in nature. The nearly parallel-sided cone of Dentalium, or the widely separated whorls of Lituites, are evidently cases where ö£ nearly approaches unity in the one case, and is still large in the other, öý being correspondingly small; while we can easily find cases where öý is very large, and ö£ is a small fraction, for instance in Haliotis, or in Gryphaea.
For the purposes of the morphologist, then, the main result of this last general inôÙvesôÙtiôÙgaôÙtion is to shew that all the various types of ãopenã and ãclosedã spirals, all the various degrees of separation or overlap of the successive whorls, are simply the outward expression of a varying ratio in the rate of growth of the outer as compared with the inner border of the tubular shell.
The foregoing problem of contact, or intersection, of the successive whorls, is a very simple one in the case of the discoid shell but a more complex one