366 PROCEEDINGS OF THE ACADEMY OF [1887. 



variable number of radii in different cases. Tenthly, if the digits of 

 higher forms represent the distal extremities of one or two dichoto- 

 mously divided single rays, each derived from a single somite, it is 

 not possible to state with certainty to which order of secondary 

 branches they belong, because the epiphyses and diaphyses of the 

 proximal long bones may represent elements which should be taken 

 into account. The digits would probably represent the second sub- 

 division, if the ej)iphyses of the long bones were thrown out of the 

 reckoning. 



The following suggestion seems very important. The manifest 

 impossibility of deriving a chiropterygium from a given or known 

 uniserial or biserial ichthyopterygiura, which will serve, as a start- 

 ing point for the limb? of all known higher vertebrates, forcibly im- 

 presses the conclusion that, firstly, the limbs of all vertebrates are 

 not necessarily exactly homologous and that, secondly, the chirop- 

 terygium has in all probability been independently developed sev- 

 eral times and indirectly from different segments along the sides of 

 the primitive vertebrate body. 



The importance of this conclusion, as qualifying the prevalent 

 doctrines regarding the homologies of the limbs of vertebrates, may 

 be inferred since it has been found by Albertina Carlson (Kongl, 

 Svensk. Vet. Akad. Handl. xi, 1887,) that in the Ophidia the post- 

 plexus may be developed opposite the intervals between the 275th, 

 to the 278th, vertebrae. Besides this. Miss Carlson has shown that 

 there is great variation in the position of the postplexus in different 

 genera of Ophidians. 



It seems almost unnecessary to note here, that the modifications of 

 the position of the limb in reference to the same segments along the 

 body, also implicates the homologies of the muscles and blood vascu- 

 lar supply. 



The view which has been suggested above as to the origin of the 

 limbs of the higher vertebrates, implies that the distinction between 

 the uniserial and biserial archipterygium is simply formal; that 

 whether a fin shall become provided with series of radii on one or 

 both sides depends on the manner in which coalescence of the pri- 

 mar}"^ radii took place ; Avhether, in fjict, from one or both borders. 

 The usual type in Elasmol)ranchs occurred by coalescence from be- 

 hind. In liala coalescence occurred from both the anterior and pos- 

 terior borders of the pectoral as shown by its ontogeny, giving rise 



