ON VARIATIONS IN THE VALUE OF THE MONETARY STANDARD. 287 



difficult, for instance, to trace evidence of lopsidedness in the five-year averages 

 given by Soetbeer.' 



The evidence adduced appears to afford a reasonable presumption that 

 the required method of combination is some form other than the arith- 

 metic mean, of the general character of the geometi'ic mean. Those who 

 have followed Jevons' investigations will be familiar with the pi'oposal 

 that the logarithm of the required mean or general percentage should be 

 equated to the arithmetic mean of the logarithms of the percentages 

 special to each article. To which it is now to be added that this arith- 

 metic mean need not be nimble, but may be iveighted in the sense above 

 indicated (p. 283) ; e.g. — 



W 1 log Xi + W2 log X2 + &C. 



loy: x= 



lVi+lV.2 + 



What then are these weights to be ? is our second inquiry. 



(2) The theory of errors supplies the following rules— of which the first 

 two have been already implied in our statement of the problem — (a) In 

 the first place no weight should be attached to a class of observations 

 known to be affected with what is called a constant error, or uniform bias 

 in one direction. It is supposed of course that only the fact, but not the 

 amount, of the error is known ; otherwise it would be possible to get rid 

 of it. In our case this rule dictates to reject all prices which are not 

 amenable to that play of a perfect market whose change of level we 

 have to investigate. • The writer is far from pretending that this region 

 of permeability can at present be marked off" with precision. However, 

 a rough delimitation may be effected by researches like Dr. Kraemer's. 



Assuming then that we have selected a set of percentages which may 

 be regarded as accidental deviations from a common mean, on what 

 principle should more importance be attached to one indication of change 

 rather than another ? The second (/3) maxim which we have to apply is 

 that the observations should be independent. This condition excludes 

 the prices of the same commodity at different stages of production, since 

 these prices are closely interdependent. Or, if we must take account that 

 at each stage some fresh cause of fluctuation — source of ' error ' — is intro- 

 duced, at any rate each price-return is not to count for one, but only for 

 a fraction. 



Here arises the question whether a commodity extensively consumed 

 like meat or cotton ought not to count for more, in so far as its price is a 

 mean of a greater number of transactions, than cloves and pepper. The 

 answer is that these tiansactions are not independent. The law that there 

 can be only one price in a market prima facie removes the presumption in 

 favour of the more largely consumed commodity. There is no analogy be- 

 tween the average price of such a commodity and a mean founded upon a 

 specially large number of independent observations in theory at least, and 

 for the purpose of a first approximation ; for it will appear in the next 

 section that this abstract proposition is qualified by the inevitable imper- 

 fections of our statistical data. 



(y) A third principle is that less weight should be attached to 

 observations belonging to a class which are subject to a wider deviation 

 from the mean. Such, in our case, would be the prices of articles which, 

 exclusive of the common price-movement of all the selected articles, are 



' Materialen, pp. 99-114. 



