ON VAKIATIONS IN THE VALUE OF THE MONETARY STANDARD. 157 



well-known analogies between the unity of price in the same market and 

 the equilibrium of fluids in the same vessel, the change of price in a 

 large market is not more indicative of the sought mean variation than a 

 change of price in a small market. F rim a facie, for tlie purpose in hand, 

 each observation should count for one. Or, if more weight attaches to 

 a change of price in one article rather than another, it is not on account 

 of the importance of that article to the consumer or to the shopkeeper, 

 but on account of its importance to the calculator of probabilities, as 

 affordinf an observation which is peculiarly likely to be correct — 

 peculiarly likely to coincide with that type which he is seeking to elicit. 



This type of mean variation may be generally defined as that figure 

 which Avonld be presented most frequently if we were to continue in- 

 definitely the long series of price-ratios, or at least that return in whose 

 neio'hbourhood the greatest number of these statistics cluster. It is, in 

 other words, the Greatest Ordinate of the complete curve, or the highest 

 column of the rectilinear diagram, which represents by its abscissa ratio 

 between the prices of two compared epochs, and by its ordinate the fre- 

 quency with which that ratio would be returned if the statistics were 

 extended over every region of industry which is subject to independent fluc- 

 tuations. It is even allowable to imagine series of statistics still longer,' 

 namely, those which would ideally occur if we could go on and on mul- 

 tiplying observations under unchanged conditions. As Dr. Venn says : — 



' We say that a certain proportion begins to prevail among the events 

 in the long run ; but then, on looking closer at the facts, we find that we 

 have to express ourselves hypothetically, and to say that, if present cir- 

 cumstances remain as they are, the long run will show its characteristics 

 without disturbance.' 



The grounds for thus defining our qticesitum were stated in that part 

 of the former paper which referred to semi- objective averages or types. A 

 reference should be added to the sections on the Greatest Ordinate in 

 Dr. Venn's ' Logic of Chance.' ^ Compare also the following weighty 

 words in the masterly study on ' Cambridge Anthropometry ' which he has 

 recently contributed to the Anthropological Institute : ' The ordinary 

 mean here is obviously an imperfect guide. . . . What we ought to do, 

 owing to the obvious asymmetry of the curve of frequency, is to take, not 

 the arithmetic mean, but what is called "the point of maximum frequency," 

 as this is a far truer index of what may be considered the normal length of 

 vision.' Dr. Venn is discussing a problem analogous to ours, namely, how 

 to extricate from an unsymmetrical group of observations that mean value 

 which may be taken as a representative type. 



Such being the question, it might seem appropriate to put as answer 

 that return which occurs most frequently in the statistics actually given. 

 But it must ever be remembered, though it is often forgotten by statis- 

 ticians, that the statistics of prices with which we have to do are of the 

 nature of samples : specimens taken at random from a much larger, if not 

 an indefinitely large series. In interpreting these evidences, in inferring 

 the typo from a limited number of individuals, we must be guided by the 

 methodical rules which the Calculus of Probabilities prescribes. The 

 theory of errors of observation is here as high above ordinary induction 



' Compare Dr. Venn, Logic of Chance, cliap. i. § 14. 



- The third edition of this unique work, especially the first two chapters and the 

 last two chapters, should be studied by all who wish to contemplate that phase of 

 our problem which is now under consideration. 



