240 



H. M'COLL ON THE GROWTH AND 



I finally resolved the problem into a form which brought 

 it within the reach of the integral calculus ; in other 

 words_, Iliad somehow determined the limits of integration, 

 though I hardly knew how. I applied the same method 

 successfully to two or three other problems in the ' Edu- 

 cational Times/ but without being able to make any mate- 

 rial improvement in it. Whilst occupied with these 

 researches^ the editor of the ' Educational Times ' sent me 

 a very neat and simple geometrical solution by Mr. G. S. 

 Carr of the very problem which had given me so much 

 trouble. This so discouraged me (in the belief that I was 

 only wasting my time) that I threw up the whole subject in 

 disgust, and determined for the future to eschew all 

 mathematics that did not fall within the very narrow limits 

 of my requirements as a teacher. 



When, six years afterwards, I broke my resolution and 

 again took up the subject of probability, my mind natu- 

 rally reverted to the old abandoned method;- and it then 

 struck me that, with all its defects, it had one important 

 merit, namely independence of geometrical diagrams, and 

 that, consequently, it would be well worth my while to 

 apply myself patiently to the task of removing its defects 

 and developing it, if possible, into something better. 



My first step was to drop the letter p {ior probability), 

 which I thought might, without ambiguity be left under- 

 stood ; so that, for instance, 1.2.3 should replace 

 j3(i . 2 . 3) as an abbreviation for " the probability of the 

 event i . 2 . 3.''^ My next step was to use letters instead 

 of numbers, as ABC instead of i . 2 . 3, and an accent to de- 

 note non-occurrence, as ABC instead of 1.2:3. ^^^ ^^ 

 this point a difiiculty j^esented itself: how was ABC, the 

 chance of the compound event ABC, to be distinguished 

 from ABC, the product of the chances A, B, C ? for the 

 chance of the compound event would not generally be the 



