OF THE CALCULATION OF CHANCES. 71 



ciently precise to render their numerical appreciation of any 

 practical value, the numerical data are not drawn from know 

 ledge of the causes, but from experience of the events them 

 selves. The probabilities of life at different ages, or in diffe 

 rent climates ; the probabilities of recovery from a particular 

 disease ; the chances of the birth of male or female offspring ; 

 the chances of the destruction of houses or other property by 

 fire ; the chances of the loss of a ship in a particular voyage ; 

 are deduced from bills of mortality, returns from hospitals, 

 registers of births, of shipwrecks, c., that is, from the ob 

 served frequency not of the causes, but of the effects. The 

 reason is, that in all these classes of facts, the causes are 

 either not amenable to direct observation at all, or not with 

 the requisite precision, and we have no means of judging of 

 their frequency except from the empirical law afforded by the 

 frequency of the effects. The inference does not the less 

 depend on causation alone. We reason from an effect to a 

 similar effect by passing through the cause. If the actuary of 

 an insurance office infers from his tables that among a hundred 

 persons now living, of a particular age, five on the average 

 will attain the age of seventy, his inference is legitimate, not 

 for the simple reason that this is the proportion who have 

 lived till seventy in times past, but because the fact of their 

 having so lived shows that this is the proportion existing, at 

 that place and time, between the causes which prolong life 

 to the age of seventy, and those tending to bring it to an 

 earlier close.* 



* The writer last quoted says that the valuation of chances by comparing 

 the number of cases in which the event occurs with the number in which it 

 does not occur, &quot;would generally be wholly erroneous,&quot; and &quot;is not the true 

 theory of probability.&quot; It is at least that which forms the foundation of 

 insurance, and of all those calculations of chances in the business of life which 

 experience so abundantly verifies. The reason which the reviewer gives fur 

 rejecting the theory, is that it &quot; would regard an event as certain which had 

 hitherto never failed ; which is exceedingly far from the truth, even for a very 

 large number of constant successes.&quot; This is not a defect in a particular 

 theory, but in any theory of chances. No principle of evaluation can provide 

 for such a case as that which the reviewer supposes. If an event has never 

 once failed, in a number of trials sufficient to eliminate chance, it really has all 

 the certainty which can be given by an empirical law : it is certain during the 



