A SWARM OF METEORITES, AND ON THEORIES OF COSMOGONY. 
65 
swarm would probably settle down ^to the condition of convective ecjuilibrium 
throughout. 
It may be conjectured, then, that the best hypothesis in the early stages of the 
swarm is the isothermal adiabatic arrangement, and later an adiabatic sphere. It has 
not seemed to me worth while to discuss the latter hypothesis in detail at present. 
The investigation of § 11 also gives the coefficient of viscosity of the quasi-gas, and 
shows that it is so great that the meteor-swarm must, if rotating, revolve nearly 
without relative motion of its parts, other tlian the motion of agitation. But, as the 
viscosity diminishes when the swarm contracts, this would probably not be true in the 
later stages of its history, and the central portion would probably rotate more 
rapidly than the outside. It forjns, however, no part of the scope of this paper to 
consider the rotation of the system. 
In § 12 the rate of loss of kinetic energy through imperfect elasticity is considered, 
and it appears that the rate estimated per unit time and volume must vary directly 
as the square of the quasi-pressure and inversely as the mean velocity of agitation. 
Since the kinetic energy lost is taken up in volatilising solid matter, it follows that 
the heat generated must follow the same law. The mean temperature of the gases 
generated in any part of the swarm depends on a great variety of circumstances, but 
it seems probable that its variation would be according to some law of the same kind. 
Thus, if the spectroscope enables us to form an idea of the temperature in various 
parts of a nebula, we shall at the same time obtain some idea of the distribution of 
density. 
It has been assumed that the outer portion of the swarm is in convective 
equilibrium, and therefore there is a definite limit beyond which it cannot extend. 
Now, a medium can only be said to be in convective equilibrium when it obeys the 
laws of gases, and the applicability of those laws depends on the frequency of collisions. 
But at the boundary of the adiabatic layer the velocity of agitation vanishes, and 
collisions become infinitely rare. These two propositions are mutually destructive of 
one another, and it is impossible to push the conception of convective equilibrium to 
its logical conclusion. There must, in fact, be some degree of rarity of density, and of 
collisions, at which the statistical treatment of the medium breaks down. 
I have sought to obtain some representation of the state of things by supposing 
that collisions never occur beyond a certain distance fi’om the centre of the swarm. 
Then, from every point of the surface of the sphere, which limits the regions of 
collisions, a fountain of meteorites is shot out, in all azimuths and inclinations to the 
vertical, and with velocities grouped about a mean according to the law of error. 
These meteorites ascend to various heights without collision, and, in falling back on to 
the limiting sphere, cannonade its surface, so as to counterbalance the hydrostatic 
pressure at the limiting sphere. 
The distribution of meteorites, thus shot out, is investigated in § 13, and it is 
found that near tbe limiting sphere the decrease in density is somewhat more rapid 
MDCCCLXXXIX. —A. 
K 
