•206 Professor Whewell on the Matliematical Exposition 



(?oni is p shillings (units of money), and that the annual return 

 requisite to replace a capital c with the usual profit, is qc {q—\ 

 being a fraction which expresses the rate of profit.) 



In general, w^e shall have to consider only the average produce 

 and rate of all the soils, except the last quality; the last quality 

 being that which is brought into cultivation, or thrown out, by 

 the changes which we have to consider. 



Let a be the whole number of acres in cultivation, c the 

 average capital employed on an acre, r the average produce per 

 acre. Then the whole produce is ar, and its price arp; the whole 

 capital rs ac, and the sum requisite to replace it with profit is 

 acq; and hence by the 1st Axiom, the whole rent is arp — acq, 

 it being supposed that there are no taxes. 



If we now suppose taxes (viz. a tax affecting agricultural 

 imdertakings only) to be paid on each acre, depending in any 

 manner on the quality; viz. on the 1st quality t^ per acre, on 

 the second L, on the wi"" t,„, on the n'" <„: the whole tax will be 

 n^t^ + a^L + a^t,... + a„,t,„ + ...a„t„; and we may suppose this to be 

 at, where t is the average tax per acre: {t^, &c. are expressed in 

 units of money.) 



The rent will now be the excess of the price of the produce 

 above the deductions, which are the tax and the profits on the 

 capital ; for the capitalist cannot pay more Or less, as will appear 

 by the same reasonings as those which were used when there 

 was no tax. That is, the whole rent will now be 



arp — at — acq. 



In this case a, r, p, c, may be different from what they were 

 before, in consequence of the introduction of t, and we have to 

 examine what the alterations are which will thus take place : 

 q is supposed to be unaltered by Axiom 6. 



In consequence of the tax, let it be supposed that the price 

 p becomes p'; and that the last quality of soil a„ is thrown out of 



