116 
ASTRONOMY: H. N. RUSSELL 
Proc. N. a. vS. 
The numerical factor is independent of the physical units which are 
employed. The factor q is introduced to take account of the complica- 
tions which occur when the size of the particle becomes comparable with 
the wave-lengths of light. ^ For particles more than two or three wave- 
lengths in diameter q is sensibly equal to unity. For smaller particles 
it increases and is a maximum, 2.56, when the circumference of the parti- 
cle is 1.12 times the wave-length. It then rapidly diminishes and becomes 
nearly equal to 14/3 X (27rf/X)^ for particles of less than half this diameter. 
The ratio g/r is a maximum, 2.42, when the circumference equals the wave- 
length. 
For clouds of the same mean density d the opacity reaches a sharp max- 
imum when the particles are of this size. At the same time the absorption 
changes from the non-selective type to the selective type, varying as 
X""*. For visual light the maximum opacity occurs when the radius is 
0.086 p. A cloud of particles of this size, and of the density of rock (2.7), 
will exert an absorption of one magnitude if it contains only 1 /86 of a milli- 
gram of matter per square centimeter of cross-section, regardless of its 
thickness. If the particles are of half this size, or smaller, the selective 
absorption is almost as complete as for a gas, but may be nearly 100 million 
times as great. 
Obscuration of light in space, therefore, whether general or selective 
with respect to wave-length, will be produced mainly by dust particles 
a few milHonths of an inch in diameter, unless such particles form a negli- 
gible proportion by weight of the obscuring cloud. 
3. It is just these particles, however, which will be most influenced by 
the pressure of the radiation of the stars. Calculations from more ac- 
curate data confirm Schwarzchild's conclusion that for a particle of the 
optimum size and the density of water, the repulsive force of the sun's 
radiation is about ten times the gravitational attraction, and show that 
for stars of the same brightness, but other spectral types, the radiation 
pressure will be about two-thirds as great for Class M and increase for 
the whiter stars, till for Class B it is fully ten times as great as for solar 
stars. 
Dwarf stars will hardly repel dust at all, but giant stars, and especially 
the very luminous one of Class B, will repel it very powerfully. Only 
the coarser particles can come near such a star — the finer ones being driven 
away. This selective removal, from the vicinity of bright stars, of the 
particles which are most efficient in cloud formation, may explain the 
fact that the luminous portions of these dark nebulae, though centered 
upon stars, do not brighten up in their immediate neighborhood as much 
as might have been anticipated. 
The finest dust must continue to be repelled by the stars, whatever 
their distance. It may congregate to some degree in interstellar regions, 
