132 MR. R. J. TILLYARD ON THE RECTAL BREATHING-APPARATUS 



Clock-Face Notation to indicate these positions. As there are always six 

 holobranchs arranged at equal intervals from one another, it will be clearly- 

 seen that, in a transverse section, the middle lines or axes of symmetry of the 

 holobranchs must lie at the six angles of a regular hexagon inscribed in the 

 circle which represents the transverse section of the branchial basket. Now, 

 if we take the numerals 1 to 12 and place them in their ordinary positions on 

 the clock-face, the raid-dorsal position will be represented by 12, the mid- 

 ventral by 6, and the other numbers will lie at intervals of 30° along the 

 circumference. In the Simplex System the positions of the six holobranchs 

 will then be found to correspond with the numbers 2, 4, 6, 8, 10, 12. But in 

 the Duplex System we shall find that the middle line, or axis of symmetry, 

 of each holobranch (which, in this case, is actually the line lying midway 

 between each pair of hemibranchs) lies in one of the positions 1, 3, 5, 

 7, 9, 11. 



Now it happens that in all Odonate nymphs the six so-called " rectal 

 glands " of the anal portion of the rectum lie in the positions 2, 4, 6, 8, 

 10, 12. Sadones, who only examined the gills of the larva of Libellula 

 depressa, which belong to the Duplex System, noticed that their positions did 

 not correspond with those of the "rectal glands." He therefore fell into the 

 serious error of announcing that the rectal gills could not be homologous 

 with these latter structures, since they did not correspond with them in 

 position. It will be one of the main purposes of this paper to show that the 

 six main longitudinal folds in the Simplex System are the homologues of the 

 six " rectal glands,'^ and also to explain how it is that the more complicated 

 Duplex System has apparently shifted its position. Sadones's error shows, 

 indeed, how dangerous it is for a biologist to study the complex mechanism 

 of the very highest term in a phylogenetic series, without any reference to, 

 or knowledge of, those less specialized forms that hold the key to the 

 situation. 



The Tracheal System of the gill-basket is physiologically an efferent system, 

 and may be considered as such in proposing the nomenclature for its parts. 

 It must not, however^ be forgotten that it was originally an afferent system, 

 and is developed as such in the embryo. The efferent function begins almost 

 immediately after the hatching of the young larva. It will be found, perhaps, 

 simpler to follow the ramifications of this system as if it were an afferent 

 system, ^. e. starting from the main longitudinal tracheal trunks, and follow- 

 ing the branches into the gills. The names, however, which we shall propose, 

 will be such as are suggestive of the efferent function. 



Starting then either from the great dorsal or the visceral trunks, a series 

 of large tracheal branches may be seen branching off to the gill-basket. 

 There are six of tliese series altogether, corresponding to the six rows of gills. 

 These trachese are the primary efferent trachea; of the gill-basket. 



Arrived close to the outer surface of the gill-basket, each primary eff^erent 



