30 * BULLETIX 931, U. S. DEPAETMEXT OF AGRICULTURE. 
that experiments 71 and 72. in which they showed the least virulence, 
vrere conducted in a colder greenhouse than any of the other tests 
may have had something to do with the lower activity indicated for 
these strains. Variation in the temperature requirements of different 
strains in accordance with the temperature of the source locality has 
already been demonstrated by Edgerton (35) for one of the anthrac- 
noses. It is hoped later to determine the temperature and acidity 
preferences of these two strains as compared with the others used. 
It should be noted that the consistently weak strain Xo. 189 (fig. 2). 
was abnormal in habit, lighter brown, and produced fewer sclerotia 
than typical strains. The other strains appearing in the graphs 
showed no conspicuous morphological or cultural differences that 
were identical. The only other strain which was noticeably abnormal 
in culture was one from pine seedlings in Kansas, intermediate in 
habit and color between Xo. 189 and the typical strains and indicat- 
ing little more virulence than Xo. 189 in the few experiments in 
which it was used. It does not appear in figures 1 and 2, but was 
included in the experiments reported in the following paragraph. 
Peltier (99) believes low sclerotium-forming capacity to be a sign 
of degeneration and low virulence; the writer's experience agrees 
with his as to virulence, but these two strains showed no other evi- 
dence of lack of vigor. 
As a further check on the reality of the apparent differences in 
virulence between different strains, all of the original strains avail- 
able at the time, a total of 29. were used in the practically duplicate 
experiments 71 and 72 and the relative survivals of the same strains 
in the two series mathematically and graphically' compared (fig. 11). 
The very decided correlation between the two experiments indicated 
by the graph has a coefficient 3 of 0.813 ±0. 0-12. nineteen times its 
3 The correlation coefficient, a .very useful thing for many kinds of biological work, 
which unfortunately has received little attention from plant pathologists, is explained 
by Secrist (124, p. 43 et seq.) and the process of computation described (124, p. 453-467). 
A shorter method of computation is given by E. Davenport (30, p. 465—467) : the 
example he gives is of a series with a large number of varieties, in which the correlation 
table is employed. Davenport's method is. however, just as useful in such a case as 
this, in which the number of varieties is too small to make the formal tahle advantageous. 
In such a case the computation should be arranged as by Secrist (124. p. 460-461). but 
the guessed rather than the true mean used and Davenport's formula employed. If the 
coefficient is + 1, the correlation is perfect : if it is there is no correlation, and if 
— 1, perfect negative correlation. The significance of a coefficient less than 1 is judged 
from its relation to its probable error. King (84), in an excellent discussion of cor- 
relation, gives rules for judging the degree of significance of the coefficient. The 
correlation coefficient has its greatest potential usefulness in examining apparent causal 
relations. It is so used in connection with the relation between the hydrogen-ion exponent 
and damping-off in considering figure 12 of the present bulletin. Intel-experimental, 
or, as Harris calls them, " interannual '* correlation coefficients of the sort used for 
these Corticium strains have been used by Norton (96, p. 51) in measuring the constancy 
of rust resistance of asparagus strains, by Harris (54) in demonstrating the constancy 
of differences in various characters between strain- or individuals, and they appear to 
be useful for this purpose in the present case. 
