GROWTH-GRADIENTS & GROWTH-INTENSITY 85 



The only references I can find to these striking changes in 

 the proportions of heterogonic Crustacean limbs are those of 

 Kemp and his fellow-workers (Kemp, 1913, 1914, 1915 ; Hen- 

 derson and Mathai, 1910). But they only draw attention to 

 the change in percentage length of the joints, and have not 

 proved the existence of constant differential growth-ratios, or 

 propounded the idea of a growth-gradient. The figures for 

 Palaemon rudis have, however, been analysed by Miss I. Dean 

 (unpublished) and in both series show a definite growth- 

 gradient with growth-centre in the propus (Table VII ; Fig. 46). 



In general, measurements of crustacean limbs show that 

 wherever there is marked heterogony, there is a comparatively 

 steep growth-gradient within the limb, with well-marked 

 growth-centre near the tip (apparently always in the propus) ; 

 when the heterogony is only slight, the growth-gradient is far 

 less steep, and its centre usually near the middle of the limb : 

 in most cases examined either in the merus or carpus. Thus, 

 although the joints of the small (female-type) chela of male 

 Uca do not, to simple inspection, appear to alter in propor- 

 tionate size, measurement shows that in respect at least of 

 linear dimension, they do so, albeit slightly ; the growth- 

 centre here is in the carpus (Huxley and Callow). (It will 

 later be shown that precisely similar relations hold for those 

 brachyuran abdomens which have been measured.) 



Benazzi (1929) has given results on the regeneration of the 

 limbs of the larva of the dragonfly Aesckna grandis from which 

 it can be calculated that for regeneration during two instars, 

 the growth-coefficients (k) of femur, tibia and tarsus, relative 

 to the sum of the three parts, are as follows : femur, 1-12 ; 

 tibia, 1-02 ; tarsus, 072. There is thus a regeneration-gradient 

 in the limb with high point proximally. 



Whereas the gradients of most organs appear to be of 

 the simple form above described, there are some of unusual 

 type in which part of the organ has growth-coefficients 

 above unity, the rest below unity. This is the case with 

 the first antennae of certain copepods (Seymour Sewell, 

 1929) (see Fig. 47). There is a positive growth-centre at 

 the eighth or ninth segment, and a negative growth-centre 

 at the extreme tip. The change from positive to negative 

 heterogony of the segments, relative to total antenna-length, 

 occurs close to the joint between the eighteenth and nine- 

 teenth segments. It is worth noting that when a hinge is 

 developed in the male's grasping antenna, it is formed at this 



