X. 
314 ASTRONOMY: F. H. SHARES 
Hertzsprung has determined by an entirely different method — that of 
effective wave-lengths — the colors of nearly 200 stars in the cluster 
N. G. C. 1647. These can be expressed as color indices and compared 
with similar results derived directly from photographic and photo- 
visual magnitudes. The agreement or disagreement of the two series of 
values immediately checks the relative errors of the scales. 
To execute this comparison, the polar scales were transferred to the 
region of the cluster by 10 plates of dupHcate exposure — 5 for each 
scale. All possible care was taken to avoid errors in the zero points, 
for uncertainties here also enter to their full amount into the color 
indices. 
In this manner color values were obtained for about 50 stars between 
magnitudes 11 and 14.5, which had also been observed by Hertzsprung. 
There is some uncertainty involved in the transformation of the effective 
wave-lengths into color indices ; but it is not likely that the mean differ- 
ence in the two series of values exceeds a tenth of a magnitude, and there 
is some evidence that it is even less. The relative errors of the scales 
between the sixth magnitude, which defines the international zero 
point, and the thirteenth or fourteenth magnitude can therefore scarcely 
exceed this limit. 
Comparisons of the individual scales for the Pole with the results 
of other observers are also important in their indications. The only 
other investigation covering the entire range of brightness is that of 
the photographic scale carried out at the Harvard Observatory. With 
proper allowance for color, the Harvard and Mount Wilson results are 
in close agreement, that is, the scales are parallel, from the tenth to the 
fifteenth magnitude. For the fainter stars there is a large divergence, 
which has arisen from differences in the method of reduction (the Har- 
vard scale for the fainter stars is based upon Mount Wilson plates). 
For the bright stars there is also a divergence, amounting to about 
6%, whose origin is not yet fully explained. 
Other investigations of the photographic scale have been made at 
Greenwich and Potsdam. These extend from the ninth to the sixteenth 
or seventeenth magnitude; after correction for color to reduce to the 
system of the reflector, both show a close accordance with the Mount 
Wilson results. In addition, the bright stars between the fourth and 
eighth magnitudes have been observed at Gottingen and at the Yerkes 
Observatory. These results are also in close agreement with the Moimt 
Wilson scale. 
The material for the photovisual scale is less abundant. Visual 
magnitudes of the Polar Sequence stars have been determined at Har- 
