28 GENESIS OF THE ARIETIDiE. 



We reproduce this conclusion in full, though, as may be seen by reading the 

 preceding pages, we differ essentially as to the causes that produced parallelism 

 between different series in the same or different localities. Nevertheless, Waagen 

 agrees with us in rejecting the doctrine of natural selection as a fundamental 

 cause of parallelism, and has also stated in 1875, from independent observations, 

 the possibility of doing what we have been putting in practice ever since 1866 ; 

 namely, predicting what sort of species would be found as descendants of certain 

 given forms, and then subsequently finding them. This experience has also 

 been shared by Professor Cope, who makes similar statements of his own obser- 

 vations among fossil and recent Batrachians and Reptiles. The method pursued 

 by both of us differs from that ordinarily used by naturalists in predicting the 

 existence of new forms, in that it relies upon the action of the law of accelera- 

 tion, and the constant recurrence of similar forms in different series of the 

 same stock, or, as we have explained above, upon the law of morphological 

 equivalence. 1 



Theory of Radicals and Morphological Equivalence in 

 Retrogressive Forms. 



There are certain species among complicated acmic forms which became the 

 ancestors of uncoiled degenerate series, that can be properly termed nostologic 

 forms on account of their complete reversion to the uncoiled forms of the radical 

 groups among Nautiloids. These were not confined to any special class of forms, 

 though more frequent among the higher than among the trunk stock of radical 

 forms. They are what we have called geratologous radicals. Thus Lobites of 

 the Trias must have sprung from some geratologous radical among the Goniati- 

 tina3; and Hauer's Cochloceras with its turrillites-like whorls, and the straight 

 Rhabdoceras, both have sutures which indicate derivation from some genus like 

 Helictites or Choristoceras among Ceratitinaa of the Trias, ribbed shells with very 

 simple sutures. 2 Choristoceras, also, had discoidal species in the Rhoatic beds. , 

 We treat these forms as probably degradational, because of their simpler 

 ornamentation and sutures, and also because the similar uncoiled shells among 

 Gasteropoda and among Ammonitina3 may be followed until they grade into 

 closely coiled and more complicated shells, from which they probably arose. 3 

 The geratologous forms have a most important bearing on the conclusions reached 

 in this essay. They terminate the geologic history of their suborders, just as the 

 Turrillites and Baculites, and others, appear as the final forms of Ammonitinoe. 

 They were also coextensive with the existence of the cephalopod type, and were 

 evidently liable to be evolved at any time in their history, and to increase in 



1 The law of acceleration and of morphological equivalence has been stated in the Preface, pp. iv. and v. 



2 These lines were written before Zittel's superb work, " Handbuch der Paleontologie," had appeared, 

 in which (p. 431) he associates these forms in exactly the same order. Although his text does not allude to 

 the genesis of the forms, his mode of arrangement shows that he probably had the same idea in mind. 



8 Parallelisms of Individuals and Order among Tetrabranchiate Mollusks, Mem. Bost. Soc. Nat. Hist., 

 I., 1866-67, and Proceedings of same, 1., 1866, p. 302. Genetic Relations of Stephanoceras, Proc. Bost. 

 Soc. Nat. Hist., 1876, XVIII. p. 380. Also Genesis of Tertiary Species of Planorbis at Steinheim, p. 8. 



