338 EDWIN S. GOODiaClI. 



muscle-buds are given off by eacli myotome to the paired fins 

 in Elasmobranclis ; that tliese pass outwards into tlie fin-fold, 

 dividing into upper and lower halves, Avhich give rise to the 

 dorsal and ventral radial muscles. Between each pair of 

 corresponding upper and lower buds develops a cartilaginous 

 radial. Thus, as Rabl showed, since two radial muscles and 

 cartilages correspond to each segment, the relation between 

 tlie number of radials in the fin-skeleton, and the number of 

 trunk vertebra; belonging to those segments which contributed 

 to the formation of the fin, may be expressed in the formula 



^^ ^ = vertebrjB. Brans has endeavoured to prove that 

 2 _ 



this formula does not hold good (p. 444, 3). But it is quite 



obvious that, although in the main correct, it can only be 

 intended to give approximate results when applied to whole 

 fins. In most paired fins of Elasmobranclis the anterior and , 

 posterior regions are much modified by excessive concentration 

 and reduction, and here the cori-espondence between muscles 

 and radials becomes much disturbed. The formula applies 

 perfectly over the greater part of a fin which is normally 

 developed, as is seen in Braus's own figures (4, 6). More im- 

 portant is the contention that the adult radial fin-muscles 

 do not correspond to the muscle-buds in the embryo. It is 

 urged that the muscle-buds become mixed and that the adult 

 muscles are no longer unisegmental and haploneurous, but 

 are compound and polyneurous, and, in fact, bear no definite 

 relation to the segments from which they arose. 



It is true that, as Mollier has shown (24), the muscle-buds 

 in Elasmobrauch fins may be connected together at their base, 

 at all events temporarily, by strands of tissue. It is also true 

 that the mixed motor and sensory nerves form a complicated 

 plexus at the base of, and round about, the radial muscles. 

 But it does not follow that these muscles are either compound 

 or polyneurous. So far as I am aware, it has never been proved 

 that muscle-forming substance actually passes from one bud 

 to ancjther (]). 359) ; nor has it ever been proved tliat one 

 radial muscle is really innervated by more than one motor 



