August 10, 1900.] 



SCIENCE. 



205 



sion reached by this inquiry was that a 

 Laplacian ring could not have contracted 

 directly into a gaseous globe, and that the 

 nebula out of which the solar system was 

 evolved must have been one of great hetero- 

 geneity rather than one of the pronounced 

 homogeneity assumed in the Laplacian hy- 

 pothesis. 



The further question whether the equa- 

 torial matter of a spheroid of gas whose 

 rotation was increasing would separate in- 

 termittently as rings or go off continuously 

 is not new, but it was thought worth while 

 to reconsider it in the light of modern con- 

 ceptions of the outer border of an atmos- 

 phere or of a globe of gas. This outer 

 border is not now regarded as a defined 

 surface where gravity and ' repulsive force' 

 balance ; on the contrary, the outer portion 

 is somewhat like a fountain in which indi- 

 vidual molecules are thrown by the rebound 

 from collisioQS to varying heights, from 

 which they return in elliptical paths, possibly 

 to be thrown back again or to assist in pro- 

 jecting other particles through like paths. 

 There is no theoretical limit to the extent 

 of these excursions short of escape from the 

 control of the main body. The actions of 

 the molecules in this outer portion are 

 therefore more individual and free than 

 those of the denser mass, and in the course 

 of their long free curving paths they may 

 collide in such a way as to become satellites 

 to the main body. 



]S"ow the extreme tenuity of the Lapla- 

 cian nebula seems not to have been con- 

 sidered in connection with ring-formation. 

 One of us has computed that the average 

 density of the solar nebula, when extended 

 to the orbit of ISTeptune, would be 1/191,- 

 000,000,000 of that of water.* The tenu- 

 ity of the extreme outer portion must there- 

 fore have been quite beyond the limits of 

 the imagination. In view of this extreme 

 tenuity and the peculiar constitution al- 



* Paper III., above cited, pp. 114. 



ready cited, it is scarcely possible that there 

 could have been any effective cohesion to 

 prevent the separation of the peripheral 

 portion particle by particle as the individual 

 centrifugal force of each came to equal the 

 centripetal force. It is clear that in a mass 

 of gas densest at the center the centrifugal 

 force would overtake the centripetal force 

 first at the equatorial surface.* The con- 

 clusion is therefore that the peripheral 

 matter would have been left behind con- 

 tinuously and that separate rings would not 

 have formed. 



Some minor arguments that merely touch 

 the probability of the Laplacian hypothesis 

 may be passed by.f 



Arguments of the foregoing class, though 

 they seem entitled to great weight, lack 

 something in rigor, for, at present, exhaust- 

 ive data cannot be commanded and treated 

 by precise mathematical methods. We, 

 therefore, had recourse to lines of attack of 

 a more mechanical sort. These were found 

 in the relations of mass and momenta. We 

 attempted (1) a comparison of the moment 

 of momentum of the supposed nebular sys- 

 tem with the moment of momentum of the 

 actual system, and (2) a study of the ratios 

 of masses to momenta. 



1. It is a firmly established law of me- 

 chanics that any system of particles rotat- 

 ing about a common axis retains a constant 

 moment of momentum whatever change of 

 form may take place as the result of its 

 own evolution. The evolution of the solar 

 system under the Laplacian hypothesis is 

 such a case. If, therefore, we can restore, 

 theoretically, the supposed nebulous system 

 and compute its moment of momentum, it 

 must be found at all stages the same as at 

 present. The only serious difSculty of the 

 method lies in determining the distribution 

 of density through the postulated nebu- 

 lous mass. Fortunately this has been at- 



* Paper III., above cited, pp. 114, 115. 

 t Paper III., pp. 107-111. 



