148 Dr. WHEWELL, ON THE MATHEMATICAL EXPOSITION OF 



168 (=4x6x7) yards of linen. But this quantity is reduced to 144 (=4x6x6) by the 

 expense of carriage to England. Hence by exporting cloth and importing linen, England 

 would only obtain 144 yards, instead of 147 which she could obtain by the same labour 

 employed on linen at home. 



Hence, though the price of linen as compared with cloth is only - as great in Germany as 



4 



in England, the expense of carriage prevents the trade being profitable. 



65. In Mr. Mill's example (Polit. Econ. 11. 125) the cost of carriage of each, Cand D, is 

 supposed equal, nearly, to — of the price of D ; which is equal, nearly, to — of the price 



of C, or nearly to — . Hence u = — , U = — . 



'....../ 29 29 17 



(1 + C7)(1+m) 30x18x3 1620 1 



= 1 , nearly. 



Pp 29x17x4 1772 5 



2 1 

 = - , and making k = - , 



3 5 5 



l - n (1 - Mk') 15 - 13ra 



2 , 1 



And taking, as in (40), m = M = - , and making k = - , 



m -n{\ - M) 10- 5n' 



In order that there may be an applicable value of x, we must have (47) n between 



15 , 13 

 — and — . 

 13 12 



If n be — , which is between those limits, 



5 1 



x = — = -. 

 40 8 



Also for X, (1 - X) (1 - x) = 1 - k' = 1 - - ; 



5 



v * 8 32 j v 3 



whence 1 — AT = -x- = — , and X = — . 



5 7 35 35 



7 7 2 



The relative price of D and C in England is p' - p - - — , for p = - f (40). 



S 1 ~ o 



32 64 13 

 The relative price of C and D in Germany isP^P— = — = — nearly, for P = 2, (40). 



In England 7 yards of cloth exchange for 12 of linen ; in Germany 7 yards of cloth for 13 

 of linen nearly ; the difference depends on the cost of carriage both ways. 



66. In the preceding investigations, I have done little more than put into a general and 

 algebraical form the reasonings which Mr. Mill has presented to his readers in numerical examples. 

 But I think it will have appeared that by this mode of dealing with the subject, the limits of 

 the truth of the theorems of the solutions of the problems are much more easily brought into 



