38 SHINKISHI HATAI 



when the value of this constant is equal to zero, the resulting 

 curve will be parallel to the abscissa with the distance corre- 

 sponding to the value of the constant A, therefore the increase in 

 the constant "h" means that the curve becomes steeper as the 

 frog becomes larger, at the same time with an increasing distance 

 of the entire curve from the base line. For the latter statement 

 we find one exception in group 3, in which the value of the con- 

 stant "A" is smaller than that of the smallest frog. If however 

 we examine the observed mean values in that group, a peculiarity 

 can be found at once; that is the mean values in both the lower 

 and upper ends of the curve are too small compared with the 

 values found in the middle. Since our determination of the con- 

 stants is based on the observations, such an aberrant result for 

 this particular group is inevitable. Nevertheless, the higher 

 value of the other constant "h" indicates a higher probability 

 that all the mean values for group 3 should have been greater than 

 they actually were. 



Therefore with a single exception in the one constant in group 

 3, the equations are in harmony with the general feature in the 

 growth of the internodes. When we come to an actual test, 

 the observed values are too irregular to make valuable a detailed 

 comparison with the corresponding values obtained by the 

 equation. 



On account of the difficulty just mentioned, the question of 

 fit between the theoretical values and the observed can best be 

 judged by an actual comparison of the tw T o graphical represen- 

 tations of the values (see chart 3). 



As we notice from the curves, the fit of the theoretical curve 

 to the observed is very satisfactory in the first three groups, and 

 the continuous lines run about the middle of the observed points. 

 In groups 4 and 5 it is not as good as in the former three groups, 

 nevertheless when the irregularity of the observed values in these 

 two groups is considered, the continuous lines should be regarded 

 as the best approximation to the observed values. At least the 

 continuous lines run very close to the observation in the best part 

 of the curve, that is the middle portion where the number of obser- 

 vations is large. 



