THE ORIGIN OF THE EARTH. 67 



The collisions of isolated planetesimals with one another may be 

 neglected, for it is uncertain whether the planetesimals would rebound 

 from one another or would unite; probably the former when they 

 were highly elastic, and the latter when inelastic; and probably much 

 would also depend on their velocities and their modes of impact; but 

 in any case, the result would only affect the size and number of the 

 planetesimals. The important consideration is the 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. 



The evolution of circularity. — When two bodies in concentric 

 elliptical orbits unite, their conjoined 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 pre- 

 vious orbits, and may be less eccentric than both, as illustrated in 

 Figs. 25 and 26. While a mathematical demonstration that this is 

 universally true is possible, the illustrations suffice to show that it holds 

 for most normal cases falling within the problem in hand. It follows 

 that the union of an indefinite number of orbits progressively reduces 

 the resulting orbit toward circularity. In application, there arises 

 the obvious corollary that the planets which have grown most have, 

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

 have grown least most nearly represent the original eccentricity. The 

 significant application of this to the planets of the solar system will 

 appear later. 



The time involved. — 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 contingen- 

 cies of collision for the entire number of planetesimals will be spread 

 over a protracted period, and that collisions can succeed one another 

 rapidly only as the immensity of the possible number insures this. 

 Individually, the chances of collision 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. 



