284 EEPOET— 1887. 



Lastly, the supposed tacit combination which everywhere exists between 

 dealers may prevent prices falling as low as from time to time they otherwise 

 would according to the law of supply and demand. 



There is therefore at any rate no a priori presumption against the proposition 

 that price-returns are apt to group themselves in an unsymmetrical curve of 

 which the range in excess is greater than in defect. In favour of this proposition 

 the following empirical evidence is adduced : — 



In the first table are examined the prices of twelve commodities during the 

 two periods 1782-1820, 1820-1865. The maximum and minimum entry for each 

 series having been noted, it is found that the number of entries above the ' middle 

 point,' half-way between the maximum and minimum, is in every instance less, 

 and in some instances very much less, than half the total number of entries in the 

 series. In the twenty-four trials there is only one exception to the rule, and in 



Fig. 3. 



very few cases even an approach to an exception. "We maj- presume then that the 

 curves are of the lopsided character indicated by the accompanying diagram. For 

 the ' median ' [or point having as many entries above as below it], which upon 

 the supposition of symmetrj' ought to be about coincident with the ' middle 

 point ' as above defined, or at any rate as often above as below it — this median is 

 in every instance but one (fodder, 1798-1820) below the middle point. 



Fig. 3 annexed very well represents the prices of corn during the periods 

 1261-1400, and 1401-1540 given in Professor Rogers' ' History of Agriculture.' 

 The abscissa in the figure represents prices, and the ordinate the number of years 

 in which the corresponding price was enjoyed. It will be found that in both 

 cases the maximum elevation, the greatest ordinate of the cm-ve, occurs between 

 five and six (shillings). Below that maximum-point, in both cases the curve does 

 not sink more than two or three shUliugs (2s. lO'^d. is the lowest entrj'), while 

 above that point one curve stretches out to 14, the other to 16. There can be no 

 doubt about the fulfilment of an unsymmetrical law. Further verification of 

 the law may thus be obtained from the earlier series of statistics. Compare the 

 decennial averages (of corn prices) given by Professor Rogers with the annual re - 

 turns on which they are based. The ' middle point,' half-way between the maxi- 

 mum and minimum of each decade, is in almost every case above the average. 

 There are only three exceptions out of the fourteen decades, viz., 1271-1281, 

 1281-1291, 1371-1381 ; and one of these exceptions is not an instance to the 

 contrary, the middle point exactly coinciding with the average. 



If the prices are similarly examined by decades for linen (vol. i. p. 593), 

 clouts, and other commodities it vrAl be found that the rule holds, with no excep- 

 tions, or trifling ones. Thus for clouts there is not a single exception during 

 twelve decades, 1271-1390. The only exception which Professor Rogers' statistics 

 show is the decade 1391-1400. 



penses with empirical verification. For the same presumption exists not only in the 

 case of many anthi-opometrical and other statistics which prove to be symmetrical, 

 but also in cases where there is an asymmetry in the sense contrary to the theory, 

 an extension of the lon-er limits of the representative curve. Such are the statistics 

 of barometrical height arranged by Dr. Venn in Nature, Sept. 1, 1887; the statistics 

 of eyesight given by Dr. Chas. Roberts in the Medical Times, Feb. 1885 ; the grouping 

 of Italian recruits by Signor Perozzo in Annali di Statistica, 1878. 



