612 THE POPULAR SCIENCE MONTHLY. 



fortunately, as the whole requirement is that we should have certain 

 sentiments, there is nothing in the facts to forbid our having a hope, 

 or calm and cheerful wish, that the community may last beyond any 

 assignable date. 



It may seem strange that I should put forward three sentiments, 

 namely, interest in an indefinite community, recognition of the possi- 

 bility of this interest being made supreme, and hope in the unlimited 

 continuance of intellectual activity, as indispensable requirements of 

 logic. Yet, when we consider that logic depends on a mere struggle 

 to escape doubt, which, as it terminates in action, must begin in emo- 

 tion, and that, furthermore, the only cause of our planting ourselves 

 on reason is that other methods of escaping doubt fail on account of 

 the social impulse, why should we wonder to find social sentiment 

 presupposed in reasoning? As for the other two sentiments which I 

 find necessary, they are so only as supports and accessories of that. 

 It interests me to notice that these three sentiments seem to be pretty 

 much the same as that famous trio of Charity, Faith, and Hope, which, 

 in the estimation of St. Paul, are the finest and greatest of spiritual 

 gifts. Neither Old nor New Testament is a text-book of the logic 

 of science, but the latter is certainly the highest existing authority 

 in regard to the dispositions of heart which a man ought to have. 



Such average statistical numbers as the number of inhabitants per 

 square mile, the average number of deaths per week, the number of 

 convictions per indictment, or, generally speaking, the number of oc's 

 per y, where the cc's are a class of things some or all of which are con- 

 nected with another class of things, their y's, I term relative numbers. 

 Of the two classes of things to which a relative number refers, that 

 one of which it is a number may be called its relate, and that one 

 per which the numeration is made may be called its correlate. 



Probability is a kind of relative number; namely, it is the ratio 

 of the number of arguments of a certain genus which carry truth with 

 them to the total number of arguments of that genus, and the rules 

 for the calculation of probabilities are very easily derived from this 

 consideration. They may all be given here, since they are extremely 

 simple, and it is sometimes convenient to know something of the ele- 

 mentary rules of calculation of chances. 



Rule I. Direct Calculation. To calculate, directly, any relative 

 number, say for instance the number of passengers in the average trip 

 of a street-car, we must proceed as follows : 



Count the number of passengers for each trip ; add all these num- 

 bers, and divide by the number of trips. There are cases in which 

 this rule may be simplified. Suppose we wish to know the number 



might be assigned which that evidence might not cover, yet further evidence would 

 cover it. 



