OF THE CALCULATION OF CHANCES. 69 



sources we derive our assurance. The probability of events as 

 calculated from their mere frequeucyin past experience, affords 

 a less secure basis for practical guidance, than their proba- 

 bility as deduced from an equally accurate knowledge of the 

 frequency of occurrence of their causes. 



The generalization, that an event occurs in ten out of every 

 hundred cases of a given description, is as real an induction 

 as if the generalization were that it occurs in all cases. But 

 when we arrive at the conclusion by merely counting instances 

 in actual experience, and comparing the number of cases in 

 which A has been present with the number in which it has 

 been absent, the evidence is only that of the method of Agree- 

 ment, and the conclusion amounts only to an empirical law. 

 We can make a step beyond this when we can ascend to the 

 causes on which the occurrence of A or its non-occurrence will 

 depend, and form an estimate of the comparative frequency of 

 the causes favourable and of those unfavourable to the occur- 

 rence. These are data of a higher order, by which the empirical 

 law derived from a mere numerical comparison of affirmative 

 and negative instances will be either corrected or confirmed, 

 and in either case we shall obtain a more correct measure of 

 probability than is given by that numerical comparison. It 

 has been well remarked that in the kind of examples by which 

 the doctrine of chances is usually illustrated, that of balls in a 

 box, the estimate of probabilities is supported by reasons of 

 causation, stronger than specific experience. "What is the 

 reason that in a box where there are nine black balls and one 

 white, we expect to draw a black ball nine times as much (in 

 other words, nine times as often, frequency being the gauge of 

 intensity in expectation) as a white ? Obviously because the 

 local conditions are nine times as favourable, because the hand 

 may alight in nine places and get a black ball, while it can 

 only alight in one place and find a white ball; just for the 

 same reason that we do not expect to succeed in finding a 

 friend in a crowd, the conditions in order that we and he should 

 come together being many and difficult. This of course would 

 not hold to the same extent were the white balls of smaller 

 size than the black, neither would the probability remain the 



