SUMMARY. 129 



both the earth and moon were of the same density and shape as at present, 

 the distance from the surface of one body to the surface of the other was 

 immediately after fission 4,155 miles. Since this result is altogether incom- 

 patible with the obvious implications of the fission theory, we must either 

 abandon the theory or show that this number would be very largely reduced 

 by including the effects of the neglected factors. Consequently we examine 

 the effects of various neglected conditions and influences. 



If the earth were rotating in 4.93 of our present hours it must obviously 

 have been very oblate instead of spherical as was assumed in the computa- 

 tion. In the absence of certain knowledge we may assume that its equa- 

 torial radius reached out to the surface of the moon when the distance of 

 its center was 9,194 miles, that the oblateness was such that the volume 

 was the same as at present, and that the law of density was such that its 

 rotational moment of momentum was the same as it would have been if 

 it were spherical and the Laplacian law of density prevailed. We find 

 that under these hypotheses the polar radius would have been only 942 

 miles. A scale drawing shows that this oblateness is out of the question, 

 and a little consideration shows that the equatorial zone must have been 

 60 rare as to make it impossible to account for the mass of the moon. 



If we waive the condition that for a given period of rotation the law 

 of density was such as to keep the rotational moment of momentum the 

 same as when the body was supposed to be a sphere, we shall have to sup- 

 pose the moment of momentum was greater than this in order to get suffi- 

 cient matter in the periphery to account for the origin of the moon. But 

 this supposition leads to the conclusion that the nearest possible distance 

 of the moon was greater than the 9,194 miles found before. 



Another hypothesis is that the earth was initially larger than at present, 

 and has shrunk to its present dimensions as it cooled. It was found in this 

 case also that the initial distance of the moon must have been greater than 

 the 9,194 miles found on the original hypothesis. 



An examination was made of the hypothesis that the earth originally 

 had a radius of 9,194 miles and a density such as to keep its moment of 

 momentum the same as if it were of its present size. It was supposed the 

 density varied according to the Laplacian law and the constants of the law 

 were worked out by the conditions of the hypotheses. It turned out that 

 the density of the surface must have been negative, a result having no 

 physical interpretation and proving the falsity of at least one of the hypoth- 

 eses upon which the computations were made. 



In sections VII and VIII the problem was treated without neglecting 

 the rotational moment of momentum and energy of the moon, but keeping 

 the earth and moon spherical. It turned out that the initial distance of the 

 earth and moon could not have been less than 9,200 miles. That is, when 

 this factor is included the result becomes less favorable to the fission theory 

 than when it was omitted. 



Then in sections X and XI the hypothesis was made that the moon's 

 rotational moment of momentum and energy may be neglected, but the 

 eccentricity of the moon's orbit was given the value assigned by observa- 

 tions. It was found under these hypotheses that the initial distance of the 



