13 
n-13] Distribution of Stars in Space 
at the rate of about one star per 10 cubic parsecs. Known stars establish 
this uniform distribution up to less than 4 parsecs. After this the density 
appears to fall off so long as we take account only of stars whose distances are 
known, but this is merely because most of the stars beyond 4 parsecs have 
not had their distances measured. 
It is nevertheless quite obvious that the uniform distribution of stars 
which prevails in the near neighbourhood of the sun cannot go on for ever. 
If it did, the sky would exhibit a uniform blaze of light, since, in whatever 
direction we looked, we should in time come to a star. Moreover, the infinite 
mass of stars would produce gravitational forces of infinite intensity, and these 
would cause the sun and stars to move with infinite speed. Actually the 
comparative faintness of starlight and the observed finite velocities with which 
the stars move through space, fix definite calculable limits to the extent of 
the field of stars surrounding the sun. The limit set by the speed of motion 
of the stars will be discussed in a later chapter, but we may consider at once 
the limit set by the observed brightness of the sky. 
The naked eye can see some 6000 stars in both hemispheres of the sky. 
A one-inch telescope has about five times the aperture of the naked eye, and, 
because it has 25 times the area, admits 25 times as much light. If any star 
can just be seen with the naked eye, a similar star at five times the distance 
ought to be just visible in a one-inch telescope. In brief, we may say that 
the range of vision of the one-inch telescope for a given object is five times as 
great as that of the naked eye because its aperture is five times as great, and 
in general the ranges of vision of different telescopes for similar objects are 
proportional to their apertures. 
Thus if the distribution of stars around the sun extended uniformly to 
infinity, the number of stars visible in different telescopes would be proportional 
to the cubes of their apertures. A one-inch telescope would shew 5 3 , or 125, 
times as many stars as the naked eye, and, as the naked eye can see 6000 
stars, a one-inch telescope should shew 750,000 stars. Actually it only shews 
about 120 , 000 . Part of the discrepancy no doubt arises from the loss of light 
caused by passing through the three lenses of the telescope. If this could be 
eliminated, a one-inch telescope would enable us to see somewhat more than 
the 120,000 stars which it actually shews, but it would not shew as many as 
750,000. A five-inch telescope ought in the same way to shew 125 times as 
many stars as a one-inch telescope but the ratio actually observed is far less 
than this. The explanation is that the remaining stars are not there to see; 
somewhere within the range of a five-inch telescope the star field surrounding 
the sun must begin to thin out quite perceptibly. 
This method of investigation can be extended and refined almost indefi 
nitely. On examining the numbers of stars visible in different directions in 
space, the star field is found to thin out differently in different directions; a 
detailed study gives particulars of the way in which the star field thins out