USE OF A SYMBOLICAL LANGUAGE. 241 



product of the chances of the separate events. To gaard 

 against this risk of confusion I decided to use capitals, as 

 ABC, when the chance of the whole compound event was 

 meant, and small italic letters, abc, when the product of 

 the separate chances a, b, c was meant. Thus, though the 

 chances A, B, C were separately equal to a, b, c, the 

 symbol ABC would not (except in the case of independent 

 events) be equivalent to the symbol abc. The equivalence 

 of A(B + C) and AB+AC, and of similar expressions, I 

 discovered before I introduced letters instead of numbers. 



So far, I had made no real advance : the substitution of 

 a literal for a numerical notation improved perhaps the 

 appearance of the method ; but it did not affect it practi- 

 cally. In applying the method to such questions as 

 required the integral calculus it still remained a tentative 

 method ; I still groped my way towards conclusions in 

 particular cases without the help of any general rules of 

 procedure. At last I was struck by the fact that the 

 events registered in my tables, and whose chances were 

 denoted by the letters, were all of the form x>x^^ Xj>x, 

 Xj_>x^, y>}/i, yz>y, yz>J/i) &c., and had all reference to 

 the limits of the different variables. This suggested the 

 idea of a partial return to the original numerical notation 

 and classifying the events according to the variable spoken 

 of. I denoted the event and also the chance of the event 

 x>x^ by <a?^, the eyent x^>x and its chance by x^>, and 

 so on for x^,, Xj<^ x^, x^', y,, y,-, &c. This was a very impor- 

 tant step so far as my method related to integration limits ; 

 and after this its development in this direction was com- 

 paratively rapid — too much so for me to remember very 

 accurately its different stages. Still, I looked upon the 

 method as essentially and inseparably connected with pro- 

 bability ; and even when I had decided that it would be 

 more convenient and less confusing to let my symbols de- 



SER. III. VOL. VII. K 



