222 Professor Whewell on the Mathematical Exposition 



— TR = ac(q- l)s — acv{q- l) s ~ arpio (1 —u) 



f(9-0sw ) 



=:ac{q- \)s — arj)W-arp {— lout. 



The two first terms are the most considerable. 



Using the equations of price, according to Axioms 5 and 6, 

 both with and without the tax, we have 



p'r„_i =c„_i9 + s(9-l)c„_i, 

 pr„ = Cnq. 



t/ 7* C I O ~^ lis 



Whence - — "~' " = 1 + ~ — ; or usinff w and p as before, 



pr„c„_, q 



Also as before, w = eu, p = m{fi-i)u, and, therefore, omitting 

 n\ &c. 



/ X ((7—1)5 

 CM + m (/U — 1 ) M = -^^ — , 



? 



(q-l)s {q-l)es 



q{e + m(,uL-l)}' q{e+m{fi-l)] 



Putting for w its value in -tR, and omitting the latter term 

 which involves s" 



n , N (q—1)s e 



— tK = ac {q-l)s — arp~ ; -. tt . 



^^ ^ q e + m(M— 1) 



arnu 

 or smce ac= — - — 

 qv 



„ (o- l)s |m e ) 



~tR= arp^ ^— \ -. -rf . 



q (v e + m(n-\)> 



Also, since the effect of the tax cannot diminish the rate of 

 profits, by Axiom 6, 



„ (?-i)s 1 



— TQ=:acqv = arpu=arp— — — -. -r, 



^ ^ *^ q e + m{/x—l) 



TP=arp {{\ +w) {l-u)-l}=arp ^^-J^ e + m(^-l) ~ '"'^^" " 



