USE OF TABLES. 87 



lies between certain limits, and its converse. The 

 latter problem contains a consideration of some diffi- 

 culty, namely,, the probability of a probability, or, as we 

 have called it, the presumption of a probability. To 

 make this idea more clear, remember that any state of 

 probability may be immediately made the expression of 

 the result of a set of circumstances, which being in- 

 troduced into the question, the difficulty disappears. 

 Thus, suppose a large number of urns containing 

 various proportions of black and white balls. Let 

 there be 100 urns, and let one of them only contain 

 equal numbers of black and white balls. If then 

 I lay my hand upon one of these urns with the intention 

 of drawing, it is, before the drawing, 99 to 1 against 

 my having placed my hand upon an urn from which, 

 in the long run, equal numbers of both sorts of balls 

 will be produced : the presumption that black and 

 white balls have an even chance is only T -J^ ; the pre- 

 sumption that the probability of a white ball is -J, is 



TFo* 



In speaking of compound probabilities, writers have 



employed six words synonymously probability, chance, 

 presumption, possibility, facility, and expectation. Re- 

 jecting only the word possibility, as indicating a thing 

 of which there cannot be different degrees., the five 

 remaining terms have their advantages, each one 

 pointing out a peculiar and useful view of the main 

 idea. Thus the word presumption refers distinctly 

 to an act of the mind, or a state of the mind, while in 

 the word probability we feel disposed rather to think of 

 the external arrangements on the knowledge of which 

 the strength of our presumption ought to depend, than 

 of the presumption itself. When, therefore, having 

 observed an event, we want to know how strongly we 

 are to suppose that the observed event was preceded by 

 a given arrangement of circumstances, the term pre- 

 sumption of probability is very appropriate. The word 

 facility applies particularly to the notion which we 

 form when we see one event happen more often than 



