XI] 



CONCERNING GNOMONS 



513 



collection of either equal or similar figures, similarly situated, 

 as in Figs. 256, 257, there we can always discover a series of 

 inscribed or escribed logarithmic spirals. 



Once more, then, we may modify our definition, and say that : 

 "Any plane curve proceeding from a fixed point (or pole), and such 

 that the vectorial area of any sector is always a gnomon to the 

 whole preceding figure, is called an equiangular, or logarithmic, 

 spiral." And we may now introduce this new concept and 

 nomenclature into our description of the Nautilus shell and 

 other related organic forms, by saying that: (1) if a growing 



Fig. 257. The same in a system of hexagons. 



structure be built up of successive parts, similar and similarly 

 situated, we can always trace through corresponding points 

 a series of logarithmic spirals (Figs. 258, 259, etc.) ; (2) it is 

 characteristic of the growth of the horn, of the shell, and of 

 all other organic forms in which a logarithmic spiral can be 

 recognised, that each successive increment of growth is a gnomon 

 to the entire pre-existing structure. And conversely (3) it follows 

 obviously, that in the logarithmic spiral 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 



T. G. 33 



