ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 713 



be white, and in two-thirds black. In one-third of those urns of which 

 the first ball was white, and also in one-third of those in which the 

 first ball was black, the second ball would be white. In this way, 

 we should have a distribution like that shown in the following 

 table, where w stands for a white ball and b for a black one. The 

 reader can, if he chooses, verify the table for himself. 



wwww. 



wwwb. 

 wwwb. 



wwbb. 

 wwbb. 

 wwbb. 

 wwbb. 



wbbb. 

 wbbb. 

 wbbb. 

 wbbb. 

 wbbb. 

 wbbb. 

 wbbb. 

 wbbb. 



bbbb. 

 bbbb. 

 bbbb. 

 bbbb. 

 bbbb. 

 bbbb. 

 bbbb. 

 bbbb. 

 bbbb. 

 bbbb. 

 bbbb. 

 bbbb. 

 bbbb. 



bbbb. 

 bbbb. 

 bbbb. 



wwbw. 

 wwbw. 



wbwb. 

 wbwb. 

 wbwb. 

 wbwb. 



bwbb. 

 bwbb. 

 bwbb. 

 bwbb. 

 bwbb. 

 bwbb. 

 bwbb. 

 bwbb. 



wbww. 

 wbww. 



bwwb. 

 bwwb. 

 bwwb. 

 bwwb. 



bbwb. 

 bbwb. 

 bbwb. 

 bbwb. 

 bbwb. 

 bbwb. 

 bbwb. 

 bbwb. 



bwww. 

 bwww. 



wbbw r . 

 wbbw. 

 wbbw. 

 wbbw. 



bbbw. 

 bbbw. 

 bbbw. 

 bbbw. 

 bbbw. 

 bbbw. 

 bbbw. 

 bbbw. 



bwbw. 

 bwbw. 

 bwbw. 

 bwbw. 



bbww. 

 bbww. 

 bbww. 

 bbww. 



In the second group, where there is one b, there are two 

 sets just alike ; in the third there are 4, in the fourth 8, and in 

 the fifth 16, doubling every time. This is because we have 

 supposed twice as many black balls in the granary as white 

 ones; had we supposed 10 times as many, instead of 



16 



sets we should have had 



10, 



100, 



1000, 



10000 



sets ; on the other hand, had the numbers of black and white 

 balls in the granary been even, there would have been but 

 one set in each group. Now suppose two balls were drawn 

 from one of these urns and were found to be both white, what 

 would be the probability of the next one being white ? If the two 

 drawn out were the first two put into the urns, and the next to be 

 drawn out were the third put in, then the probability of this third 

 being white would be the same whatever the colors of the first two, 

 for it has been supposed that just the same proportion of urns has 

 the third ball white among those which have the first two white-white, 

 white-black, black-ichite, and black-black. Thus,'in this case, the chance 



