CHANCE, AND ITS ELIMINATION. 59 



arising from the irregular changes in the state of the at- 

 mosphere, was discovered hy comparing the average height 

 of the barometer at different hours of the day. When this 

 comparison was made, it was found that there was a small 

 difference, which on the average was constant, however the 

 absolute quantities might vary, and which difference, there- 

 fore, must be the effect of a constant cause. This cause was 

 afterwards ascertained, deductively, to be the rarefaction of 

 the air, occasioned by the increase of temperature as the day 

 advances. 



5. After these general remarks on the nature of chance, 

 we are prepared to consider in what manner assurance may be 

 obtained that a conjunction between two phenomena, which 

 has been observed a certain number of times, is not casual, but 

 a result of causation, and to be received therefore as one of the 

 uniformities of nature, though (until accounted for a priori) 

 only as an empirical law. 



We will suppose the strongest case, namely, that the 

 phenomenon B has never been observed except in conjunction 

 with A. Even then, the probability that they are connected 

 is not measured by the total number of instances in which 

 they have been found together, but by the excess of that 

 number above the number due to the absolute frequency of 

 A. If, for example, A exists always, and therefore coexists 

 with everything, no number of instances of its coexistence 

 with B would prove a connexion ; as in our example of the 

 fixed stars. If A be a fact of such common occurrence that 

 it may be presumed to be present in half of all the cases that 

 occur, and therefore in half the cases in which B occurs, it 

 is only the proportional excess above half, that is to be 

 reckoned as evidence towards proving a connexion between 

 A and B. 



In addition to the question, What is the number of coinci- 

 dences which, on an average of a great multitude of trials, may 

 be expected to arise from chance alone ? there is also another 

 question, namely, Of what extent of deviation from that 

 average is the occurrence credible, from chance alone, in some 



