n to the fuller discussion of
this extension. For the present it is sufficient to assume these values.
The whole system of the Galaxy then has a volume of 200 million cubic
siriometers. Suppose further that the total number of stars in the
Galaxy would amount to 1000 millions, a value to which we shall also
return in a following chapter. Then we conclude that the average number
of stars per cubic siriometer would amount to 5. This supposes that the
density of the stars in each part of the Galaxy is the same. But the sun
lies rather near the centre of the system, where the density is
(considerably) greater than the average density. A calculation, which
will be found in the mathematical part of these lectures, shows that the
density in the centre amounts to approximately 16 times the average
density, giving 80 stars per cubic siriometer in the neighbourhood of
the sun (and of the centre). A sphere having a radius of one siriometer
has a volume of 4 cubic siriometers, so that we obtain in this way 320
stars in all, within a sphere with a radius of one siriometer. For
different reasons it is probable that this number is rather too great
than too small, and we may perhaps estimate the total number to be
something like 200 stars, of which more than a tenth is now known to the
astronomers.

We may also arrive at an evaluation of this number by proceeding from
the number of stars of different apparent or absolute magnitudes. This
latter way is the most simple. We shall find in a later paragraph that
the absolute magnitudes which are now known differ between -8 and +13.
But from mathematical statistics it is proved that the total range of a
statistical series amounts upon an average to approximately 6 times the
dispersion of the series. Hence we conclude that the dispersion
([sigma]) of the absolute magnitudes of the stars has approximately the
value 3 (we should obtain [sigma] = [13 + 8] : 6 = 3.5, but for large
numbers of individuals the total range may amount to more than 6
[sigma]).

As, further, the number of stars per cubic siriometer with an absolute
magnitude brighter than 6 is known (we have obtained 8 : 4 = 2 stars per
cubic siriometer brighter than 6m), we get a relation between the total
number of stars per cubic siriometer (_D_0_) and the mean absolute
magnitude (_M_0_) of the stars, so that _D_0_ can be obtained, as soon
as _M_0_ is known. The computation of _M_0_ is rather difficult, and is
discussed in a follow