a Spherical Gaseous Nebula, 707 
of radius R is therefore 
W 
</rrV/p=^ rfn»- .... (47). 
§ 42. From equations (45) and (47) we obtain, as the 
ratio of the intrinsic energy within the sphere of gas to 
the work done by gravity in collecting the whole mass from 
an infinite distance, 
w = S < 48 >- 
If K ;; be the specific heat of the gas at constant pressure, we 
have S = K P — K„ and equation (48) may now be written in 
the form 
1= 1e = 3— = * rm 
W 3(1^ -K,) 3(*-l) 3 > 4 ^" 
§ 43. According to this theorem, it is convenient to divide 
gases into two species : species P, gases for which the 
ratio (h) of thermal capacity pressure constant to thermal 
capacity volume constant is greater than 1J ; species Q, 
gases for which fc is less than 1^. And the theorem ex- 
pressed mathematically in equations (48) and (49) may be 
stated thus: — "A spherical globe of gas, given in equi- 
librium, with any arbitrary distribution of temperature having 
isothermal surfaces spherical, has less heat if the gas is of 
species P, and more heat if of species Q, than the thermal 
equivalent of the work wdrich would be done by the mutual 
gravitational attraction between all its parts, in ideal shrink- 
age from an infinitely rare distribution of the whole mass to 
the given condition of density " *. 
§ 44. It is easy to show from the theorem of §§ 42, 43 
that the equilibrium of a globe of Q gas is essentially 
unstable. Let us first suppose for a moment that by a slight 
disturbance of the equilibrium condition the ratio I/W for 
the globe of Q gas becomes greater than that required 
for equilibrium by equation (49). Unless the excess of 
internal energy were quickly radiated away, the repulsive 
force which the globe of gas possesses by virtue of its 
internal energy w 7 ould more than balance the condensing 
influence of gravity, and the globe would tend to expand. 
Since the internal energy lost in expansion is exactly equi- 
valent to the work done against gravity, we see that the 
* Quoted from " On Homer Lane's FroHem of a Spherical Gaseous 
Nebula," * Nature,' Feb. 14, 1907. 
