ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 613 



of inhabitants to a dwelling in New York. The same person cannot 

 inhabit two dwellings. If he divide his time between two dwellings 

 he ought to be counted a half-inhabitant of each. In this case we 

 have only to divide the total number of the inhabitants of New York 

 by the number of their dwellings, without the necessity of counting 

 separately those which inhabit each one. A similar proceeding will 

 apply wherever each individual relate belongs to one individual cor- 

 relate exclusively. If we want the number of sk's per y, and no x be- 

 longs to more than one y, we have only to divide the whole number 

 of jc's of y's by the number of y's. Such a method would, of course, 

 fail if applied to finding the average number of street-car passengers 

 per trip. We could not divide the total number of travelers by the 

 number of trips, since many of them would have made many passages. 

 To find the probability that from a given class of premises, A, a 

 given class of conclusions, B, follow, it is simply necessary to ascer- 

 tain what proportion of the times in which premises of that class are 

 true, the appropriate conclusions are also true. In other words, it is 

 the number of cases of the occurrence of both the events A and B, di- 

 vided by the total number of cases of the occurrence of the event A. 



Rule II. Addition of Relative Numbers. Given two relative 

 numbers having the same correlate, say the number of jc's per y, 

 and the number of z's per y it is required to find the number of tc's 

 and s's together per y. If there is nothing which is at once an x and 

 a z to the same y, the sum of the two given numbers would give the 

 required number. Suppose, for example, that we had given the aver- 

 age number of friends that men have, and the average number of 

 enemies, the sum of these two is the average number of persons in- 

 terested in a man. On the other hand, it plainly would not do to add 

 the average number of persons having constitutional diseases to the 

 average number over military age, and to the average number ex- 

 empted by each special cause from military service, in order to get 

 the average number exempt in any way, since many are exempt in 

 two or more ways at once. 



This rule applies directly to probabilities. Given the probability 

 that two different and mutually exclusive events will happen under the 

 same supposed set of circumstances. Given, for instance, the proba- 

 bility that if A then B, and also the probability that if A then C, 

 then the sum of these two probabilities is the probability that if A 

 then either B or C, so long as there is no event which belongs at 

 once to the two classes B and C. 



Rule III. Ifultiplication of Relative Numbers. Suppose that we 

 have given the relative number of x's per y also the relative num- 

 ber of z's per x of y ; or, to take a concrete example, suppose that we 

 have given, first, the average number of children in families living in 



