XI] OF VARIOUS CEPHALOPODS 807 



or any stichlihe phylogenetic hypotheses*. If we have two shells 

 in which the constant angle of the spire be respectively 80° and 

 60°, that fact in itself does not at all justify an assertion that the 

 one is more- primitive, more ancient, or more "ancestral" than the 

 other. Nor, if we find a third in which the angle happens to be 

 70°, does that fact entitle us to say that this shell is intermediate 

 between the other two, in time, or in blood relationship, or in 

 any other sense whatsoever save only the strictly formal and 

 mathematical one. For it is evident that, though these particular 

 arithmetical constants manifest themselves in visible and recog- 

 nisable differences of form, yet they are not necessarily more 

 deep-seated or significant than are those which manifest themselves 

 only in difference of magnitude; and the student of phylogeny 

 scarcely ventures to draw conclusions as to the relative antiquity 

 of two allied organisms on the ground that one happens to be 

 bigger or less, or longer or shorter, than the other. 



At the same time, while.it is obviously unsafe to rest conclusions 

 upon such features as these, unless they be strongly supported 

 and corroborated in other ways — for the simple reason that there 

 is unlimited room for coincidence, or separate and independent 

 attainment of this or that magnitude or numerical ratio — yet on 

 the other hand it is certain that, in particular cases, the evolution 

 of a race has actually involved gradual increase or decrease in 

 some one or more numerical factors, magnitude itself included — 

 that is to say increase or decrease in some one or more of the 

 actual and relative velocities of growth. When we do meet with 

 a clear and unmistakable series of such progressive magnitudes or 

 ratios, manifesting themselves in a progressive series of ''aUied" 

 forms, then we have the phenomenon of "orthogenesis."' For 

 orthogenesis is simply that phenomenon of continuous Unes or 

 series of form (and also of functional or physiological capacity), 



* Phylogenetic speculation, fifty years ago the chief preoccupation of the 

 biologist, has had its caustic critics. Cf. {int. al.) Rhumbler, in Arch. f. Entw. 

 Mech. VII, p. 104, 1898: " Phylogenetische Speculationen . . , werden immer auf 

 Anklang bei den Fachgenossen rechnen dlirfen, sofern nicht ein anderer Fachgenosse 

 auf demselben Gebiet rait gleicher Kenntniss der Dinge und mit gleicher Scharfainn 

 zufallig zu einer anderen Theorie gekommen ist. . . .Die Richtigkeit 'guter' phylo- 

 genetischer Schliisse lasst sich im schlimmsten Falle anzweifeln, aber direkt 

 widerlegen lasst sich in der Regel«iicht." 



