ON VARIATIONS IN THE VALUE OF THE MONETARY STANDARD. 267 



between two periods of revision, we see by the theory of errors that the price 

 which fluctuates least is {ccBteris paribus) the best representative of mean price. 

 And accordingly, in the combination of the different indications of change in 

 the value of money, there is a prima facie presumption that pecuhar weight should 

 be assigned to those indications which are peculiarly accurate. 



But the validity of this principle turns upon very nice considerations. Where 

 we have several measurements of one and the same thing it is indisputable that 

 more weight attaches to the less fluctuating measures. This is true not only in 

 the case of a real objective measurable, such as the distance between two points, 

 but also where the qucesitum is a subjective mean, such as lliomme moyen. If, as 

 in a case mentioned by Dr. Baxter,^ we have two sets of measurements of heights 

 of American citizens, the one executed -ftith the utmost precision, the other rough- 

 and-ready, then, in order to obtain the best value for the mean height of the 

 American man, it would be best to affect those careless measurements with 

 inferior weight. 



But it may be otherwise when we are seeking not a single mean, but the sum 

 of two or more. If we have to determine the distance from Dover to York via 

 London, and we have very good measurements for the first distance, and very bad 

 for the second, the best that we can do, though bad may be the best, is to add 

 together without quaUfication the two means. So if we have to determine the 

 income of a nation consisting, say, of two classes, upper and lower, for one of which 

 the returns are very accurate, for the other very - loose, still the best combination 

 of data which is available is the simple addition of the two estimates. 



Yet again, if we have several estimates of such a compound mean as has been 

 supposed, the principle of iveight may again make its appearance. Suppose that, as 

 Laplace proposes ^ (in the case of birth-rates), it were the practice to ascertain 

 the statistics of ' a great empire ' by way of sample. Let observations be taken 

 on several villages or districts, consisting each of an upper, middle, and lower class. 

 In combining these observations so as to obtain the mean income for the empire, 

 it would be proper to assign less weight to those localities where the returns were 

 obtained in a more summary fashion, by a less accurate method. Further, although 

 each estimate might not be based upon all the classes in each district, but only on a 

 miscellaneous selection from them, still if we could divide such estimates into two 

 classes, contrasted in respect of accui-acy and differentiated by no other attribute, 

 the best method of combLaation would be a weighted mean. 



To apply these principles : (1) if, like Jevons, we content ourselves with taking 

 samples of commodities rather than all commodities — a perfectly legitimate pro- 

 cedure, and j ustified alike by the theory of Laplace and the practice of statisticians, 

 e.g., Jevons in his enumeration of sovereigns — then undoubtedly, the principles of 

 inverse pirohability becoming applicable to this mode of measurement, greater 

 weight should attach to -the less fluctuating species of returns. It might indeed be 

 a nice question how much the principle of quantity should be cut into by the 

 consideration of fluctuation. Thus, if we took Mr. Gifl'en's ' statistics of the 

 variation in the prices of exports and imports as a sample (or part of one) of the 

 change in the purchasing power of money, C(5tton perhaps, on account of its unique 

 importance in respect of quantity, stands out by itself, and ought to receive full 

 weight. But if we have several articles of about the same importance in respect 

 of quantity but differing in fluctuation, a higher combination-weight should be 

 assigned to the less fluctuating mass of value. 



(2) A similar principle should govern oiu- procedure, if we had to base our 

 calculation upon returns relating not to the whole population, but only to 

 specimens thereof. Suppose, for instance, it was sought to determine the change 

 in the value of money in China, and that statistics could only be obtained for 

 certain representative localities. If we make a complete enumeration of com- 



' United States Sanitary Commission. 



- Supposing, of course, no aninnis mensurandi or constant error in one direction 

 such as that of underrating income. 

 ' Thcorie Analytique. 

 ^ Pari. Papers, 1881-85. 



