1887.] NATURAL SCIENCES OF PHILADELPHIA. 365 



posterior radii may be swept forward proximally or anterior ones 

 may be swej^t backward proximally ; or both processes may occur 

 simultaneously ; or certain radii may be so accelerated in their growth 

 and others so retarded as to give rise to a uniserial or biserial pe- 

 dunculate limb. Sixthly, the evidence as to occurrence of the abor- 

 tion and extensive loss of radii in any part of the ichthyopterygium 

 is clear, as well as the frequent dichotomous subdivision of the dis- 

 tal ends of single radii* as in the pectorals of Raia, and cephalic 

 fins of Torpedo. Such secondary or divided radii may indeed be 

 homologous with the digits of higher forms, as it seems might be 

 countenanced by the fact that the limbs of some Amphibia have but 

 two digits at first, and that the others afterwards bud out at one 

 side or edge as was first noted by Prof. Baird, and subsequently con- 

 firmed by Cope and Baur. Such a view is also to some degree coun- 

 tenanced by the manner in which supernumerary digits develop in 

 Amphibia and by the simple structure and variability of the manus 

 and pes of Amphiuma or Muraenopsis. Seventhly, the obviously 

 compound nature of the mesopterygium of Polypterus as is proved 

 by the presence of serially or segmentally arranged foramina, per- 

 forating it for the passage of nerves, and which has been supposed 

 to be shoved outward to give rise to the intermedium, which in 

 the chiropterygium, must accordingly represent twelve fused radii, 

 whereas, it ought not at most, represent more than three or four. 

 Eighthly, the lack of correspondence or agreement in the structure of 

 the tarsi and carpi of higher forms, some of which are believed to pre- 

 sent traces of not less than six digits ; and in others as many as seven, 

 and the impossibility of determining with absolute certainty, the 

 homologues of the tarsal and carpal bones, as the centrale is some- 

 times represented by two elements or is so obscured as to be too in- 

 distinct to be clearly made out ; the same may be said of the inter- 

 medium. Ninthly, the impossibility of determining from which bor- 

 der of the primitive fold the elision or abortion of radii first began, 

 owing to the fact that the torsion of the fold on its own base, does not 

 always appear to occur or at least is not recapitulated, this torsion 

 varies from 90 to nothing at all. Whether the suppression of radii 

 was metapterygial or propterygial at first, we cannot now determine 

 with certainty, and all that we can justly say is, that it has probably 

 occurred on both borders in various types, and to the extent of a 



*The radii of Elasmobranchs as here understood are in no sense the homo- 

 logues of the rays of Teleosts, which are mainly derived from actimtricliia. 



