"4 
ON THE USE OF INDEX NUMBERS. 859 
On the Use of Index Numbers in the Investigation of Trade 
Statistics. By STEPHEN Bourne, F.S.S. 
[A communication ordered by the General Committee to be printed in extenso 
among the Reports. ] 
WHATEVER opinions may be held on the oft-mooted question whether 
statistics are to be deemed a science or merely as an art, there can be no 
denying that statistical research may, and ought to be conducted on scientific 
principles. The collation of facts, the method in which they are grouped 
and treated, and the results attained by such treatment, is as truly the 
pursuit of science as is the study of many another branch of knowledge 
directed to the discovery and promulgation of truth. Many of the 
elements with which statisticians have to deal are obscure and variable, but 
the conclusions they may be made to support are capable of being of 
as definite establishment as those worked out by the processes of the more 
exact sciences. One of the methods resorted to is the use of an ‘ index 
number,’ which as its name denotes, indicates certain conditions and 
connections of figures which it is otherwise difficult to associate with 
each other. The use of this method is not without difficulty, and two or 
three instances in whichit has been adopted may serve to illustrate both 
its merits and its disadvantages, as well as an introduction to the special 
occasion for its application which forms the subject of this paper. 
The late Professor Jevons, in a pampblet on the fall in the value of gold 
published in 1863, sought in this manner to indicate the various changes 
which had taken place in the price of the various articles of commerce 
following upon the then recent gold discoveries in Australia, and from 
thence to infer that the altered nominal values were in reality due to a 
depreciation in the value of the precious metal in which these prices were 
expressed. Later on, the same evidence of a fall in price was adduced in 
proof of the subsequent appreciation of gold, which more recently both Mr. 
Goschen and Mr. Giffen have asserted to be still in progress. Collecting 
together the average mean prices of thirty-nine different commodities 
during the six years of 1845-50, the Professor took these as the datum 
line with which to compare those of the three years 1860-2. Subsequently 
adding to these seventy-nine new commodities, and by logarithmetic cal- 
culations dividing the arithmetical averages of the former period into that 
of the later three years, he obtained a ratio or percentage which repre- 
sented the rise of prices presumed to be due to the fall of gold. Having 
thus reduced prices expressed in various coins—pence, shillings, and 
pounds—and appertaining to quantities denoted by various weights, 
measures, and numbers, to a series of index numbers each having a 
definite and proper relation to the commodity it represented, it became 
possible to add together the equivalents of that which could not be other- 
wise combined, and so to obtain an average marking a distinct alteration 
with respect to gold. This was taken to establish a universal rise in 
price corresponding to a depreciation of gold by about 9 per cent., which 
was thereby deemed to be proved to have taken place. 
The ‘ Economist,’ commencing with the average price for the same 
six years, 1845-50, of each of twenty-two separate articles or groups of 
