THE COEFFICIENT OF OPACITY 
243 
167. I have considered elsewhere* the emission and absorption of 
radiation at encounters of free electrons with one another. For Capella 
the absorption coefficient due to this process was found to be k = -038, 
so that the contribution is negligible. My investigation, however, did not 
take account of the interference of the waves from the two accelerated 
electrons. Rosseland has pointed out that this interference reduces the 
emission almost to zero. The algebraic sum of the accelerations of the two 
charges is zero, and it is well known in classical theory that this is the 
condition for the absence of radiation. 
Scattering of radiation by the free electrons must be included in the 
opacity. It is shown in (53-5) that the contribution from this source is 
only 0-2. 
Complex processes such as the simultaneous encounter of three bodies 
(ions or electrons) could be considered; but these would give an absorption 
varying as the square of the density, and cannot constitute an important 
part of the astronomical absorption which is found to be proportional to 
the first power of the density. 
The possible radiation from ions encountering one another will not be 
important. The velocities of the ions are comparatively small, their high 
charges ward off collisions, and they can scarcely come close enough to 
disturb the remnants of their electron systems. 
It seems that we cannot discover any other important source of 
absorption to supplement that of which Kramers’ theory claims to be a 
full treatment. 
Effect of Chemical Constitution. 
168. Denote the opacity calculated from the observed mass and 
luminosity by k a and the opacity calculated by Kramers’ theory by k t . 
As the comparison stands at present k a = 10 k t . By combining (158-2), 
(87-1) and (90-1) we obtain 
= 0-0443 
k a 
fe 2 Zff L ß 1 
Chu 0 A M (1 - ßY (1 + f) T o i 
(168-1), 
where a has been taken as 2-5 in the numerical factor. 
By taking an element heavier than iron the factor Z 2 /A is increased. 
It might seem that the discrepancy between k t and k a could be partly 
accounted for by supposing that the stars are composed mainly of the 
heaviest elements. This hypothesis turns out to be useless because the 
assumption of heavier elements involves consequential changes in ¡3 which 
neutralise the improvement. 
For example, if Capella were made of gold Z 2 /A would be 2-6 times 
greater than for iron. But the molecular weight for completely ionised 
Monthly Notices, 84, p. 117.