14 NATURE AND DESIGN OF THIS WORK. [CHAP. I. 



Again, although questions in the theory of Probabilities 

 present themselves under various aspects, and may be variously 

 modified by algebraical and other conditions, there seems to be 

 one general type to which all such questions, or so much of each 

 of them as truly belongs to the theory of Probabilities, may be 

 referred. Considered with reference to the data and the qucesi- 

 tum, that type may be described as follows : 1st. The data are 

 the probabilities of one or more given events, each probability 

 being either that of the absolute fulfilment of the event to which 

 it relates, or the probability of its fulfilment under given sup- 

 posed conditions. 2ndly. The qucBsitum, or object sought, is the 

 probability of the fulfilment, absolutely or conditionally, of some 

 other event differing in expression from those in the data, but 

 more or less involving the same elements. As concerns the data, 

 they are either causally given, as when the probability of a par- 

 ticular throw of a die is deduced from a knowledge of the consti- 

 tution of the piece, or they are derived from observation of 

 repeated instances of the success or failure of events. In the 

 latter case the probability of an event may be defined as the 

 limit toward which the ratio of the favourable to the whole num- 

 ber of observed cases approaches (the uniformity of nature being 

 presupposed) as the observations are indefinitely continued. 

 Lastly, as concerns the nature or relation of the events in ques- 

 tion, an important distinction remains. Those events are either 

 simple or compound. By a compound event is meant one of 

 which the expression in language, or the conception in thought, 

 depends upon the expression or the conception of other events, 

 which, in relation to it, may be regarded as simple events. To 

 say "it rains," or to say "it thunders," is to express the occur- 

 rence of a simple event; but to say "it rains and thunders," or 

 to say " it either rains or thunders," is to express that of a com- 

 pound event. For the expression of that event depends upon 

 the elementary expressions, " it rains," " it thunders." The cri- 

 terion of simple events is not, therefore, any supposed simplicity 

 in their nature. It is founded solely on the mode of their ex- 

 pression in language or conception in thought. 



14. Now one general problem, which the existing theory of 

 Probabilities enables us to solve, is the following, viz. : Given 



