238 Professor Whewell on the Mathematical Exposition 



Hence the increase of rent, omitting terms involving 



wu, s„u, i/„v, &c. is 



= apr{z — y — vo + u) — acqv, 



(since acqv = apru,) = apr{z — y — w). 



Putting for w its value, this is 



^ m(,-x){z-y-ez) ^_ mi.-l)\{e-x)z-y} ^ 



'^ c + m(jii— 1) e + m(/u— 1) 



in this case we have a diminution also of the rent till the 

 increased demand comes into action. 

 The increase of return and profit is 



qac' + qa„c„'- qac = qacy +acqv {l+y„) 



= aqcy + apru, omitting vy„. 



If we suppose the demand to have increased, so that with 

 the new system of production prices are the same as before, we 

 shall have the rent increased from arp~acq to 

 ar'p + pa„r'„ — ac'q - qa„c„'. 



Therefore the increase is 



arpz — acqy + apru (l + z„) — aqcv (1 + i/„), 



also apru = aqcv, 

 and omitting the smaller terras, the increase of rent is 



arpz — acqy, 



which is the whole increase of produce minus the return and 

 profit on the increased outlay. 



W. WHEWELL. 



Trinity Collkoe, 

 March 30. 1829. 



