FUNDAMENTAL PROBLEMS OF GEOLOGY. 227 



equally open to the supposedly fatal weakness. So indeed is the 

 concentration of an>' kind of an assemblage of discrete matter in 

 which the individual molecules or aggregates revolve independently. 



The supposed fatal difficulty is as follows: In a ring revolving as 

 a unit, as the Laplacian rings are supposed to have done, the outer 

 part moves faster than the inner part, and so, if a planetary ring 

 breaks at its weakest point and gathers into a globe about the center 

 of its cross-section, it will xoX.'aX.q. forward . If, on the other hand, 

 the particles of the ring revolve bidependently, the inner ones must 

 move faster than the outer ones, and if they collect about the middle 

 part, it has been held that the rotation must be retrograde.-^ 



By way of exception, to meet the singular cases of Uranus and 

 Neptune, it has been suggested that if the matter of the planetary 

 rings, revolving as units, happened to collect about some point other 

 than the center of the cross-section, the foregoing conclusions would 

 not hold ; but if the matter were drawn together by gravity simply, 

 as usually supposed under the L,aplacian hypothesis, it is not evident 

 why it should not collect about the middle part. 



Now, as a matter of fact, the six inner planets and their satellites 

 rotate forzvard. The satellites of Uranus revolve backward in a 

 plane inclined 82.2° to the ecliptic; those of Neptune also revolve 

 backward in a plane inclined 34.5° to the ecliptic. The rotations of 

 the planets themselves have not been determined . These exceptional 

 inclinations and rotations have been interpreted as very oblique or 

 partially overturned rotations. Accepting the foregoing premises, the 

 prevalence of direct rotation has been regarded as strongly confirma- 

 tory of an origin from gaseous rings rotating as units, and as strongly 

 adverse to accretion from bodies revolving independently. The force 

 of this line of reasoning has apparently been felt to be so strong as to 

 be essentially fatal to the latter conception. It therefore requires 

 critical consideration. 



The reasoning is good for the special case cited, that of a symmet- 

 rical 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 planetesimals were arranged in strictly circular concentric orbits, 



* For ampler statements of this difficulty, see Faye, Sur I'Origiuedu Monde, 

 pp. 165, 270-2S1, 1896; also Young's General Astronomy, pp. 518-520. 



