784 THE EQUIANGULAR SPIRAL [ch. 



each will cut or intersect its predecessor, as in an Ammonite or 

 the majority of gastropods, and so on. 



A similar relation of velocities suffices to determine the apical 

 angle of the resulting cone, and give us the diflFerence, for example, 

 between the sharp, pointed cone of Turritella, the less acute one of 

 Fusus or Buccinum, and the obtuse one of Harpa or^of Dolium. 

 In short it is obvious that all the differences of form which we 

 observe between one shell and another are referable to inatters of 

 degree, depending, one and all, upon the relative magnitudes of the 

 various factors in the complex equation to the curve. This is an 

 immensely important thing. To learn that all the multitudinous 

 shapes of shells, in their all but infinite variety, may be reduced to 

 the variant properties of a single simple curve, is a great achieve- 

 ment. It exemphfies very beautifully what Bacoi^ meant in saying 

 that the forms or differences of things are simple and few, and the 

 degrees and coordinations of these make all their variety*. And 

 after such a fashion as this John Goodsir imagined that the naturahst 

 of the future would determine and classify his shells, so that 

 conchology should presently become, hke mineralogy, a mathe- 

 matical science I . 



The paper in which, more than a hundred years ago, Canon Moseleyf 

 gave a simple mathematical account, on fines fike tfies^, of the 

 spiral forms of univalve shells, is one of the classics of Natural 

 History. But other students before, and sometimes long before, 

 him had begun to recognise the same simpficity of form and 

 structure. About the year 1818 Reinecke had declared Nautilus 

 to be a well-defined geometrical figure, whose chambers followed 



* For a discussion of this idea, and of the views of Bacon and of J. S. Mill, see 

 J. M. Keynes, op. cit. p. 271. 



t On the employment of mathematical modes of investigation in the determina- 

 tion of organic forms^ in Anatomical Memoirs, ii, p. 205, 1868 (posthumous 

 pubhcation). 



X The Rev. Henry Moseley (1801-1872), of St John's College, Cambridge, 

 Canon of Bristol, Professor of Natural Philosophy in King's College, London, was 

 a man of great and versatile ability. He was father of H. N. Moseley, naturalist 

 on board the Challenger and Professor of Zoology in Oxford; and he was grand- 

 father of H. G. J. Moseley (1887-1915) — Moseley of the Moseley numbers — whose 

 death at Gallipoli, long ere his prime, was one of the major tragedies of the Four 

 Years War. 



