216 Professor Whewell on the Mathematical Exposition 



If ^ = —, e = 3, m{fi- l) = 12; we shall have/= ~, and the 



1 

 9' 



last term in the above expression is — 



30375 



which may be neg- 



/ 



lected without error. 



Hence, m = , / ^^ , 



which is the result that we should have obtained from equation 

 (d) by omitting u". 



27. Substituting this value, and omitting m\ &c. equations 

 {D) become 



l+m(M-l) 



— tR = arpf 



— tQ = acqv, &c. 



or putting apru for aqcv 



„ „ wi (m - 1 ) 



- -rR == arp/.-— 



1 T 



acqv 



tQ^ arpf. - 



m (/u-l)j 

 1 

 + 7n{M-l) 

 e- 1 



(£). 



tP = arpf.- -. -, 



^•^ 1 — m(/u— I) 



T=arp/ 



Hence, tP — tQ — tR=T, as it should be. 



28. Hence the portions of the tax which fall on rent, profits 

 and prices, are as m(M— 1), 1, e — l, respectively. 



Thus if the average produce be four times, and the greatest 

 produce seven times, that which jiays mere profits (e being 3), 

 we have m = 4, /i = 7; and the portions which fall on rent, profits, 

 and prices will be respectively as 24, 1, 2: on these suppositions 



less than -— the tax falls on prices. 



If in this case the tax be — the produce, 



