42 SHINKISHI HATAI 



The above table shows clearly that for any given diameter the 

 length of the internodes which are nearer to the proximal end of 

 the leg are shorter than those away from it. This observation 

 suggests the possible existence of an exponential relation between 

 the internodes from different segments of the leg in the same 

 frog. In order to investigate this point, the total averages were 

 taken as shown in the above table. I took this average for the 

 reason that first, all frogs are mature, and second, on account of 

 higher variability of the length of the internode, the sum of the 

 larger number is important. From the average we see that the 

 diameter which is approximately 6 micra gives 659 micra for the 

 internode at the upper end of the thigh, and 855 micra for the 

 internode found at the upper portion of the foot (cruro-tarsal 

 joint), that is the relation between the two is 1:1.29. 



To determine whether or not a similar relation can also be 

 found between the length and diameter of the internode in differ- 

 ent sized frogs, I selected two values of the internode for the 

 diameter of 6 micra; one from group 4 and the other from group 5, 

 as these two mean lengths are the nearest values giving a diam- 

 eter comparable with the averaged figures in Takahashi's table. 

 We have here 780 micra and 963 micra for the internodes in 

 groups 4 and 5 respectively. 2 In this case the proportion between 

 the two internodes is 1 : 1.23 as contrasted with 1 : 1.29 in the 

 other. 



These two ratios agree very well for the diameter of 6 micra. 

 This agreement is necessary for the argument, but does not per- 

 mit us to conclude that the relation between the diameter and the 

 length of the internode in the different segments of the leg of the 

 same frog is also exponential, since we cannot determine the form 

 of the curve. For this reason we must seek for further evidence. 



An examination of the figs. 3 to 6 in Takahashi's paper gives 

 us an additional reason for the above conclusion, since there we 

 find that not only the length of the internode for a given diam- 

 eter increases towards the periphery, but the three lines repre- 



2 Takahashi has pointed out thai the internodes on the fibers from the American 

 frog, R. pipiens, are shorter than those found by Boycott on the fibers of R. tem- 

 poraria (fusca). 



