GROWTH 



291 



One method of illustrating this was introduced by D'Arcy Thompson 

 (1916), although he used it to compare adult forms which are evolution- 

 arily related rather than ontogenetic stages of a single individual. He took 

 one adult form as a standard, drew it in outline as seen when projected on 

 to a plane, and superposed on the drawing a rectangular network. He 

 showed that if this network is treated as a grid of co-ordinates, and is 

 then distorted in the appropriate manner, the drawing of the original 

 shape will be distorted at the same time into a fairly good outline of some 

 other type of animal (Fig. 13.4). Such distortions of a co-ordinate network 

 will produce alterations which are continuously gradated over the whole 

 area, and thus the growth gradients which are affected are probably also 

 continuously graded, since they are likely to depend on the same funda- 

 mental mechanisms as produce the distortions which differentiate one form 

 from the other. More recent workers have in fact shown that the same 

 method can be used to compare different developmental stages of a single 

 species. 



12 3 4 5 6 



Figure 13.4 



A transformation of a co-ordinate grid which converts the outline ofDtodon 

 (left) into that of its relative the sunfish Orthagoriscus. (After D'Arcy Thomp- 

 son 1942.) 



