140 Dr. WHEWELL, ON THE MATHEMATICAL EXPOSITION OF 



8 1 



If we suppose n to be - , we find x = — . 



Hence the price of D in terms of C falls - in England ; that is, the price of D becomes 



2 5 10 



- x - C = — C, which is one of Mr. Mill's suppositions. 



3 6 18 rr 



1 ■■ tYt ffl 1 



On this supposition, since q ' = q = q — , the quantity of (D) consumed in England 



is greater by — than it was before the trade. 



3 Q 1,1- MX 28 



Also (1 - x) (1 - X) = -. Hence i-X= — , X = — ; Q'=« ~ = Q— • 



v ' v ' 4 10 10 J - X 27 



The quantity of (C) consumed in Germany is — greater than it was before the trade. 



41. If we suppose n to be — , we find x = - , -3f = 0. 



9 4 



Hence the price of D in terms of C in England falls - ; that is, the price of D becomes 



3 2 10 



- x - Cor ^C The quantity of (Z?) consumed in England becomes — q. 



In this case the relative price of C and D in Germany is not altered by the trade, and Q 

 is not altered. 



If we suppose n to be - , we find x = 0, X = - , Q' = — Q. 



In this case the relative price of C and D in England is not altered by the trade, and q 

 is not altered. 



6 . .5 



42. If we suppose n to be greater than - , for instance, if x = — , we should find from 



5 4 



1 5 



the formulae, x = — - , A" = — . 

 6 14 



But this solution, implying that the price of D in England is increased by the trade, 



is of course inapplicable. 



In like manner if n be less than — we shall find X negative, and have an inapplicable 

 solution. 



43. We can now trace the gain of each country by the trade on the above suppositions. 



8 8 4 



Let n = - and P = 2 as above (40). Then PQ = -q, and since P = 2, Q = -q. 



In this case, before the trade, England produces for her own consumption a quantity q 



28 

 of (X)) and a certain quantity of (C). During the trade she exports — Q of (C) with 



