GROWTH-GRADIENTS IN NEGATIVE HETEROGON Y 87 



by a continuous growth-gradient with the positive centre in 

 the region of the ninth segment. Further, we may safely 

 assume that the copepods, in common with almost all other 

 animals, show a negative heterogony of the head region : 

 accordingly this centre of low growth-intensity will again be 

 connected via a continuous growth-gradient with the positive 

 growth-centre of the antenna. Since the gradient is of the 

 same type in both sexes, the functional differentiation of the 

 terminal region of the male antenna as a clasping organ cannot 

 have any causal significance in determining the low growth- 

 rate of this region. On the other hand, the fact that the 

 heterogony passes from positive to negative at about the 

 eighteenth or nineteenth segment may have had something to 

 do with the fixing of the hinge- joint between the clasping 

 region and the rest of the male antenna at this spot ; such 

 a suggestion must, however, be regarded for the moment as 

 purely speculative. 



§ 3. Reversal of the Sign of the Growth-gradient in 



Negative Heterogony 



Those pereiopods which are used as walking legs appear 

 usually to show slight but distinct positive heterogony, and 

 to have a definite but slight growth-gradient with centre in 

 the merus (Bush, 1930). It is of interest that in the actively- 

 running shore-crab Ocypoda, the young (like the active young 

 of Ungulates) must be provided from the start with relatively 

 large legs if their speed is to be sufficient, so that their pereio- 

 pods show a definite negative heterogony, or decrease in rela- 

 tive size with increase of absolute size : and that here the 

 low point of growth, or ' negative growth-centre ', is also in 

 the merus 1 (Cott, I.e.; Huxley, 1931B). 



A similar reversal of gradient-sign appears to occur in the 

 individual development of Ungulates. D'Arcy Thompson (1. c.) 

 gives a figure (Fig. 48), of the proportions of the foot in ox, 



1 This is from length-measurements kindly supplied in answer to a 

 query of mine by Mr. Cott ; unfortunately, he only had a few speci- 

 mens available for measurement, and the results, while clearly showing 

 the merus as the joint of lowest growth-ratio, are not sufficient to 

 construct a growth-gradient. The indication is that the gradient is 

 complex, first rising above the level for the body-standard (carapace 

 length), then sinking well below it in the merus, then rising again. 

 It would be of great interest to establish this by obtaining statistically 

 adequate data, as this is the only indication so far obtained of a com- 

 plex growth-gradient with two points of inflexion within a single limb. 



