of some Doctrines of Political Economt/. 213 



2*2. We shall now suppose the average rate of produce r to 

 be a known multiple of the lowest rate of produce r„; (it may 

 perhaps in this country be two or three times the latter.) Gene- 

 rally let r-mr„, and since uar = a„r„, we ha\e mua = a,„ or mu = 



a„ 

 a 



Also the quantity of the last soil a„ will depend upon the 

 interval which it is found necessary to take between its fertility 

 and that of the next quality a„_i. If, in order to reduce the 

 problem to calculation, we suppose the worst soil (including' all 

 from rate r,„ to rate r„_i) to consist of qualities improving by in- 

 sensible shades, and of each of which there is an equal quantity, 

 we can easily express this dependence: and this supposition 

 must bring us very near the truth. Let the rate at which 

 these worst qualities of soil improve be such, that if the same 

 rate of improvement continued for the whole quantity of land 

 in the country (which is a), the best soil would yield a produce /'. 

 Let this be called the hypothetical greatest rate of produce. 

 It may probably not differ much from r, the actual greatest 

 rate of produce. But let generally r = fji.r„, or let the hypothetical 

 greatest rate be m times the least. Then we shall have, since 

 the rate of improvement is uniform, 



rn-i-Tn ^a^ ^^ r„_,-r„ ^ a^ 

 r' - r„ a' {/u-l) ?■„ a ' 



.'. -^^ = I + U-l) —. And as before — = mu, 

 .-. ^^= 1 + m (m-1) M. But ^^ = 1 + p, (if c„_, = c„) ; 



.'. p =: 7}l {fJi — 1) U, 



Also if in equation (b) we put for lo its value eu, we have 

 an equation which expresses that the price arising from dimi- 



