34 Arrangement and Formation of the Series. [CHAP. II. 



&amp;lt; Frequency of Error ... is incorrect in many groups of vital 

 and social phenomena.... For example, suppose we endeavour 

 to match a tint ; Fechner s law, in its approximative and 

 simplest form of sensation = log. stimulus, tells us that a 

 series of tints, in which the quantities of white scattered on a 

 black ground are as 1, 2, 4, 8, 16, 32, &c., will appear to the 

 eye to be separated by equal intervals of tint. Therefore, in 

 matching a grey that contains 8 portions of white, we are 

 just as likely to err by selecting one that has 16 portions as 

 one that has 4 portions. In the first case there would be an 

 error in excess, of 8 ; in the second there would be an error, 

 in deficiency, of 4. Therefore, an error of the same magnitude 

 in excess or in deficiency is not equally probable.&quot; The con 

 sequences of this assumption are worked out in a remarkable 

 paper by Dr D. McAlister, to which allusion will have to be 

 made again hereafter. All that concerns us here to point out 

 is that when the results of statistics of this character are 

 arranged graphically we do not get a curve which is sym 

 metrical on both sides of a central axis. 



8. More recently, Mr F. Y. Edge worth (in a report of 

 a Committee of the British Association appointed to enquire 

 into the variation of the monetary standard) has urged the 

 same considerations in respect of prices of commodities. He 

 gives a number of statistics &quot; drawn from the prices of twelve 

 commodities during the two periods 17821820, 18201865. 

 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 1 , 

 is in every instance less than half the total number of entries 

 in the series. In the twenty-four trials there is not a single 

 exception to the rule, and in very few cases even an approach 



1 We are here considering, re- of statistics; so that there are actual 

 member, the case of a finite amount limits at each end. 



