August 10, 1900.] 



SCIENCE. 



207 



planets, the estimates of Darwin being used 

 throughout. 



Just previous to the supposed separation 

 of the Jovian ring, the moment of momen- 

 tum of the parent nebula, reckoned from 

 the present moments of momenta of the 

 bodies derived from it, was 14.1816. Now 

 Jupiter has 13.469, or about 95%, of this. 

 But the mass of Jupiter is only 1/1047 of 

 the parent nebula, or less than one-tenth 

 of one per cent. Neglecting for the moment 

 any transfers of momentum that may have 

 taken place afterwards, it appears that, by 

 hypothesis, the Jovian ring carried aivay less 

 than one-thousandth of the mass of the nebula, 

 tvhile at the same time it took off 95'fo of the mo- 

 ment of momentum. Is such a thing possible 

 in a gaseous spheroid evolving under gas- 

 eous laws, or evolving in any form of con- 

 vective equilibrium? One nineteen-thou- 

 sandth more of the mass thrown off with an 

 equal proportion of momentum would have 

 left none in the central body ! 



A similar comparison in the case of the 

 other planets reveals not only very extra- 

 ordinary ratios but such large and irregu- 

 lar variations in the ratios as couldL hardly 

 be expected in the systematic evolution of a 

 gaseous body. 



To the inquiry whether these discrep- 

 ancies can be due to subsequent transfers 

 of momentum by tidal friction, the compu- 

 tations of Gr. H. Darwin have given an 

 emphatic negative ; and these are supported 

 by other considerations.* 



The general conclusion from these several 

 attempts to test the nebular hypothesis of 

 Laplace is altogether adverse to its tena- 

 bility. It is equally adverse to any meteor- 

 oidal hypothesis which assumes a quasi- gas- 

 eous behavior, or an aggregation controlled 

 by the laws of convective equilibrium, 

 as set forth by G. H. Darwin in his mem- 

 oir 'On the Mechanical Conditions of a 

 Swarm of Meteorites and on Theories of Cos- 



* Paper II., pp. 70-71. 



mogony.' The inquiry into the relations 

 of masses and momenta points to an un- 

 symmetrical distribution of matter and en- 

 ergy quite inharmonious with an original 

 spheroidal form of any kind. On the con- 

 trary, it seems to indicate that the origin of 

 the system icas such that the outer part acquired 

 all but a trivial part of the momentum while it 

 possessed only a trivial part of the mass. In 

 specific terms, the outer or planetary part 

 now embraces only about 1/700 of the mass, 

 while it carries more than 97% of the 

 moment of momentum. The sun has no such 

 residual rotatory momentum as to imply 

 that he ever ' threw off ' any planets from 

 his equator. If the solar system were con- 

 verted into a gaseous nebula controlled by 

 Boyle's law and given the existing moment 

 of momentum and allowed to contract, the 

 centrifugal force would not overtake the 

 centripetal until long after the orbit of Mer- 

 cury had been passed. 



The ratios of masses to momenta and the 

 discrepancies of the system clearly have a 

 high value in the construction of a tenable 

 hypothesis, whatever that may prove to be ; 

 for they are specific criteria which must be 

 met. In an attempt to construct such a 

 hypothesis, the matter of the system must be so 

 brought together as to give loiv mass, high mo- 

 mentum and irregular distribution to the outer 

 part, and high mass, low momentum and spher- 

 icity to the central part. In speculation in 

 this direction the possibility of the initia- 

 tion of the system by the peripheral collis- 

 ion of a very small nebula upon a large one 

 has seemed worthy of consideration. As- 

 suming that the collision was essentially 

 due to mutual gravitation, the smaller 

 nebula must, from the nature of the case, 

 have had a relatively high velocity, and 

 hence a high ratio of momentum to mass, 

 while the larger nebula may have had little 

 initial rotation, or may even have had a 

 rotation contrary to the present one, which 

 was reversed by the impact, or the recur- 



