CONSTANT DIFFERENTIAL GROWTH-RATIOS 9 



will reproduce the actual figures for weight. 1 But we can be 

 perfectly sure that the actual growth-rate of the crab and of 

 its claw slows off with age, that it differs in summer and 

 winter, and is further subjected to all kinds of irregular fluc- 

 tuations due to temperature, food and other factors. The 

 actual rates may be as 8,000 : 5,000 in early life, as 160 : 100 

 later, as 4 : 2-5 in maturity, and as 0-08 : 0-05 in extreme old 

 age ; yet so long as the ratio 8 : 5 is preserved, claw-size will 

 always be the same function of body-size — a body of given 



100 ZOO 300 400 600 BOO 1000 IZSO H00 1750 Z000 ZZSO 



weight of rest of body.mg 



Fig. 2. — Increase of absolute and relative chela-weight in the large chela of 

 the male fiddler-crab, Uca pugnax. 



(Constructed from the data of Huxley, 1927A.) 



weight will have attached to it a claw whose weight would 

 be the same whether the body had taken three weeks or three 

 years to reach its present size. 2 The differential growth-ratio re- 

 mains the biologically and morphogenetically important factor. 

 The expression^ = bx k can be written log y = log b + k log x. 



1 y = 2, x = 100. At time t, y, = y e om , x t = A' o e 005( . After ten 

 years, y 10 = 2e os = ^4-45, and x 10 = iooe ' 5 ' = ^164-92. After twenty 

 years, y 20 = ze 16 = ^9 - 9i. and x 20 = iooe 10 = £271-9, and so on. 

 Double logarithmic plotting of these figures gives a straight line. 



2 In all probability this is only true as an approximation. It is a 

 priori unlikely that there is no differential effect of environmental 

 agencies on the growth-rates of body and chela respectively. 



