72 GEOLOGY. 



ring of perfectly circular form, in which the inner bodies, in uniting 

 with the outer ones, are supposed to strike their inner sides. To bring 

 about this delicate adjustment systematically, the orbits must remain 

 closely concentric, and the inner ones must be enlarged, or the outer 

 ones be reduced, so that they will approach concentrically to within 

 the sum of the semi-diameters of the bodies to be united. If plane t- 

 esimals were arranged in strictly circular concentric orbits, and were 

 separated from one another at the distances the case requires, the 

 mechanics by which they could be brought into this special 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 as- 

 sumed. 1 On consideration it will be seen that the postulated case 

 is a very special and quite artificial one, for all the present planetary- 

 orbits are elliptical, and are by no means strictly concentric. 



It becomes evident, on studious consideration, that \n 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 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 necessarily assigned very notable eccentricities. In all 

 these cases, the most available mode of aggregation, if not the sole 

 practicable one, lies in 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 01 

 less aphelion portion of its orbit coincides with a more or less perihelion 

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

 orbit can come into contact with a planetary 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, as shown in Fig. 29. 

 To illustrate by a pronounced case, a planetesimal, P, in the orbit A (Fig. 



1 This has been discussed mathematically by Moulton — ' ' An Attempt to Test the 

 Nebular Hypothesis by an Appeal to the Laws of Dynamics," Astrophys. Jour. Vol. 

 XI, pp. 115-126, 1900. 



