590 SYSTEMATIC RELATIONS OF FISHES. 
on the lower side of the column, those on the upper side remaining 
rudimental, it will be necessary that such enlarged portion should 
strike the water in the plane transverse to the longitudinal axis of 
the body in order that the weight of the body be propelled with 
the least expenditure of force. This will necessarily cause the 
distal vertebrae, or end of the chorda dorsalis, to be turned up- 
ward, so that the inferior rays of the fin shall be brought as near 
‘to the vertical line of the superior as possible. This is the type 
of tail known as the heterocercal, as called by Agassiz. 
We find among the Physoclysti that the lower rays of the fin are 
more and more strengthened, and the hemal spines which support 
them, are more and more enlarged. Consequently the end of the 
column is more curved upwards, as seen in Amia. The superior 
rays and neural spines are also strengthened, and the inferior so 
extended upwards as to pass round the extremity of the column 
and come into contact with them. And now the vertebral centra 
are successively atrophied from the extremity. Counting from the 
extremity to the bases of the first supports of the outer rays of 
the caudal fin above and below, we find that ten vertebra remain 
in the tail of Notopterus. In the Hyodontide, Albulide, Elopide, 
Alepocephalide and Salmonide, there are but two left, while one 
only appears in the Osteoglossidw, Aulopide, Lutodiridw, Butyrini- 
dæ, Coregonide, Clupeide and Chirocentride. In most other fam- 
ilies, especially of Physoclysti, the last one has disappeared, and 
the numerous hzemal arches are arranged like radii diverging up- 
wards and downwards from the last caudal vertebra. In the high- 
est groups, as Pharyngognathi, etc., they become codssified, and 
the tail has completed specialization. This is the type called 
homocereal or diphycercal by later writers. 
These types are thus plainly stages in the development of this 
member, the first and second being simply arrests of development 
of the last. Thus the young salmon commences with an eel-like 
vertebral column, or is isocercal; it presently, by the upward 
curvature of the column, and unequal development of the caudal 
fin, becomes diphycercal, but ceases to grow before it has quite 
accomplished this stage. The Polypterus, the eels, Gymnarchus 
and other fishes ossify the vertebre in the isocercal stage. The 
heterocercal type is seen in the Chondrostei, where the vertebra 
never ossify. In Lepidosteus and Amia, they ossify in this stage. 
I further specify the characters of the orders of Physostomi and 
the families they contain, in the paper itself. 
