MATHEMATICAL SECTION. 125 
In the data cited by Mr. Gilbert from Finley’s tornado predic- 
tions, s = 2803, o= 51, p = 100, andc = 28. By Mr. Gilbert’s 
formula, 
a) cs — op 
“= 8(0--p —¢) — op 
he obtains 
t= 216. 
Prof. Peirce obtains 
4= .523. 
I obtain 
4= .142. 
By making s, 0, and 7 constant, and imposing conditions on p and 
¢, we may obtain hypothetical data involving equal skill. Putting 
e = p, I infer that Mr. Finley would have manifested equal skill if 
he had made no false predictions of tornadoes, and, out of the 51, 
had predicted 7.35. Mr. Gilbert’s formula gives 11.18, and Prof 
Peirce’s 26.67. Putting c=o0,I infer that he would also have 
manifested equal skill if he had included all the 51 tornadoes by 
making 323.7 predictions. Mr. Gilbert’s formula gives 221.5, and 
Prof. Peirce’s 1364. 
_ Mr. Finley’s entire success in predicting tornadoes is 
ee = .154; 
op 
and since the portion due to skill = .142, we may infer that .923 
of this success is due to skill, and only .077 to chance. On the 
other hand, of his success in predicting the non-occurrence of tor- 
nadoes, only .147 is due to skill, and .853 is due to chance. 
Prophecy and fulfillment are effects of a common cause. Neither 
causes the other. The problem, broadly stated, requires a nume- 
rical expression for the causal relation between two classes of phe- 
nomena either in co-existence or in sequence, when the presence of 
one corresponds sometimes to the presence and sometimes to the 
absence of the other, and sometimes both are absent. In case of 
sequence it is immaterial which is antecedent. The quantities de- 
noted by o and p should therefore be interchangeable. 
My formula responds properly to every test proposed by Mr. 
Gilbert. The value of 7 increases rapidly with that of c, and 
