DIASTROPHISM AND THE FORMATIVE PROCESSES 4it 
would constantly give rise to perturbations and these, on the 
whole, would favor the gathering in of the planetesimals, but 
just how fast is beyond the reach of rigorous computation. It 
can only be reached roughly by approximations. A period some- 
where between one billion and three billion years seems most 
probable.* 
66. While the total heat of planetesimal infall was great, the 
melting effects were conditioned by the rate of fall and by the 
extent of atmospheric surface into which they fell. At the stage 
when the earth was one-third grown, there would remain to fall 
in 4X107° planetesimals averaging 1/50 lb.; or about 3 X10% 
planetesimals per square foot of earth surface. Taking the 
radio-bio-geologic estimate (2.410% years), as the time, the 
average rate of plunge into the upper part of each one-square-foot 
air-column would be one planetesimal in 6.7 days. Even at the 
time estimate based on the older geologic scale—probably much 
too short—a planetesimal would fall into the top of each square- 
foot air-column not oftener than once in 40 minutes. Now in the 
upper air, half the heat would be promptly radiated outward, and 
the rest would act at a disadvantage in heating the earth’s surface 
some miles below. The mean intervals between falls would quite 
surely be much too great to produce the melting of the earth’s 
surface.” 
_ For a cross test, let the method be reversed by selecting a rate 
supposed to be sufficient to produce melting and testing this by 
the time. Let it be supposed that one fall per second per square- 
foot air-column would have been a melting rate. All the plane- 
tesimals would, at this rate, have been collected in a little over 
4,000 years, an impossibly short time. It can scarcely be held 
that a rate of one fall per hour per column would produce surface 
melting; and yet, at that rate, all would have fallen in less than 
15,000,000 years. We found that the impossibly speedy demon- 
directed method required 100,000,000 years. The melting of the 
surface during the last two-thirds of the earth’s growth seems out 
of the question.’ 
t Tbid., pp. 679-81. 
2“The Rate of Planetesimal Infall,”’ zbid., pp. 681-86. 3 Ibid., pp. 683-86. 
