CHAPTER IV. 



THE LAW OF DISTRIBUTION (CONTINUED). 



COMPARISON BETWEEN THE METHODS OF THE TWO PRECEDING CHAPTERS. 



61. THE problem of the present chapter will be to consider the relation 

 between the methods of procedure adopted in Chapters II. and III. 



The discussion of Chapter II. was based upon certain questions of pro- 

 bability, and an answer to these questions was made possible and was ob- 

 tained by the help of the assumption of molecular chaos enunciated in 15. 



The discussion of Chapter III. also rested, although in a different sense, 

 upon the theory of probability. The generalised space filled with fluid 

 supplied a basis for the calculation of probabilities, and as the motion of the 

 fluid was proved to be steady-motion, it followed that this basis was inde- 

 pendent of the time. For the present, we continue to take this generalised 

 space as the basis of probability calculations. The question " What is the 

 probability that a system satisfies condition p?" will be taken to mean: "For 

 what proportion of the generalised space is condition p satisfied?" The 

 further question : " Given that a system satisfies condition p, what is the 

 probability that it also satisfies condition q ? " will be interpreted to mean : 

 " A point is selected at random from all those parts of the generalised space 

 in which condition p is satisfied : what is the probability that at this point 

 condition q also is satisfied ? " And if v p is the total volume of that part of 

 the space in which condition p is satisfied, and v pq that of the space in which 

 condition q also is satisfied, the value of the probability required is of course 

 the ratio 



^ (103). 



v p 



If v is the whole volume of this generalised space (or of any part of it to 

 which we choose to limit our consideration) the chance that condition q shall 

 be satisfied independently of condition p is 



V JL ...(104). 



