Raymond Pearl 67 
TABLE VI. 
Index Correlations in Ghilomonas. 
Series 
Characters 
Gross (p) 
Spurious* (pd) 
Net* {p-p,) 
A (Poor conditions) 
B (Good „ ) 
A (Poor „ ) 
B (Good „ ) 
Index and Length 
n n »i 
„ „ Breadth 
}) J1 5) 
- -446 + -038 
- -389 + -043 
+ -407 + -040 
+ -426 + -042 
- -723 ± -023 
- -689 + -027 
+ -7231 -023 
+ -689 + -027 
+ •277+ -044 
+ •299+ -046 
- -317+ -043 
- -263+ ^047 
In this table the column headed " Gross " gives the observed correlations 
between the designated characters; the column headed "Spurious" gives the 
value which this correlation would take if the organic correlation between length 
and breadth did not exist ; and finally the column headed " Net " gives the portion 
of the " gross " coefficient which is due to the existence of an organic correlation 
between the index and the particular character under consideration. 
From the values in Table VI we see that : 
(a) The net organic correlation between the length-breadth index and length 
is positive, while the correlation between the index and breadth is negative. 
Thus the net correlations are opposite in sign to what the gross correlations are. 
The sign of the gross coefficients is in each case what we should expect it to be 
for arithmetical reasons, because the length is the denominator and the breadth 
the numerator of the index fraction. 
(h) The net coefficients are of considerable magnitude, and represent clearly 
a sensible real correlation between the index and the absolute dimensions. They 
show that there is a definite correlation in this form between shape and size of 
body. The theoretical bearing of this result will be discussed farther on in the 
paper. 
(c) The index correlations are of sensibly the same magnitude in both series, 
as are the correlations for absolute size characters (cf supra, p. 64). 
(d) The index is correlated more closely with breadth than with length in 
Series A, where the environment was unfavourable, while the opposite relation 
prevails in Series B, with a favourable environment. The differences are small, 
however, and no great stress is to be laid on them. 
Without at this time entering upon any discussion of the matter, I should like 
merely to call attention to the fact that the values for the variation and correlation 
constants for Ghilomonas agree very well with what we have found for similar 
characters in other Protozoa. From Table V we see that the coefficients of 
* The probable errors in the "spurious " and "net" columns are calculated from the usual formula 
1 _ j-2 
for the probable error of a correlation coefScient, P.E. r=: '07449 — , — . This assumes that the probable 
■Jn 
error of these constants is the same as it would be if they had been determined from the product 
moment. The error involved in this assumption is probably insignificant. 
9—2 
