QUANTITATIVE ANALYSIS 



ii5 



end : the gradient is not only steepened but tilted round a 

 point within its length (cf. Hammond's sheep limbs, p. 88). x 



Fig. 62 shows the essential facts. It will be seen that besides 

 the parts mentioned, there is also a slight heterogony of the 

 male antennae and prothorax (and see Table XIa) ; further, 

 that in the regions of the body measured, heterogony in 

 length and breadth is quantitatively different. The most 

 significant point is that the heterogony of the three pairs of 

 legs is graded in an antero-posterior direction. The facts in 

 general support the conception that there exists a growth- 

 gradient with centre in the mandibles, grading down pos- 

 teriorly 2 (Fig. 63). 



Theoretically, two further points appear to me particularly 

 interesting. The first is this, 

 that we can exclude functional 

 hypertrophy as the cause of 

 the correlated increase of the 

 other parts. In fiddler-crabs, 

 for instance, and other Crus- 

 tacea, it might be suggested 

 that the increased weight of 

 the large chela caused extra 

 strain to be put on neigh- 

 bouring limbs, which then re- 

 sponded by functional hyper- 

 trophy. It would be difficult 

 to reconcile this with the 

 correlated decrease of the limbs 

 anterior to the highly heter- 

 ogenic appendage, which will 



be discussed later in this chapter, but the interpretation is 

 wholly ruled out in a holometabolous insect, in which the 

 male legs have never had to support the weight of the 

 enlarged mandibles before they appear in their definitive, 



1 Champy's figure (1929, p. 198) of the beetle Oryctes rhadama 

 indicates a similar gradient with high point anteriorly, but here affect- 

 ing {inter alia) two sexual heterogonic organs, the two ' horns ' of the 

 male. The heterogony of the more anterior, cephalic horn is clearly 

 greater than that of the thoracic horn. 



2 Some of the quantitative data for the thorax do not fit in with the 

 idea of a uniform gradient. It will be necessary to make additional 

 measurements on other species to clear up this point : as previously 

 indicated, however, there is no necessity to suppose that such gradients 

 are always uniform and not complex in shape. 



Fig. 63. — Probable growth-gradients 

 in the body of male and female stag- 

 beetles (Liicamts cervus). 



