PROBLEMS OF RELATIVE 



GROWTH 



CHAPTER I 

 CONSTANT DIFFERENTIAL GROWTH-RATIOS 



§ i. Introductory 



THE problem of differential growth is a fundamental 

 one for biology, since, as D'Arcy Thompson especially 

 has stressed (1917), all organic forms, save the simplest 

 such as the spherical or the amoeboid, are the result of dif- 

 ferential growth, — whether general growth which is quantita- 

 tively different in the three planes of space, or growth localized 

 at certain circumscribed spots. But the subject has received 

 little consideration. D'Arcy Thompson's own treatment, 

 though exhaustive on certain points (e.g. the logarithmic 

 spiral), profoundly original and important in others (e.g. his 

 use of Cartesian transformations to illuminate the evolution 

 of one form from another), and interesting throughout, is 

 admittedly incomplete. Certain large bodies of data, such as 

 those included in Donaldson's The Rat (1924) and in various 

 treatises on physical anthropology, e.g. R. Martin (1928 ) exist 

 on differential growth in mammals, but have so far not been 

 analysed save by the use of purely empirical formulae ; Champy 

 (1924) has written a very stimulating book on differential 

 growth of such extreme type as to warrant the term ' dys- 

 harmonic ', and has later given further examples (1929) ; 

 Przibram has recently (1930) collated some of his interesting 

 results and ideas. But, apart from this, little that is con- 

 nected or general has been written on the subject ; and even 

 the individual papers dealing with the topic are few and on 

 the whole disconnected. 



Since 1920 I have been studying certain phases of the 

 problem : the purpose of the present review is to bring to- 

 gether the various aspects which have presented themselves, 



