XI] CONCERNING GNOMONS 765 



outline of the shell or of the horn we can always inscribe an endless 

 variety of other gnomonic figures, having no necessary relation, 

 save as a mathematical accident, to the nature or mode of develop- 

 ment of the actual structure*. But observe that the gnomons to 

 a square may form increments of any size, and the same is true of 

 the gnomons to a Haliotis-sheW ; but" in the higher symmetry of a 

 chambered Nautilus, or of the successive triangles in Fig. 359, 

 growth goes on by a progressive series of gnomons, each one of 

 which is the gnomon to another. 



Fig. 362. A shell of Haliotis, with two of the many hues of growtii, or generating 

 curves, marked out in black: the areas bounded by these hnes of growth being 

 in all cases gnomons to the pre-existing shell. 



Of these three propositions, the second is of great use and 

 advantage for our easy understanding and simple description of 

 the molluscan shell, and of a great variety of other structures whose 

 mode of growth is analogous, and whose mathematical properties 

 are therefore identical. We see that the successive chambers of a 

 spiral Nautilus or of a straight Orthocems, each whorl or part of a 

 whorl of a periwinkle or other gastropod, each new increment of the 

 operculum of a gastropod, each additional increment of an elephant's 

 tusk, or each new chamber of a spiral foraminifer, has its leading 

 characteristic at once described and its form so far explained by the 



* For many beautiful geometrical constructions based on the molluscan shell, 

 see S. Colman and C. A. Coan, Nature a Harmonic Unity (ch. ix, Conchology), 

 New York, 1912. 



