198 
MR. J. H. JEANS ON THE CONFIGURATIONS 
The Influence of other Physical Factors. 
43. The discussion from § 10 onwards has been limited to material in which the 
relation between pressure and density is of the form 
p = Kf? — cons.,.(169) 
an equation which implies that the mass is composed of matter of similar properties 
throughout. In an actual mass there must be at least some tendency for the 
substances of greater atomic or molecular weight to sink towards the centre, 
although it is far from clear to what extent this tendency will actually prevail 
under astronomical conditions. 
In equation (169), y is usually regarded as expressing the measure of a property 
of the material, being the ratio of the specific heats when the matter is gaseous. We 
have, however, only used this equation in its differential form 
dp = Kyp y ~ 1 dp .(l70) 
Now with any structure whatever of the mass of matter under consideration the 
surfaces of constant pressure and density must coincide. Our use of equation (170) 
has in no sense referred to a change of state of a single element of matter, it has 
referred to a passage from one surface of constant density to the next. Thus, in 
strictness, y refers to the arrangement of the matter and not to a physical property 
of the matter. In the case so far considered in which the matter has been supposed 
to have the same physical properties throughout, the two meanings become identical, 
but when the mass under discussion is an aggregate of imperfectly mixed types of 
matter, it becomes important to distinguish clearly between the two meanings. 
When p and p both vanish at the surface of the mass, equation (170) is equivalent to 
d log p — —d log p, 
7 
(171) 
where the differentials are supposed to refer to passage from one surface of constant 
density to the next. In passing from one surface to the next, p will increase partly 
on account of the increase of pressure, but partly also on account of the higher 
atomic weight of which the materials of the layer of higher density may be supposed 
composed. Thus we may suppose equation (171) replaced by 
d\og P = (— + —) d log p, .(172) 
Wm yd 
where y M is the value of y defined by equation (169) as a property of the material, 
while y A is such that the additional term on the right of equation (172) represents 
the increase in d log p owing to increase of atomic weight of the materials as we pass 
to layers of greater density. 
