84 Papers from the Marine Biological Laboratory at Tortugas. 



the time of operation antl the first molt and considers the quotient as the 

 " specific rate of regeneration per unit of thoracic length per day." As 

 quoted above, " the members of the series with the greater injury molt more 

 rapidly than those of the series with the lesser injury." Thus it clearly 

 follows that any " constant " divided by fewer days (a smaller number) 

 will give a greater quotient (specific rate of regeneration per day) than 

 the same " constant " divided by a greater number of days. The calcu- 

 lations included in Zeleny's tables 6 and 7 (1905) then, to my mind, fail 

 to show that the greater degree of injury causes a faster regeneration, but 

 merely that those most injured molt sooner after the operation ; and since 

 all regenerate the same specific amount at the end of the first molt re- 

 gardless of the time, of course the ones molting soonest will appear to grow 

 that specific amount quickest. 



A more plausible line of reasoning would seem to be the following: 

 Since all have the same specific amount of regeneration after the first 

 molt, whether it takes 27 or 181 days for the molt to occur, this specific 

 amount probably begins to be formed soon after the operation and con- 

 tinues until it is prevented by the chitinous covering of the crayfish, just as 

 the animal's increase in body-size is always checked by the amount of 

 expansion possible within its inflexible case. When the growth is so checked 

 it must stop and remain quiescent until the molt occurs. The full amount 

 of growth may be attained in 10, 20, or 30 days — no one can say — but 

 after it is once attained all succeeding days until the molt occurs are not 

 days of growth at all, but merely a quiescent period. That some such 

 process as this is followed is strongly suggested by the fact that the specific 

 amount of regeneration is a " constant " for all at the time of the first molt. 



It is not at all certain, then, that the regeneration is continuous through- 

 out the period elapsing between molts ; therefore, one is in error to divide 

 the specific amount of regeneration, a " constant," by the number of days 

 between molts and to consider the quotient obtained as the specific rate 

 of regeneration per day. The columns of specific rates in Zeleny's tables 

 6 and 7 mean nothing, unless it can be proven that the regeneration is 

 continuous during all of the 27 or 181 days, and since the columns of specific 

 amounts show this element to be practically constant it seems likely that 

 all of the individuals regenerate as much as possible soon after the opera- 

 tion and then the process stops until the molt occurs. 



To further illustrate the insufficiency of such a method of calculation 

 we may consider the line of averages at the foot of Zeleny's table 6. The 

 specific amount of regeneration for series x\ averages 0.444 ^"^^ ^c"" series 

 B (the ones with greater injury) 0.435 (practically equal), while the 

 average specific rate of regeneration for A is 0.0049, ^"d for B almost 

 twice as much, 0.008. The columns including the number of days before 

 the molts are not averaged, but if one will make the calculation for tlie 14 



