288 



PRINCIPLES OF EMBRYOLOGY 



But if we adopt a more realistic formulation of the growth rates of x 



doc 

 and y, making — =f{x, t), when /(a:, () is one of the functions discussed 

 at 



in the previous section, it can be shown that although the allometry 

 formula is often a good approximation, it will only be exactly true in 

 exceptional cases. 



There are other reasons why the formula cannot be accepted as a strictly 

 accurate description of the situation. The most important is that if two 



2 dist. 

 segments 



Log wt. carpus 



Figure 13.3 



A, the log weight of the two distal segments (crosses) and the two proximal 

 segments (circles) plotted against the log weight of the middle segment 

 (the carpus) of the claw of the Fiddler crab Uca pugnax. The slope of these 

 lines defines the allometric growth constants B, the gradient in growth 

 constants along the claw in Uca (full line) and the spider crab Maia (dotted 

 line). (After Huxley 1932.) 



segments of an organ, y^ and y2, are each related heterogonically to the 

 whole organism, then the sum of the two segments cannot be so related, 

 since if jx = ^i^:"^ and ji = ^2^"^ then y-^ + 72 cannot be of the form 

 hx"^, though the discrepancy is usually not very large. 



One must conclude that the allometry formula, like the other growth 

 equations discussed previously, can at best be taken as a useful empirical 

 summary of a set of data, but that it is not a firmly based theoretical prin- 

 ciple. 



Even with this limitation, a number of conclusions can be drawn from 

 it. In the first place, as long as a remains constant, the rates of growth of 

 the two parts are preserving a constant relation to one another; and it is 



