THE CURVES OF LIFE: A CRITICISM 399 



forms of organic objects. He deals with spirals in general, 

 from those of the smallest spirillum to those of the starry 

 nebulae, touching on the way whirlwinds, water-spouts, crystals, 

 shells, trees, plants, human organs and parts, horns, and also the 

 decorative use of the spiral ; and some of these are dealt with 

 at great length and with much detail and necessary diffuseness. 

 But although the spiral is one of Nature's commonest and most 

 widely diffused ciphers, one has hitherto looked in vain for a 

 key to this wondrous cipher-writing. 



Mr. Cook quotes the following sentence of Leonardo's : 

 " In this the eye surpasses Nature, inasmuch as the works of 

 Nature are finite, while the things which can be accomplished 

 by the handiwork, at the command of the eye, are infinite"; 

 which he would explain by saying " that the logarithmic spiral 

 (for instance) can never be reached in Nature," for " Nature 

 is finite, while the logarithmic spiral is infinite, and goes on 

 for ever, as no living organism does." Apparently the logar- 

 ithmic spiral is the nearest mathematical expression we can use 

 for the relation of form to growth : the other factor which 

 would enable us to express the whole accurately is the life 

 of the object itself. So, also, in a work of art the " baffling 

 factor ... is its beauty." There is something more than the 

 mere mathematical statement, some variation, some inflection 

 which is life in the one case and beauty in the other. " All 

 beautiful lines," said Ruskin, "are drawn under mathematical 

 laws organically transgressed." 



Mr. Cook is very careful to insist that the $ ratio does not, of 

 course, provide a recipe by which any modern mathematician 

 could produce sculpture like the Greek, or painting like that of 

 the great masters ; but it does show that both Beauty and 

 Growth are " visibly expressed to us in terms of the same fun- 

 damental principles." 



The first examples given are those of upright and flat spiral 

 formation in shells, of which Mr. Cook gives a number of illus- 

 trations, many of which are well known, for it is easier to examine 

 spiral formation in shells than in any other natural object. Mr. 

 Cook's explanation of spiral growth in shells on physical 

 grounds alone seems to us hardly sufficient. He says it is in 

 need of " a complete scientific explanation," but surely no 

 physical agency alone can account for the diversity of forms 

 in nature, unless this agency be unduly tortured for the sake 



