it follows 

 that we must assume that the orbit immediately after separation 

 was somewhat eccentric. But since the rotations would be 

 sensibly uniform while the revolution would be such as to fulfil 

 the law of areas, there would be relative motion of the various 

 parts and therefore tidal evolution. The question whether this 

 friction would drive the moon farther from the earth or bring it 

 back and precipitate it again upon the earth is treated in section 

 X, and it is found there, under the assumption that the loss of 

 energy is proportional to the square of the tide-raising force and 

 the square of the velocity of the tide along the surface of the 

 earth, that the tides would bring the moon again to the earth. 

 Thus, unless some of the neglected factors can offset this result, the 

 direct implications of the theory destroy it, and it may be noted 

 here that these remarks apply with equal force to the hypothesis 

 that the binary stars have originated by fission and that their 

 present distances from each other and the eccentricities of their 

 orbits are a result of tidal friction " (pp. 130, 131). 



"It is well known that a comparison of ancient and modern 

 eclipses shows that the moon has an acceleration in longitude of 

 about 4" per century which is not explained by perturbations. 

 Let us assume that this is due to tidal friction and is the measure 

 of it at the present time. At this rate it will take over 30,000,000 

 years for the moon to gain one revolution. Consequently we see 

 without any computation that it must have been an extremely 

 long time in the past when its period was a small fraction of its 

 present period. 



" The problem was treated in section XV, and it was found there 

 that, if the physical condition of the earth has been essentially 

 constant, the length of the day was 20 of our present hours, and 

 of the month 24 of our present days, not less than 220,000,000,000 

 years ago. It is extremely improbable that the neglected factors, 

 such as the eccentricity of the moon's orbit, could change these 

 figures enough to be of any consequence. This remarkable 

 result has the great merit of resting upon but few assumptions 

 and in depending for its quantitative character upon the actual 

 observations. If it is accepted as being correct as to its general 

 order, it shows that tidal evolution has not affected the rotation 

 of the earth much in the period during which the earth has here- 

 tofore been supposed to have existed even by those who have 

 been most extravagant in their demands for time. And if one 

 does not accept these results as to their general quantitative 

 order, he faces the embarrassing problem of bringing his ideas 

 into harmony with the observations" (p. 132). 



"In a word, the quantitative results obtained in this paper are 

 on the whole strongly adverse to the theory that the earth and 



