IS erroneous, and in many cafes produdlive of abfuidi'iy. JVlAtVic- 

 maticians, who have treated this fubjed: with the moft rigoroiij 

 accuracy, follow a very different method. They denote certainty 

 by an unit, and probability by fradions of which the denominator 

 confifts of the number of times or trials in which the experiment 

 has either happened or failed, and the numerator of one of thetn 

 exhibits the number of trials in which it has happened, and that 

 of the other the number of trials in which it has failed ; and 

 then they confider their ratios, and irot their difference. Thus if 

 an event has happened ten times, and has failed five times, the 

 probability that it will happen again is fi, and the probability 

 that it will not happen again is 7^-; then its probabiHty is as 

 two to one. Whereas by Mr. Hume's rule of fubtradion, the 

 fuperior probability would be only Jj, and thus would be con- 

 verted into an improbability ; for an experiment that has fucceeded 

 in half the number of trials to which it had been expofed, is 

 juftly confidered as doubtful, it having failed as often as it fuc- 

 ceeded : but if it has not fucceeded even in half the number of 

 trials, it muft be confidered as improhahle. 



Ibid, " There is no fpecies of reafoning more ufeful or ne- 

 *' ceffary to human life, than that derived from the teftimony of 

 '* fpedators. We may even deny it to be founded on the rela- 

 " tion of caufe and effed -, but it is fufficient to obferve, that our 

 ** affurance in any argument of this kind is iblely derived from 



" ouf 



