214 Professor Whewell on the Mathematical Exposition 



nished supply is the same as the price of production on the 

 new limiting soil. We obtain thus 



23. Substituting in equations (C), the values 



(1 + Ui-A:) == ^ + ^"' |0 = »« (ii^- 1) w» we have 



„ {H-m(*t — 1)}m 

 — tR = arp ~ 7 -~ acqv 



' \ +vi{ix—V)u ^ 



-tQ = acqv } (D). 



tP = arp {(e — 1) u-eu^} 

 T=arpk (1 + ew) (1 - m) 



Also by the equation 



Y^ = (l+e?/) {l+m(M-l)«} (d), 



u is known when k is given, and vice versa. 



24. We may obtain also the relation between u and v. For 

 we have 



prn = ?c„, pa„r„ = qa„c„, puar = qvac. 



Hence, aqcv = apru. 

 Substituting this in equations {D), we have 



— tR = arpumU— 1) -. — — 



' ^ ' 1 +m(,u - Dm 



— tQ = arpu. 



25. When u is small we may simplify the expressions. 

 Since a„ was thrown out of cultivation by the imposing of the 



tax, it is manifest by Axiom 2, that we have 



p' (1 -k) r„ < Cnq; .: r„ < JJ^rjTy 



