ON VARIATIONS IN THE VALUE OF THE MONETARY STANDARD. 139 



Nor is it to be objected that, in the present state of statistics, it would 

 be impossible to obtain returns under several of the headings, that many- 

 important articles would have to bo omitted altogether. For the plan 

 still may pi-esent an ideal in the direction of which it may be thought ad- 

 visable to move as far as possible. It may supply a rationale to some 

 practical method. Thus, any large aggregate of miscellaneous articles, 

 finished and unfinished, may be regarded as a sample taken at random 

 from the immense incalculable series which forms the data of the ideal 

 Index-number. For instance, such a sample may be afforded by the 

 statistics of foreign trade, which we now proceed to consider. 



Section III. 

 Mr. Olffeii's Methods. 



The next solution of our problem which calls for some additional 

 remarks is that which is deduced from the Statistics of Foreign Trade. 

 It is proposed first to examine the principles upon which Mr. Giifen's 

 masterly calculations are based. • 



The primary object of the whole investigation appears to have been to 

 compare the volume of trade in different years. ^ The purpose is, in 

 the language of this Committee's first report, to enable us, ' given the 

 increase of value [of exports or imports in one year as compared with 

 another], to estimate the increase in quantity of the class of commodities 

 under consideration.' 



But there is room for casuistical discrimination when we inquire 

 what is the meaning and measure of increase in the volume of trade or 

 quantity of commodities. 



At first sight the following method of comparing the volume at dif- 

 ferent epochs might seem plausible. Compare the (given) quantity of 

 one article, say a, in one year, say year x, with the quantity of the same 

 commodity in the compared year y. We thus obtain a ratio 



Quantity of commodity a in year y 

 Quantity of commodity a in year x 



Form now a similar ratio for article h, and again for c, and so on. The 

 circumstance that the unit of a is avoirdupois, that of h, it may be, liquid 

 measure, and so on, need not clog these calculations of ratio. We shall 

 thus obtain as many ratios as there are articles, say fifty, as approximately 

 in some of Mr. Giffen's computations. Now take the mean of these fifty 

 ratios. That mean ratio represents the variation in the volume of trade 

 between the years x and y. 



This solution of the problem is by no means to be despised as naif. 

 It presupposes no doubt a certain sympathy and conformity to a common 

 type on the part of several augmentations of which an average is taken. 

 But it will be shown first that this hypothesis is adequately verified ; and 

 Becondly, that it is equally postulated by the more familiar solutions of 

 the problem. 



As to the first point, consider the following figures, which are obtained 

 by dividing the quantity of every export in 1883 by the corresponding 



' Pari. Paper/, 1878-9, C 2247 ; 1880, C 2484 ; 1881. C 3079 ; 18S4-5, C 445G. 

 * Consider the title and introductory sentences of the Reports. 



