features as these, unless they be strongly supported and corroborated in other ways,ãfor the simple reason that there is unlimited room for coincidence, or separate and independent attainment of this or that magnitude or numerical ratio,ãyet 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,ãthat 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 ãalliedã forms, then we have the phenomenon of ãorthogenesis.ã For orthogenesis is simply that phenomenon of continuous lines 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 ãorigin of species,ã or of the nature and origin of ãfunctional adaptations.ã And to my mind, the mathôÙeôÙmatôÙiôÙcal (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 charôÙacôÙterôÙisôÙtic of the molluscan shell, that complete regularity is apt to be departed from. We have clear