VISCERAL ARCHES OF THE GNATHOSTOME FISHES. 365 
in a plane perpendicular to the axis of the body, but this 
plane later became inclined to that axis, the acute angle 
lying posterior to the plane ; and still later it acquired, in the 
Elasmobranchii, the well known sigma form. What impressed 
this sigma form on these arches is not known, but it would 
seem as if it must have been related to the relative lengths of 
the pharyngeal cavity and the occipital portion of the chondro- 
cranium. But, whatever the cause, this sigma form of arch 
has definitely associated with it, in recent fishes, the presence 
of cartilaginous branchial rays, of musculi constrictores super- 
ficiales, and of musculi adductores arcuum branchialium of the 
plagiostoman type; while associated with the other, or straight, 
form of arch is the absence of the above cited features, the 
presence of supporting rods in the branchial filaments and of 
musculi levatores arcuum branchialium, and the occasional 
presence of musculi adductores arcuum branchialium that are 
innervated by nerves that pass over the posterior edge of the 
branchial bar of the related arch. 
In Ceratodus, it is probable (Allis, 1915) that there are 
much reduced pharyngobranchials and that they are directed 
postero-mesially, as they are in the Elasmobranchii, while the 
hypobranchials are directed antero-mesially, as in the Teleos- 
tomi ; and in this fish there are no adductores and apparently 
no supporting rods to the branchial filaments, but there are 
so-called musculi interbranchiales which are probably persist- 
ing remnants of the plagiostoman constrictores superficiales. 
This limitation of cartilaginous branchial rays or sup- 
porting rods in the branchial filaments, together with certain 
other associated and distinctive features, to the Elasmo- 
branchii and Teleostomi respectively, and the probable 
absence of both branchial rays and supporting rods in 
Ceratodus, would seem to favour the view that the Teleostomi 
were descended from a fish in which the cartilaginous 
branchial rays had not yet been acquired. I have, however, 
quite recently (Allis, 1915) concluded that the basal portions, 
at least, of the cartilaginous extrabranchials are archaic struc- 
tures, and that they are found, in modified form, either in the 
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