388 
DIFFUSE MATTER IN SPACE 
the absorption. The energy of emission of the Balmer series is in fact 
derived from absorption in the principal series of hydrogen. Dark lines 
of the latter series will cross the spectrum of the stimulating stars but they 
are in the far ultra-violet beyond the region which can be observed*. 
Probably the Orion Nebula is nearly transparent to Balmer radiation in 
spite of the fact that it is emitting it, so that the brightness is a direct 
measure of the gross emission—a very unusual simplification. (This may 
be contrasted with the chromosphere, where the brightness is by no means 
a measure of the number of emitting atoms since there is high internal 
absorption.) Probably a great deal of interesting information as to the 
density of the hydrogen distribution and the probabilities of transition 
between the different quantised states of the atom, etc. could be obtained 
from absolute measures of the emission of the Orion Nebula. 
We naturally assume that the diffuse and dark nebulae are local 
condensations of the general cloud of interstellar matter revealed by the 
fixed calcium lines. It is, however, by no means easy to account quantita 
tively for the great opacity of the dark nebulae. Most theories lead to an 
extravagantly high mass, as has been pointed out by A. Pannekoek. We 
may take as typical the dark nebula in Taurus studied by Pannekoekf. 
He found an obscuring patch of area 140 square parsecs, which in general 
reduced the light of the stars behind it by 2 magnitudes. Interpreting the 
darkening as Rayleigh scattering he found a mass of at least 4.10 9 x O. 
Adopting electron scattering the required mass is less, but the difficulty 
is not wholly removed. To reduce by 2 m we require 10 gm. per sq. cm. of 
fully-ionised material or say 200 gm. per sq. cm. of singly-ionised material. 
The whole mass is then 140 x 200 x (3.10 18 ) 2 = 2-5 .10 41 gm. = 120 million 
suns. If the depth is taken as 12 parsecs (corresponding to the transverse 
dimensions) the density is 5.10 -18 gm. per cu. cm. or 500 times our 
estimate of p 0 in § 260. A star approaching this nebula would, under its 
gravitational attraction, acquire a velocity of 300 km. per sec. at the 
boundary and 350 km. per sec. on reaching the centre. The mass is clearly 
too high. To avoid abnormal stellar velocities the mass should be 
divided by 100. Accepting reduction by a factor T ^, the density is 
about 1000 times our assumed density of ordinary interstellar matter, 
and the mass is 2 gm. per sq. cm. It is doubtful if 2 gm. per sq. cm. can 
give the observed opacity in any other way than by solid obstruction, 
e.g. by particles like sand. The problem of the masses of the dark nebulae 
is fraught with difficulty, and we do not venture to suggest any conclusion. 
* Our upper atmosphere is practically opaque to radiation of wave-length less 
than 2850 A, and even the solar spectrum cannot be observed beyond this limit. 
f Proc. Akad. van Wetenschappen, Amsterdam, 23, p. 720 (1920).