406 
Note on Dr Simpsons Memoir 
The least examination of these two series shows that one cannot be considered as a random 
sample of the other. Not only are the means of breadth and index sensibly different, but there 
has been a general lowering of the direct and a raising of the cross-correlations, which is far 
beyond the limits suggested by even the large probable errors. As for the index-correlation, 
its immense change is very mysterious*. There has been either considerable change in envi- 
ronment, in average interval from division at which measurements were taken, or, as suggested 
in (1), the breadth to 5 /x is really not close enough to get consistent results. 
It appears therefore that, as the second sei'ies cannot be looked upon as a random sample 
of the first, it would be idle to attempt to use results for growth deduced from it to correct 
for the growth factor the values of the correlations obtained in the first series. Accordingly 
all that seemed possible was to apply the growth results obtained for the short series to the 
correlations obtained for the short series and so reach some appreciation of the screening in- 
fluence of growth on pui'e homotyposis. 
(3) The interval after division was accordingly correlated with length, breadth and index 
for the 44 cases, with the following results : 
TABLE VII. 
Interval and Size. 
Organ 
Correlation 
Length and Interval ... 
Breadth and Interval... 
Index and Interval 
•547 + -071 
•538 +'072 
•273 + ^094 
It will be seen at once that growth-correlation is a most sensible factor in the resemblance 
between individuals when pairs of them are measured at the same interval after division. It 
is least for the index, but is quite sensible even in this case. In other words, the index is 
a more reliable character than absolute length or breadth to deduce pure homotyposis fromt, 
but clearly the average percentage growths in length and in breadth are not equal, and 
accordingly the index itself alters with the interval from division. 
The lengths between 3 and 38 hours interval from division were plotted to the intervals ; the 
results were, of course, very irregular, but a straight line certainly would represent them as 
efiectively as any curve. For the data available accordinglj' the regression line of age and size 
was taken as the average curve of growth. In other words, for an organ x the growth in time 
T was taken to be ^ where r^.; was the correlation for interval from division and size 
tabled above in VII, the standard deviation of the organ x and o-j that of the intervals of 
time given in Table V. Thus if x be the observed size of an organ at time t its most probable 
size, at the mean interval t after division, would be 
a;' = x--^^ (t-t). 
* The value of the index-correlation was also determined for the second series indirectly from the 
formula R. S. Proc. Vol. 60, p. 493. The value found was •130, which agrees as well as could be 
expected with the direct value -114 given above. 
t Used by K. Pearson for gills of mushrooms and by E. Warren for ivy leaves for this reason: 
see Phil. Trans. Vol. 197, A, pp. 240, 338. 
