Karl Pearson 
409 
the observed frequency is placed alongside each point. It may be doubted whether 
the ultimate decrease of breadth with increasing length is real and not solely 
due to the two abnormally narrow corpuscles of maximum length. Still there is 
some sign of a tendency to reduced breadth before these are reached. 
(4) I had much hoped that the index of the blood corpuscle would be a 
character free from growth changes, but the previous section shows that in this 
respect it is not available. A direct investigation of the correlation of the body 
length of the tadpole and the index of its blood corpuscles (Table F) gives for the 
coefficient of correlation, 
r= + -179 + -016. 
Thus the index alters with the growth of the tadpole quite significantly, but not 
so intimately as in the case of the length of the corpuscle. The change is of 
course in the opposite direction since the index = breadth/length, and the small 
decrease in breadth is more than compensated by the greater decrease in length. 
The corpuscle tends to become rounder with the growth of the tadpole. 
For comparative purposes, we find : 
TABLE V. 
Comparison of Corpuscle Indices for Tadpoles of Toad and Frog. 
Number 
Mean 
Standard 
Deviation 
B. vulgaris 
R. temporaria ... 
725 
1775 
•751 
•732 
•0810 
•1047 
14^31 
+ •081 
+ •179 
It would thus appear that the corpuscle in the toadpoU is somewhat more 
orachycalic than in the tadpole, sensibly less variable and less modified by growth. 
On plotting the means of the index arrays to the successive body lengths 
for tadpoles, the resultant regression line was a very irregular polygon, but showed 
distinct signs of a non-linear regression. Accordingly the correlation ratio was 
found for the indices and body length, and gave the value rj = •348, thus demon- 
strating that the index does not increase uniformly with the body length. It rises 
in fact quickly with body lengths from 5^6 to 7^8, and then remains nearly constant. 
I may remark that for a somewhat different series of tadpoles, the correlation ratio 
between index and total length, not body length, was found to be somewhat higher, 
i.e. 77 = •405. There is thus more relation between index of corpuscle and growth 
of the tadpole than is indicated by the correlation coefficient •179. In the case of 
toadpoll's corpuscles, the regression is again not linear and the correlation ratio, 77, 
is equal to •273. To get rid of the lumpiness due to taking only 25 corpuscles from 
71 tadpoles and 29 toadpoUs, we need probably 50 to 100 corpuscles from four or 
five hundred individuals. 
Biometrika vi 52 
