THROUGH LONG PERIODS OF TIME. 151 



while the probabilities of subsequent events may often be 

 determined from the probabilities of prior events, it is rarely 

 the case that probabilities of prior events can be determined \j 

 from those of subsequent events, for we are rarely justified in 

 excluding the consideration of the antecedent probability of 

 the prior events. 



It is worthy of notice that to take a system at random from 

 an ensemble at a date chosen at random from several given 

 dates, t', t", etc., is practically the same thing as to take a sys- 

 tem at random from the ensemble composed of all the systems 

 of the given ensemble in their phases at the time ', together 

 with the same systems in their phases at the time t /; , etc. By 

 Theorem VIII of Chapter XI this will give an ensemble in 

 which the average index of probability will be less than in 

 the given ensemble, except in the case when the distribution 

 in the given ensemble is the same at the times t r , t' f , etc. 

 Consequently, any indefiniteness in the time in which we take 

 a system at random from an ensemble has the practical effect 

 of diminishing the average index of the ensemble from which 

 the system may be supposed to be drawn, except when the 

 given ensemble is in statistical equilibrium. 



