404 'SCIENCE PROGRESS 



The book is so suggestive in each of its directions that one 

 could wish they could have been treated more as separate 

 entities, but by doing this no doubt the book would have lost 

 much of its charm, which is rather suggestiveness in many 

 directions than proof in any one direction. 



The large collection of facts recorded in the book are, as 

 Mr. Cook modestly claims, spadework, but excellent spade- 

 work. The <f> ratio around which the facts are placed is a 

 very brilliant piece of work, and it should have a wide 

 extension of use. The most difficult parts of the book to form 

 a judgment on are those which attempt to correlate the facts and 

 the <f> ratio. Are the approximations to the logarithmic 

 spiral in Nature accidental, or have they any meaning, and, 

 if so, what meaning? Are the </> ratios which are found 

 in Nature and in many forms of Art accidental, or have they 

 any relation to the impression of beauty received by us 

 when looking at a beautiful thing? Is the power of an artist 

 to produce beautiful works of art, is his feeling for beauty, 

 nothing else than the unconscious use of these proportions? 

 These are a few questions which arise, which will require 

 much more work yet to settle. Is it possible that, having a 

 preconceived idea, you can fit such a thing as a ratio to 

 anything ? For instance, if you take a large photograph of 

 Leonardo's Last Supper, it is a remarkable fact that the 

 space proportions can be planned out according to this ratio. 

 The twelve Apostles are divided into four groups, and in each 

 group the heads are so arranged as to correspond to the ex- 

 treme and mean proportion ; also the distances of the two 

 groups on the right and those on the left from the central figure 

 are in the same proportion ; and even the width of the two 

 parts of the tablecloth. 



Mr. Cook gives the Venus of Botticelli as an example which 

 shows the </> ratio in its proportions. It is curious that these 

 proportions should so nearly fit this type of the beautiful con- 

 sumptive girl; and also that this type should have persisted 

 in art as far, at any rate, as Burn e-J ones. The model of the 

 Venus is said to have been Simonetta Catanea, who died of 

 tuberculosis in 1476, at the age of twenty-three. 



It may be that the discovery of this (f> ratio will so stimulate 

 work on these fascinating problems of proportion in Nature 

 and Art that their real meaning may be discovered. At 



