224 CARNEGIE INSTITUTION OF WASHINGTON. 



have shifted, the attitudes of their orbital planes must have varied, 

 and their eccentricities must have been modified. It will suffice to 

 consider the shifting of the major axes of the orbits, technically 

 ' ' the motion of the line of apsides, ' ' as that is the' most vital factor 

 in the process of aggregation. 



So long as the major axes of the orbits were essentially parallel 

 to one another, the bodies would remain apart and aggregation be 

 prevented ; but when they became shifted differentially the orbits 

 would be liable to touch, and conjunction be po.s.sible if the orbital 

 planes were appropriately related to one another. 



The shifting of the lines of apsides is in constant progress in the 

 present system, and must of necessity take place in any such system, 

 as shown by the investigations in celestial mechanics. The shifting 

 is differential and subject to various perturbations, involving alter- 

 nate movement forward and backward, but the average result is an 

 advance* for all the planets except Venus. At present the line of 

 apsides of quickest revolution is that of Saturn, which completes its 

 circuit in 67,000 years, roundl)^ speaking, while that of Neptune 

 requires 540,000 3'ears, and that of the earth a little more than 100,000 

 years. t In the course of time the major axis of each orbit is thrown 

 athwart that of its neighbors, and whenever the longer axis of the 

 smaller orbit is equal to the shorter axis of the larger orbit, and the 

 planes of the orbits are properly related, collision is rendered con- 

 tingent. Actual collision is dependent, of course, upon the bodies 

 reaching the crossing of their paths at the same time. The planes 

 of the planetary orbits now lie near to one another and are presumed 

 always to have done so. These planes, though not necessarily the 

 orbits, intersect one another, and the lines of intersection are shift- 

 ing, so that in time all assignable intersections are realized. Under 

 these conditions the mechanics of such a system furnish the requisite 

 contingencies for collisions between the planetesimals and the nuclei 

 if sufficient time be granted. 



The collisions of isolated planetesimals with one another may be 

 neglected, for it is uncertain whether the planetesimals would re- 

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

 they were highl}^ 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 



* Celestial Mechanics, F. R. Moulton, p. 245. 

 t Young's General Astronomy, p. 313. 



