THE ASTRONOMICAL DEDUCTIONS. 17 



kind made so familiar to us by the geologic rhetoric of the last century. 

 Until the outward reach of this atmosphere was escaped by the receding 

 moon, the atmospheric friction must have kept the moon in consonant 

 revolution with itself and tidal action could not have been inaugurated. 

 This must have prolonged the critical stages and made the triumph of 

 contraction over the solar tides all the more doubtful. 



The separation of the moon from the earth after the common mass 

 became a liquid spheroid is subject to another serious contingency, based 

 upon the same principle of differential attraction as the tides themselves. 

 Roche has shown that a satellite revolving within a given distance from its 

 primary will be torn to fragments. The fragments must revolve at velocities 

 strictly dependent on their distances from the center of the primary and 

 hence must disperse themselves into a ring of the Saturnian type.^ The 

 fragments so produced would be subject to further reduction by collisions 

 with one another, by changes of temperature, and by internal reactions, 

 and would probably only reach an approximately stable condition as to 

 size when they were well comminuted. For the earth-moon combination 

 the Roche limit of disruption lies about 11,000 miles from the earth's 

 center.^ The cogency of Roche's reasoning, supported by that of Clerk- 

 Maxwell and others, and the example of the rings of Saturn, seems to leave 

 no alternative but to suppose that a body of the mass of the moon could 

 not pass from the earth outward by tidal reaction without being torn to 

 fragments and converted into a ring, unless the fission of the earth-moon 

 mass and the initiation of the lunar tide took place outside the Roche 

 hmit, which is difficult to believe under the Darwinian hypothesis, though 

 consistent enough with the Laplacian. The laws of revolution seem to 

 forbid the supposition that the fragments produced by tidal disruption 

 could have been aggregated for any appreciable length of time on one 

 side of the earth so as to act jointly in producing an effective tide. Even 

 if some tide could be so produced there would still remain the question 

 whether it would have carried the fragments outward by reaction suffi- 

 ciently far for them to have escaped the dangers of reversal by the solar 

 tides, as pointed out in a preceding paragraph. There seem to be no 

 cogent theoretical grounds upon which it can be affirmed that the frag- 

 ments of a disrupted body of this kind would evolve into any other condi- 

 tion than that of a ring of discrete particles during the time available for 

 starting the recessional movement of the moon. They might perhaps 

 move outside the Roche limit or be drawn down to the planet in a period 

 sufficiently long, but probably not in the available period. The fact that 

 the Saturnian rings are present at this stage in the history of the solar 

 system suggests, if it does not definitely imply, that this form of organiza- 

 tion is one of much persistence. 



If we pass by these peculiar difficulties that embarrass the supposed 

 separation of the moon from the earth, and if we set aside the special 

 consequences assigned to a molten or viscous earth-body, the remaining 



* On the stability of motion of Saturn's rings. < Scientific Papers of James Clerk- 

 Maxwell, vol. 1, pp. 288-376. 



2 Darwin's "Tides," pp. 358-360. 



