The Determination of Size 



625 



genetic force, in accordance with the princi- 

 ple of similitude (cf. Thompson, '41). 



RELATIVE GROWTH 



Studies in relative growth or allometry are 

 essentially studies of changing shape with 

 increase in size, generally in the simplest 



growth lies in D'Arcy Thompson's illumi- 

 nating employment of Cartesian transforma- 

 tions for comparing the shapes of related 

 forms, for these implied the existence of a 

 general gradient-pattern in growth. 



The effort to find the simplest relation 

 between two growing dimensions has led 

 generally to the use of a power equation of 



Lcnglh soo mm. 



LENGTH OF BODY IN MM. 



lO 



lOO 



lOOO 



Fig. 215. Relative growth in Polyodon (from D. H. Thompson, '34). Logarithmic plot of rostrum- 

 length/body — length. 



form, that is, as exhibited between two vary- 

 ing measurable dimensions, usually linear. 

 The literature is extensive and has become 

 progressively mathematical in a numerical 

 sense. It has also acquired a formidable 

 terminology, and both features have done 

 much to obscure the issues. The terminology 

 is discussed at some length by Needham 

 ('42), Reeve and Huxley ('45), and Richards 

 and Kavanagh ('45). 



The inspiration for the work on relative 



the form y=bx^ or, in a linear form, log 

 y=k log X + log b (Huxley, '24, '27). The 

 exponent k is the ratio of two specific growth 

 rates and its values are obtained, in a sense, 

 by cancelling out time, so that k becomes 

 a correlation or partition coefficient. The 

 value of b depends on the measuring scales 

 employed and it possesses no unique bio- 

 logical significance, k is a pure number and 

 is not constant, but may be so when specific 

 growth rates change in such a manner as 



