‘860 REPORT—1885. 
articles, to which it gave the index number of 100, has year by year 
calculated for a new index number the percentage of variation in price 
and thus indicated the specific yearly rise or fall down to the present 
time. Thus cotton wool, the price of which was represented at the 
commencement of the series by 100, the actual price being 8d. per lb., 
103 x 100 
a 
In the interval it had risen in 1866 to the equivalent of 267, and in 1883 
9@ 9R7 
fell solowas 71. It is evident that a ie 
26 + 167 — 29 
rising to 103d. in 1873, was represented by 126, the result of 
=1544, or leaving out 
from each the original 100, = 542 would give the index 
numbers for the average price or increase of price for those three years, 
‘and by conversion back into pence show the actual price and increased 
price: for as 100 : 1542::81 : 122 and 100: 54°6::8-25 : 4°51, and so 
on for every succeeding year. Each of the twenty-two articles being on 
the datum line as 100, the total index number becomes 2,200, and the 
several new numbers in the following years being added together, we get 
3,964 and 2,947 as the totals for 1866 and 1873, with 1,564 and 747 as 
the respective indications of the general rise in prices. The index for Ist 
January, 1885, is but 2,098, showing, so far as this table is evidence, that 
we have now reached the lowest prices for at least thirty-five years. 
This table however—good as it is so far as it goes—is defective, 
inasmuch as it only deals with the quotations for forty-four distinct 
-articles out of the numerous commodities in which we deal, and it takes 
no account of the relative importance of the articles, either in the range 
of value, or the quantities bought and sold. Thus wheat at 30s. to 50s. 
per quarter, of which we grow some 80,000,000 bushels, and import some 
120,000,000 more, reckons for no more than indigo at 2s. to 8s. per lb., 
the transactions in which must be limited to the 100,000 cwts. we import. 
Again, including as it does four descriptions of cotton, each numbering 
as one out of twenty-two, the unusual fluctuations to which this article is 
subject affects the index number, for the years in which this may occur, in 
a fourfold degree. The same to less extent may be said of iron. These 
sources of derangement, together with that of the entire omission of such 
an important article as coal, Jed me, in a paper on the silver question 
read before the Statistical Society in 1879,! to substitute corrected index 
numbers in which these two sources of error were avoided. The effect 
of these corrections was to reduce amongst others the average index 
number of 1865 from 162 to 138, and to increase that of 1873 from 134 
to 142. It is obvious also, as the ‘ Economist’ itself remarks, ‘that in the 
course of so long a period of years, 1845-84, some variations have 
inevitably arisen in the mode of quoting prices.’ 
It must be evident therefore that imperfections in the data upon 
which these calculations are made prevent entire confidence in their 
results, notwithstanding the scientific accuracy in the methods employed. 
It is probable, however, that for the purpose of comparing one year with 
another or others, especially with those not separated by long intervals, 
the ratio of progress is accurate. In such statistics as these, which em- 
brace a multitude of small items, and thus afford opportunities for minor 
errors to balance each other, the results are not far from the truth, even 
» «Some Phases of the Silver Question.’ Stat. Journal, vol. xliii. 
