150 REPORT— 1889. 



period of twenty years as quite permissible ; then by the formula above 

 reached we find the total number of available arrangements to be more 

 than a billion. All these billion schemes are on the whole about equally 

 good, some having a slight advantage in respect of safety, and others 

 of ease. 



Section IY. 

 Mr. Bourne's Method, 



These elucidations assist us in discerning the character of a method 

 which was proposed by Mr. Bourne so long ago as 1873, and more 

 recently has been submitted to the British Association together with 

 some criticism of Mr. Giffen's celebrated computations. > It will be found 

 that Mr. Bourne has discovered, not the method, but only a method — a 

 very good method, no doubt, but not much better than many others, not 

 more serviceable than hundreds, not more accurate than millions that 

 are available. 



A little attention will show that the reasoning is virtually identical 

 with that which Mr. Giffen employs in his fourth table when he compares 

 the quantities in any year at the prices of that year with the same quan- 

 tities at the prices of 1883 ; and goes on, as, for instance, in his first Report, 

 page V, to compare the measure (for the level of prices) so obtained in 

 order to deduce the comparative volume of any year from its value. It is 

 not to be denied, indeed, that this method, under the neat handling of 

 Mr. Bourne, has acquired great elegance. But we must take care not 

 to exaggerate its pre-eminence over other methods. 



In the first place it does not seem to have any advantage over the 

 twin-method which was noticed along with it above.^ This method is, in 

 brief, to take as the measure of changed level of prices 



Quantities of 1883 at prices 1887 

 Quantities of 1883 at prices 1883' 



There is no reason to think that this method would be less accurate 

 than its converse. And it would enjoy the distinction of not having 

 been worked out in detail by Mr. Gifien (in his latter tables). 



A certain precedence, perhaps, attaches to these twin-methods in virtue 

 of a slight superiority in ease and elegance.-* But this slight distinction 

 must not be mistaken for a serious ditference in worth or power. Nor is 

 Mr. Bourne's position defensible when he disapproves the method set 

 forth in Mr. Giffen's first three tables. The gist of Mr. Bourne's objec- 

 tions is contained in the following passage, of which the context should 

 be studied : — * 



' The proportions of [quantities of] cotton yam for 1865, 1875, 1883 

 stood as 104 : 216 : 265, but by value as 10 : 13 : 14, and the percentages 

 of increase or decrease from the standard of 1861 were as +91-23 

 : -1-16-91 [misprinted in the Report 41-63] : —2-3. It is difficult to see 

 how any combination of these factors, so widely diS'ering in their ratios, 

 can bring about the result that the Index-numbers for cotton yarn should 

 be altered as -}-5-38 : +1-00 : —0-14 as shown in the Board of Trade 

 tables.' 



' Brit. Assoc. Rejport, 1885 and 1888. 2 Above, p. 146. 



s Above, p. 147. « Brit. Assoc. Report, 1885, p. 868. 



