A detailed discussion of these is found in a paper by Dr. John A. Ryder "On the Origin of Heterocercy" in the Report of the U. S. Fish Commissioner for 1884. In this paper a dynamic or mechanical theory of the causes of change of form is set forth, parts of this having a hypothetical and somewhat uncertain basis. Dr. Ryder proposes the name _archicercal_ to denote the cylindroidal worm-like caudal end of the larva of fishes and amphibians before they acquire median fin-folds. The term _lophocercal_ is proposed by Ryder for the form of caudal fin which consists of a rayless fold of skin continuous with the skin of the tail, the inner surfaces of this fold being more or less nearly in contact. To the same type of tail Dr. Jeffries Wyman in 1864 gave the name _protocercal_. This name was used for the tail of the larval ray when it acquires median fin-folds. The term implies, what cannot be far from true, that this form of tail is the first in the stages of evolution of the caudal fin. To the same type of tail Mr. Alexander Agassiz gave, in 1877, the name of _leptocardial_, on the supposition that it represented the adult condition of the lancelet. In this creature, however, rudimentary basal rays are present, a condition differing from that of the early embryos. The diphycercal tail, as usually understood, is one in which the end of the vertebral column bears "not only hypural but also epural intermediary pieces which support rays." The term is used for the primitive type of tail in which the vertebræ, lying horizontally, grow progressively smaller, as in _Neoceratodus_, _Protopterus_, and other Dipnoans and Crossopterygians. The term was first applied by McCoy to the tails of the Dipnoan genera _Diplopterus_ and _Gyroptychius_, and for tails of this type it should be reserved. [Illustration: FIG. 64.--Heterocercal tail of Bowfin, _Amia calva_ (Linnæus). (After Zittel.)] [Illustration: FIG. 65.--Heterocercal tail of Garpike, _Lepisosteus osseus_ (Linnæus).] The heterocercal tail is one in which the hindmost vertebræ are bent upwards. The term is generally applied to those fishes only in which this bending is considerable and is externally evident, as in the sharks and Ganoids. The character disappears by degrees, changing sometimes to diphycercal or leptocercal by a process of degeneration, or in ordinary fishes becoming _homocercal_. Dr. Ryder uses the term heterocercal for all cases in which any up-bending of the axis takes place, even though it involves the modification of but a single vertebra. With this definition, the tail of salmon, herring, and even of most bony fishes would be considered heterocercal, and most or all of these pass through a heterocercal stage in the course of development. The term is, however, usually restricted to those forms in which the curving of the axis is evident without dissection. [Illustration: FIG. 66.--_Coryphænoides carapinus_ (Goode and Bean), showing leptocercal tail. Gulf Stream.]