[2] Dr. whewell, on the mathematical exposition of 



must be a perpetual import of those metals, to supply the wear and tear, both of coin, and 

 of the other uses of gold and silver, all which we may include in the term plate. According 

 to Mr. Jacob {Of the Precious Metals^ chap, xxni.), the loss by friction annually, is on 

 gold coin g^-jy, on silver coin, ^-q, of the value. If we suppose that the compound loss on 

 the gold and silver is g-J-Q, we should require, in order to keep up a metallic currency of 30 

 millions, an import of gold and silver to the amount of £60,000 annually. If the import of 

 the precious metals were greater than this, the amount of the currency would be increased, 

 and prices would rise. If the amount of the precious metals imported were less than £60,000, 

 prices would fall: and according to the principle just stated, if the excess or defect of 

 metallic import were permanent, the rise or fall of prices would be permanent, and would 

 not cease till a new position of equilibrium was attained. If, for instance, the annual import 

 of gold and silver, which went to supply the currency, were continually £80,000 instead of 

 £60,000, prices would go on rising, till the currency was 40 millions instead of 30 millions ; 

 and then there would be an equilibrium, because £80,000 exactly supplies the wear and tear 

 of a currency of 40 millions. Prices would, in this case, have risen by one third, as we have 

 already stated. If the regular annual import of gold and silver were £40,000, instead of 

 £60,000, prices would fall till the currency was reduced to 20 millions, which amount of cur- 

 rency is exactly kept up by an annual supply of £40,000; and prices would be reduced in 

 the ratio of 3 to 2, as above stated. 



71. In the mode of treating the subject here adopted, we consider only states of equi- 

 librium, like those just spoken of. For although, as I observed at the close of the last 

 memoir (67), a state of equilibrium is never attained, the state of equilibrium is that to 

 which all the motions tend ; and an equilibrium theory is the best attempt at a theory of 

 trade which we can at present make. We must, further, point out some other principles 

 of equilibrium which we here adopt. 



We assume, as in the former memoir (37). the equality of import and export. But in 

 the former memoir, we spoke only of commodities in general, as exchanged for one another, 

 without considering the precious metals in particular. It is plain that when we say that in 

 a state of equilibrium the total exchange values of the imports and of the exports are equal, 

 we must include, in the imports, the gold and silver which are annually imported. But as 

 the metals which are used as currency require peculiar consideration in the present discussion, 

 we shall separate them from the other imports. Let / be the whole of the annual imports, 

 exclusive of gold and silver, P the quantity of those metals annually required to supply the 

 wear and tear of plate ; Q the quantity annually required to supply the wear and tear of the 

 currency ; E the whole annual value of the exports ; then we have 



E = I + P + Q, 

 and this is now the equation of imports and exports. 



72. Let us now consider what the effect upon international trade would be, if the 

 equation of imports and exports were deranged by some considerable addition to the imports. 

 Suppose, for instance, that some commodity (K), which had hitherto been principally pro- 



