QUANTITATIVE ANALYSIS 113 



progressively more left-handed. The same is true for females, 

 but the right-handedness is less in the right-handed region, 

 the left-handedness greater in the left-handed region. In 

 accordance with this greater right-handedness of the males 

 (which is doubtless correlated with the extreme right-handed- 

 ness of the male chela), the male is still slightly right-handed 

 at the level of the fourth pereiopod, while the female is here 

 symmetrical ; i.e. the change from right- to left-handedness 

 is not associated with a particular appendage, but takes place 

 in relation with a graded distribution of growth-intensity. 



An extremely interesting case of a large-scale growth-gradient 

 extending through much of the body is provided by the stag- 

 beetles (Lucanidae). It is well known to Coleopterists that 

 large males are characterized, not only by relatively large 

 mandibles, as we have already seen, but also by relatively 

 large heads, prothorax and prothoracic legs, although the 

 relative increase for these is much less than for the highly 

 heterogenic mandibles. So far as I am aware, however, no 

 measurements have been available until those recently made 

 by Mr. Edwards at my suggestion and analysed by me (Edwards 

 and Huxley, unpublished). They refer to L. cervus. 



The partition-coefficients of various organs, against elytron- 

 length, in males are as follows (between elytron lengths 15 

 and 21 mm.). 



There is thus, in general, a decrease in growth-intensity from 

 front of head to hind limb, in other words, a growth-gradient 

 with centre in the mandibles. Heterogony changes from 

 positive to negative between the first and second leg. (It may 

 be noted in passing that the gradient is a little steeper in the 

 femora than in rest-of-leg — evidence of a graded effect within 

 the legs.) 



The data for the females are not so full, but indi- 

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