148 DR. R. J. TILLYARD ON THE 
negative triads viz. E2a( — ), R2b( + )j a"d R3( — ). The second and third 
members of tliis triad remain unbranched to the margin; but the first, 
E2a, develops another negative triad, from the third branch o£ which a 
further negative triad is also developed. To save complications in the 
notation, I have named the five veins lieveloped on the wing-margin by 
these two latter triads IRja, 2R2a 3R2a, 4R2a and -5R2a ; it will be noticed 
that they are alternately concave and convex. 
The triad system, as will be clearly seen, always results in tlie formation 
of alternately convex and concave veins along the wing-margin. There is a 
large body of evidence to show that, apart from the Mayflies, this system 
was the original system of branching of the veins in the insect wing. 
Consideration of this evidence is beyond the scope of this paper, but attention 
is drawn to it in the hope that students of other Orders will attempt to 
recognise the remains of triads in the wings before them. As examples 
of archaic triads, we may take the universally recognised primitive set of 
three branches of R, viz., Rj, R2+3, R.1+5, which is formed from an original 
positive triad with the intermediate vein developed from the lower branch Rs. 
A similar archaic triad appears also to have developed from M, viz. Mi( — ), 
M2(4), and M3+4( — ), as shown in Protereisma, though this triad often 
appears in other insects as Mi_|_2(~)j ^3(4-), and M4( — ), owing to a 
difference in the position of the origin of the intermediate vein. It will 
readily be seen how easily . a pectinate series can be developed from the 
triadic system ; an example of this can be seen in the vein Cuj in Protereisma. 
Simple dichotomies, on the other hand, may be explained by either the non- 
development or suppression of the middle member of a triad, as in the case 
of the secondary branches of Rs in most insects. 
We now pass from the consideration of the triad to the application of the 
rule of alternate convexity and concavity of veins as it affects the problem of 
the elucidation .of the homologies of the wing-veins in an archaic Mayfly such 
as Protereisma (text-figs. 1, 3). The general rules applicable to all except 
very highlj'-specialised wing-types may be stated as follows :■ — • 
(1) Two strongly convex veins can always be recognised lying between 
the costal margi*i and the anal furrow, viz., Rj and Cuj. 
(2) The conutve vein lying between Ri and the costal margin is Sc. 
(3) M is a w'eakly concave vein lying between two ridges of Ri and Cuj. 
In many archaic types it gives off a posterior branch close to the base, which 
joins with Cu], thus forming the cuhito-median Y-vein, the main stem of 
which is properly denoted by Mj + CXii, though usually called simply Cuj. 
If this Y-vein can be recognised, any doubts as to the limits of M and Rs 
should be finally removed. 
(4) The vein lying either in or slightly anterior to the anal furrow is the 
vena dividens, Ou,. 
