8 
PROFESSOR G. H. DARWIR OR THE MECHARICAL CORDITIORS" OF 
With these values 
Uq = 1Q6-46323 _ 2,905,600 cm. per sec. 
= 106-68329 _ 4^800,600 cm. 
To = I00'253fi6 _ 1-79334 sec. . (1^) 
106-79204 ^ 6,195,000 I 
''0 J 
The dimensions of Iq and Tq are not those of length and time ; but, if meteorites 
of 1 gramme mass, with sphere of action 1 centimetre, and “ velocity of mean square ” 
of agitation equal to the Earth’s velocity in its orbit, bave density of distribution 
equal to one-third of the mean density of the sphere M, then Iq, tq will be the mean 
free path and time, as stated in centimetres and seconds. We may thus regard Iq, Tq 
as a lengTh and time, provided care be taken in the subsequent use of the s}nnbols to 
adhere to the c.g.s. system of units. 
§ 4. On the Equilibrium of a Gas at Uniform Temq^erature in Concentric Spherical 
Layers under its own Gravitation. 
It is assumed iirovisioually tlrat the conditions are satisfied which permit us to 
regard the swarm of meteorites as a quasi-gas, subject to the laws of hydrostatics. 
The solution of this problem, then, becomes a necessary preliminary to the discus¬ 
sion of the kinetic theory of meteorites. The equilibrium of a gas under its own 
gravitation has been ably discussed by Professor Pitter in one of his series of ]iapers 
on gaseous planets.'” The intrinsic interest of the problem renders an independent 
solution valuable. Suppose, then, that a mass M-^ of gas is enclosed in a spherical 
envelope of radius a^, and is in equilibrium in concentric spherical layers. Let vf, 
the mean square of the velocity of agitation of the gaseous molecules, be defined by 
reference to the potential of the mass at the radius cq, so that 
2 piA 
where is a numerical coefficient, and y is the attractional constant. 
Let y* and w be the pressure and density of the gas at radius r, and L: the modulus 
of elasticity, so that 
20 — h w, 
h = 
2 — 
* “ Untersucliungen iiber die Hobe dei’ Atmosphare und die Constitution gasformigei- Weltkoi-per,” 
‘Wiedemann’s Annalen ’ (Rew Series), vol. 16, 1882, p. 166. A very elegant solution of part of my 
problem has also been given by Mr. G. W. Hill in the ‘ Annals of Mathematics,’ vol. 4, No. 1, p. 19 
(Februai’y, 1888). Mr. Hill’s paper only reached my hands after my own calculations had been 
completed, and I therefoi-e adhere to my own less elegant method. Mr. Hill has obviously not seen 
M. Ritter’s papers. 
