60 
PROFESSOR G. H. DARWIN ON THE MECHANICAL CONDITIONS OF 
The evaluation of mean mass in the fringe (see § 1 3), where collisions are supposed 
to be non-existent, is not very difficult, although it involves some troublesome algebra. 
I do not give the investigation, merely remarking that it leads to almost exactly the 
same kind of law of diminution of mean mass as we have found in the adiabatic 
layer. 
§ 17. Summary. 
The first and second sections only involved arguments of a general character in 
which mathematical analysis was unnecessary. The reader who does not wish to 
concern himself with details may therefore be supposed to have passed from §§ 1 and 2 
to this Summary. 
In order to submit the theory to an adequate test, it is necessary to discuss some 
definite case of the aggregation of a swarm of meteorites, and it is obvious that the 
only system of which we possess any knowledge is our own. It is accordingly 
supposed that a number of meteorites have fallen together from a condition of wide 
dis23ersion, and have ultimately coalesced so as to leave the Sun and planets as their 
progeny. The object of this paper is to consider the mechanical condition of the 
system after the cessation of any considerable sujjply of meteorites from outside, and 
before the coalescence of the swarm into a star with attendant planets. 
For the sake of simplicity, tbe meteorites are considered to be spherical, and are 
treated, at least 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 distribution of the meteorites in space. No account being taken of 
the rotation of the system, tlie meteorites wdll be arranged in concentric spherical layers 
of equal density of distribution, and the quasi-gas, whose molecules are meteorites, 
being compressible, 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 molecules ; 
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 
swarm 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 equilibrium. 
In other words, we have a quasi-isothermal sphere surrounded by what may be called 
an atmosphere in convective equilibrium, and Avith 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. PbiTTER “ 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 
