of some Doctrines of Political Economy. 219 



lowest soils is properly estimated by assuming the same capital 

 to be applied to an acre of each, and comparing the results, 

 whereas it may be that from the nature of the agriculture of these 

 soils the same capital is not applied to each. Also it is assumed 

 in Art. 22, that if we have among the lowest cultivated soils, 

 10000 acres which gives an excess of not more than 6 per acre 

 above the least produce, we shall have 20000 acres which gives 

 an excess of not more than 12, and so on proportionally. These 

 are assumptions made to reduce the problem to mathematical 

 definiteness and regularity. But their inaccuracy will affect the 

 result only by quantities much less tlian those which we inves- 

 tigate. The errors will be changes of the second order, or often 

 of lower orders still. In the same manner the assumption is in- 

 troduced that there is a limiting soil which pays exactly profits 

 and nothing more. But if we suppose that though there may 

 not be exactly any such soil, the soils above this limit will be 

 cultivated, and those below it will not, we come to nearly the 

 same conclusions. 



31 . Let us now consider the effect of a land-tax : and let 

 the tax be a given sum (0 per acre. Resuming the equations 

 of Art. 15, we have (a„ being thrown out of cultivation by the ' 



tax), 



— tR = arp — ar[\ — u)p' + [a — a„) t — acqv 



— tQ = acqv, 



tP = ar[\ — u)p' — arp, 

 T={a-a„)t,. 

 as before, let />' = (!+«))/), and we have 



— TR = arp{\ — (1 +w) (1— m)} +(a -a,)t — acqv. 



A1.SO for the limiting soils with and without taxes respectively, 



we have 



p'r„.,-l„.^=zc,_,q, 



pr„ = c„q; and eliminating; q, 



EE 2 



