370 BOTANICAL GAZETTE [NOVEMBER 
two populations of Ranunculus ficaria, but MAcLEop (1899) has 
shown that similar changes may be found in that spec‘es at d'fferent 
times in a single season. I have also found (SHULL 1902) that the 
coefficients of correlation in Aster prenanthoides may be very different 
at different parts of the season. 
Before the significance of such changes can be understood it will 
be necessary to investigate the nature of correlation when considered 
in this statistical way. Some biologists use the term “correlation” 
to designate a relation between two organs or characters, such that 
the development of the one determines that of the other, as for instance 
the dependence of the secondary sexual characters upon the primary 
in animals, or the relation of the internodes to the leaves in plants. 
In this kind of correlation the failure of the one organ or character 
to develop, or its removal at an early stage of development, invariably 
prevents or modifies the development of the other. Every degree of 
correlation in this sense is found in different cases, and it probably 
exists to some extent even between organs whose immediate relations 
to each other are little understood. It is only rarely, however, that 
this kind of correlation is not insignificant as compared with biometr- 
cal correlation. Thus, in the biometrical sense there is a very high 
correlation between the index fingers of the right and left hands, 
but the removal of one of these would have no appreciable effect 
upon the development of the other. 
For convenience we may speak of “immediate” 
correlation when one organ or character stands in a 
relation to another, and “mediate” or “indirect” correlation in cases 
of correlated variation in which no such direct dependence exists. 
Statistcal measures of correlation make no distinction between these 
two kinds of correlation, but as a notable degree of immediate corre- 
lation is comparatively rare, while mediate correlation 1S almost 
universal, the correlation of parts as spoken 0 
may be considered as mediate or indirect. 
between two organs or characters may be defined, 
mutual relation to the combination of common causes, a 
ity, nutrition, etc., which determine their quantitative sees 
It is the relation which results in proportion and symmetry: 
. ans OF 
mediate correlation is perfect, 7. e., when p=1; the two OFS 
or ‘direct ” 
d rect causal 
