XI] OF VAKIOUS CEPHALOPODS 549 



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 "allied" 

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

 orthogenesis is simply that phenomenon of continuous Hnes or 

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

 which was the foundation of the Theory of Evolution, alike to 

 Lamarck and to Darwin and Wallace ; and which we see to exist 

 whatever be our ideas of the "origin of species," or of the nature 

 and origin of "functional adaptations." And to my mind, the 

 mathematical (as distinguished from the purely physical) study 

 of morphology bids fair to help us to recognise this phenomenon 

 of orthogenesis in many cases where it is not at once patent to 

 the eye ; and also, on the other hand, to warn us, in many other 

 cases, that even strong and apparently complex resemblances in 

 form may be capable of arising independently, and may sometimes 

 signify no more than the equally accidental numerical coincidences 

 which are manifested in identity of length or weight, or any other 

 simple magnitudes. 



I have already referred to the fact that, while in general a 

 very great and remarkable regularity of form is characteristic of 

 the molluscan shell, that complete regularity is apt to be departed 

 from. We have clear cases of such a departure in Pupa, Clausiha, 

 and various Buhmi, where the enveloping cone of the spire is 

 not a right cone but a cone whose sides are curved. It is plain 

 that this condition may arise in two ways: either by a gradual 

 change in the ratio of growth of the whorls, that is to say in 

 the logarithmic spiral itself, or by a change in the velocity of 



