PHYSIOLOGY OF GROWTH-GRADIENTS 167 



those that had thus been regenerating for one instar, are plotted 

 on a double logarithmic grid against body-size, an interesting 

 result is obtained. Both sets of points approximate nicely 

 to straight lines ; but the line for the regenerates is inclined 

 at a slightly higher angle than that for the normal claws — 

 k = 1-20 instead of 1*15. In other words, during the first instar 

 after operation, large crabs regenerate a slightly greater frac- 

 tion of their claws than do small ones, and the absolute amount 

 of increase is multiplied by a constant factor for each unit of 

 multiplicative increase in absolute size. The amount of this 

 factor is, of course, obtained by dividing the ' growth-ratio ' 

 determined from the slope of the line for the regenerating 

 claws by the actual growth-ratio as found for the normal 

 claws. This paradoxical result may possibly be accounted 

 for on the principle, which holds in many cases, that the 

 rate of regeneration increases with the amount removed. 



We have already seen (p. 52) that when a heterogenic 

 organ is grafted on to a body relatively too large for it, its 

 growth-rate is decreased, so that here too it tends towards 

 its proper relative size. Thus here also the idea of a partition- 

 coefficient, representing an equilibrium between the amount 

 of material in the organ and in the body, is supported. 



§ 2. The Initial Determination and Physiological 

 Basis of Growth-gradients 



An important question is that of the physiological and 

 biochemical bases of heterogony and of growth-gradients. 

 Some experiments of Morgan (1932A) on male fiddler-crabs 

 give some indications on this problem. His results may be 

 summarized as follows. Young male fiddler-crabs, at a very 

 early instar of their post-larval existence, produce two claws 

 of male type. If one of these be amputated, the other is very 

 shortly afterwards fixed as permanently male-type, and will 

 regenerate male-type if later amputated. The amputated 

 claw regenerates of female type and is from thenceforth fixed 

 in this condition. Normally, it is the loss of one claw during 

 the first few instars which determines the right- or left- 

 handedness of the males. 



If both claws are cut off during this early symmetrical stage 

 when both are of male-type, both regenerate of female type, 

 and remain so permanently. Occasionally, however, a male 

 is found in nature which has lost neither of its claws during 



