30 On a Fai-viulafor the Relative Importance of the BorougJis. 



ber 711 to a given number n ; that is, let xH : j/T ::m:n; we 

 have now a third equation; 



3/ _ «H 

 X m T ' 



Which being substituted in the other two, they become 



B = {m + n): 



and from these, by division, &c. we get 



B ( h t -) 



m + 7i \ H 1/ 



The same formula as was found by a very different process. 



The controversy concerning the just rule for estimating 

 borough importance may be explained briefly as follows : 

 All parties agree in deducing it from the two fractions 

 _h^ t 



H' T' 

 Lieutenant Drummond has placed the boroughs in the scale 

 of relative importance by the formula 



' = ^{-^-4} 



or at least by a rule equivalent to this formula. 

 Mr. Pollock proposed the formula 



/A J 

 ~ V H ■ T 



Dr. M'Intyre strongly insists that the true formula should 



be 7 _ _h^ _^ 



H • T • 



The two last will place the boroughs exactly in the same order. 

 The first, however, is the only rule founded on true principles: 

 the others have been formed from confused or mistaken no- 

 tions about the doctrine of ratios. 



The question comes at last simply to this : — shall we take 

 an arithmetical or a geometrical mean between the two frac- 

 tions -Tj- and -7p- as the measure of the importance of a 



borough? In a practical point of view it hardly signifies 

 which rule be followed ; yet it would have been discreditable 



