135 



low, the efFect being proportional to the momentary thres- 

 hold itself. 



We thus are led, by the simple considération of the 

 frcquency curve, to the law of F e c h n e r — W e b e r (see 

 also Ist paper p. 42). 



In ail cases like the présent in which the reaction curve 

 is an inclined straight line, the curve of the z is a loga- 

 rithmic one. Mathematically this is proved with the utmost 

 ease. As we wish to avoid mathematical considérations 

 however, the resuit may be hère taken on trust ^). 



If therefore, we had treated as observed quantities, not 

 the minimum weights which still produce a sensation of 

 pressure, but the logarithms of thèse quantities, we would 

 hâve been led to a normal curve. 



Examplc IIL Valuation of house property in England 

 and Wales, years 1885 — 1886 as given by Pearson. Phil. 

 Trans. Vol. 186 p. 396 (tab. 6, fig. 4). 



This is the curve which in art. 3 was considered as a 

 rough substitute for the wealth-curve. The fig. shows that 

 the reaction curve is again well represented by an ii'clined 

 straight line which passes somewhere near the origin. 

 We conclude that the reaction is approximately propor- 

 tional to the degree of wealth reached, just what, according 

 to art. 1 1 we had to expect. 



The curve of the z must again be a logarithmic one ^). 



This is ail that can be maintained. Whether the reac- 

 tion curve passes absolutely through the origin or not 

 cannot be decided with any certainty. This is not owing 

 to any defect in the method but to a defect in the data. 

 The method tries to solve the problem: Given the observed 

 frequency curve, find the reaction curve. In the présent 



') If the reaction curve passes through the origin the équation of the 

 z curve will be z = log. x; if it cuts the .r axis at x = k, the équation 

 will be z = log. (x — A:). 



