Vol. 1.] Woodivorth. — Wifig Veins of Insects. 69 



at the margin and become weaker as they proceed inwardly 

 (proximally), the ending being similar to that of the outgrow- 

 ing veins, bnt in the opposite direction. In some cases, however, 

 they have gained an attachment to an outgrowing vein through 

 a cross vein, becoming so completely united to it that they 

 have all the characteristics of branches. There is nothing in 

 the structural peculiarities to determine whether a particular 

 vein arose as a branch or as an independent vein; the only 

 criterion being a comparison with the venation of other mem- 

 bers of the same group, the principle being to class as an inde- 

 pendent vein anything that anywhere exhibits structures 

 characteristic of independent veins. It is not certain that 

 branches in the strictest sense may not, under some circum- 

 stances, especially that of their relation to a cross vein, take on 

 some of these characteristics. Such appears to be the belief 

 of several recent students of venation, who, having adopted a 

 typical number of branches as belonging to the vein we have 

 called the primary, include among them in man}'^ instances 

 veins which show very evident signs of their independent 

 nature. I am convinced that there is no reason vvhy, in any 

 group, branches might not be decreased or increased in this way 

 to any extent, and that the application of the typical-number 

 hypothesis can not be depended on as conclusive evidence of 

 the nature of a supposed branch. At the same time, while there 

 is a theoretical typical number of independents in any area — 

 that is, one, three, seven, fifteen, etc. — a very little inspection 

 of venations will convince one that the typical number is 

 rarely attained. The reason is that an independent vein only 

 approximates the middle of an interspace, so that a vein in 

 the next series will commonly be quicker to develop on one 

 side than on the other, and this difference may become more 

 and more exaggerated as time goes on. In some groups the 

 evidence may be so plain that there can be but little doubt as 

 to the source of the vein appearing as a branch; but whether 

 we can homologize and clearly distinguish between true 

 branches and independent veins throughout the whole class, 

 is open to doubt. 



A matter which somewhat complicates the question of inde- 

 pendent veins is that specialization of the wing membrane 

 which results in what have been called convex and concave 

 veins. There has been no satisfactory explanation of the cause 



