ON VARIATIONS IN THE VALUE OF THE MONETARY STANDARD. 293 



of the median. For instance, if we are certain beforehand that the mean 

 is below 100, we may dispose the entries above that figure in any order, 

 just as they occur in the table from which they are taken. 



We have shown how to construct a type of price-variations analogous 

 to the typical mean of statures or other attributes defined as that height, 

 or it may be weight, which appertains to a greater number of a certain 

 population than any other height or weight does.' But here it may be 

 asked, Why rest satisfied with a type if there exists a more substan- 

 tial qucesituni ? Why seek the mean variation of shadows instead of the 

 objective movement of the bodies, that declination of the sun or revo- 

 lution of the earth of which the varying shadows are the expression ? 

 Why not penetrate beneath the superficies of shifting prices to the real 

 relations between the quantity of money and commodities ? ^ 



The matter is simple as long as we keep to the abstract theory of the 

 text-books. Imagine a purely metallic currency, the amount of which 

 is, say, Q, and let the rapidity of circulation or duty of money be called 

 C ; then we may simply express the quantity of metallic money in terms 

 of prices and volumes of transaction in our notation 



lifow let prices vary with the quantity of money, other things being 

 constant, and we have for the variation in the quantity of money the 

 simple expression 



apa+/3j3g-H&C. _Q 



a'p'a+/3y^+&c. Q" 



where -=c^=l, &c., nearly, or upon an average. 

 « P 



Let us now introduce the several concrete circumstances, first that 

 a proportion, say the ratio K, of transactions is effected by credit ; 

 secondly, that the volume of transactions varies between the epochs \;nder 

 comparison, say is multiplied upon an average by the factor P ; thirdly, 

 that the proportion of credit transactions, and fourthly , the duty of money, 

 the coeflBcients C and K, do not remain constant. 



When we introduce the first attribute alone, no diflBculty is felt. The 

 factor K disappears and leaves our formula in its initial simplicity. 

 Again, when we introduce by itself the attribute of increased volumes, no 

 great complication arises. We have only to multiply the simple formula 

 by P in order to obtain the diminution of metallic money relative to the 

 volume of transactions, per unit volume as one may say. 



This proposition may appear at first sight still to hold good when we 

 combine the two attributes hitherto considered separately. But this 

 presumption is negatived by the fact that legal-tender money is largely 



' The Mean as defined in Dr. Charles Roberts" writings, not quite identical with 

 Quetelet's homme moyen in case of asymmetrical curves like that on p. 284. 



" What we have so far found is a mere ratio, comparable in point of objectivity 

 to the ratio between male and female births (about 1,040: 1,000 in England). 

 But might the analogue be the proportion of black and white balls in large groups of 

 balls wiiich have been drawn at random from a huge urn ? Beneath the typical 

 mean presented by those groups there is a more objective fact ; the relative numbers 

 of black and white balls, the masses of ebon and ivory. 



' By o, o', &c., for the purpose in hand we should understand not so much the 

 amount of things sold as the amount of sales (per imit of time). 



