ON TARIATIONS IN THE VALUE OF THE MONETARY STANDARD. 151 



This passage, with its context, presents great difficulties. As Mr. 

 CJifi'en's 'Index -numbers' do not purport to be measures of volume, but 

 of changed level of prices, there is no reason for surprise that the 

 ' factors ' of quantity and value should have no visible cfi'ect on^the 

 'result that the Index-numbers for cotton yarn should be altered' by 

 certain additions. The additions to the Index-number are proportional 

 to the percentages of increase or decrease of price ( + 5'38, +1, —014; 

 proportional to +91-23, +16-91, —2-31), and that is all that is to be ex- 

 pected. It seems as if the original writer had stated the relation between a 

 yard and a metre as a preliminary to comparing the height of an English- 

 man and Frenchman, the former height having been given in yards, the 

 latter in metres. The critic gives the relative height of the Englishman 

 and Frenchman, and then complains that this factor has no correspondence 

 with the relation between a yard and a metre. 



Such appears at first sight to be the drift of the passage above cited. 

 It will be found, however, from the context that the critic has not over- 

 looked the fact that the object of the ' Index-number ' in question is, to 

 continue our metaphor, the comparison of the two scales, yard and 

 metre. But he seems under the mistaken impression that this comparison 

 can best be effected by giving the Frenchman's height in metres and also. 

 in feet, and comparing these figures. Now, it is here contended that the 

 two scales may equally well be compared by taking the Englishman's 

 height both in metres and feet.' Nay, a German will do equally well for 

 the purpose of comparing the two scales of measurement.^ But, in order 

 to bring out the truth which is here implied, it will be well to employ a 

 metaphor which is more nearly an analogy. 



The following apologue may put the whole matter in a clear light. 

 Suppose there Avere given the increase per cent, in the number of births 

 in a certain district, the increase per cent, in the number of the popula- 

 tion, and in the number of persons to a birth (or the inverse birth-rate) 

 for several years. There would, of course, be a visible connection between 

 these figures ; and any one set, in particular the proportionate popula- 

 tion, could be deduced from the other two. Now, if a statistician had 

 assigned an Index-number purporting to represent the alteration in the 

 numbers of the population, and the alterations so assigned were not de- 

 ducible from the first and third sets of data, and not coincident with the 

 second, it would, no doubt, be reasonable to complain that it was difficult 

 to see how the given factors brought about that result. 



But our problem is by no means so simple. It is like those problems 

 in vital statistics which Laplace, in the absence of a complete census, 

 proposed to solve by the aid of the Calculus of Probabilities. He supposes 

 that the total number of births in a country has been ascertained from 

 registers of baptisms, and that the birth-rate, or its reciprocal, the 

 number of persons to one birth, has been observed at two or more epochs 

 in several districts, which are taken as fairly representative of the whole 

 country. If the birth-rate were constant from year to year, we might 

 reason thus : — 

 Population in year y : Population in j-ear z :: Total No. of births in y 

 : Total No. of births ina; (x being the standard year). 



But if the birth-rate is considered as varying between the two epochs 

 • Tlie twin-method alluded to on our page 150. = Mr. Giffen's first method. 



