682 T. C. CHAMBERLIN 



into the core to complete the growth of the earth. The earth-core, 

 taken at 6,000 miles in diameter, would have a surface area of 

 3X10'^ square feet. As there were 4X10^^ planetesimals in all, 

 13X10"' planetesimals must fall upon each foot of earth-core 

 surface, on the average, to build the body up to its present 

 mass. 



Now, if we take the total period of infall, as given above on 

 the radio-geo-biologic scale, at 2.4X10' years, a planetesimal 

 one-fiftieth of a pound in weight, falling upon each square foot 

 every 6 . 7 days, or a little less than once a week, would have com- 

 pleted the growth of the earth in the time specified. It will be 

 agreed, I think, that this does not remotely approach a rate suffi- 

 cient to melt the earth surface. If there is any doubt as to the 

 dissipation of energy following the impact of a falling body, see 

 later discussions. 



If we take as the period of infall the biological requirements as 

 estimated on the older geologic time-scale, 6X10^ years, a planet- 

 esimal falling upon a square foot once in about forty hours would 

 build the earth up to its present mass in the time estimated. This 

 again, I think it will be agreed, is not near the melting-rate for 

 the general surface. 



If we make the time of infall equal to the highest of our range 

 of estimates from the mechanics of the case, 3X10' years, an 

 average fall of a planetesimal on each square foot once in a little 

 over eight days would suffice, or if we take the minimum of the 

 estimates, 18X10^, a planetesimal once in about five days would 

 answer, in either case far from a general melting-rate. 



If we fall back upon the untenable assumption that the planet- 

 esimals distributed themselves after the manner of gaseous par- 

 ticles — made merely as a first step in approach — and take the 

 computed 26X 10'' years as the total time, the average rate of infall 

 upon each square foot would be about one planetesimal in seven- 

 teen hours. Even this does not seem to be a rate that would 

 threaten the melting of the earth, and yet it is much more rapid 

 than is permitted by the mechanics of the real case under the basal 

 assumptions made. 



