Mr Galton, for instance,--to whom every branch of the theory of statistics owes so much,--has insisted[7] that the "assumption which lies at the basis of the well-known law of '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." The consequences 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 symmetrical on both sides of a central axis. 8. More recently, Mr F. Y. Edgeworth (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 "drawn from 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,[8] 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 to an exception. We may presume then that the curves are of the lop-sided character indicated by the accompanying diagram." The same facts are also ascertained in respect to _place_ variations as distinguished from time variations. To these may be added some statistics of my own, referring to the heights of the barometer taken at the same hour on more than 4000 successive days (v. _Nature_, Sept. 2, 1887). So far as these go they show a marked asymmetry of arrangement.