32 
ASTRONOMY: F. H. SEARES 
The last two columns of the table give the weighted mean differences 
between the Mount Wilson color-indices and the color-values derived 
from the exposure-ratios, and the number of stars included in each 
group. 
The close agreement in the two series of results shows clearly enough 
the usefulness of the exposure-ratio method, and indicates that the 
photographic and photo visual magnitude scales for the North Polar 
Standards are substantially in the proper relation to each other. The 
agreement affords no test of the presence of errors affecting the two 
scales equally; but there can be no important divergence of either scale 
relative to the other, for the differences in the color-values derived by 
the two methods would then show a progressive change with magnitude. 
In general, the precision of the method of exposure-ratios is excellent. 
For example, the probable error of a color-index derived from a single 
exposure-ratio is about 0.07 magnitudes. This value is based upon the 
results for the 36 stars for which there are five or more separate deter- 
minations, and speaks well for the uniformity of different plates of the 
same emulsion. Puzzling abnormalities have occasionally occurred, but 
the cases thus far met with are perhaps to be attributed to causes 
external to the plates themselves. Each emulsion will undoubtedly 
require a special investigation for the determination of factors which 
will reduce it to the standard curve connecting exposure-ratio and color- 
index, but this should not be a matter of any great difficulty. Never- 
theless, the limitations of the method can not be fixed until a number of 
questions of this sort have been examined. 
In the meantime, however, it may be noted that the colors of the 
Polar Standards, brighter than the 13th magnitude, have been deter- 
mined to about the same precision as was reached in the investigation 
of the magnitude scales, with an expenditure of time and labor which 
was perhaps a tenth of that required for the earHer investigation. All 
of the observational data for the present investigation, including about 
80 photographs and nearly 400 separate determinations of color, were 
obtained during three nights with a total of less than 22 hours observ- 
ing time. 
One of the most interesting consequences of this recent determination 
of the colors of stars near the Pole is to be found in the confirmation it 
affords of a result previously announced,^ namely, that there are no 
faint stars in this region with negative or small positive color-indices. 
The lower limit of the color-index gradually increases as the fainter 
stars are approached, and at the 16th photographic magnitude its value 
is of the order of +0.5 magnitude. Although this state of affairs was 
