bactriticones, the loosely coiled forms as gyroceracones or mimoceracones, the more closely coiled shells, in which one whorl overlaps the other, as nautilicones or ammoniticones, and so forth. In such a succession of forms the biologist sees undoubted and unquestioned evidence of ancestral descent. For instance we read in Zittelãs Palaeontology27: ãThe bactriticone obviously represents the primitive or primary radical of the Ammonoidea, and the mimoceracone the next or secondary radical of this orderã; while precisely the opposite conclusion was drawn by Owen, who supposed that the straight chambered shells of such fossil cephalopods as Orthoceras had been produced by the gradual unwinding of a coiled nautiloid shell28. To such phylogenetic hypotheses the mathôÙeôÙmatôÙiôÙcal or dynamical study of the forms of shells lends no valid support. If we have two shells in which the constant angle of the spire be respectively 80ô¯ and 60ô¯, that fact in itself does not at all justify an assertion that the one is more primitive, more ancient, or more ãancestralã than the other. Nor, if we find a third in which the angle happens to be 70ô¯, 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 mathôÙeôÙmatôÙiôÙcal one. For it is evident that, though these particular arithmetical constants manifest themselves in visible and recognisable 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. {549}
At the same time, while it is obviously unsafe to rest conclusions upon such