228 CARNEGIE INSTITUTION OP WASHINGTON. 



aud were separated from one another at the distances the case re- 

 quires, the mechanics by which they could be brought into this spe- 

 cial mode of collision consecutively is not evident and has not been 

 explicitly pointed out. It is certain that their union into a spheroid 

 would not be by any means the simple, direct, and rapid process 

 usually assumed.* On consideration it will be seen that the postu- 

 lated case is a very special and quite artificial one, for all the present 

 planetary orbits are elliptical and are by no means strictl}- concentric. 



It becomes evident, on studious consideration, that in any case 

 which could probably arise from any actual antecedents, the planet- 

 esimals must have had elliptical orbits ; for even if they arose from a 

 gaseous ring of the Laplacian type the rebounds of the molecules as 

 they collided and separated must have given rise to non-concentric 

 elliptical orbits. Even in this case the measure of the eccentricities 

 must probably have been many million times the sum of the semi- 

 diameters of the particles. In the case of planetesimals derived 

 from a spiral nebula, the orbits are necessarilj' assigned very notable 

 eccentricities. In all these cases the most available mode of aggre- 

 gation, if not the sole practicable one, lies i7i the crossing of the orbits 

 brought about by the constant shifting of their major axes, as already 

 set forth. 



Now, a planetesimal in a smaller elliptical orbit can come into con- 

 tact with a planetary nucleus in a larger orbit only when a more or 

 less aphelion portion of its orbit coincides wiih a more or less peri- 

 helion portion of the larger orbit of the nucleus, and a planetesimal 

 in a larger orbit can come into contact with a planetar\' nucleus in a 

 smaller orbit only when a more or less perihelion portion of its orbit 

 coincides with a more or less aphelion portion of the nucleus' orbit. 



Now, the vital point lies in the fact that at the point of collision 

 the body in the smaller orbit is moving sloiver than the one in the 

 larger orbit, though on the average it moves the faster. 



If the body in the outer orbit were alwa^^s to strike the outside of 

 the body in the inner orbit, the impact would contribute to forw^ard 

 rotation ; but the orbits may cross one another, and the bod)^ in the 

 inner orbit may have passed the crossing before it is overtaken by 

 the body in the outer orbit, and so the inertia of the overtaken bod)' 

 may be felt on the outer side of the nucleus and tend to produce ret- 

 rograde rotation. It is, therefore, necessary to take account of two 



*This has been discussed mathematically bj- F. R. Moulton : An Attempt to 

 Test the Nebular Hypothesis by an .\ppeal to the Laws of Dynamics. Astrophys. 

 Jour., Vol. XI, pp. 115-126, 1900. 



