188G.] PROCEEDINGS OF UNITED .STATES NATIONAL MUSEUM. 73 



pareutly form a kind of tympanic meuibrauc on either side just be- 

 hind the scapuhir arch. 



It is thus rendered evident that the mutations of development of three 

 or four structures may be sufficient to supply characters of ordinal vahie 

 to the taxonomist; that, iu fact, we may get a far greater variety of small 

 diflereuces between the many species belonging to the orders, founded 

 on such a small number of prominent characters, than might be supposed 

 possible if it was assumed that a permutation of the number of charac- 

 ters used in the ordinal definitions would give the number of species to 

 be included by the supposed orders, for each character is capable, within 

 very wide limits, of infinitely small amounts of variation, which may 

 serve as the marks of species or varieties. We are thus forced to infer 

 that in the " genesis of species" we are dealing with a permutation, the 

 exact number of terms in which, and in which the capacity for the varia- 

 tion of each terra is unknown, so that it would, if all the structural char- 

 acters of a group were given, be impossible to predicate how many 

 species or possible combinations of characters that group was capable 

 of yielding under the stress of environing infiueuces competent to pro- 

 duce changes iu the relative developmeut of parts. 



For instance, the one feature which Cyprmus and Aminrus retain in 

 common is the possession of a barbel at the augleof the mouth, yet the 

 one has no cartilaginous basis and appears late, whereas the other has 

 at first a cartilaginous support which afterwards ossifies at its base. 

 Now it is absolutely no proof whatever that these structures in the two 

 forms are not indicative of affiliation, if we assume that this is so, be- 

 cause in the one there is no skeletal support, while it is present in the 

 other. Because, if we attended to the development of both forms we 

 might find reasons for the belief that what had failed to develop in the 

 one was nevertheless possibly as salient a feature iu the ancestor of 

 Cyprinus as iu Amiurus, and that the tendency to suppress or retard the 

 development of the barbels iu the one and exaggerate them in the other 

 was due to the operation of the very forces which we found capable of 

 producing a complex series of permutations. This idea may be rendered 

 somewhat clearer if we bear in mind that it seems to be a frequent em- 

 bryological rule that structures which are disappearing in an organism 

 disappear part by part in an order just tlie reverse of that iu which they 

 are normally developed to their fullest importance. 



This principle in embryology may be very clearly illustrated .by the 

 succession of events in the course of the developmeut of the rays of the 

 median fins of a few types in which the gamut of chai'.ges traversed by 

 the process of development is analyzed. 



(1) Taking the Dipnoi as the lowest and simplest type, it seems that 

 the following is the method of development of the median fins which 

 will be found to exist : First, a perfectly eradiate, lojdiocercal, median 

 lin-fold, into which mesoblast is proliferated, between which and the 

 epidermis a single row of actinotrichia are developed on either side of 



