30 BULLETIN 934, U. S. DEPARTMENT OF AGRICULTURE. 



that experiments 71 and 72, in which they showed the least virulence, 

 were 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 No. 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 No. 189 and the typical strains and indicat- 

 ing little more virulence than No. 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 sclerotrum-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 0.042, 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 table 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. Interexperimental, 

 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 strains or individuals, and they appear to 

 be useful for this purpose in the present case. 



