ASTRONOMY: F. H. SHARES 
523 
points, which at present are likely to prove troublesome. With care 
satisfactory results can be obtained, but the operation is tedious at 
best, and the uncertainties are greatest for just those objects whose 
colors we should like most to know — the faint stars. 
The third method, although spectroscopic in character, gives real 
values of the color, and not merely the spectral type. It is also free 
from the zero-point and scale errors which complicate precise determi- 
nations of the color-index; and although subject to its own peculiar errors, 
these do not seem to be very serious. The chief objection is that the 
method is wasteful of light, the limiting magnitude for the determi- 
nation of effective wave-lengths being about three magnitudes less than 
that for direct photography If a large telescope is to be used, the size 
and weight of the objective grating are also objectionable and make it 
difficult to pass quickly from the determination of effective wave- 
lengths to other kinds of observational work. 
The following method seems to offer some advantages, and has 
also the merit of simplicity and convenience. The limiting magni- 
tude to which it can be applied should be about the same as that for 
which photovisual magnitudes can be determined. It consists simply 
in determining the ratio of exposure-times necessary to produce photo- 
graphic and photovisual, or more briefly blue and yellow, images of the 
same size. For convenience, and also as a matter of precision, the 
images should be on the same plate. An isochromatic plate exposed 
behind a yellow filter registers the yellow image as usual The same 
plate used without filter gives the blue image. This will include to 
some extent the effect of the longer wave-lengths, but owing to the 
relatively small sensitiveness of the isochromatic plate to the yellow 
and orange rays, the shorter wave-lengths will still be of predominating 
influence. 
In the simplest case there will be for each star one yellow image and a 
series of three or four blue images, with the exposure times for the 
latter increasing in geometrical progression — as a constant ratio, 2 
seems to be the most convenient. The diameters of the blue images, 
or their scale readings,^ are plotted against the logarithm of the exposure, 
and from the nearly linear curve thus derived can be read the exposure 
time for a blue image of the same size as the yellow image. The ratio 
of the interpolated exposure to that which produced the yellow image — 
the exposure ratio — compared with similar ratios for stars of known 
color, gives at once the color-index or color-class.^ 
Various modifications necessary to meet special conditions immedi- 
ately suggest themselves; but whatever the details, consideration should 
