ON VAUIATIONS IN THE VALUE OF THE MONETARY STANDARD. 145 



tude of the quantities of commodity increases in general from year to 

 year; but the proportions between the respective masses of commodity 

 are, by hypothesis stated at page 142, constant. Thus we are to imagine 

 each set of ratios q„^ : jj,, j^j ■ !Z62> ^^-^ %n '■ iimi as quantities of the same 

 order hovering about a mean or diverging from a type which we may 

 denote by y^ '. ji- Similar suppositions are made with respect to the 

 other articles. The annexed arrangement of the symbols brings these 

 relations clearly under view : — 



Year I 

 Year 2 



Here each y stands for any of the g's in the column above it ; or, rather, 

 the ratio of any one y to another ; e.g., y^ '■ Jb stands for the ratio of the 

 corresponding g's for any year. , 



Similarly let pa\ denote the price of the article a in the year \,Pa2 

 the price of the same article in the year 2, and so on. Here the abso- 

 lute magnitude of the prices varies from year to year with the apprecia- 

 tion or depreciation of money ; but the proportions between the prices of 

 the respective commodities are regarded as fairly constant. Then we 

 have a scheme for the ^'s like that of the j's : — 



Yearl 

 Year 2 



Year n p„„ i',,„ 



Tft 



Here each of the tt's is typical of the column above it ; or, rather, the ratio 

 of any one -k to another is typical of the ratio between the corresponding 

 ^j's for any year. 



Upon these hypotheses the following appears to be the most general, 

 or at least a sufficiently general, representation of the proportionate 

 volumes of trade for the series of years. 



Volume of imports [or exports] in year x is proportional to value of 

 imports [or exports] in year.?; -f- Index-number indicating the ratio of the 

 price-level in the year x to the level of prices which is taken as standard. 



.*. Volume of imports [or exports] in year x is proportional to value 

 of imports [or exports] in year x 



7a T„ + y6 Tj + Ac. ' 



where, as already explained, y,., y;,, &c., tt,,, itj,, &c., are the typical quan- 

 tities and prices. 



So far we have supposed both the quantities and prices of the articles 

 imported or exported to be given. In the concrete case where these data 

 are wanting for a considerable set of articles of which the value only ia 



1880. L 



