138 
[CH. IV 
The Source of Stellar Energy 
at all in the earth’s atmosphere the flux of energy per square centimetre 
would produce over a million ions per second, representing a flux of energy of 
about 0*00003 ergs per second. The actual flux must be far greater than this, 
partly because the figure of 1*4 ions per second represents the activity of 
the radiation after it has suffered absorption by the earth’s atmosphere, and 
partly because the main part of this radiation must expend its energy in other 
ways than in the ionisation of molecules. To allow for absorption we may 
multiply our estimate by about 10, increasing it to about 0*0003 ergs per 
second; but it seems impossible to estimate the second source of error. 
According to Hubble (§ 17) the extra-galactic nebulae are so evenly 
spaced that we can regard them, to a first approximation, as forming a distribu 
tion of uniform density round the earth, with a density of matter, at least up 
to about 100 million light years, of about 1*5 xlO -31 grammes per cubic cm. 
Giving p this value in equation (126*1), we find that a flux of 0*0003 ergs 
per square cm. requires that 
G(r 2 -7*0 = 6 x 10 27 . 
If we put the outer radius r 2 equal to the 140 million light years distance 
of the furthest visible nebulae (r 2 = 1*4 x 10 20 ) we obtain G = 43. Thus we 
can account for the amount of highly penetrating radiation received by the 
earth’s atmosphere, by supposing all the nebulae within 140 million light years 
to be generating energy at the rate of 43 ergs per gramme per second. The 
calculation is of course very rough ; the energy actually received is greater 
than 0*0003 ergs per second for the reasons already stated; against this no 
doubt a large amount of highly penetrating radiation reaches us from nebulae 
at distances greater than 140 million light years. 
Setting these various corrections off against one another,a rate of generation 
of energy of G = 43 ergs per gramme per second would seem to be of the right 
order of magnitude to account for the observed reception of highly penetrating 
radiation; we notice at once that it is of the same order of magnitude as the 
rate of generation of fairly young stars—for Sirius, for instance, G — 29; for 
Capella, G — 50. We shall return to a fuller discussion of this fact later; for 
the present we note that the agreement as regards order of magnitude confirms 
our conception of stellar energy originating in the annihilation of matter. 
The wave-length of the observed radiation might be expected to disclose 
its source. If the radiation originated in the annihilation of matter, the 
minimum wave-length ought to be 1*31 x 10 -13 cms., the energy of a quantum 
being 0*00150 ergs, and that of an electron 940 million volts. But the only 
quantity susceptible of direct measurement is the penetrating power of the 
radiation, and the theoretical relation between this and wave-length is still 
uncertain. The original formula of Compton and a later formula of Dirac and 
Gordon agreed in assigning a wave-length far greater than 1*31 x 10~ 18 cms. 
to the observed radiation, but a more recent investigation of Klein and Nishina* 
* Nature, cxxn. (1928), p. 399.