THE CURVES OF LIFE: A CRITICISM 405 



present it seems impossible to speak with any certainty upon 

 the results of these inquiries. That this ratio appears so con- 

 stantly in Nature and Art is certain, but it is not yet possible 

 to give it the dignity of a law. The present work has brought 

 together a larger mass of facts bearing on the subject than has 

 ever been collected before, which facts are essential to all 

 future endeavours to solve the biological and artistic meaning of 

 spiral formations and of this ratio which is connected with 

 them. It may certainly be said of this <£ ratio that it is the ideal 

 to which all additive series have now, but not till now, attained : 

 it gives exact expression to them all ; and, moreover, it does 

 express certain tendencies of growth in natural objects, and 

 certain pleasing proportions of form in artistic objects and 

 is an expression of that truth of form which we call beauty. 

 It is therefore of very profound significance, and should 

 stimulate to further work, so that its relations to Nature and 

 Art can be made clear and explicit. Mr. Cook's idea is that 

 the logarithmic spiral and this ratio are standards which are 

 never quite reached in Nature or Art, and that it is this 

 divergence, slight as it is, that predicates life in the one case 

 and beauty in the other. This is perhaps the safest view to 

 take at the present time. 



The present writer once made a series of measurements of 

 models and statues, from the point of view of the Sectio aurea, 

 and he found that the statues approached much more nearly to 

 this proportion than the models. Bacon, it will be remembered, 

 treats with ridicule the idea of confining proportions by rigid 

 rules. He says : " There is no excellent beauty that hath not 

 some strangeness in the proportion. . . . Not but I think a 

 painter may make a better face than ever was ; but he must do 

 it "by a kind of felicity (as a musician that maketh an excellent 

 air in music), and not by rule." This " felicity" is the word we 

 were trying to find before ; it is like Keats's " magic hand of 

 chance," and Ovid's " Ars casum simulet " : it is "the little more 

 and how much it is" which Mr. Cook insists upon. 



But it may be found, when much more work has been done, 

 that this remarkable ratio stands in a nearer relation to Nature 

 and to Art than we can at present imagine : then Mr. Cook's 

 dream, that the biologist shall lie down with the artist and the 

 mathematician with the botanist, will be fulfilled. 



