DIASTROPHISM AND THE FORMATIVE PROCESSES 679 



2. To make a first approach of a natural kind that can be 

 treated mathematically, Dr. MacMillan has suggested that the 

 planetesimals might be treated as though they were particles of 

 gas which would close in upon the track of the earth-core as it 

 revolved through the center of the tract, though the dynamics of 

 gases are radically different from those of planetesimals, and cor- 

 rections must be made accordingly. To gather in all the planet- 

 esimals under these conditions would take an indefinite period; 

 to gather in 90 per cent would require somewhat over 260,000,000 

 years. Keeping in mind that this is not the real case, but merely 

 one that can easily be treated, it is worth while to note that one- 

 fifteenth of the earth-mass would fall in after 260,000,000 years 

 had passed and that nine-fifteenths would be systematically dis- 

 tributed over this period with infall greatest at the start in due 

 proportion, but it does not give warrant for excessive concentra- 

 tion in the early stages. If that is assumed, it makes the more 

 certain a non-melting rate in the later stages and the infall during 

 these would furnish the outer shell of the earth to a depth beyond 

 the reach of most problems of immediate geologic interest. The 

 vital point, however, is that in this substitute case, like the real 

 one, the laws of mechanics require a distribution of infall over long 

 periods. 



3. The next step toward the real case is the substitution of 

 heterogeneously revolving particles for the previous gaseous par- 

 ticles. A gaseous organization is a failing structure in the sense 

 that when any inner portion of it is removed the rest collapses 

 sufficiently to fill the space. In an orbital organization no such 

 collapse takes place, each remaining body is sustained in its orbit 

 by its own moving force. This makes a radical difference in the 

 rate of ingathering by a body like the earth-core in the case in 

 hand. Those planetesimals whose paths had actual crossings with 

 that of the earth-core would be picked up, if not disturbed by per- 

 turbation, whenever their time schedules became coincident at 

 the crossing, but not before, normally. Those planetesimals — by 

 far the greater number — which had no such actual crossings at 

 the start, would circle through their independent orbits indefinitely, 



