366 Charles Zelejiy. 



other attempts at explanation. The factor that they bring up 

 may be supposed in every case to cause a difference in food- 

 material distribution which in turn causes the difference in rate of 

 growth. Under the present head it is therefore pertinent to dis- 

 cuss only the supposition that the direct mechanical disturbance 

 of the channels of food-distribution shunts the materials off in 

 such proportions into the new channels as to make probable an 

 explanation purely on these grounds. At the very beginning the 

 pure assumption must be made that the total amount of food 

 materials elaborated and involved in chela-building in our case is 

 a constant (K) in all individuals regardless of the character of the 

 injury. The source and distribution of the food stuffs may be 

 indicated by the diagrams shown in Figs. 4, 5 and 6. The facts 

 to be explained are that chela C in Series A (Fig. 5) regenerates 

 less rapidly than either chela C or C^ in Series B (Fig. 6). The 

 assumption according to the hypothesis now being tested is that 

 the rate of growth and regeneration is determined by the amount 

 of food material, an increase in the amount of food material gomg 

 to a part determming the increase in rate of growth or regenera- 

 tion of that part. The assumption is also made that the same 

 kind of material is used m the growth of an uninjured chela as in 

 the regeneration of a removed one and that the total amount of 

 this food-material being distributed is a constant (K). 



The distribution of the food-material may be represented for 

 the three cases given in Figs. 4, 5 and 6 by the following formulae: 



K = C + O + D + D' + E + Ei. (Unoperated series, Fig. 4.) 

 = reg. budC + C' + D + D' + E + E>. (Series A, Fig. 5.) 

 = reg. bud C+ reg. bud C'+ D + D' + reg. bud E + reg. bud E^ (Series B, Fig. 6). 



Now the rate of regeneration of chela C in Series B is greater 

 than that of chela C in Series A. Therefore according to the pres- 

 ent hypothesis the amount of food material going to the former 

 chela bud is greater than that going to the latter or reg. bud C (in 

 series B) > reg. bud C (in Series A). 



Therefore 



reg. budC'+D +D' + reg. bud E + reg. bud E^>0 + D + Di + E + E'. 

 (Series B). (Series A). 



But D +DMs the same in the two series. 

 Therefore 



reg. bud C + reg. bud E + reg. bud E^ < C + E + E' 



