440 WILLIAM K. GREGORY 



Boulenger's classification is true to British tradition in the 

 fewness of its larger divisions; and many families, suborders, and 

 orders of the American system are not recognized as distinct 

 divisions. Thus the differences between the English and Ameri- 

 can systems are very salient. By the American method as- 

 exemplified in Dr. Jordan's latest work, 18 orders, about 33 sub- 

 orders, and considerably more than 200 families of true Teleosts 

 are recognized; by the English method all are swept into the 

 single "order" Teleostei which is coordinate in value with the 

 orders Crossopterygii, Chondrostei, Holostei, and which is sub- 

 divided into thirteen suborders which for the most part have 

 the value of the orders of the American system. Boulenger's 

 treatment of the "suborder" Ostariophysi may serve as an in- 

 stance of this extensive synthesizing. Since this assemblage is 

 regarded as a natural one the divisions Heterognathi, Eventog- 

 nathi, Nematognathi are not used, and the Characins, Carps, 

 and Catfishes are all united as families in the suborder Ostario- 

 physi. In Boulenger's definitions of these families the trench- 

 ant structural differences between them are revealed, but so far as 

 the classification itself indicates they might be no more separated 

 than, say the Tarpons (Elopidae) from the Lady-fishes (Albu- 

 lidas) , or the Herrings (Clupeidae) from the Salmons (Salmonidae) . 



These differences in method seem to arise from the dual 

 nature and function of a natural classification in the modern 

 sense. A natural classification must necessarily express, first, 

 degrees of homological resemblances and differences and, second, 

 degrees of genetic relationship ; but it cannot at the same time 

 express both with equal accuracy, and its primary purpose is 

 to express degrees of homological resemblances and differences. 



In comparing the end forms of diverging lines of descent we 

 find that between any two forms degrees of genetic relationship 

 are solely a function of time and of the rate of reproduction, 

 while degrees of homologous structural relationships are a 

 function of varying rates of evolution. To borrow an illustration 

 from mammalogy, we may suppose that a certain group of 

 pre-Tertiary mammals has given rise to the modern Insecti- 

 vores on the one hand and to the Bats on the other. Between 

 this ancestral group and each of the two modern groups a number 



