436 PROCEEDINGS OF THE AMERICAN ACADEMY 



A few examples may serve to elucidate the above principles. 

 A bag contains black and white balls in an unknown ratio. The 

 probability of drawing a white ball will be one half. But the facility 

 will be represented by the ratio of the white balls to the whole num- 

 ber, supposing them to be mixed indiscriminately, and when this ratio 

 is known, it will also be the probability. 



So long as the deaths of individuals in any particular country all 

 proceed from independent causes, we expect their number to agree 

 with those deduced from a table of mortality, within certain limits of 

 error. If, however, the country were ravaged by an epidemic, or any 

 change were to take place in its climate, we should no longer expect 

 the deaths to follow the laws of the tables of mortality. Here, how- 

 ever, would be a single cause, producing, or effecting in some way, the 

 deaths of a number of individuals. 



The neglect of the distinction between probability and facility has 

 never led to any error, (except, perhaps, of interpretation,) because 

 every answer to a question in chances must represent a probability. 

 If we are ignorant of any of the constant causes, we can only deduce 

 the most probable value of the facility, which may not be the real 

 value ; — if we know the law of action of all the constant causes, the 

 probability and facility are the same. 



Let us now consider a question which has been the subject of some 

 dispute, viz. the nature of the argument by which, from the fact of the 

 near approach of several stars, it is deduced that their proximity is not 

 the result of chance. Writei-s on probabilities have generally agreed 

 that such proximity indicates a physical connection between the stars. 



The real argument for the connection is to be expressed in the fol- 

 lowing form : — 



1. If the causes which fixed the position of each star were entirely 

 independent of those which fixed the position of every other ; or, in 

 other words, if the stars were scattered by chance, it is exceedingly 

 improbable that these (two, three, or seven) stars should be found as 

 near each other as they actually are. 



2. It is not very improbable that such proximity should result from 

 the existence of a common element in the causes which determined 

 their positions. 



3. Therefore, such proximity being an ascertained fact, it is in the 

 highest degree probable that it resulted from the existence of a com- 

 mon element, etc. 



