ON THE USE OF INDEX NUMBERS. 869 
“%be, from sound bases in the Board of Trade tables does not affect the total 
results so much as might be supposed, from the fact that the year 1875 on 
which the calculations are made was one unmarked by any great 
irregularity in any of the articles, either in quantity or price, and also 
from the deviations happening to take different directions, so as to 
‘neutralise cach other. The effect of the two systems may be shown side 
by side for the five years already detailed in a previous table, where the 
alteration in the index numbers, and the export values they represent, 
were based upon the prices of 1883, thus: 
Prices of 1883 Prices of 1861 
| Actual Values Index No. | Altered Value | Index No. ' Altered Value 
£ | / £ £ 
18835 240,000,000 | 1,000 240,000,000 59°85 | 264,000,000 
1879 192,000,000 | 798 192,000,000 | 59°70 212,000,000 
1875 224,000,000 | 739 177,000,000 | T£AT 198,000,000 
1873 255,000,000 | 127 174,000,000 85°73 196,000°000 
1865 166,000,000 | 460 111,000,000 | 89°26 122,000,000 
| 
The prices of 186] having been 10 per cent. higher than those of 1883 
would make that difference between the calculated values in each of the 
years. These index numbers of 1861 will not however permit of being 
added together, either in the whole or the several parts, for the different 
articles, because they are in each year percentages of varying totals, 
‘whilst those for 1883 are in every case a percentage of the same amount, 
mamely the total of that year, 240,000,0001. 
But having got these altered values by applying the prices of one year 
to others and deducting from them the actual values of the respective 
years, it would appear in the case of the three years that the bulk of our 
‘trade in 1883 is to be measured as more than 1875 by 83,000,0001., than 
1873 by 96,000,0007., and than 1865 by 193,000,000/. But both 1865 and 
1873 are abnormal years in which the extravagant prices of coals, and 
therefore of iron, or of cotton, ran the total values up to an undue extent, 
and so by the large proportion they are of our whole trade had an unfair 
influence, not only upon the values of these goods themselves, but upon 
the average of the non-enumerated as well. For instance, the price of 
cotton in 1865 raised the index number in comparison with 1883 by 
adding 243 to 299, being 81 per cent., whereas all the other enumerated 
articles together only added 107 to 405, being 24 per cent. In like 
manner the cost of coals in 1873 added 54 to 44, at the rate of 123 per 
cent., and the other goods, excepting metals which were almost equally 
affected, were increased 309 on 521, or but 59 per cent. For the ultra 
free-trader therefore to compare the results of these two exceptional years, 
as has often been done, with 1883, is about as absurd as should some 
opponent of sanitary reform in Spain compare the death-rate of some 
fature year, when cholera has ceased its ravages, in proof of the superior 
healthiness of the nation in the later over the previous year. The true 
worth of such investigations is historical, as furnishing one factor amongst 
the many which are combined in influencing the prosperity of trade, and 
sets of tables thus constructed may possibly be of great help in the 
collection of information towards solving the problems committed to the 
consideration of the recently appointed Royal Commission on Trade. 
