The data are now available for deriving a value for the order of the
density of space. This is accomplished by means of the formulae for the
numbers of nebulae to a given limiting magnitude and for the distance
in terms of the magnitude. In nebulae per cubic parsec, the density is
$\begin{align}
\log \rho & = \log N - \log V\\
& = (0.6 m_{T} - 4.45) -\ log\frac {4π}{3} - 3(4.04 + 0.2 m_{T})\\
& = -17.19
\end{align}$ (11)
This is a lower limit, for the absence of nebulae in the plane of the
Milky Way has been ignored. The current explanation of this phenomenon
in terms of obscuration by dark clouds which encircle the Milky Way
is supported by the extra-galactic nature of the nebulae, their
general similarity to the galactic system, and the frequency with
which peripheral belts of obscuring material are encountered among the
spirals. The known clouds of dark nebulosity are interior features of
our system, and they do not form a continuous belt. In the regions
where they are least conspicuous, however, the extra-galactic nebulae
approach nearest to the plane of the Milky Way, many being found within
10°. This is consistent with the hypothesis of a peripheral belt of
absorption.
The only positive objection which has been urged to this explanation
has been to the effect that the nebular density is a direct function of
galactic latitude. Accumulating evidence[26] has failed to confirm this
view and indicates that it is largely due to the influence of the great
cluster in Virgo, some 15° from the north galactic pole. There is no
corresponding concentration in the neighborhood of the south pole.
If an outer belt of absorption is assumed, which, combined with the
known inner clouds, obscures extra-galactic nebulae to a mean distance
of 15° from the galactic plane, the value derived for the density of
space must be increased by nearly 40 per cent. This will not change the
order of the value previously determined and is within the uncertainty
of the masses as derived by Öpik’s method. The new value is then
ρ = 9×10^{–18} nebulae per cubic parsec. (12)
The corresponding mean distance between nebulae is of the order of
570,000 parsecs, although in several of the clusters the distances
between members appear to be a tenth of this amount or less.
The density can be reduced to absolute units by substituting the value
for the mean mass of a nebula, 2.6×10^8 ☉. Then, since the mass of
the sun in grams is 2×10^{33} and 1 parsec is 3.1×10^{18} cm,
ρ = 1.5×10^{–31} grams per cubic centimeter. (13)
This must be considered as a lower limit, for loose material scattered
between the systems is entirely ignored. There are no means of
estimating the order of the necessary correction. No positive evidence
of absorption by inter-nebular material, either selective or general,
has been found, nor should we expect to find it unless the amount of
this material is many times that which is concentrated in the systems.