INDIVIDUATION— FORMATION OF PATTERN AND SHAPE 423 



and the appearance of six tentacles, to such a mechanism. But tliis does 

 not seem very convincing. One of the most important characteristics of 

 embryonic development is that the patterns which arise tend to be accom- 

 modated to the total amount of material available. For instance, a normal 

 embryo can be formed from half an egg, or from two eggs fused together; 

 or if a flatworm is cut longitudinally into strips each much narrower 

 than the normal breadth of the worm, nevertheless each of these will 

 regenerate a complete head. In patterns which behave in this way, the 

 distance apart of the various elements cannot be fixed by any defmite 

 chemical wave-length dependent on the unchanging values of rate con- 

 stants, diffusion constants, etc. Rather the pattern must arise as a whole 

 within the boundaries of the material available. 



The simultaneous rhythms of Henke or the chemical rhythms of 

 Turing cannot, then, provide a general explanation of the periodic 

 patterns which are important to animal morphology. It seems in any 

 case improbable that fundamental rhythmic patterns, such as those of the 

 somites of the vertebrate body, would be dependent on such an inherently 

 chancy mechanism as that investigated by Turing. Probably the processes 

 which he and Henke have discussed play a part only in the quasi-periodic 

 dapphngs and mottlings which often fill up relatively unimportant spaces. 

 The fact that a developmental pattern is usually found to become either 

 enlarged or diminished in scale so as to fit into the available material sug- 

 gests that the boundaries of the mass of substance play a major part in the 

 processes by which the pattern is formed. For instance, in a regeneration 

 blastema of a flatworm, it may be that some process always attains a 

 critical value in the midline and falls off to zero at the two lateral edges. 

 If this, or something like it,, were the case, one could understand how a 

 complete head appears even on a very narrow strip. Again, in Henke's 

 wings which are characterised by a central field, we may suppose that the 

 position on the anterior margin from which the diffusion of the field 

 starts is always midway between the base and the tip, however large or 

 small the wing may be. It is only by some such relations as this, in which 

 the pattern is produced in dependence on the boundaries of the material 

 available, that the facts as they are observed can be adequately under- 

 stood. 



Although, as has been stated above, developmental patterns often 

 retain their completeness even when the material available is considerably 

 greater or less than normal, this is not always the case. The relation 

 between pattern and mass is certainly not simple and probably 

 differs in different cases. A number of other instances will be mentioned 

 below. 



