1916] Chandler: Structure of Feathers 265 



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 

 growth 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 num,her of harhules per unit of measure 

 on the harhs 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). Al- 

 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- 



