ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 615 



regard to probabilities), that the proportion of males among all the 

 children born in New York is the same as the proportion of males born 

 in summer in New York, and, therefore, if the names of all the chil- 

 dren born during a year were put into an urn, we might multiply the 

 probability that any name drawn would be the name of a male child 

 by the probability that it would be the name of a child born in 

 summer, in order to obtain the probability that it would be the 

 name of a male child born in summer. The questions of proba- 

 bility, in the treatises upon the subject, have usually been such as re- 

 late to balls drawn from urns, and games of cards, and so on, in 

 which the question of the independence of events, as it is called that 

 is to say, the question of whether the probability of C, under the 

 hypothesis B, is the same as its probability under the hypothesis 

 A, has been very simple ; but, in the application of probabilities to 

 the ordinary questions of life, it is often an exceedingly nice ques- 

 tion whether two events may be considered as independent with suf- 

 ficient accuracy or not. In all calculations about cards it is assumed 

 that the cards are thoroughly shuffled, which makes one deal quite in- 

 dependent of another. In point of fact the cards seldom are, in prac- 

 tice, shuffled sufficiently to make this true ; thus, in a game of whist, 

 in which the cards have fallen in suits of four of the same suit, and 

 are so gathered up, they will lie more or less in sets of four of the 

 same suit, and this will be true even after they are shuffled. At least 

 some traces of this arrangement will remain, in consequence of which 

 the number of "short suits," as they are called that is to say, the 

 number of hands in which the cards are very unequally divided in re- 

 gard to suits is smaller than the calculation would make it to be ; so 

 that, when there is a misdeal, where the cards, being thrown about 

 the table, get very thoroughly shuffled, it is a common saying that in 

 the hands next dealt out there are generally short suits. A few years 

 ago a friend of mine, who plays whist a great deal, was so good as to 

 count the number of spades dealt to him in 165 hands, in which the 

 cards had been, if anything, shuffled better than usual. According to 

 calculation, there should have been 85 of these hands in which my 

 friend held either three or four spades, but in point of fact there were 

 94, showing the influence of imperfect shuffling. 



According to the view here taken, these are the only fundamental 

 rules for the calculation of chances. An additional one, derived from 

 a different conception of probability, is given in some treatises, which 

 if it be sound might be made the basis of a theory of reasoning. 

 Being, as I believe it is, absolutely absurd, the consideration of it 

 serves to bring us to the true theory ; and it is for the sake of this 

 discussion, which must be postponed to the next number, that I have 

 brought the doctrine of chances to the reader's attention at this early 

 stage of our studies of the logic of science. 



