<J Prof. G. H. Darwin. On the Mechanical [Nov. 15, 



able size fall upon the earth, and, unless Mr. Lockyer lias mis- 

 interpreted the spectroscopic evidence, the nebula? do now consist of 

 meteorites. Hence it would seem as if fracture was not of very 

 frequent occurrence. It is easy to see that if two bodies meet with a 

 given velocity the chance of fracture is much greater if they are large, 

 and it is possible that the process of breaking up will go on only until 

 a certain size, dependent on the velocity of agitation, is reached, and 

 will then become comparatively unimportant. 



When the volatilised gases cool they will condense into a metallic 

 rain, and this may fuse with old meteorites whose surfaces are molten. 

 A meteorite in that condition will certainly also pick up dust. Thus 

 there are processes in action tending to counteract subdivision by 

 fracture and volatilisation. The mean size of meteorites probably 

 depends on the balance between these opposite tendencies. If this is 

 so, there will be some fractures, and some fusions, but the mean mass 

 will change very slowly with the mean kinetic energy of agitation. 

 This view is at any rate adopted in the paper as a working hypothesis. 

 It was not, however, possible to take account of fracture and fusion in 

 the mathematical investigation, but the meteorites are treated as 

 being of invariable mass. 



The velocity with which the meteorites move is derived from their 

 fall from a great distance towards a centre of aggregation. In other 

 words, the potential energy of their mutual attraction when widely 

 dispersed becomes converted, at least partially, into kinetic energy. 

 When the condensation of a swarm is just beginning, the mass of the 

 aggregation towards which the meteorites fall is small, and thus the 

 new bodies arrive at the aggregation with small velocity. Hence 

 initially the kinetic energy is small, and the volume of the sphere 

 within which hydrostatic ideas are (if anywhere) applicable is also 

 small. As more and more meteorites fall in, that volume is enlarged, 

 and the velocity with which they reach the aggregation is increased. 

 Finally the supply of meteorites in that part of space begins to fail, 

 and the imperfect elasticity of the colliding bodies brings about a 

 gradual contraction of the swarm. I do not now attempt to trace the 

 whole history of a swarm, but the object of the paper is to examine 

 its mechanical condition at an epoch when the supply of meteorites 

 from outside has ceased, and when the velocities of agitation and dis- 

 tribution of meteorites in space have arranged themselves into a 

 sub-permanent condition, only affected by secular changes. This 

 examination will enable us to understand, at least roughly, the secular 

 change as the swarm contracts, and will throw light on other 

 questions. 



The foundation for the mathematical investigation in the paper is 

 the hypothesis that a number of meteorites which were ultimately to 

 coalesce, so as to form the sun and planets, have fallen together from 



