ON VAKIATIONS IN THE VALUE OP THE MONETAEY STANDARD. 281 



market-forces. That this condition does hold approximately with respect 

 to a large group of articles is shown in the case of Austria by Dr. Kraemer 

 in his important work on Austrian Paper-money. From the statistics 

 given in his Chapter III. there can be no doubt that a change in the 

 ' valuta ' of currency does enter into, and might be extricated from, the 

 prices of a certain set of commodities. The following articles may be 

 instanced as particularly sensitive : — Wool, spirits, rape-seed, undressed 

 leather, and, in genei'al, articles of foreign trade. These observations are 

 supported by the copious statistics adduced by Herska, Bela Foldes, and 

 others. The only question is whether we ought not to regard all com- 

 modities, rather than only some commodities, as varying with the agio. 

 No doubt it is a delicate question, and only to be decided by the proper 

 mathematical methods of statistics, whether it is possible to extricate a 

 mean variation in the value of money from the changes of particular 

 prices. It seems to be so in the case of Austria. In the case of the 

 United States, if we could accept the law laid down by Mr. Delmar as 

 to the propagation of a change in price, we could not hope for a suffi- 

 ciently large group to aSbrd a real average. But the statistics adduced 

 by Hock, in his history of the finance of the United States, show con- 

 clusively that in correspondence with the condition of the inconvertible 

 currency and the state of credit there did extend pretty uniform waves 

 of disturbance over a part, if not indeed the whole, of American industry. 



The proposition which has been proved for inconvertible currency is 

 shown to be true for metallic money — as regards, at least, a certain zone 

 of industry — by the index numbers of the Economist, the statistics adduced 

 by Soetbeer, Laspeyres, and others. 



Assuming, then, that there is, or may be, over a certain region of the 

 industrial world a mean disturbance of the sort described, it would be 

 a significant operation to take the average of all the price-variations, ' 

 irrespective of the quantities of the corresponding commodities. We should 

 thus obtain a mean elevation or depression which may be described as a 

 figure such that, if we took any ware at random, that figure ' would be 

 more likely than any other to be equal to the price-variation of the 

 selected ware. A similar typical mean of human heights (irrespective of 

 other attributes) has proved a useful implement of statistical induction 

 in the hands of Mr. Galton, Dr. Charles Roberts, and others. 



A more exact illustration is afforded by the following physical analogies. 

 Suppose it were required to measure the force of gravitation in the neighbourhood 

 of a mountain. Our data might consist of a set of penduhims, all disturbed from 

 the vertical by the attraction of the mountain, and each further subject to proper 

 disturbances. The displacement from the vertical constituting the required 

 measurement might be found by taking a mean of the displacements suffered by 

 all the pendulums. Now, /»-(mh tvhat we know of the action of gravity, there is no 

 reason to think that the displacement of a larger mass gives in general a better 

 measure of the common disturbing agency, the gravitation force, than a smaller 

 mass does. Hence, in taking the mean of the displacements, there is no propriety 

 in assigning more importance to the displacement of the more massive pendulum. 

 If we do assign preferential importance, it should he on other grounds, namely, 

 that the proper disturbances of some pendulums are apt to be less serious than 

 those of others. The comhinution weights (or ' multiplier weights,' in Sir G. 

 Airy's phrase) determined by such considerations must be carefully distuiguished 

 from the ' weight ' in the ordinary sense. The pendulum weightiest in the former 



' In short, the greatest ordinate of the curve of price-variations. 



