102 Gaseous Stars [ch. m 
Since T e r is constant it follows that the radius of the star is inversely pro 
portional to the square of its luminosity. 
These are the laws which would be obeyed if all the quantities which we 
have assumed to be uniform were actually uniform and if the gas-laws were 
accurately obeyed throughout stellar interiors. 
Observation reveals no tendency for these laws to be obeyed. As we 
shall see below (§ 167) the least luminous stars of a given mass generally 
have the smallest radii and the highest central temperatures. We shall see 
at once that the laws are not obeyed, since the atomic weights of stellar 
atoms, calculated on the supposition that the gas-laws are obeyed, will be 
found to vary widely from one star to another. 
The Atomic Weight of Stellar Matter. 
93. Equation (92-3) may be written in the form 
Nf 18-3 T) 
A 
.(931), 
^•c(^c + 1) $ 
and so provides a means of determining N 2 /A for the atoms of which actual 
stars are composed. Indeed, we have already calculated T c and \ c for a 
number of stars, and since G is readily calculated from the star’s luminosity, 
the value of A 2 /A is obtained at once. 
It must of necessity be possible to determine N*/A from observations on 
a star’s structure, because the coefficient of opacity, by which the star’s whole 
structure is determined, is proportional to N' 2 /A. If we cut every atomic 
nucleus in a piece of matter into two equal halves, we halve both N and A 
and so also N 2 /A, with the result that the substance becomes twice as trans 
parent as before. This is the theoretical basis of the well-known physical fact 
that a large clot of matter in the form of a massive nucleus is far more effective 
in absorbing X-radiation than a large number of small clots of equal total mass. 
It is for this reason that the physicist and surgeon both select lead as the 
material with which to screen their X-ray apparatus; a ton of lead is far 
more effective in stopping unwanted X-rays than a ton of wood or of iron. If 
we knew the strength of an X-ray apparatus, and the total weight of shielding 
material round it, we could form a very fair estimate of the atomic weight 
of the shielding material by measuring the amount of X-radiation which 
escaped through it. 
In using formula (93T) we are in effect using just such a method to 
determine the atomic weight of the atoms of which the stars are composed. 
A star is in effect nothing but a huge X-ray apparatus. We know the total 
mass of many stars, and we can readily calculate the rate at which they are 
generating X-rays—it is merely the rate at which they are radiating energy 
away into space. If we could shut a Maxwell demon inside a star and make 
him cut each atomic nucleus in half, keeping the star’s mass and rate of