150 THE RATE OF CxROWTH [ch. 



it has a higher "coefficieDt of growth," and accordingly, as age 

 advances, the disproportion between the two claws becomes more 

 and more evident. Moreover, we must assume that the character- 

 istic form of the claw is a "function" of its magnitude; the 

 knobbiness is a phenomenon coincident with growth, and we 

 never, under any circumstances, find the smaller claw with big 

 crushing teeth and the big claw with little serrated ones. There 

 are many other somewhat similar cases where size and form are 

 manifestly correlated, and we have already seen, to some extent, 

 that th^ phenomenon of growth is accompanied by certain ratios 

 of velocity that lead inevitably to changes of form. Meanwhile, 

 then, we must simply assume that the essential difference between 

 the two claws is one of magnitudej with which a certain difEerentia- 

 tion of form is inseparably associated. 



If we amputate a claw, or if, as often happens, the crab "casts 

 it off," it undergoes a process of regeneration, — it grows anew, 

 and evidently does so with an accelerated velocity, which accelera- 

 tion will cease when equilibrium of the parts is once more attained : 

 the accelerated velocity being a case in point to illustrate that 

 vis revulsionis of Haller, to which we have already referred. 



With the help of this principle, Przibram accounts for certain 

 curious phenomena which accompany the process of regeneration. 

 As his experiments and those of Morgan shew, if the large or 

 knobby claw (A) be removed, there are certain cases, e.g. the 

 common lobster, where it is directly regenerated. In other cases, 

 e.g. Alpheus*, the other claw (B) assumes the size and form of that 

 which was amputated, while the latter regenerates itself in the 

 form of the other and weaker one; A and B have apparently 

 changed places. In a third case, as in the crabs, the yl-claw re- 

 generates itself as a small or 5-claw, but the B-claw remains for a 

 time unaltered, though slowly and in the course of repeated moults 

 it later on assumes the large and heavily toothed ^-form. 



Much has been written on this phenomenon, but in essence it 

 is very simple. It depends upon the respective rates of growth, 

 upon a ratio between the rate of regeneration and the rate of 

 growth of the uninjured limb : complicated a little, however, by 



* Wilson, E. B., Reversal of Symmetry in Alpheus heterochelis, Biol. Bull, rv, 

 p. 197, 1903. 



