376 CARNEGIE INSTITUTION OF WASHINGTON. 



ment is less restrictive. It is concluded, therefore, that there is a 

 notable gap between the smallest planetoids formed by this phase of 

 collective concentration and the largest planetesimals built up from 

 molecules or precipitate-aggregates by orbital accessions. 



The state of aggregation of the planetesimals has really little bearing 

 on the fluidity or solidity of the earth, for the more they were united 

 before they fell to the earth the fewer there were to fall. In uniting 

 they exhausted some of their potential energy, which otherwise they 

 might have carried into the earth, while in compensation the united 

 masses were more effectual in overcoming the resistance of the atmos- 

 phere. 



The rate of infall of planetesimals was studied from the probable 

 frequency with which in the pursuit of their orbits they would cross the 

 orbit of the growing planet, combined with the chance that the planet 

 would be there at that instant. The case can be illustrated in its most 

 favorable aspect by considering the courses of the molecules that escaped 

 from the earth nucleus into planetesimal paths by reason of high mole- 

 cular velocities during its hot early stage. It is easily shown that such 

 escaping molecules would, with extremely rare exceptions, take planet- 

 esimal orbits, whatever the direction in which they were shot forth 

 from the earth nucleus. After being shot forth into such orbits they 

 would come back to the vu'tual point of escape in about a year's time, 

 but the chance of reaching the node at the instant the planet was pass- 

 ing would be adverse unless they had acquired an orbit of the same pe- 

 riodic value, which would not be the common case, for most molecules 

 escaping in this way would take either larger or smaller orbits or else 

 more elliptical or less elliptical orbits, or both. Their future chances 

 would depend on modifications of their orbits due to perturbations 

 and precessions, whose effects would be slow and uncertain. 



Somewhat less definite conditions controlled the relations of the 

 orbits in the case of planetesimals formed directly by the original solar 

 outburst. On the whole these were less favorable to capture by the 

 earth nucleus. The conclusion, therefore, seems imperative that infalls 

 at least could not be precipitate. There seems little ground for assign- 

 ing a sufficient frequency to cause a general molten condition of the 

 earth, even if it were not protected by its atmosphere. 



The atmosphere probably reached a protective depth and density 

 by the time the earth was one-tenth grown, if indeed the nucleus itself 

 was not more massive than this at the start. At present, very small 

 infalling bodies — many of which have velocities much higher than can 

 be assigned planetesimals — are generally consumed or arrested above 

 30 miles from the earth's surface. Very little thermal effect on the solid 

 substance of the earth can therefore be assigned infalling bodies of such 

 sizes, even if their number were vastly increased. Even the larger 

 meteorites bring little heat to the surface of the earth, for their moving 



