212 LIFE OF SIR JOHN LUBBOCK oh. 



illustrative election, however, surprised and con- 

 vinced him ; so that far from moving an amend- 

 ment he offered to second, and did second, the 

 resolution in favour of the system. 



By way of making sure of the correctness of 

 the arithmetical calculation that he had applied 

 to Proportional Representation, Sir John con- 

 sulted Sir G. Stokes, stating the case thus : 



High Elms, Hayes, Kent, 

 Feb. 3rd, 1885. 



My dear Professor Stokes — The opponents of 

 Proportional Representation continually object that, 

 under the system we have proposed, much would depend 

 on chance. 



This of course might be entirely obviated by dis- 

 tributing the second votes in proportion, but we have 

 not thought this necessary because the chance is so 

 small. 



According to our calculation, supposing a Constitu- 

 ency of 25,000 Electors, returning 3 members, and that 

 a candidate receives 10,000 votes of which one-half are 

 marked in the second place for a candidate " B " and 

 one-half for " C," and suppose that 4000 have to be 

 distributed, the element of chance would generally 

 affect the result by less than 20. 



Your authority on such a question would of course be 

 accepted as conclusive. Will you therefore allow me 

 to ask you whether this is so, and also to state what the 

 odds would be against the result being affected by 

 chance to the extent of 100. — I am, yours very truly, 



John Lubbock. 



Prof. Stokes, M.A., D.C.L., etc. 



To this enquiry Sir G. Stokes replied : 



I have carefully calculated the chances, and quite 

 verify your result. I find that the average difference 

 from 2000 in the votes assigned to B or C in the case 

 you mention would be as nearly as may be 16, and that 

 the odds against the difference being as great as 100 

 would be in round numbers 44,000 to 1. 



