Mr. Drummond's Rule for Boroughs, signed G.V. 361 



« H denoting the houses, T, the taxes, B, the relative im- 

 portance of any borough ; also, h, t, b, and A', t', V denotmg 

 the same things of two other boroughs; the problem requires 



the ratio -^ to be expressed by the two ratios -pj- and tj- 



(p. 220*); and-g-, by-jj and -^. 



This I allow to be a correct view of the question. 

 The result, however, to which we are conducted, by an 

 ingenious use of the calculus, is thus expressed (p. 222): 



« ^ = m-YY + n -^, whence b = 'Q\m-^ +n ^^•" 



Again (p. 223), " Lieutenant Drummond assuming vi and n 



to be equal, the formula becomes 6 = 13 ^ -^ "^ T j 



This is just the analytic expression of his rule." 



sl„ce,.,^=^+^=iit^ (fori depend, 



on -5— and ) ; we have 



n t ' 



^T + ^ H A^ ^,2) inverted). 



.-. A^T^ + f^H^ + 2^ATH = ^ATH, orA'T^ + f'H* 



+ ^ATH = O! 



Otherwise, lest equation (2) should be said to be a forced 



construction of the rule, 



h AT+m ,6' A'T+^'H. 

 Since g- = -3px^' a"d -^ = jpj, , 



^, + 5' (/,+A')T + (; + OH 

 ■we have, by addition, ., = — - ^j'p * 



But, by " the third principle" (seep. 221), i + &' = B, A + A' 

 = H, and i + ^'=T. „t^TH 



Therefore, by substitution, -^ - jpj^ — > tnai is, 



1 1 ■ ■ 



• These quotations are somewhat shorter than the original sentences. 

 XS. Vol. 11. No. 65. May 1832. 3 A It 



