684 T. C. CHAMBERLIN 



convection and radiation. As radiation increases with the fourth 

 power of the temperature, it would be very effective as the red- 

 hot stage was approached. 



As the case is beyond the reach of experiment or rigorous com- 

 putation, specific estimates of rate can be little more than matters 

 of judgment. Let us therefore resort to the serial method, which 

 sometimes leads to a decisive conclusion even when definite quan- 

 titative values are unavailable.' Let each reader fix upon such 

 rate of infall as seems to him competent to produce a molten 

 state of the earth surface under the given conditions. Let us 

 then see how such a rate fits into the range of rates which the 

 mechanics of the case permits. Too great a discrepancy may be 

 about as decisive as if the precise rates were known. The working 

 test is the final arbiter. 



If one's assumption is that a plane tesimal plunged into the 

 upper end of each square-foot air-column once every second, the 

 column would be built up to the present surface in 4,119 years. 

 It will be recalled that our first, but wholly arbitrary and excep- 

 tionally speedy mode of sweeping up the planetesimal field required 

 100,000,000 years and the most speedy natural method 260,000,000, 

 and that both of these hypothetical cases required less time than 

 the real case. 



If one planetesimal fell upon each square foot once per minute, 

 tlie total time would still be only 247,140 years. The competency 

 of such a rate to melt the earth surface would, I think, at least 

 be open to question. 



If the rate were one planetesimal per hour, the total period 

 would be 14,828,400 years, which is about one-seventeenth of the 

 time of ingathering required on even the gaseous assumption. 

 Moreover this rate would give a cooling period to every column 

 of air more than 3,000 times as long as the glowing period, 

 estimated from the mean duration of ''shooting stars." 



At one planetesimal per day per square foot, the total time 

 would be 355,881,600 years. I think it will be agreed that this 

 rate of infall would fall far below a liquefying rate, and yet even 



'"The Methods of the Earth Sciences," Pop. Set. Mo. (November, 1904), 

 pp. 70 and 71 ("The Method of Multiple Series"). 



