STELLAR NUMBERS AND DISTANCES: 
BY MEANS OF PHOTOGRAPHIC STAR GAUGING. * 
The mere equal-surface counting of the stars visible with the same 
instrument in different sections of the sky gives results open to mis-in- 
terpretation. Admirable in itself, the method fails because it encoun- 
ters what we may call “‘ systematic errors” in the distribution of the 
stars. With incidental anomalies it is fully competent to deal; they 
should, on a large average, be mutually compensatory; but it breaks 
down before the clustering tendency which pervades, more or less mark- 
edly, the entire sidereal system. Not only are certain parts of space 
more crowded than others, but the crowded parts are related according 
to an obvious plan. They do not occur casually. Their effect is then 
heightened, instead of being eliminated, by multiplied observations. 
The present resources of science, however, seem to offer the means of 
discriminating, to some extent, between real crowding and the simple 
extent of star-strewn space. Although the total number of the stars vis- 
ible in each case with the same telescope might be precisely the same, 
their relative numbers, counted by magnitudes, would in all probability 
be very different. In a stratum, supposing the distribution of the stars 
equable and their size uniform, their numbers should be nearly quad- 
rupled at each descent of a magnitude. This, of course, is an ideal 
law of progression which we can not expect to find anywhere strictly 
obeyed; but even approximate conformity to it must be held to indicate 
with tolerable certainty that the lessening ranks of the stars are, on 
the whole, at distances from us corresponding with their light. Now it 
is approximately conformed to by the stellar multitude down to the 8.9 
magnitude over the general expanse of the sky, as well as over the zone 
of the Milky Way. Butin that zone stars of the ninth and higher mag- 
nitudes very much exceed their due numerical proportions; in other 
words, they are physically, no less than optically, condensed. 
From these circumstances two very important inferences may be de- 
rived: First, that the lower margin of the galactic aggregations lies at 
a distance from us corresponding roughly to the mean distance of a 
ninth magnitude star, costing light some fourteen hundred years of 
travel; next, that the aggregated objects are average stars, neither 
hes Bae a 1 es = 
: * From Nature, August 8, 1889, vol. XL, pp. 344-346. 
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