CHAP. I.] NATURE AND DESIGN OF THIS WORK. 13 



regards the character of the solutions to which it leads. In con- 

 nexion with this object some further detail will be requisite con- 

 cerning the forms in which the results of the logical analysis are 

 presented. 



The ground of this necessity of a prior method in Logic, as 

 the basis of a theory of Probabilities, may be stated in a few 

 words. Before we can determine the mode in which the expected 

 frequency of occurrence of a particular event is dependent upon 

 the known frequency of occurrence of any other events, we must be 

 acquainted with the mutual dependence of the events themselves. 

 Speaking technically, we must be able to express the event 

 whose probability is sought, as a function of the events whose 

 probabilities are given. Now this explicit determination belongs 

 in all instances to the department of Logic. Probability, how- 

 ever, in its mathematical acceptation, admits of numerical mea- 

 surement. Hence the subject of Probabilities belongs equally to 

 the science of Number and to that of Logic. In recognising the 

 co-ordinate existence of both these elements, the present treatise 

 differs from all previous ones ; and as this difference not only 

 affects the question of the possibility of the solution of problems 

 in a large number of instances, but also introduces new and im- 

 portant elements into the solutions obtained, I deem it necessary 

 to state here, at some length, the peculiar consequences of the 

 theory developed in the following pages. 



13. The measure of the probability of an event is usually 

 denned as a fraction, of which the numerator represents the num- 

 ber of cases favourable to the event, and the denominator the 

 whole number of cases favourable and unfavourable ; all cases 

 being supposed equally likely to happen. That definition is 

 adopted in the present work. At the same time it is shown that 

 there is another aspect of the subject (shortly to be referred to) 

 which might equally be regarded as fundamental, and which 

 would actually lead to the same system of methods and conclu- 

 sions. It may be added, that so far as the received conclusions 

 of the theory of Probabilities extend, and so far as they are con- 

 sequences of its fundamental definitions, they do not differ from 

 the results (supposed to be equally correct in inference) of the 

 method of this work. 



