140 



EEPORT — 1889. 



quantity in 1880. The quantities are taken from Mr. Giffen's Table V., 

 Part I. ; ' and the quotients are given in the order in which those quan- 

 tities occur. Thus for Alkali the quantity (of cwts.) is for 1880, 6,888, 

 and for 1883, 6,947 ; the figures after the first four being neglected. 

 Accordingly, the quotient is 1"01, or I'O. The figures are true to the 

 first place of decimals. 



The grouping of these ratios is exhibited in the annexed diagram ; 

 where each upright line, surmounted by a figure expressing its length, 

 represents the number of times that a certain ratio occurs. Thus the 

 ratio I'l is presented eleven times ; the ratio 1"2 ten times. The median, 

 is 1*1 ; a result which agrees with that obtained by Mr. Giffen's more 

 elaborate and accurate method. He, in effect, weighting each of 

 tiiese ratios witb the values of the corresponding article for 1883, finds 

 for the ratio of the volume of 1883 to the volume of 1880 the quotient 

 146,371,015 -J- 188,032,674 = 1-06, or approximately 1-1. 



Again, comparing 1886 with 1883, and taking each of the fifty-two 

 ratios to two decimal places, I find for the median I'OO ; while Mr. Giffen's 

 Weighted Mean is -98. 



This consilience might have been predicted by the Calculus of 

 Probabilities, if cotton and perhaps one or two other articles whose values 

 constitute abnormally large weights had been omitted.^ The fact that 

 even without that omission the results coincide shows an even greater 

 symmetry in the movement of trade than might have been expected. 



The objection to this plan of taking a simple average between the 

 ratios of quantities is that equal importance is assigned to a growth in 

 the quantity of an insignificant article like valonia and a staple like wheat, 

 of which the quantity imported had in 1875 a pecuniary value some 150 

 times as great as that of the unimportant dye-stuff instanced. We re- 

 quire, then, a measure of the importance to be attached to different articles 

 of trade. It is assumed that such a measure is afforded by money, or 

 should be, but that the Monetary Standard is itself liable to variation. 

 We require, therefore, to measure the variation of that standard, and thus 



' ' Reports on Recent Changes in the Valuf of Foreign Trade, Pari. Papers, 1885, 

 «. 4456 ; and 1888, c. 5386, Part III. table 2. 



- The verification holds good when one, or more than one, of the returns for 

 cotton are omitted. 



