312 
ASTRONOMY: F. H. SEARES 
which were 2 minutes each: (1) intermediate stars, full aperture; (2) 
bright star with reduction of intensity, usually three or four exposures 
with different arrangements of diaphragms and screens ; (3) intermediate 
stars, full aperture. The magnitudes of the reduced-intensity images 
were found by comparison with those of the intermediate stars, which 
had already been investigated; the subtraction of the reduction con- 
stants then gave values for the real magnitudes. 
The method possesses many advantages and, when applied with 
sufficient elaboration, apparently gives a scale of high precision. For 
example, suppose that a screen absorbing 6 mags, is used. Since stand- 
ards between the tenth and fifteenth magnitudes are presupposed, 
bright stars between magnitudes 4 and 9 are within reach; and since in 
each case the same constant is subtracted from the magnitude of the 
reduced-intensity image, the slope of the resulting scale will be inde- 
pendent of any error affecting the constant. The process is, in effect, a 
transference of the adopted scale for the intermediate stars to the region 
of the brighter objects. 
To provide the necessary checks, it is desirable that all possible 
arrangements of apertures, covering a wide range of reduction con- 
stants, should be used. There will thus be accumulated a number of 
separate, but overlapping, determinations of the scale, each of which 
should be homogeneous with that of the intermediate stars ; their inter- 
comparison controls the errors* of the constants, and their mean is the 
final result. When the data are extensive, as is here assumed, the re- 
ductions can be modified so that the result is no longer dependent upon 
that for the intermediate stars. 
To keep the labor within reasonable Kmits, this part of the investiga- 
tion was restricted to the stars of the North Polar Sequence, the brightest 
of which is Polaris; but in order that there might be a satisfactory 
connection with the intermediate group, a number of the latter were 
reobserved by the bright-star method. These considerations led to the 
selection of 32 objects distributed between magnitudes 2.5 and 12.3, pho- 
tographic. More or less complete series of observations were obtained 
with 10 different arrangements of the aperture, besides partial series 
for several others, the constants ranging from 1 to 11 mags. The 
overlapping scales, which are based upon 213 plates and 662 individual 
magnitudes, are in good agreement; not only are they sensibly parallel, 
but the constant systematic differences are small, which indicates that 
the reduction constants are well determined. 
With the completion of the investigation of the bright stars, it be- 
came possible to reduce the entire series of results to the international 
