692 T. C. CHAM BERLIN 



infalls, in proportion to the time between falls. As these last 

 impacts left no conclusive evidence of molten residue, it follows 

 that no previous infall, in itself, can be consistently supposed to 

 have left any greater molten residue and if their inheritance was 

 greater it could apparently only come from a closer succession of 

 infalls. Apparently, then, the only way in which a general molten 

 condition can reasonably be supposed to have arisen was from the 

 cumulative effects of such inherited residues of heat from the 

 earlier infalls in excess of those of the later infalls. How tenable 

 is this ? There were by computation less than two hundred infalls 

 of the specified kind to each disk-area during the whole accretion 

 period of the moon. If that accretion period were essentially the 

 same as that of the earth, as it should theoretically be, and if we 

 compute the rate of infall by using the minimum accretion period 

 assigned the earth based on mechanical and biological evidences, 

 to make the rate as high as consistent, the mean interval between 

 impacts would be about 3,000,000 years. If the mean accretion 

 period had been used, the mean interval between infalls would 

 have been more than twice this time. Very little inheritance of 

 heat from a surficial bump can be postulated over an interval of 

 this order. 



But we are not left wholly to computations on estimated require- 

 ments. There is the direct evidence of the craters themselves. 

 Some are fresh and their debris lines lie straight across older pits 

 and older features of all sorts. Some pits and rims are worn or 

 buried to the very limit of recognition, and there are all grades 

 between. These features offer no warrant for the hypothesis that 

 there was a closely crowded infall. They distinctly imply that the 

 formation of the visible craters stretched over a long period. This 

 evidence is the more cogent when the limited means of denudation, 

 owing to the absence of an atmosphere and hydrosphere on the 

 moon, are considered. 



Now let us turn to the theory itself. If it be supposed that the 

 five-mile bolides are planetesimals, the supposition itself hides under 

 its cloak a quasi-assertion of the rate of their infall, for, as we have 

 seen, all planetesimals started as very minute bodies controlled by 

 a system of dynamics that imposed upon them slow growth as a 



