No.412.] SMALLER NORTH-AMERICAN .SHRIKES. 277 
in size. An exposure of seventy-five seconds was ordinarily 
sufficient to obtain a picture, which appeared on development 
as a white area on a black ground. A magnification of 3% 
diameters was secured, care always being taken to have the 
distance of the bill from the lens constant. An outline of 
the culmen of practicable working size having been thus 
obtained, the next step was the analysis of the curve. 
It was highly desirable to have one simple criterion of the 
curvature, if one sufficiently representative could be found. 
In Fig. 3, which represents the outline in a representative case, 
a great increase in the sharpness of the curvature is seen 
D 
Fic. 3. — Diag f bill showing hod of ing f cul A B equals distance 
of A from nearest margin of nostril; CD, tangent to outline of culmen parallel to A B; ZF, 
perpendicular at point of tangency, Z; ZAF, angle embraced between the two chords 
of the culmen, 4B and AE. 
towards the distal end of the culmen ; the sharpness of curva- 
ture varies in different individuals. The point where the rapid 
increase begins was found on inspection to be sufficiently 
uniform in position to suggest the idea of comparing in dif- 
ferent individuals the angle embraced between two chords of 
the curve of the culmen, each of them terminating at the distal 
end of the culmen. The proximal ends of the two chords were 
selected by the following method: one was established at a 
point on the culmen as far from its apex as the apex was from 
the nearest margin of the nostril. The distance of the nostril 
from the tip of the culmen, of course, could not be measured on 
the photographic silhouette print; it was therefore determined 
