3o8 Sir W illiam Herschei/s observations and experiments 
The catalogue contains 1161 stars of the 5th magnitude, 
whereas the 5th order of distances has only room for 602. 
Of the 6th magnitude the catalogue contains not less than 
6103 stars, but the 6th order of distances will admit only 
866 . 
And lastly, the same catalogue points out 6146 stars of the 
7th magnitude, while the number of stars that can be taken 
into the 7th order of distances is only 1178. 
The result of this comparison therefore is, that if the order 
of magnitudes could indicate the distance of the stars, it 
would denote at first a gradual, and afterwards a very abrupt 
condensation of them ; but that, considering the principle on 
which the stars are classed, their arrangement into magni- 
tudes can only apply to certain relative distances, and show 
that taking the stars of each class one with another, those of 
the succeeding magnitudes are farther from us than the stars 
of the preceding order. 
IV. Of a criterion for ascertaining the Profundity , or local situ- 
ation of celestial objects in space. 
It has been shown that the presumptive distances of the 
stars pointed out by their magnitudes can give us no infor- 
mation of their real situation in space. The statement, how- 
ever, that one with another the faintest stars are at the great- 
est distance from us, seems to me so forcible, that I believe 
it may serve for the foundation of an experimental investi- 
gation. 
It will be admitted, that the light of a star is inversely as 
the square of its distance ; if therefore we can find a method 
