the relative Importance of a certain Number of Boroughs. 2 1 9 

 persons have proposed very different methods of accomplish- 

 ing it. x^ , -r. • i_ 



Lieutenant Drummond of the Royal Engmeers, to whom 

 the arrangement of the boroughs according to the proposed 

 scale was entrusted, proceeded according to the following pre- 



" I. Take the average number of houses contained in the 

 boroughs to be arranged : divide the number of houses in 

 each borouo-h by this average number, and a series of numbers 

 will be obtained denoting the relative importance of the diffe- 

 rent boroughs with respect to houses. 



" 11. Take the average amount of the assessed taxes paid by 

 the same boroughs, and proceed precisely in the same manner 

 as described with respect to the houses : a series of numbers 

 will result, showing the relative importance of the different 

 boroughs with regard to assessed taxes. 



" 111. Add together the numbers in the two lists which relate 

 to the same borough, and a series of numbers will be pro- 

 duced denoting the relative importance of the different boroughs 

 with respect to houses and assessed taxes combined." 



These very simple precepts were objected to in the House 

 of Commons as unnecessarily complex ; and it was affirmed 

 that the scale might have been formed with the boroughs in 

 the very same order, by simply taking the sum of the numbers 

 expressing the houses and taxes : probably this assertion was 

 made wifhout due consideration, for certainly the boroughs 

 would not have been placed in the same order by this process 

 as by Lieutenant Drummond's rules. 



The subject has also been handled in the newspapers ; and 

 in one it has been proposed to construct the scale of disfran- 

 chisement by taking a geometrical mean between the number 

 of houses and assessed taxes of each borough. The author of 

 this rule, said to be a scientific friend of the editor of the news- 

 paper, affirms this to be " by far the most simple and accurate 

 way of proceeding." 



It could hardly have been expected that there would be such 

 a difference of opinion on so simple a question. The subject 

 is by no means difficult ; truth is but a little way below the 

 surface. Since, however, the matter to which it relates is of 

 the highest importance, it is most desirable to place it beyond 

 further controversy, by discussing it on principles strictly ma- 

 thematical. 



But before the subject can be brought within the power of 

 nuilheniatical investigation, the things to bo considered must 

 be invested witli the properties of mathematical quantity. This 

 may be done by the following principles : — 



2 F 2 1 • Boroughs 



