[4] Dr. WHEWELL, ON THE MATHEMATICAL EXPOSITION OF 



now Q, but (1 - m) Q, the quantity of currency will be annually diminished ; and there will 

 be no equilibrium till the currency is diminished in the same ratio, since the amount of the 

 currency is a certain multiple, (500 in our supposition) of the annual supply. Hence, prices will 

 be reduced in the ratio 1 : 1 - «i. This diminution of prices will produce an increase, F, of the 

 exports ; and we have to consider in what way F may be supposed to depend upon m. 



75. The quantity F consists of commodities sent to the general market of the world as 



supply. It will include all commodities which our country can export at such a rate as to 



compete with other countries. The lower are prices in our country, the greater will be F. 



As a plausible hypothesis, made for the sake of reducing the relation to a formula, we 



may suppose that F, the value added to the exports, is proportional to the fall of price : for 



instance, that a general fall of our prices of one tenth would add £100,000 to our exports; 



that a fall of prices of two tenths would add £200,000 to the exports ; and so on. On this 



supposition, we may put F = mG, where G is a quantity depending on the manufacturing 



skill and activity of our country, as shewn in providing articles of export. Then our equation 



becomes • 



K 



mG=K-mQ; whence m 



G+Q 



76. We thus find the fall of price produced by the importation of K. For instance, let 

 K, the value of the new import, = £100,000, and, as before, let Q, the original annual 



import of money, =£60,000. Also let mG =£100,000, when m = — , as above (75); there- 

 fore G = £1,000,000. 



100,000 5 

 XlGnCG wz — — 



1,000,000 + 60,000 53 ' 



In this case, the prices in our country are lowered by less than one tenth. In the new 



conditio n of equilibrium, the annual import of gold and silver to keep up the currency will be 



48 5 



£54,340 = — x 60,000. The new exports, F, will be — x 1,000,000 = £Q4,340, which compared 



with the new imports, £100,000, leaves a new balance against us of £5660. On the old exports 

 and imports, the balance in our favour was £60,000. Therefore in the new state, it is £54,340, 

 which just keeps up the currency. 



77- If, the other data being the same, K be 1,000,000 instead of 100,000, we shall find 



100 



w = — 7;. 

 106 



Hence 1 - m = = — nearly. 



106 18 ' 



In this case, according to the suppositions which we have made, the prices in our country 



would be reduced to one eighteenth of what they were before, in consequence of the scarcity 



of the precious metals arising from the exportation of them to pay for the new import K. 



But it is evident that such a reduction of prices would produce so great a difference between 



neighbouring countries, that it could not long subsist, while there was trade between the 



