310 
ASTRONOMY: F. H. SHARES 
that the same quantity of energy distributed over different patterns 
produces the same photographic result; the use of a coarse objective 
grating or screen of wire gauze is unobjectionable from the standpoint 
of diffraction, but requires a troublesome laboratory investigation for 
the determination of its constant; the diversion of a certain fraction 
of the Hght into a secondary image by means of a prism of small angle 
is subject to disturbances by diffraction and absorption. Other meth- 
ods are subject to similar uncertainties; and, in addition, all which 
involve successive exposures upon the same plate, Hke the majority of 
those just enumerated, have to contend with irregularities in the atmos- 
pheric conditions. 
In arranging the program of observations it was considered that the 
latter could be disregarded, because of the favorable situation of Mount 
Wilson and the moderate exposure times which would be required. 
Moreover, the considerable accumulation of material necessary for the 
investigation would render atmospheric disturbances wholly accidental. 
Other difficulties, it was hoped, would be sufficiently controlled by 
the use of a wire gauze screen and a series of circular diaphragms cover- 
ing a wide range of aperture. For the latter, the following diameters 
in inches were adopted: 40, 32, 14, 9, 8, and 6. Two large screens of 
wire gauze were used, one of single thickness and one of double thick- 
ness, the wires of the latter being crossed at an angle of 45°; smaller 
screens for use over the diaphragms of 14 inches and less were also 
available. The constants depend upon laboratory determinations of 
the absorption for point sources, controlled by the measurement of 
the absorption for surfaces. 
It was found convenient to separate the investigation into three 
parts, with a corresponding variation in the treatment: (a) bright stars, 
including objects brighter than the tenth magnitude; (b) intermediate 
stars, from the tenth to the eighteenth magnitude; (c) faint stars, 
fainter than the eighteenth magnitude. The Hmits refer to the photo- 
graphic scale. 
For both scales the work was begun with the second group — the 
intermediate stars. The details of observation, measurement, and re- 
duction have been described elsewhere. ^ For the photographic scale, 
to which the following paragraphs refer, the exposure times fall into 
two groups, one of 11 minutes or less, the other ranging between 30 
minutes and 60 minutes. Forty-two separate determinations of the 
scale were derived from the data on 15 plates of shorter exposure; from 
those of longer exposure there were fourteen determinations, from an 
equal number of plates. The former series involved the use of the 
