708 Lord Kelvin : The Problem of 
ratio I/W would continue to increase and the globe would 
become farther from an equilibrium condition than before. 
The expansion of the globe would therefore go on at an ever 
increasing speed till the density of the gas becomes infinitely 
small throughout. 
If, on the other hand, through a slight disturbance of the 
equilibrium condition, the ratio I/W becomes less than that 
required for equilibrium, the globe of gas would in this case 
tend to contract. The increase in the internal energy due 
to any slight condensation would be exactly equal to the 
thermal equivalent of the work done by gravitation ; and 
the ratio I/W would therefore go on diminishing instead of 
increasing, as it would require to do if the gas is to be 
restored to a condition of equilibrium. 
§ 45. " From this we see that if a globe of gas Q is given 
in a state of equilibrium, with the requisite heat given to it 
no matter how, and left to itself in waveless quiescent ether, 
it would, through gradual loss of heat, immediately cease to 
be in equilibrium, and would begin to fall inwards towards 
its centre, until in the central regions it becomes so dense 
that it ceases to obey Boyle's Law : that is to say, ceases to 
be a gas. Then, notwithstanding the above theorem, it can 
come to approximate convective equilibrium as a cooling 
liquid globe surrounded by an atmosphere of its own 
vapour " *. 
§ 4:6. But if, after being given in convective equilibrium 
as in § 45, heat be properly and sufficiently supplied to the 
globe of Q gas at its centre, the whole gaseous mass can be 
kept in the condition of convective equilibrium. 
§ 47. The theorem of §§ 42, 43 is given by Professor 
Perry on page 252 of 'Nature'' for July 13, 1899 ; and in 
the short article " On Homer Lane's Problem of a Spherical 
Gaseous Nebula," published in 'Nature,' February 14, 1907, 
I have referred to it as Perry's theorem. Since this was 
written, however, I have found the same theorem given by 
A, Bitter on pp. 160-162 of Wiedemann's Annalen, Bd. 8, 
1879, with the same conclusion from it as that stated in 
§ 44 above, namely, that when Z:<1J the equilibrium of the 
spherical gaseous mass is unstable. 
§ 48. In the theorem of Bitter and of Perry, given in 
§ 42. convective equilibrium is not assumed. For the pur- 
poses of our problem, indicated in § 21, it is desirable to 
obtain expressions for the energy and the gravitational work 
of a mass ]\I in equilibrium with a stated density at its 
* Quoted from " On Homer Lane's Problem of a Spherical Gaseous 
Nebula/' 'Nature,' Feb. 14, 1907. 
