oO 
1916] Chandler: Structure of Feathers 26 
Although the narrowness of the outer vane in the primaries is 
brought about partially by an actual shortness of the barb, it is 
accentuated by the relatively narrower angle which the barbs of the 
outer vane make with the shaft. In all but the most generalized 
remiges, there is a tendency for the barbs of the outer vane to be 
inserted farther apart on the shaft, but at a more acute angle than 
those of the inner vane. As a rule, the number of barbs per unit of 
measure changes in a very definite manner, following a mathematical 
curve analogous to some of those worked out by Pearl (1907) for 
erowth in the whorls of leaves of the aquatic plant Ceratophyllum. 
Beginning at the tip there is a slight decrease in number per unit 
of measure, then a very slowly accelerating increase for the greater 
length of the feather, terminating in a very quickly accelerating in- 
crease as the superior umbilicus is approached, accompanied by a 
transition to a downy form. It is interesting to note in this con- 
nection that the change in number of barbules per unit of measure 
on the barbs follows a very similar curve, and probably varies with a 
similar mathematical equation. 
The barbs of remiges, with the exception of the meager basal 
downy structure already mentioned, are always highly developed in 
birds of flight, consisting of a thin lamelliform ramus bearing highly 
developed distal and proximal vanules (Fig. B). The pith of the 
ramus, as shown by Mascha (1904), is composed either of a single 
dorso-ventral plate of cells, one cell in thickness, or of a network of 
cells, more than one cell in thickness (Fig. C). 
Without exception, the rami of the inner vane are narrower than 
those of the outer, though often almost imperceptibly so. Distal to 
the notch of the incised primaries this difference is especially notice- 
able, the rami of the outer vane being often as deep as the shaft, 
while those of the inner vane are less than half as deep. In the 
majority of birds where the rami are not as deep as the shaft, there 
are fine ridges on the shaft from the insertion of the ramus to the 
ventral edge. As pointed out by me (1914), the deep type of ramus 
is probably the more primitive condition. 
The ventral edges of the rami (fig. C) are produced into horny 
keels, usually with no evident cell structure, known as the ventral 
ridges (see Pycraft, 1893; Mascha, 1904; and Stubbs, 1910). AlI- 
though in the great majority of birds this ridge forms only a nar- 
row, inconspicuous border for the ramus, in a few birds it is extra- 
