CALCULATION OF CHANCES. 81 



Disbelief, that he has been led by it into serious 

 practical mistakes when attempting to pronounce 

 upon the circumstances which render any statement 

 incredible. 



4. From the preceding view of the foundation of 

 the doctrine of chances, its general principles may be 

 seen to be applicable in a rough way to many subjects 

 which are by no means amenable to its precise calcu- 

 lations. To render these applicable, there must be 

 numerical data, derived from the observation of a 

 very large number of instances. The probabilities of 

 life at different ages, or in different climates ; the 

 probabilities of recovery from a particular disease ; 

 the chances of the birth of male or female offspring; 

 the chances of the loss of a vessel in a particular 

 voyage ; all these admit of estimation sufficiently pre- 

 cise to render the numerical appreciation of their 

 amount a thing of practical value; because there are 

 bills of mortality, returns from hospitals, registers of 

 births, of shipwrecks, &c., founded on cases suffi- 

 ciently numerous to afford average proportions which 

 do not materially vary from year to year, or from ten 

 years to ten years. But where observation and expe- 

 riment have not afforded a set of instances sufficientlv 



f 



numerous to eliminate chance, and sufficiently various 

 to eliminate all non-essential specialities of circum- 

 stance, to attempt to calculate chances is to convert 

 mere ignorance into dangerous error by clothing it in 

 the garb of knowledge. 



It remains to examine the bearing of the doctrine 

 of chances upon the peculiar problem for the sake 

 of which we have on this occasion adverted to it, 

 namely, how to distinguish coincidences which are 

 casual from those which are the result of law ; from 



VOL. II. G 



