104 STELLAR NUMBERS AND DISTANCES. 
larger nor smaller than those in our nearer neighborhood. Both con- 
clusions seem inevitable should the facts turn out, on closer investiga- 
tion, to be as above stated. A regular increase in the numbers of the 
successive photometric orders of stars, tallying with the increased cub- 
ical contents of the successive spheres of which the radii are the theo- 
retical mean distances of those same orders, affords strong, if not de- 
monstrative, evidence of a corresponding real penetration of space.* 
And since the sequence continues unbroken down just to the ninth 
magnitude, we see that the galactic condensations of ninth magnitude 
stars can not be situated nearer to us than their brightness would lead 
us to suppose—can not, in other words, be stars on a lower than the 
ordinary level of luster. 
It is tolerably certain however that the denser star clouds of the 
Milky Way lie far beyond ninth magnitude distance. The ground for 
this assertion is not the apparent minuteness of their components, but 
the singular fact, adverted to by Argelander, that, in the divided Milky 
Way, running from Cygnus to the Centaur, the shining branches are 
nearly on a par with the dark rift separating them as regards the dis- 
tribution of stars even fainter than the ninth magnitude. The nebu- 
lous effect to the eye distinguishing the branches is then presumably 
due to more remote collections. As to the further limits of these we 
know as yet nothing, except that Herschel’s gauge numbers left it to 
be inferred that ‘‘ thinning-out” had become marked before the attain- 
ment of fourteenth magnitude distance. On these and similar subjects 
enlightenment may be hoped for through the judicious use of means 
already at hand. 
For simple star-counts, we have only to substitute star-counts by 
magnitudes over selected areas of the sky.t The relative numbers of 
the photometric ranks can hardly fail to give highly valuable indica- 
tions as to real distribution; provided only that the assumption of a 
general uniformity in the brightness of the stars be valid. Not (it need 
scarcely be said) of a uniformity such as to preelude any extent of in- 
dividual variety; all that need be supposed is that the average size of 
a Star remains constant throughout sidereal space. This hypothesis 
has far more probability in its favor than any other which could be set 
up instead of it; though it may receive corrections as our inquiries ad- 
vance. 
The photometric classification of small stars is one of the many 
branches of sidereal science which will henceforth be prosecuted only 
with the assistance of the camera. Visual methods are inadequate and 
insecure. Those by photography, it is true, have also their difficulties, 
~The idea of determining distance by distribution seems to have presented itself 
to Dr. Gould in 1874. See American Journal of Science, vol. V1. 
tThis plan was first suggested by Prof. Holden in 1883, as a mode of investigating 
the composition of star-groupings (‘‘Washburn Publications,” vol. u, p. 113), 
Counts with varied telescopic apertures gayeehim the numbers in the successive 
photometric ranks. We believe that a photographic method of determining them 
has since been adopted by him. 
rl 
