STELLAR NUMBERS AND DISTANCES. 105 
‘not yet completely vanquished; they will, however, evidently prove 
manageable. Prof. Pickering is tentatively establishing methods in 
photographic photometry which will doubtless before long be brought 
to perfection. They depend mainly upon comparisons of stellar im- 
pressions upon any given plate, exposed under known conditions, with 
standard impressions of standard stars obtained with varied exposures 
or apertures. For the purpose we have in view, accidental errors of 
estimation, even if very large in amount, are of no importance. What 
is essential is that the integrity of the series should be preserved—that 
the proportionate change of light from one magnitude to the next should 
remain invariable from the first term to the last. The realization of 
this aim, now virtually attained, is one of the most weighty services 
rendered to astronomy by the sensitive plate. 
We may now describe the process of photographic star-gauging. It 
consists in the enumeration, by magnitudes or half magnitudes, of the 
stars down, say, to the fifteenth magnitude, self-pictured from distinet- 
ively situated patches of the sky. Each such area should be wide 
enough to insure the elimination of minor irregularities in distribution; 
but a single large field would often suffice to show the characteristic 
grouping of the smaller telescopic stars. 
The Milky Way would naturally be the first subject of inquiry; and 
the comparison of several plates taken in different sections of its course 
might be expected to yield data of great significance as regards its 
constitution. From simply calling over the muster-ro]l by orders of 
brightness of the stars contained in them, answers may be derived to 
the following questions: 
(1) How far does the regular sequence of increasing numbers extend? 
That is, down to what grade of brightness do the stars continue nearly 
to quadruple with each additional magnitude? 
(2) Is the progression interrupted by defect or excess, or by each alter- 
nately? In other words, does the stellar system embrace systematic 
vacancies as well as systematic groupings? 
(3) Supposing an accumulation of stars to set in at a definite stage of 
space-penetration, where does it stop? Down to what magnitude is 
the augmented ratio of increase maintained? 
(4) Are there symptoms of approaching total exhaustion of the stel- 
lar supplies beyond? 
These should be found in a concurrent decrease of density with 
brightness, “‘ density ” being understood as the proportion of the num- 
bers present to the space theoretically available for stars of a given 
magnitude. For one of two things seems certain: either the thinning 
fringe of stars is composed of really small objects interspersed among 
larger ones, or of average stars at average distances from us, but fur- 
ther and further apart from cach other. In the first case the system 
ends abruptly; in the second, it is,as it were, shielded by outliers from 
the absolute void. 
