382 
DIFFUSE MATTER IN SPACE 
temperature of diffuse matter applies also to the nebulae, we take the 
conditions to be isothermal with T — 10,000°. Then by (63-4) with /x = 10, 
B = 1 
r r = 3-14.10V*z, 
or if r is measured in parsecs 
r — (10 20 p o r^2 (260-1). 
Take, for example, the unit of z to be 1 parsec ; the density then diminishes 
from p 0 at the centre of the nebula to ^ p 0 at 5 parsecs from the centre and 
^oPo at 10 parsecs distance (Table 7). I suppose that this corresponds very 
well to the size of typical nebular aggregations. Accordingly by (260-1) 
Po = IO" 20 . 
Even if the scale of the nebula is 3 times larger or smaller p 0 is only changed 
by a factor 9, so that the central density of the nebulae is rather well 
determined if this theory is valid. At 150 parsecs distance from any one 
nebula we probably reach the general average conditions of interstellar 
space undisturbed by exceptional attracting masses. By Table 7 the 
density has there fallen to 10 _4 p 0 . This then indicates a density 10~ 24 or 
about -fa of the upper limit which we have been adopting. This last result 
happens to be nearly independent of the determination of p 0 ; and it seems 
impossible to strain the data so as to give a result near the lower limit 
of 10~ 6 atoms per cu. cm. 
We judge therefore that the interstellar medium is much denser than 
would be necessary to give the fixed calcium lines if all the calcium were 
in the state of Ca + . It is probable therefore that most of the calcium is 
doubly ionised—a conclusion favourable to Fowler’s argument (§ 258). 
A rough determination of the state of ionisation of the diffuse matter 
can be made in the following way. Assume as in § 257 that all the stars 
have the same effective temperature T —approximately the same as the 
temperature of the interstellar matter. Then the radiation in space is 
evenly diluted equilibrium radiation, that is to say, the density for 
frequency v to v + dv is j ^ ^ 
where I (v, T) is the equilibrium intensity and 8 is a constant “factor of 
dilution.” The degree of ionisation is determined by equating the number 
of captures to the number of expulsions. The former number is propor 
tional to the density of the electrons and the latter to the density of the 
radiation. If the radiation density and the electron density are both 
multiplied by the same factor 8 the balance will be unaltered. This multi 
plication brings the radiation up to its equilibrium density ; hence we have 
the rule— 
The conditions of ionisation in interstellar material are the same as in 
material of density p8 in thermodynamical equilibrium at temperature T. 
Equilibrium radiation at 10,000° has a density 76 ergs per cu. cm.;