28 Reply to Dr. M'Intyre's Remarks on 



borough, let us suppose A = H and ^ = T ; then we ought 

 to have i = B, and therefore 



B = B im'^ +«'-^}; 



Hence it appears that m' + n' = 1: This condition will be 

 satisfied if we make 



, m , n 



in' = , ?i' = : 



?« + n m + 11 



Our general formula now becomes 



B r ■ /i t 



b = 



^m-^ +n~^\ (2) 



7)1 + 71 



Where, as before, ?« and 7i are conventional numbers, which 

 are to satisfy the hypothesis of some supposed relation between 

 the house- and tax-importance : if these are to have equal 

 •weight, then in = ??, and the formula becomes 



' = -|{^-4-};-- W 



Dr. M'Intyre may now try his criterion of absurdity on 

 either of the formulae (2) (S) ; namely, the supposition that 

 B = b + b', H = k + h' and T = t + t'; and he will find that 

 they both stand the test. But in his remarks, he has also re- 

 quired that our formula should at the same time satisfy the 

 two conditions 



m + 

 b 



B = 



— < m-x- 

 m-\-n l_ li 



h t \ ^ 



H T ) I 



Let us suppose, if possible, that they satisfy these condi- 

 tions; and, taking the product of the two equations, and 

 leaving out common factors, &c. we obtain 



{m-\-n)' = 771- + ?r+ mn ^-yr '^ + "T" •'nFJ 5 

 and hence again, 



and 



h t I h 



^ "" H • /; "•■ A • T 



^ H • T ~ ^ H / "^ ^ T ^ ' 



