1 6 Charles Zeleny. 



4. Discussion. 



We must, therefore, conclude that when more than one arm is 

 removed the regenerative energy as expressed in the replacement 

 of the lost arms is greatly increased. Not only is the total regen- 

 erative energy greater in this case, but the energy expressed in each 

 arm is greater than the total energy when only one arm is 

 removed. 



Expressing this in mathematical form, if Ej represents the 

 regenerative energy exhibited m the replacement of the lost arm 

 when only one is removed, assuming that increase in length is a 

 measure of such energy, and E„ represents the energy exhibited 

 in regeneration when more than one arm is removed, ?7 being the 

 number of absent arms, then not only is E,; > Ej but also 



— > Ej or E« > n Ef 



n 



Therefore, when we remove « arms we increase the total regenera- 

 tive energy by more than n times the amount exhibited when only 

 one is removed. The force of this statement is made especially 

 strong when we consider that throughout the experiments the 

 animals received no food supply whatever. 



Expressing the relation in still another way, let us take a brittle- 

 star with arms A, By C, D and E, in which a^, h^, c^, d^ and e^ 

 represent the respective lengths these arms will attain after a 

 definite period of regeneration, supposing that one alone is cut off 

 in each case. Now let us suppose instead that the first four are 

 cut off, then after this same period of time we get for the regener- 

 ated lengths a4>fli, h^yb^, c^>c^, d^yd^. Now in the first case 

 we cannot assume that the stimulus of removal and the resultant 

 reaction of regeneration are purely local and concern only the 

 tissues in the immediate vicinity of the cut surface, for we then 

 get into difficulty as soon as we try to explain the cases where four 

 arms are simultaneously removed. Here we find we must add a 

 considerable quantity (r^) to each of the original single regenera- 

 tion lengths to get the new regeneration length, e. g., a^= a^+r^. 

 Then a.+b. + c^+d^ = a^+b^+c^+d^-^R^ where R^ ( = I r^) 

 represents the total response of the organism as a whole which 

 must be added to the local effects of the operation stimulus. If, 

 on the other hand, we consider the influence of the organism as a 



