210 THE RATE OF GROWTH [ch. 



The facial and cranial parts of a dog's skull tend to grow at 

 different rates (Fig. 56) ; and changes in the ratio between the two 

 go a long way to explain the differences in shape between one dog's 

 skull and another's, between the greyhound's and the pug's. But 

 using Huxley's own data (after Becher) for the sheepdog, I find the 

 ratio between the facial and cranial portions of the skull to be, once 

 again, a simple linear one. 



Measurements of skull of sheep-dog (30 specimens) * {mm.) 



Mean length of facial region (y) 



Mean length of cranial region- (x) 



Calculated values for cranial 

 region: x = 22-7 +0-88y 



And now, returning to the fiddler-crab, we find that after the 

 crab has reached a certain size and the first phase of rapid growth 

 is over, claw and body grow in simple linear relation to one another, 

 and the heterogonic or compound-interest formula is no longer 

 required: 



Fiddler-crab (Uca pugnax): ratio of growth-rates ^ in later stages ^ 

 of claw and body (mgm.) 



Weight of body less 872 983 1080 1165 1212 1291 1363 1449 

 claw {x) 



Weight of large 418 461 537 594 617 670 699 778 



claw {y) 



Do., calculated: 413 480 538 590 617 665 708 759 



y=0-6a;-110 



* Data from A. Becher, in Archivf. Naturgesch. (A), 1923; see Huxley, Problems 

 of Relative Growth, p. 18, and Biol. Centralbl. loc. cit. Here, and in the previous 

 case of Cydommatus, the equation has been arrived at in a very simple way. Take 

 any two values, x^, x^, and the corresponding values, yi, y^. Then let 



x-Xj^ ^ y-yi 

 ^-^ Vz-Vx 

 Of -65-3 v-48-3 



e.g. 



or 



from which a; = 22-7+0-88y. 



We may with advantage repeat this process with other values of x and y; and 

 take the mean of the results so obtained. 



112-6-65-3 1020-48-3^ 



a; -653 _y-48-3 

 47-3 "■ 53-7 * 



