/ 
IONISATION, DIFFUSION, ROTATION 
251 
above Zi — 50. Of course, we give some attention to the changes required 
if this assumed composition is considerably in error. 
174. The fundamental formula for determining the degree of ionisation 
of an element at given temperature and density is (47*1). Since a large 
number of possible stages of ionisation and degrees of excitation may have 
to be considered simultaneously the application of the formula may become 
very complicated in practice. We give first a simplified discussion which 
may, or may not, be accurate enough for actual computation, but will in 
any case exhibit some of the more essential features of the problem. 
The series of terms on the right-hand side of (47-1) corresponds to 
atoms with successive degrees of excitation. We shall here suppose that 
excitation is rare and that only the first term corresponding to unexcited 
atoms need be considered. Further, we drop the weight factors q. Consider 
the pth. ionisation and let ifj (= — y) be the energy required to remove the 
pth electron. Then the ratio of the number of atoms with jp — 1 electrons 
missing to the number with p electrons missing is by (47-1) 
the logarithms being to the base 10. 
For example, if T = 10 7 , p — *02, p, = 2, 
conditions corresponding roughly to the centre of Capella, we have by 
where the wave-length À corresponds to the energy ¡/r according to the 
For brevity we often speak of an energy À, i.e. describe the quantity of 
energy by the wave-length of the radiation having a quantum of this 
amount. 
(174*1), 
where a is the number of free electrons per unit volume, so that 
Neglecting as usual the small correction/, we have 
(174*2) 
x = 0*1, 0*5, 0*9, 
0=ll-7i2T', 9*5 RT, 7*3 RT, 
À = 1*22 Â, 1*51 Â, 1*96 Â, 
for 
and 
quantum relation 
ijj = he /À 
(174*3).