FUNDAMENTAL PROBLEMS OF GEOLOGY. 225 



impact of the isolated planetesimals upon the planetary nuclei. In 

 this case the usual result must apparently be the capture of the 

 planetesimals by the nuclei ; and with each capture the power of 

 further capture would be augmented. 



When two bodies in concentric elliptical orbits unite, their con- 

 joined mass must move in an orbit that is intermediate between the 

 two previous orbits, and this new orbit, in all cases investigated, is 

 less eccentric than one of the previous orbits, and may be less eccen- 

 tric than both. While a rigorous mathematical demonstration that 

 this is universally true has not been found, it appears to be true for 

 all normal cases falling within the problem in hand; and if so, it 

 follows that the union of an indefini te number of orbits progress- 

 ively reduces the resulting orbit toward circularity. In application 

 there arises the obvious corollary that planets that have grown most 

 have in general lost most of their primitive eccentricity, and those 

 that have grown least most nearly represent the original eccen- 

 tricity. This has a significant application to the planets of the solar 

 system, as will appear later. 



When the slowness of the motion of the line of apsides and the 

 only partial coincidence of the planes of the orbits at any one time 

 are duly considered, it is evident that the contingencies of collision 

 for the entire number of planetesimals will be spread over a pro- 

 tracted period, and that collisions can succeed one another rapidly 

 only as the immensity of the possible number insures this. Individ- 

 ually, the chances of collisions are remote and infrequent, but as the 

 numbers involved at the outset were prodigious, the impacts upon a 

 given nucleus in a given time may have been numerous. In the 

 nature of the case, the impacts must have declined in frequency after 

 the greater number of planetesimals had been gathered into the 

 nucleus. 



The rate of accretion is a matter of radical geological importance ; 

 indeed, it is, in some measure, the most critical feature of the whole 

 nebular problem, for the rate of accretion determines whether the 

 average temperature on the surface of the growing body will be high 

 or low. The surface temperature is not determined by the total 

 heat produced by the collisions, but by the heat produced in a given 

 time, which, in turn, is determined by the frequency a?id force of the 

 collisions on a given area. If the succession of collisions on a given 

 square mile was not rapid enough to generate heat beyond the con- 

 current radiation from the square mile, a high average temperature 

 for the whole could not be reached, however great the sum total of 



