1888.] Conditions of a Swarm of Meteorites, $c. 9 



velocity to be justly deduced from hydrodynamical principles must be 

 expressible as the edge of a cube containing many molecules passed 

 over in a time containing many collisions of a single molecule ; and 

 a similar statement must hold of any other function of mass, length, 

 and time. 



Beyond these limits we must go back to the kinetic theory itself, 

 and in using it care must be taken that enough molecules are con- 

 sidered at once to impart statistical constancy to their properties. 



There are limits then to the hydrodynamical treatment of gases, 

 and the like must hold of the parallel treatment of meteorites. 



The principal question involved in the nebular hypothesis seems to 

 be the stability of a rotating mass of gas ; but unfortunately this has 

 remained up to now an untouched field of mathematical research. 

 We can only judge of probable results from the investigations 

 which have been made concerning the stability of a rotating mass 

 of liquid. Now it appears that the instability of a rotating mass 

 of liquid first enters through the graver modes of gravitational 

 oscillation. In the case of a rotating spheroid of revolution the gravest 

 mode of oscillation is an elliptic deformation, and its period does not 

 differ much from that of a satellite which revolves round the spheroid 

 so as to graze its surface. Hence, assuming for the moment that a 

 kinetic theory of liquids had been formulated, we should not be 

 justified in applying the hydrodynamical method to this discussion of 

 stability, unless the periodic time of such a satellite were a large 

 multiple of the analogue of the mean free time of a molecule of 

 liquid. 



Carrying then this conclusion on to the kinetic theory of meteorites, 

 it seems probable that hydrodynamical treatment must be inapplicable 

 for the discussion of such a theory as the meteoric-nebular hypo- 

 thesis, unless a similar relation holds good. 



These considerations, although of a vague character, will afford a 

 criterion of the applicability of hydrodynamics to the kind of pro- 

 blem suggested by the nebular hypothesis. And certain criteria 

 suggested by this line of thought are found in the paper ; they give a 

 measure of the degree of curvature of the average path pursued by a 

 meteorite between two collisions. 



After these preliminary investigations, we have to consider what 

 kind of meeting of two meteorites will amount to an " encounter " 

 within the meaning of the kinetic theory. 



Is it possible, in fact, that two meteorites can considerably bend 

 their paths under the influence of gravitation, when they pass near 

 one another ? This question is considered in the paper, and it is shown 

 that unless the bodies have the dimensions of small planets, the 

 mutual gravitational influence is insensible. Hence, nothing short of 

 absolute impact is to be considered an encounter in the kinetic theory, 



