NATURE 



[Nov. 22, 1888 



of some actual system. It is obvious that the solar 

 system is the only one about which we have sufficient 

 knowledge to afford a basis for discussion. The paper, 

 of which this is an abstract, is accordingly devoted to a 

 consideration of the mechanics of a swarm of meteorites, 

 with special numerical application to the solar system. 



When two meteoric stones meet with planetary velocity, 

 the stress between them during impact must generally be 

 such that the limits of true elasticity are exceeded, and it 

 may be urged that a kinetic theory is inapplicable unless 

 the colliding particles are highly elastic. It may, how- 

 ever, I think, be shown that the very greatness of the 

 velocities will impart what virtually amounts to an 

 elasticity of a high order of perfection. 



It appears, a priori, probable that when two meteorites 

 clash, a portion of the solid matter of each is volatilized, 

 and Mr. Lockyer considers the spectroscopic evidence 

 conclusive that it is so. There is no doubt enough 

 energy liberated on impact to volatilize the whole of 

 both bodies, but only a small portion of each stone will 

 imdergo this change. A numerical example is given 

 in the paper to show the enormous amount of energy 

 with which we are dealing. It must necessarily be 

 obscure as to how a small mass of solid matter can take 

 up a very large amount of energy in a small fraction of a 

 second, but spectroscopic evidence seems to show that it 

 does so ; and if so, we have what is virtually a violent 

 explosive introduced between the two stones. 



In a direct collision each stone is probably shattered 

 into fragments, like the splashes of lead when a bullet 

 hits an iron target. But direct collision must be a 

 comparatively rare event. In glancing collisions the 

 velocity of neither body is wholly arrested, the concentra- 

 tion of energy is not so enormous (although probably still 

 sufficient to effect volatilization), and since the stones 

 rub past one another, more time is allowed for the matter 

 round the point of contact to take up the energy ; thus the 

 whole process of collision is much more intelligible. The 

 nearest terrestrial analogy is when a cannon-ball rebounds 

 from the sea. In glancing collisions fracture will probably 

 not be very frequent. 



From these arguments it is probable that, when two 

 meteorites meet, they attain an effective elasticity of a 

 high order of perfection ; but there is of course some loss 

 •of energy at each collision. It must, however, be admitted 

 that on collision the deflection of path is rarely a very large 

 angle. But a succession of glancing collisions would be | 

 capable of reversing the path, and thus the kinetic theory 

 of meteorites may be taken as not differing materially | 

 from that of gases. 



Perhaps the most serious difficulty in the whole theory 

 arises from the fractures which must often occur. If 

 they happen with great frequency, it would seem as if the 

 whole swarm of meteorites would degrade into dust. 

 We know, however, that meteorites of considerable size 

 fall upon the earth, and, unless Mr. Lockyer has 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 volatilized 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 

 volatilization. The mean size of meteorites probably 

 depends on the balance between these opposite tend- 

 encies. 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 aggre- 

 gation 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 meteor- 

 ites 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 distribution of meteor- 

 ites in space have arranged themselves into a sub-per- 

 manent 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 a condition of wide 

 dispersion, and form a swarm in which collisions are 

 frequent. 



For the sake of simplicity, the bodies are treated as 

 spherical, and in the first instance as being of uniform 

 size. 



It is assumed provisionally that the kinetic theory of 

 gases may be applied for the determination of the distri- 

 bution of the meteorites in space. No account being 

 taken of the rotation of the system, the meteorites will 

 be arranged in concentric spherical layers of equal density 

 of distribution, and the quasi-gas, whose molecules are 

 meteorites, being coinpressible, the density will be greater 

 towards the centre of the swarm. The elasticity of a gas 

 depends on the kinetic energy of agitation of its mole- 

 cules, and therefore in order to determine the law of 

 density in the swarm we must know the distribution of 

 kinetic energy of agitation. 



It is assumed that when the system comes under our 

 notice, uniformity of distribution of energy has been 

 attained throughout a central sphere, which is surrounded 

 by a layer of meteorites with that distribution of kinetic 

 energy which, in a gas, corresponds to convective equili- 

 brium, and with continuity of density and velocity of 

 agitation at the sphere of separation. Since in a gas in 

 convective equilibrium the law connecting pressure and 

 density is that which holds when the gas is contained 

 in a vessel impermeable to heat, such an arrangement of 

 gas has been called by M. Ritter {Aiinalen der Physik 

 und Chejnie, vol. xvi., 1882, p. 166) an isothermal-adiabatic 

 sphere, and the same term is adopted here as applicable 

 to a swarm of meteorites. The justifiability of these 

 assumptions will be considered later. 



The first problem which presents itself, then, is the 

 equilibrium of an isothermal sphere of gas under its own 

 gravitation. The law of density is determined in the 

 paper, but it will here suffice to remark that, if a given 

 mass be inclosed in an envelope of given radius, there is 

 a minimum temperature (or energy of agitation) at which 

 isothermal equilibrium is possible. The minimum energy 



