678 T. C. CHAMBERLIN 



taking the width of the tract now occupied by the planetoids as 

 its breadth, and for its depth the limits of the earth's dominant 

 attraction in competition with that of Mars on the outside, and 

 that of Venus on the inside. These give roundly 55X10^ miles in 

 breadth and 58X10^ in depth. They define the cross-section of 

 the planetesimal ring which curved around the sun with the path 

 of the earth-core near its center. The actual field was much 

 larger than this, but the planetesimals outside these limits are 

 neglected to compensate for any lateral thinning inside. The area 

 of the cross-section was therefore roundly 3 X 10^^ square miles and 

 its curved length 292 X 10^ miles. For a working case of the medium 

 order, let the mass of the earth-core, at the beginning of the specified 

 period of planetesimal infall, be taken as one-third of the final 

 earth-mass, leaving two-thirds of the earth-mass in the form of 

 planetesimals to be gathered in. It will be seen that this propor- 

 tion makes the mass of the planetesimals large and favors effective 

 infall. It is taken merely as a fair working basis without any 

 intention of implying an opinion as to the ratio of the nuclear to 

 the planetesimal portions which actually obtained; that may best 

 be reserved for further study. Taking the masses and dimensions 

 of Mars and Venus as guides, in accordance with our comparative 

 studies (Article X), the earth-core should have had a diameter 

 of about 6,000 miles. Its disk would then have an area of 28 X 10^ 

 square miles, roundly. This is the fleeting target which the widely 

 scattered planetesimals must hit, if they were to take part in the 

 earth-building, or to change the simile, this is the area of the sweeper 

 that must gather in the planetesimals from their vast field to build 

 its one-third mass up to a three- thirds mass. 



I. As rigorous treatment is impracticable, modes of approxima- 

 tion are our only recourse ; and so, as a simple and purely artificial 

 first approach, suited to give a realistic impression of the immensity 

 of the field that must be swept, let us suppose that the planetesimals 

 stand still while the earth-disk sweeps through it at its normal speed, 

 changing its path in such an effective way as to clean up an entirely 

 new swath at each revolution. Even by this impossibly speedy 

 method, 100,000,000 years, roundly, would be required. 



