1887.] NATURAL SCIENCES OF PHILADELPHIA. 367 



to a uniserial (anterior) propterygium, and a similar (posterior) 

 metapterygium. 



Tlie cause of such coalescence has been in part, that other adjacent 

 functionally active parts pressed upon the radii which were growing 

 at an accelerated rate. The mode in which the radii composing the 

 fins were functional was also active in promoting coalescence, in fact, 

 there is no reason to doubt that almost exactly the same arrangement 

 of forces was potent in inducing the displacement forward of the prox- 

 imal ends of the posterior radii of the pectoral and pelvic fins, as in 

 the case of the caudal, as the writer has attempted to show in his 

 essay on the origin of heterocercy. This is also strikingly shown in 

 the dorsal and anal fins of some species. The increased pressure or 

 resistance exerted by the surrounding water on the hinder lower 

 quarter of the vertical or lateral fins while in action would constantly 

 tend, owing to the peculiar flexures assumed by the surfaces of the 

 fins while in motion, to shove the hinder border forwards and carry 

 the basal ends of the hinder radii forwards. The method of this 

 might be shown by means of a diagram, in which the force exerted 

 by the fin Avas one side and the resistence of the water the other side 

 of a parallelogram of forces, while the direction in which the base of 

 the fin was constantly tending to be dis])laced, would be determined by 

 the resultant acting against the hinder lower margin of the fin. The 

 alternating direction of the stroke of the fin does not impair the 

 efliciency of this set of active forces, but makes them more efficient, 

 since, though the action of the forces is alternately reversed as respects 

 the directions in which they act, the effect is the same. 



This hypothesis of the origin of the uniserial fin applies to all its 

 types, whether encountered in the dorsal finlets of Folypterus or in 

 the paired fins of Elasmobranchs, Chondrosteans and Chimseroids. 

 It also leads up to a more comprehensive theory of the origin of all 

 the modifications of the fins, as seen in the diverse types of fishes. 



As to the chiropterygium, we are warranted in the affirmation 

 that, whether it has arisen from the dichotomous division of the dis- 

 tal portion of a separate and single ray, or of two rays, or by the 

 modification of the distal radii of a uniserial metapterygium, or of 

 the distal end of a biserial metapterygium, our difficulties are pretty 

 much the same. And, while the view that those limbs which seem 

 to show traces of the plan of the chiropterygium, have probably 

 arisen from some type approximating the metapterygium of some 

 Elasmobranchs, we must admit that we cannot, for lack of evidence, 



