SUMMARY. 131 



separately, and supposing that they would be essentially the same when 

 acting jointly, we find that the smallest possible distance of the moon 

 compatible with present conditions is 9,241 miles. Fig. 16 shows the earth 

 and moon and their initial distance to scale, and obviously one would need 

 extremely strong confirmatory evidence to convince him that the moon had 

 just broken off from the earth. The distance from the surface of the earth 

 to the surface of the moon is 4,201 miles, or 243 miles greater than the 

 radius of the earth. 



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

 have separated by fission so that their periods of rotation 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 



\ 



FiQ. 16. 



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 eccen- 

 tricities of their orbits are a result of tidal friction. 



If we neglect the rotational moment of momentum and energy of the 

 moon, the eccentricity of the moon's orbit, and the inclination of the plane of 

 the earth's equator to the plane of the moon's orbit, then it is certain, as was 

 shown in sections V and VI, that tidal friction will at the present time 

 lengthen both the day and the month, but at such relative rates that the 

 number of days in a month will decrease. Consequently if time be measured 

 by the rotation of the earth the moon will continually get ahead of its place, 

 9 



