276 EEPOBT— 1887. 



the weights 1 , 2, 3, &c., to the percentages above cited. The weighted mean 

 Ixl7 + 2x36 + 3xl4+&c. + 16xl6 ^ 



:; : — r, — :; rr. =2S-8. If we reverse the order oi im- 



1 + 2 + .J + &C. + 16 



portance, and, beginning at the bottom of the list, assign a weight 1 to hemp, 

 2 to jute, 3 to shellac, &c., we obtain for the weighted mean 25'6. The difler- 

 enee in each case between the simple and weighted mean is even less than theory 

 predicts. Suppose the corrected unit becomes 1"26, the tallow interest will now 

 be out by eic/ht per cent, instead of ten per cent, from the standard best for them 

 exclusively— no very great gain, and partly (by hypothesis of course, not wholly) ^ 

 balanced by the loss of the sugar interest, who are now more out than before. 

 A fortiori when the number of articles is greater than sixteen. 



The general conclusion is that for the purpose in hand it does not make much 

 matter what sort of mean we take ; provided that the weights assigned to the 

 different articles are not very unequal, and provided that there is no reason to 

 think that the ideally best system of weights would be very unequal. The 

 test that factors A, B, &c., are not sensibly unequal is the condition that 

 v/A- f i>- + &c. -=- (A + B + &c.) should be small ; which is true enough 

 within very wide limits (e.r/., in the case of sixteen weights being respectively 

 1, 2, 3, (fee, 16). When there are a few relatively very large interests, such as 

 possibly in England cotton, iron, and ordinary wages, then in constructing our 

 general sliding-scale we should pay special attention to those interests ; though 

 from the considerations mentioned above (p. 273) we are not entitled to assume 

 that the weight to be attached to (the price-variation for) each interest is directly 

 proportioned to the magnitude of the transactions. 



Tt will be observed that this reasoning turns upon the unique interest of 

 particular groups of persons in the prices of particular articles, on the circumstance 

 of division of labour." The conclusion as to the worth of our result is therefore 

 not equally applicable to what may be called the eonsMiiption {A J^G) sls dis- 

 tinguished from the production (A B c) standard. For the rest the latter calculation 

 resembles the former in being amenable to similar secondary modifications (see 

 above, p. 267). For mstance, upon the third of the principles referred to a 

 variation of wages ought to affect the Utiit more than an equal variation of profits 

 as concerning a greater number of persons. 



Section VI. 



Determination of a Standard for Deferred Payments ; hased upon the amount 

 of national capital ; varying with such amount, after the mariner of a 

 sliding scale ; no hypothesis being made as to the causes of the change in 

 prices. (A B c d e.) 



The next category is distiugnislied by the condition that the 

 basis of the required sliding scale is capital rather than income. This 

 Unit might be specially adapted to certain debts ; for instance, in estimat- 

 ing the capital (but not the interest) of sums raised upon mortgage of 

 fixed capital. It is interesting to enquire what sort of weight should be 

 assigned to wages for the purpose here defined. May we measure the 

 importance of wages as a means for paying off capital by the lump sum 

 which the wage-earner is able to raise upon the prospect of his earnings 

 by way of insurance ? 



With reference to this most important application of Professor 

 Nicholson's method, it may be proper here to introduce a remark which 

 is applicable also to other uses of that method. When its originator is 

 met with the difficulty that articles do not increase uniformly, he argues 



' If we suppose the weights 1, 2, ... 16 to constitute the ideally best system, that 

 which affords the maximum sum total of advantage to all. 



- Compare the remarks of Von Jacob cited by Mr. Horton in his admirable 

 chapter on the Standard of Desiderata ; Sih-er and Gold, p. 39. 



