QUANTITATIVE ANALYSIS in 



dimensions, of numerous parts of the body ; and these must, 

 for one thing, be made at a considerable number of absolute 

 sizes, to make sure that the gradients, etc., do not change 

 with age, and for another be made on a considerable 

 number of specimens within each size-group, to exclude the 

 effects of random sampling. Such a body of measurements 

 only exists for very few animals, and even there not for 

 sufficient points or organs to give a complete picture of 

 the growth-gradients ; but in spite of these limitations, the 

 results are of considerable interest. We will begin with 

 the case of the hermit-crab, Eupagurus, analysed under 

 my direction by S. F. Bush (Bush, 1930 ; Bush and 

 Huxley, 1930). Measurements were made of the eyestalks, 

 first and second antennae, third maxillipeds, chelae (= first 

 pereiopods), pereiopods 2-5, and uropods, as well as of median 

 pre-thorax length as standard ; (in some appendages the 

 length of an arbitrary portion was taken in place of total 

 length). When groups of small and large body-size were 

 compared, the following significant facts emerged. We will 

 first consider males, and in them the left side of the body, 

 where matters are not complicated by the pronounced asym- 

 metric heterogony of the right chela. Here we find a quite 

 definite double growth-gradient, with growth-centre in the 

 third pereiopod, whose growth-coefficient is considerably higher 

 than that of the body (pre-thorax) ; from this point growth- 

 activity falls off both anteriorly and posteriorly, until it is 

 about equal to that of the body in the third maxillipeds and 

 fourth pereiopods respectively, while less in the cephalic 

 appendages and uropod (Fig. 61). There is a slight irregularity 

 in the region of the last pereiopods ; otherwise the gradient 

 is quite regular. 



This is remarkable, since the organs measured are not only 

 of very different shape, but differ vastly in absolute size ; yet 

 the short eyestalk, first antenna and third maxilliped, the 

 long second antenna, the large first to third pereiopods and 

 the small fourth and fifth pereiopods, all, as regards their 

 growth-ratios, fall into this regular graded series. 1 



The further significant fact emerges that although we are 

 only considering the growth of localized appendicular organs ; 



1 This appears doubly surprising, since the size of an appendage 

 must in the long run depend upon its relative growth (growth-ratio) ; 

 we shall meet with the probable explanation of this paradox later 

 (§3. P- 118). 



