[ 93 ] 



arrive at length at certainty ; or whether thefe increments are fo 

 limited, that diminifhing* gradually, they can at length produce 

 only a determinate degree of probability. 



M. Bernouilli has anfwered this queftion in his Treatife 

 De Arte Conjedandi, Part the Fourth. He there fhews, that the 

 probability which arifes from repeated experiments, encreafes 

 continually in fuch a manner, as to approach without limit 

 towards certainty. His calculation fhews us, provided the 

 queftion relates only to a particular cafe, how many times an 

 experiment muft be repeated in order to arrive at an afSgned 

 degree of probability. Thus in the cafe of a wheel which con- 

 tains an unknown number of white and black flips of paper^ 

 fuppofe it were required to determine the ratio of the number 

 of the white to the black ; M. Bernouilli finds, that in order 

 that it may be a thoufand times more probable, that there are 

 two black papers for three white, rather than any other ratio, it 

 would be necefTary to make 25,550 experiments; and in order 

 that it might be 10,000 times more probable, it would be ne- 

 cefTary to make 31,258 trials; and in order that it fl^ould be 

 ioo,coo times more probable, 36,966 trials would be requifitej 

 and fo on ad infinitum, continually adding- 5,708 experiments,- 

 according as the probability encreafes in a decuple proportiors. 

 So that the number of experiments is the logarithm of the degree 

 of probability produced. And fince in high numbers the 



logarithm*. 



