DIFFUSE MATTER IN SPACE 
391 
In the calcium chromosphere the back-thrust of the radiation from the 
higher part on the atoms of the lower part was of great importance; the 
net flow of radiation outwards was the same at all heights so that the force 
of radiation pressure was practically constant in all parts. In the nebula 
the radiation absorbed is re-emitted mostly in wave-lengths to which the 
nebula is transparent and there is less back-thrust. Consequently the 
force of radiation pressure decreases along the radius according to the 
ordinary absorption law. This seems to permit a stable annular distribution; 
a particle falling from the midst of the nebula would be sent back again 
by the increased radiation pressure; a particle moving towards the out 
side would fall back under the reduced radiation pressure. 
I doubt, however, whether these considerations as to the behaviour 
of radiation pressure are of much importance because, as already stated, 
the hydrogen which is conspicuous in planetary nebulae is not likely to be 
much influenced by it. 
Accretion of Stellar Mass. 
266. A star travelling through the diffuse matter in interstellar space 
must sweep up the atoms in and near its track and thereby gain mass. 
If we neglect the encounters of the atoms with one another the problem 
is very similar to that of the capture of an electron by hitting the nucleus. 
Let V be the relative velocity of the star and the cloud and R the radius 
of the star; we have first to find the radius a of the apparent target corre 
sponding to a true target R. Conservation of angular momentum and of 
energy gives crV = RV', 
V' 2 _ V 2 = 2GM/R, 
V' being the velocity of the atom as it grazes the star. Eliminating V', 
o* 
R 2 
2 GM 
" 1 + RV 2 
.(266-1). 
In practical cases 2GM/RV 2 is large so that with sufficient accuracy 
a 2 /R 2 = 2GM/RV 2 . 
Hence the amount of matter swept up per second is 
dM/dt = 7ra*Vp = 27 tGMR p /V (266-2), 
p being the density of the diffuse cloud. 
As in § 257 we adopt a density of 1-66. lO“ 23 corresponding to 1 atom 
per cu. cm. of atomic weight 10. For the sun V — 2. 10 6 , so that 
dM/dt = 4-8.10 8 gm. per sec. 
The loss of mass by radiation is 
L/c 2 = 4-2.10 12 gm. per sec.