204 



SCIENCE. 



[N. S. Vol. XII. No. 293. 



the molecules beyond the control of the 

 feeble gravity of the ring, and its dispersion 

 and cooling would seem to be inevitable.* 

 There seems therefore no good ground for 

 supposing that such a ring could maintain 

 either its coherence or its temperature. 



But if the ring were dispersed and cooled 

 might it not be reheated to the gaseous con- 

 dition in subsequently collecting into the 

 globular form ? Although a rigorous dem- 

 onstration is beyond the reach of present 

 mathematical processes, it is possible to 

 make a sufiBcient approach to a valid con- 

 clusion respecting the rate at which such a 

 ring would collect into a globe as to render 

 it improbable that it would heat itself to the 

 requisite temperature or any close approach 

 to it. It is indeed a question whether ag- 

 gregation would take place at all as the 

 direct result of its own gravitation. Bear- 

 ing upon this, one of us has attempted to 

 solve a series of specific cases purposely 

 made most favorable for aggregation.! It 

 was assumed, regardless of the probabili- 

 ties, that an aggregation had already pro- 

 gressed so far as to form a large body hav- 

 ing essentially the full gravitative power of 

 the earth and yet it seemed improbable that 

 this body could bring to itself infinitesimal 

 particles from portions of the ring more 

 than 60° distant from itself in heliocentric 

 longitude, unless this were accomplished 

 by other than the simple gravitative force 

 of the earth, the sun and these particles. 

 From this it is concluded that the tradi- 

 tional idea of a hot gaseous ring breaking 

 at some point and gathering into a gaseous 

 globe while still hot enough to maintain the 

 refractory substances of the earth in a 

 gaseous condition, is not tenable, both be- 

 cause of the molecular difiBculties and the 

 gravitative incompetencies. 



Pursuing this line further, we have in- 

 quired whether any single or dominant 



* Paper II., before cited, pp. 658-665. 

 t Paper III., before cited, pp. 115-117. 



condensation would take place in a ring of 

 tolerable homogeneity.* Students of the 

 subject are aware that the rings of Saturn 

 are composed of particles of discrete non- 

 gaseous matter and cannot aggregate into 

 satellites because of the differential attrac- 

 tion, or tidal strain, of the planet. They 

 do not illustrate gaseous rings of the La- 

 placian type on the way to the formation of 

 satellites as once supposed, but quite the 

 reverse. If satellites of equal masses were 

 substituted for them, they would be torn 

 into fragments by the tidal pull of Saturn, 

 and probably redistributed into meteoric 

 rings. The rings appear to represent a 

 state of equilibrium and not a state from 

 which rapid aggregation should naturally 

 proceed, as assumed in the case of the La- 

 plaeian rings. The limiting distance within 

 which this power of disruption is exercised 

 by the planet is dependent on its gravita- 

 tive power and is known as Rochets limit. 

 For Saturn it lies a little outside of the 

 outer ring; for the earth, according to G. 

 H. Darwin, it lies about 11,000 miles from 

 the earth's center. We attempted to ap- 

 ply and extend the principles of Eoche to 

 cases arising under the nebular hypothesis 

 and in the course of this devised a new cri- 

 terion of similar nature, applicable to at- 

 tenuated gases in the form of ellipsoids and 

 rings such as are postulated in the Lapla- 

 cian hypothesis. For the precise nature of 

 this the reader must be referred to the 

 original paper. f It will sufiQce here to say 

 that while Eoche determined the limits, 

 under assumed conditions, within which 

 disruption would take place, the new cri- 

 terion assigns the limits, under assumed 

 conditions, within which the aggregation of 

 attenuated or dispersed matter would not 

 take place as the result of its own gravita- 

 tion, in the presence of the superior differ- 

 ential gravitation of the sun. The conclu- 



* Paper III., above cited, pp. 118-129. 

 t Paper III., above cited, pp. 122-126. 



