THE UNIQUENESS OF THE INDIVIDUAL 



different rates in different parts of the body. Dr J. S. Huxley 

 has made a special study of these inequalities, and two ex- 

 amples of change of shape cited in Problems of Relative Growth 

 are shown in figs. 6 and 7. Adults of different but related 

 species acquire their distinctive shapes because they conform to 

 different but related rules of transformation. Some of their 

 end results are shown in neighbouring figures (8, 9). These 

 figures are taken from D''Arcy Thompson''s classical work On 

 Growth and Form^ and more will be said of Thompsonian pro- 

 jections later. 



The form of an object, unlike its size, cannot be expressed 

 by a scalar quantity, a simple number. No child was ever 2*5 

 Thompsons in form. Form must be expressed by a correlated 

 system of vectorial measurements, i.e. measurements which 

 take account of the disposition of the measured lengths in 

 space. But although shape is in a purely metrical sense in- 

 definable, change of shape is not. Consider a lantern slide 

 thrown on a screen that lies in its normal position at right 

 angles to the optical axis of the projector. When the screen 

 tilts one way or another, the cone of light is cut at different 

 angles and the image is accordingly transformed. The nature 

 and degree of the distortion can be expressed with mathe- 

 matical exactness. No matter how complex the pattern of the 

 image, its change of shape can be accurately defined. 



Huxley''s method of assaying change of shape in development 

 is to measure the growth rate of one part of the body in terms of 

 the growth rate of another. If transformation is an orderly 

 process, the two sets of measurements will vary in dependence 

 on each other. In the simplest case, not uncommon but by no 

 means universal, the parts in comparison multiply their sizes 

 in a constant ratio: the size of one is a fixed multiple of the size 

 of the other when the size of the other is raised to a constant 

 power. Proportions alter, therefore, but alter in geometrical 

 progression. It is only when the ratio or power is unity that the 



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