258 MR G. UDNY YULE ON TIIK ASSOCIATION 



number who did not die to whom antitoxin was not administered, 

 ,, ,, to whom antitoxin was administered ; 



and from these data a discussion of the value of the cure is required. Here there is 

 no scale of " death " ; there may be a scale of " antitoxin " if the dose varied, but 

 not otherwise. 



2. Evidently such cases are of great importance, but the theory and means of 

 handling them have received little attention from statisticians. Logicians have had a 

 monopoly of the theory, but the superior interests of pure logic seem generally to 

 have hindered them from developing it in a practical direction. The classical 

 writings on the subject are, I suppose, those of DE MORGAN,* BOOLE,! and JEVONS.:}: 

 Without attempting to criticise the work of his predecessors, to both of whom lie 

 was of course greatly indebted, the method of the latter must be allowed to far 

 exceed theirs in clearness and simplicity. BOOLE'S calculus of elective operators is 

 highly complex in its working and necessitates the remembrance of many somewhat 

 artificial rules ; JEVONS' method is practically intuitive. It is a matter of surprise 

 to me that JEVONS never made any practical application of his method (so far as I am 

 aware) during the decade or more that elapsed between the publication of his paper 

 (loc. cit.) and his death, .The following is a brief explanation of his notation and 

 method. 



3. The symbols A, B, C, &c., are used to denote objects or individuals having 

 the qualities A, B, C, &c. The terms enclosed in brackets thus (A), (B), (C), 

 &c., denote the frequency of individuals possessed of the quality or qualities 

 A, B, or C, or the total number of such individuals observed in the given " universe 

 of discourse."! A compound term like AB denotes the class or group possessed of both 

 qualities A and B, and (AB) its frequency ; compound groups may occur with any 

 number of specified qualities, i.e. (ABC), (ABCD), or (BDKMN). Corresponding 

 to each positive term there is a negative term which we shall denote by a small 

 Greek letter|| a, )8, y, &c. Thus a signifies " not A," y8 " not B," and so on ; and 

 (a), (/3), &c., their frequencies. All symbols are used non-exclusively, A signifying 

 objects having the quality A with or without others, and so on, consequently the 

 frequency of any class can be expanded in terms of the frequencies of its sub-classes. 



* Formal Logic,' chap. VIIL, " On the Numerically Definite Syllogism," 1847. 



t ' Analysis of Logic,' 1847. ' Laws of Thought,' 1854. 



J " On a General System of Numerically Definite Reasoning," ' Memoirs of Manchester Literary and 

 Philosophical Society,' 1870. Reprinted in ' Pure Logic and other Minor Works,' Macmillan, 1890. 



I have used this convenient term of the logicians for the " material discussed " throughout the paper. 

 There seems no exact equivalent in ordinary statistical language. 



|| I have substituted small Greek letters for JEVONS' italics. Italics are rather troublesome when 

 reading, as one has to spell out a group like AfoDE, " big A, little b, little c, big D, big E." It is simpler 

 to read A/JyDE. The Greek becomes more troublesome when many letters are wanted, owing to the 

 non-correspondence of the alphabets, but this is not often of consequence. 



