I 6 CHARLES ZELENY. 



Expressing this in mathematical form, if E l represents the re- 

 generative energy exhibited in the replacement of the lost arm 

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

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

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

 number of absent arms, then not only is E > E, but also E ln~>E, 



J n~^ \ n' -^ 1 



or E n >nE r Therefore when we remove n arms we increase the 

 total regenerative energy by more than n times the amount ex- 

 hibited 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, B, C, D and E, in which a r b v c v d^ and 

 e l 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 a 4 > a v b 4 > b lt c 4 > c v d > d r Now in the first case 

 mentioned we cannot assume that the stimulus of removal and 

 the resultant reaction of regeneration are purely local and con- 

 cern 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 (/- 4 ) to each of the ori- 

 ginal single regeneration lengths, e. g., <? 4 = ^ -f- ;- 4 . Then a 4 -f b 

 4- c 4 -(- d 4 = a l + b l -f c\ + d l + R 4 where R 4 (= -V 4 ) 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 whole 

 on the regeneration of its arms as one of retardation, we must take 

 the values a 4 , b, c 4 and d 4 as representing most nearly the origi- 

 nal local stimulus effect. Then without changing the values of 

 r 4 or R A we may rearrange the formulse, making a l = a 4 r 4 , 

 etc., and ^ + b^ -f c l -f </, = ^ 4 + /> 4 -f c 4 + d 4 R 4 . 



But whether we consider the influence of the organism as a 

 whole to be one of acceleration or one of retardation we must 

 recognize in either case that the regeneration rate is not a matter 

 which involves only the local conditions at the wounded surface 



