14 The Astronomical Survey of the Universe [ch. i 
in any given direction. The value of such investigations has been recognised 
since the time of the Herschels. The method of “star-gauges,” or counts of 
stars of different brightnesses in different areas of the sky, instituted by 
Sir William Herschel* and extended to the southern hemisphere by his son, 
Sir Johnf, first established that the system of stars surrounding the sun is of a 
symmetrical flattened shape like a watch or a ship’s biscuit. Investigations 
on the same lines have been made by Seeliger, Chapman and Melotte, 
Kapteyn, Seares and van Rhijn and others. 
14. The Galactic System. We have seen that stars are scattered in the 
neighbourhood of the sun, at the rate of about one star to every 10 cubic 
parsecs. We can frame a definite problem by inquiring how far from the sun 
we should have to go to find the star field thinned out to any definite fraction 
we please of this density, say, one hundredth part, or one star per 1000 
cubic parsecs. In 1922 KapteynJ gave a simple answer to this question; it is 
far from absolutely accurate, but its simplicity more than compensates for its 
inexactness. 
Looking at the sky ,on a clear night, we see the band of faint stars known 
as the Milky Way. This band forms very approximately a great circle in the 
sky, so that the plane through this circle which is called the galactic plane 
passes very nearly through the earth, and divides the sky into two approxi 
mately equal halves. Now Kapteyn found that if we go for a distance of 
8465 parsecs, or about 27,000 light-years, in any direction whatever in the 
galactic plane, the star-density is reduced to one-hundredth of its value in 
the regions surrounding the sun. But to reach a corresponding reduction of 
density in other directions, we need not travel so far; the same reduction of 
density is reached after travelling only 1660 parsecs, or 5400 light-years, in a 
direction at right angles to the galactic plane. The various points in space 
at which the star-density is one-hundredth of that near the sun, lie, according 
to Kapteyn, on a much flattened spheroid. The cross-section of this spheroid 
in the plane of the galaxy is a circle of radius equal to the 8465 parsecs 
already mentioned, but its semi-minor axis, which is at right angles to this 
plane, is of length only 1660 parsecs. 
15. This particular spheroid maps out the regions in space at which the 
star-density is one-hundredth of that near the sun. If we had selected any 
other fraction in place of one-hundredth, Kapteyn finds that we should still 
have obtained a much flattened spheroid whose axes would have been different 
from those just mentioned, although still in the same proportion of 5102 to 1. 
Kapteyn has estimated the axes of these spheroids for ten different densities, 
with the results shewn in the following table: 
* “ On the Construction of the Heavens,” Phil. Trans, lxxxv. (1785) or Set. Papers , i. p. 223. 
f Results of Astronomical Observations made during the years 1834-8 at the Cape of Good Hope 
(1847), p. 373. 
X Astrophys. Journal, nv. (1922), p. 302 or Mount Wilson Contribution, No. 230.