DIFFUSE MATTER IN SPACE 
383 
hence the density of interstellar radiation being 7-7. lO“ 13 , we have 8 = 10 14 . 
With p = 10~ 24 we have p8 = 10~ 10 , and the problem reduces to finding 
the ionisation in equilibrium conditions for density 10~ 10 and temperature 
10,000°. By (174-2) we find 
tp 0 /RT =19-8, ¡/r 0 = 17 volts. 
The second ionisation potential of calcium is 11-8 volts. The proportion 
of calcium remaining in the Ca + state is then 
e^-^/RT = -0025, 
the rest being doubly ionised. 
The second ionisation potential for sodium is 30-35 volts so that there 
is practically no double ionisation. The first ionisation potential is 5-1 volts; 
hence we find that 1 atom of sodium in 1,000,000 is neutral. If the 
abundance and the absorption coefficients for sodium are the same as for 
calcium this is barely sufficient to produce the fixed D lines*. Calcium’s 
first ionisation potential is 1 volt higher and the corresponding divisor 
is 300,000. We can now readily understand why neutral calcium is less 
abundant than neutral sodium (as the observations indicate); our results 
are Ca 1 Ca + _ 1 Na 1 
Ca + ~ 300,000’ Ca ++ — 400’ Na + ~ 1,000,000’ 
so that there is an extra divisor of 400 due to the second stage ionisation 
occurring in calcium but not in sodium. 
Any minor numerical discrepancies will probably disappear when we 
take account of the spread of effective temperatures of the stars. This 
makes the radiation richer in high frequencies and poorer in low frequencies, 
so that the second stage ionisation is more intense and the first stage less 
intense than in the foregoing results. This may well reduce the proportion 
of Ca + atoms to and increase the proportion of Na atoms to 10 times 
the above figures. All the results then become satisfactorily consistent. 
Absorption of Light in Space. 
261. Distances of celestial objects up to about 50 parsecs can be 
determined by the trigonometrical method. By the use of mean parallactic 
motions and mean cross-motions the determination of average distances 
of groups of objects can be extended to perhaps 400 parsecs. Beyond this 
we are almost entirely dependent on an optical method; if the absolute 
magnitude of a star is supposed to be known independently, then it is 
a simple calculation to find at what distance it must be situated in order to 
give the observed apparent magnitude. 
* Terrestrially sodium atoms are about 4 times as abundant as calcium atoms; 
moreover the fixed D lines are weaker than H and K. Allowing for this we still 
require a rather higher absorption coefficient—which is perhaps not unlikely.