296 OF STATISTICAL CONDITIONS. [CHAP. XIX. 



observation records, a limit to which we approach the more 

 nearly as the number of observations is increased. Now let the 

 symbol n, prefixed to the expression of any class, represent the 

 number of individuals contained in that class. Thus, x represent- 

 ing men, and y white beings, let us assume 



nx = number of men. 



nxy = number of white men. 



nx (1 - y) = number of men who are not white; and so on. 



In accordance with this notation w(l) will represent the number 

 of individuals contained in the universe of discourse, and 



will represent the probability that any individual being, selec 

 out of that universe of being denoted by n ( 1), is a man. If ob- 

 servation has not made us acquainted with the total values of 

 n(x) and n(l), then the probability in question is the limit to 



which TTT approaches as the number of individual observations 



is increased. 



In like manner if, as will generally be supposed in this chap- 

 ter, x represent an event of a particular kind observed, n (x) will 

 represent the number of occurrences of that event, n (1) the 

 number of observed events (equally probable) of all kinds, and 



-y-r , or its limit, the probability of the occurrence of the 

 n(\.) 



event x. 



Hence it is clear that any conclusions which may be deduced 

 respecting the ratios of the quantities n (x), n (?/), n (1), &c. may 

 be converted into conclusions respecting the probabilities of the 

 events represented by #, y, &c. Thus, if we should find such a 

 relation as the following, viz., 



expressing that the number of times in which the event x occurs 

 and the number of times in which the event y occurs, are toge- 

 ther less than the number of possible occurrences n (I), we might 

 thence deduce the relation, 



fe) , n (y) , i 



or Prob. x + Prob. y < 1 . 



