862 REPORT—1885. 
index number for cotton yarn. Pursuing the same course with each of 
the other articles of export for that year, which are enumerated in quan- 
tity as well as value, and adding them all together, he arrives at a total of 
61 as the index number of the whole, which stands as the index number 
or representative of 146,000,0007. ont of 240,000,000. In like manner 
dealing with any other year, say 1873, he takes 100 to represent its total 
value of 255,000,000/., and finds the index number of the enumerated 
articles to be 67:2. It should be observed here that the index number 
for 1883is “of 249,000,0000,, and that for 1873, 67 of 255,000,000, 
go that the two index numbers do not stand in a definite relation to each 
other. This is a defect, as I venture to think it, to which allusion will be 
made further on. Thus far the process has been with values only, aud 
the index numbers show no more than the actual money figures do. The 
use to be made of them is to get other index numbers that shall represent 
quantities algo, and so determine whether, and to what extent, the volame 
as well as the value of one year has changed with reference to the other. 
This is effected by the following means. In the first place, a simple 
division of the total value by the total quantity of each article in each 
year will show the average price per unit whether that be a ton, pound, 
yard, gallon, or any other measure. 
Keeping for illustration to the two articles already quoted, it appears 
that Togas tons gives 5214s, as the price per ton of pig iron in 
118,0371. 4 ; LEM aT, 
1883, and Tae Os = 12465s. the price for 1873, giving a decrease 
of 72°51s., which shows that this article was more costly by 139 per cent. 
13,509,7321. 
264,772,000 
=17:76d., from whence it is seen that 
in the earlier than the later year. So with cotton yarns 
15,895,4407. 
= 19-9 med aia Pallet is 
See eee ano 4 778 Bar 
this article was 45 per cent. higher in price in 1873 than in 1883. If 
now, we increase the index numbers of 1883 by 139 and 45 per cent. respec- 
Lif X1390 o 2°36, and 5°6 x #9 = 2°52 as additi hich 
SABIE; Ge 100 = 722 as additions whic 
will represent the alterations necessary when quantity is considered aS 
well as value. 
Mr. Giffen, however, has preferred a comparison with 186], and to 
take the proportion of each article as it was in 1875 instead of that of 
each year, and has worked out the alterations thus to be made for twenty 
of the years included in the period 1840-1873. Taking then the total 
index number ascertained for 1875 to be 65°8, he finds that 1873 is 
+ 19:93, whilst 1883 is — 5-95; that is (though he does not so state it), 
these changes would make that for 1883, compared with 1873, as 59:85 
to 85°73, in which proportion the values of the latter year must be in- 
creased to bring them into comparison with the former. Thus 146,000,0007. 
must be increased to 209,000,000/.; and assuming that the non-enume- 
rated articles vary in the same ratio 224,000,001. x ao = 321,000,0002., 
as the value to which the total exports of 1883 would have reached had 
the prices been the same as in 1873. 
Adhering to the principle of the foregoing calculations, there would 
tively, we get 
