144 DR. R. J. TILLYARD ON THE 
had any connection with R at all, and is most certainly not that vein, any 
system of homologies based on these results of Needham in the Odonata 
becomes so highly speculative in character as to cease to attract even those 
who maj' have originally accepted it. It is, therefore, necessary to enquire 
anew into the whole question of the homologies of the wing-veins of the Order. 
This I have attempted to do during the last three j^ears. The results obtained 
appear to me to shoWj not only that the system proposed by Miss Morgan 
was incorrect, but that the original system proposed by Comstock and 
Needham (1899) was also wrong, and that the true interpretation of the 
homologies is one hitherto unsuspected in an)- quarter. These results, again, 
also support some startling new results obtained for the Odonata ; and it is 
for that reason that the publication of the present paper is interpolated 
between the first and second papers of the series on that Order. 
For the purpose of obtaining a really trustworthy result in an admittedly 
difficult problem, I have attempted to combine three methods of study, viz. : 
(1) the study of the Palseozoic Mayflies ; (2) the study of the nymphal 
tracheation in archaic existing types ; and (3) the application of the principles 
of convex and concave veins, both to'fossil and recent forms. Good fortune 
favoured this plan. In the first place, when visiting New Zealand in 
1919-20, Prof. C. Ohilton, of Canterbury College, Christchurch, very kindly 
accompanied me on a visit to the Cass Biological Station, which is under his 
charge. Here we found abundant material of the larvse of the archaic types 
of Siphluridse for which New Zealand is famous. As all the necessary 
apparatus for dissections and microscopic study were at hand in the Station, 
I was able to make a thorough study of these larvse on the spot. This 
produced a surprise, in that the tracheation was found to be almost complete 
in the various instars, and fairly easy of interpretation ; whereas, in the 
Mayflies studied by Miss Morgan, the tracheation was both incomplete and 
irregular. Following on this discovery, during my visit to America in 1 920, 
through the kindness of Prof. C. Schuchert, I studied the Lower Permian 
fossils left behind by Dr. Sellards in Yale University, and was surprised to 
find among them a very fine specimen of Protereisma, so beautifull}^ pi'eserved 
that it at once gave me the key to the whole venation of the Order, and, 
incidentallj^ supported the evidence given by the study of the larval 
tracheation. It then became clear to me that, if the significance of the 
alternation of convex and concave veins had been fullj' understood, and 
applied to the solution of this problem, the homologies would at once have 
become perfectly clear. In his paper on the Lower Permian Mayflies, 
Sellards (1907) entirely ignored this important point. Consequently, no 
help was to be obtained from his worlc by Miss Morgan, and she merely 
contents herself with copying his figures (1912, pi. 9. figs. 62-66), and 
attaching thereto the results obtained by her own researches. 
Text-fig. la shows the hind-wing of a species of Protereisma with the 
homologies of the veins obtained by this new method of study. For 
