Distant Stars 
9 
6-9] 
part as much light as the sun, while the thin curve refers to stars which emit 
less than a thousandth part of the light of the sun (see Table IV, p. 33). 
8 . If all the stars were known we should expect the number of stars per 
cubic parsec to approach to a definite limit as we receded from the sun. The 
curves in fig. 1 shew no evidence of such a limit, so that we must conclude 
that nothing like all the stars in the neighbourhood of the sun are known. 
Very faint stars can only be observed if they are quite near to the sun. 
Disregarding very faint companions of brighter stars, only six stars are known 
which emit less than a thousandth part of the light of the sun, and of these 
five are within 3 parsecs of the sun. This explains why the curve of faint 
stars runs down very rapidly after about 3 parsecs. 
The brighter stars can be observed at greater distances. Actually the 
curye giving the density of bright stars shews no appreciable falling off up to 
a distance of about 4 parsecs, suggesting that practically all the bright stars 
within this distance are known. The curve suggests that the density of dis 
tribution of such stars is of the order of 0*05 stars per cubic parsec, or one 
bright star to every 20 cubic parsecs. 
It is far more difficult to estimate the true density of distribution of the 
faint stars. To make a convenient figure for future calculations, we may 
suppose this to be the same as that for bright stars, so that the density of 
distribution of stars of all kinds near the sun is one to every 10 cubic parsecs, 
this requiring 18 stars actually to exist within 3| parsecs of the sun, of which 
only 15 are known. These 18 stars are of course additional to the sun itself. 
In a statistical discussion such as the foregoing we must be careful not to 
count the sun in our statistics, since its presence is an essential to our being 
able to make the calculation at all. Our procedure is in effect to draw a 
small sphere round the sun and discuss the density of distribution of stars in 
the space bounded by this sphere on the one side and by a larger sphere of 
variable radius on the other. 
Distant Stars. 
9 . We have seen that the direct method of parallactic measurement has 
only succeeded in surveying the universe with tolerable accuracy to a distance 
of about 3£ parsecs, or let us say 10 light-years, from the sun. No doubt this 
distance will be extended in time, but there is a natural limit to the power 
of the parallactic method. At best it can only measure the distance of a star 
whose parallactic motion can be projected on a background of far more 
distant stars, so that it must inevitably fail for the most distant stars of all. 
In actual fact it is bound to fail long before this. 
The parallactic motion of a star at a distance of 100 parsecs, or 325 light- 
years, consists in the description of a circle or ellipse whose apparent size in 
the sky is that of a pin-head held at a distance of 5 miles. The apparent