Ammonite or the majority of gastropods, and so on (cf. p. 541).
In like manner (8) the ratio between the growth-factor and the rate of screw-translation parallel to the axis will determine the apical angle of the resulting conical structure: will give us the difference, for example, between the sharp, pointed cone of Turritella, the less acute one of Fusus or Buccinum, and the {528} obtuse one of Harpa or Dolium. In short it is obvious that all the differences of form which we observe between one shell and another are referable to matters of degree, depending, one and all, upon the relative magnitudes of the various factors in the complex equation to the curve.
The paper in which, nearly eighty years ago, Canon Moseley thus gave a simple mathôÙeôÙmatôÙiôÙcal expression to the spiral forms of univalve shells, is one of the classics of Natural History. But other students before him had come very near to recognising this mathôÙeôÙmatôÙiôÙcal simplicity of form and structure. About the year 1818, Reinecke had suggested that the relative breadths of the adjacent whorls in an Ammonite formed a constant and diagnostic character; and Leopold von Buch accepted and developed the idea16. But long before, Swammerdam, with a deeper insight, had grasped the root of the whole matter: for, taking a few diverse examples, such as Helix and Spirula, he shewed that they and all other spiral shells whatsoever were referable to one common type, namely to that of a simple tube, variously curved according to definite mathôÙeôÙmatôÙiôÙcal laws; that all manner of ornamentation, in the way of spines, tuberosities, colour-bands and so forth, might be superposed upon them, but the type was one throughout, and specific differences were of a geometrical kind. ãOmnis enim quae inter eas animadôÙvertiôÙtur difôÙferôÙenôÙtia ex sola nascitur diôÙversiôÙtate gyraôÙtionum: quiôÙbus si inôÙsuper exôÙterna quaeôÙdam adjunôÙgunôÙtur ornaôÙmenta pinôÙnarum, sinuum, anôÙfractuum, planôÙiôÙtierum, eminenôÙtiarum, proôÙfunôÙdiôÙtaôÙtum,