304 Sir William Herschei/s observations and experiments 
brightness. Now, as it was thought convenient to arrange 
all the stars which in fine weather may be seen by the eye 
into seven classes, the brightest were called of the first, and 
the rest according to their gradually diminishing lustre, of the 
2d, 3d, 4th, 5th, 6th, and 7th magnitudes. Then, since it is 
evident that we cannot mean to affirm that the stars of the 
5th, 6th, and 7th magnitudes are really smaller than those of 
the 1st, 2d, or 3d, we must ascribe the cause of the difference 
in the apparent magnitudes of the stars to a difference in their 
relative distances from us ; and on account of the great num- 
ber of stars contained in each class, we must also allow that 
the stars of each succeeding magnitude, beginning from the 
first, are one with another farther from us than those of the 
magnitude immediately preceding. It may therefore be said, 
that since in our catalogues the magnitudes are added to the 
two dimensions which give the superficial place of the stars, 
we have also at least a presumptive value of the third dimen- 
sion; but admitting that the naked eye can see stars as far 
from us as those of the seventh magnitude, this presumptive 
value, which can only point out their relative situation, will 
afford us no information about the real distance at which they 
are placed. 
II. Of a standard by which the relative arrangement of the stars 
may be examined. 
It is evident, that when we propose to examine how the 
stars of the heavens are arranged, we ought to have a certain 
standard of reference ; and this I believe may be had by com- 
paring their distribution to a certain properly modified equa- 
lity of scattering. Now, the equality I shall here propose, 
