A SWARM OP METEORITES, AKD ON THEORIES OP COSMOGONY. 
Hence, we have 
If we apply this formula to the solution which has been already found in Table IV., 
we obtain the following results :— 
0, 2-55, 7-66, 12-77, 16, 19-2, 24, 32, 
T years 1082, 792, 193, 59-2, 33-7, 27-5, 19-8, 61-7. 
These results are applicable to meteorites weighing 3|- grammes in a swarm 
extending to 44| a^. If the meteorites weigh 3| kilogrammes, the values of r would 
be one-tenth of the tabulated values. If the streams were ten times as broad, the 
periods woidd be a hundred times as hmg. 
Now the periods r in the above table, even if multiplied by a thousand, must be 
considered as short in the history of a stellar system. It thus appears that the quasi- 
viscosity must be such that a swarm of meteors must, if revolving, move nearly 
without relative motion of its parts, at least in the early stages of its evolution. 
But let us consider the values of r at different epochs in the history of the same 
system. If a be the radius of the isothermal sphere the formulm (9) and (10) show 
that L/a^ varies as a®, whilst v/a^ varies as a~^. Hence r varies inversely as cd. 
Thus, as the swarm contracts, the periods r increase rapidly. 
Thus, later in the history, the viscosity will probably fall off so much that equalisation 
of angular velocity may be no longer attained, and we should then have the central 
])ortion rotating more rapidly than the outside, with a gradual transition from one 
angular velocity to the other. 
The modulus v gives, besides the viscosity, the rate of equalisation of the kinetic 
energy of agitation ; this corresponds in a true gas with the conduction of heat. The 
conclusion at which we thus arrive appears to justify the assumption that the whole 
of the central part of the swarm is endued with uniform kinetic energy of agitation, 
and that the mass of the quasi-isothermal nucleus is the greatest possible. With 
regard to the assumption that the nucleus is coated with a layer in adiabatic or 
convective equilibrium, it may be remarked that the velocity of agitation must 
decrease when we get to the outskirts of the swarm, and convective equilibrium will 
probably satisfy the conditions of the case better than any other. Further considera¬ 
tions will be adduced on this point in the Summary. 
* Meyer, ‘ Kinet'4clie Tlieorie cler Gase,’ p. 321. Tlie I/tt is derived from a numerical quadi’ature 
"wliicli gives the value ’318, and it is apparently only accidentally equal to I/tt, The v \/ (S/Stt) is the 
mean velocity denoted Q by Meter. 
F 2 
