ON VARIATIONS IN THE VALUE OF THE MONETART STANDARD. 289 



within the most perfect groups which are known to exist ; for instance, the pro- 

 portion of male to female births. The mean (percentage) for the first division 

 {Urproductioneii) , containing 129 wares, is 128 ; for the second division, contain- 

 ing 85 wares, 118; for the thii-d, containing 98 wares, 108. The modulus of 

 comparison between the first and second mean is {see the writer's ' Methods of 

 Statistics') about 'iO\^~ + ^ = about 5-5; while the observed difference is 10, 

 nearly twice the corresponding modulus. Which constitutes a real, yet not enor- 

 mous, difi'erence ; not greater than the diflerences in stature which exist between 

 the sub-classes of a nation constituting a perfect type Similar statements are 

 true of the comparison between the second and third means. 



If in the light of these conceptions we actually plot the 312 price-variations, it 

 will be difficult to resist the impression that we have here a typical mean as perfect 

 as any presented in concrete statistics, with the exception of the circumstance not 

 relevant to the point now examined, that the curve representing the 312 wares, 

 however continuous, and far from being saddle-backed, is not symmetrical about 

 its greatest ordinate ; the law of price statistics above announced making itself 

 markedly felt. 



The evidence that the general average rise for the whole group of 312 articles, 

 namely, from 100 to 118, is no mere accidental appearance, but indicative of a real 

 agency, is mathematically estimated by odds of trillions to one 



So nearly complete a fulfilment of our hypothesis is doubtless not presented by 

 certain other statistics, e.(/., some oftho.se adduced by Dr. Forsell in his interesting 

 brochure. But it may be safely said that no statistical argument would stand 

 tests so severe as he applies. Consider the evidence in favour of the motion of the 

 solar system, as marshalled in the masterly papers of Sir G. Airy and Messrs. 

 Dunkin and Plummer in the ' Memoirs of the Astronomical Society.' It will be 

 found that, if you omit here, and stick in there, some star of peculiarly large 

 apparent motion, the general conclusion as to the sun's movement will be most 

 materially altered. E pur si muove. 



We see in the case of one example presented by one country that the 

 hypothesis is fairly well I'ealised by the price- variations of the majority of 

 wholesale commodities. But it is a long step from one set of statistics to 

 others, from wholesale commodities to the whole field of industry, and 

 from a single country to the entire system of countries in monetary 

 communication. Over a large area (as Leslie, Knies, and others have 

 pointed out) there is apt to arise a marked diversity between the price- 

 variations of different localities ; a diversity which may well be incon- 

 sistent with the hypothesis of a unique and general mean type. There 

 is no doubt that these considerations materially restrict the fulfilment of 

 the conditions which are prefixed to this and the following section. It is 

 possible, however, that an hypothesis, though known to be inexact, may 

 correspond with the facts sufficiently well for the purpose in hand. 



Section IX. 



Determination of an index based upon quantities of commodities : upon the 

 hypotJiesis that a common cause has produced a general variation of 

 prices, (a f.) ' 



We have seen that, upon the supposition of a change in the supply of 

 money, Jevons' method of combining the variations of prices without 

 regard to the corresponding volumes of transactions is by no means so 

 absurd as has been thought by some. The case is as if we wanted to 

 discover the change in the length of shadows due to the advance of day. 



' In the preparation of this section the writer has derived much assistance from 

 repeated conversations with Professor Foxwell. 



1887. u 



