ON THE USE OF INDEX NUMBERS. 863 
yet appear to be room for simplifying and improving upon them. In the 
first place it seems erroneous for the purpose of comparing one year with 
another or others, that the component parts from which the yearly index 
numbers are built up, or rather we should say into which each of them 
is split up, should not have a common basis to rest upon, so that they may 
be added to or subtracted from each other, and then converted back into 
the figures of actual values, as for instance, cotton yarn in 1865 is 6°2 per 
cent. of 166,000,0007., in 1883 5°6 of 240,000,000/., and therefore cannot 
be combined without previous reduction to a common denominator. It 
is proposed therefore to reduce all to one standard, and to choose 240 
millions, the total exports of 1883, for the datum amount. This too 
because in the latter year a greater number of articles are specifically 
enumerated, and we can in consequence operate upon a larger proportion 
of the whole. It is evident that whether we take 1, 10, 100, or 1,000 as 
the standard index, the figures into which it is divided will be the same, 
only differing in the place of the decimal point. In the Board of Trade 
tables 100 is chosen, which for closeness of calculation requires the 
use of decimals, and also of the plus and minus signs, whereas if 1,000 
be taken we avoid the use of both, and all our indices are in whole numbers. 
‘Thus the total value of enumerated articles in the tables, which is 
expressed by 61:0, or by adding 9-4 for articles not included in the 
enumeration of earlier years, will appear as 704, which is the same thing 
without the point. But that for 1840 will be 214 instead of 79:1. 
704 214 i : 
“baciea casei h 
Hence {000 and t000 22 be added together or otherwise dealt with, 
because the denominator signifies the same amount, but ri and for 
cannot be, because the 100 stands in one case for 24.0 and in the other for 
51 millions. The one set of tables will show at a glance the proportion 
which exists between every figure they contain, which the other requires 
an elaborate calculation to discover. 
The object to be attained, as already pointed out, is to get a number 
which shall indicate for each article, and for the whole together, the bulk 
as well as the value, and so to ascertain the very important point, whether 
the changes, both in the respective items and the grand total, are due 
wholly, or in what proportion, to an increased or diminished volume of 
goods, or to a variation in the prices at which they are valued. Hence itis 
convenient to make 1883 the year for comparison, rather than 1861, which 
Mr. Giffen uses, and this once established may be utilised for succeeding 
years, until some great alteration in the conditions of trade may make it 
necessary to adopt some new method of exhibiting its effects. 
The number of distinct articles which are specified, both as to value 
and quantity, is 65, for each of which individual calculation has to be 
made in each year. These furnish a wide enough range for assuming 
with safety that those which cannot, for want of definite information as 
to quantities, be so estimated, may be taken in the same ratio of bulk 
as the others are found to yield. The mode of estimation is first to 
convert the value for each given year into a number proportionate to that 
of 1,000, which is the index number for 1883. Then taking the price per 
unit, be it a pound, a gallon, or a yard, as deduced from the amounts and 
shown in the ‘Statistical Abstract,’ to consider that for 1883 as 1:00, and 
for other years in the percentage of increase or decrease. Having thus 
_ obtained a divider for the value index, the resulting number becomes 
‘ 
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