USE OF A SYMBOLICAL LANGUAGE. 239 



As I stated in m}- tliird paper in tlic ' Proceedings ' of 

 the London Mathematical Society, my method originated 

 in a question in probability proposed in the ' Educational 

 Times ^ for June 1871*. The question (as I understood 

 it) may be thus generalized : — " Given that the variables 

 X, y, z are each taken at random between given limits, 

 what is the chance that an assigned function of these 

 variables, say (p(a?, y, z), will be real and positive? When 

 I began to solve the pi'oblem I found that, in addition to 

 the particular event whose chance was required, I should 

 have to consider the relations in which this event stood 

 towards several other events on which it more or less 

 depended. It struck me that it would help the memory 

 and facilitate the reasoning, if I registered the various 

 events spoken of in regular numerical order in a table of 

 reference. The event whose chance had to be found 

 resolved itself into a concurrence of two distinct but not 

 independent events i and 2 ; and J denoted the chance (or 

 probability) of this concurrence by the symbol p{\ .2). 

 The compound event i . 2 implied the occurrence of a 

 third event 3, which it was necessaiy also to take into 

 account ; I had therefore to replace ^j(i . 2) by j9(i , 2 . 3). 

 But the consideration of 1.2.3 could not be separated 

 from the consideration of a fourth event 4, in conjunction 

 with which it might happen, but not necessarily ; and the 

 probability of the concurrence 1.2.3 depended mate- 

 rially upon whether it happened in conjunction with this 

 fourth event or without it. Denoting the no?i-occurrence of 

 this fourth event by the symbol : 4, 1 thus had the equation 

 ;?(i .2.3) =p[i .2.3.4) =75(1 .2.3:4). Proceeding in 

 this way, but in a somewhat groping and tentative manner, 



* The subject of probability was one which I had recently taken up at the 

 request of Mr. J. C. Miller, the matheinatical editor of the ' Educational 

 Times,' who felt great interest in it himself, and strongly recommended it 

 as " an unworked vein in which I should find many treasures." 



