110 



A comparison of fig. 3 with fig. 2 well illustrâtes the 

 anology of the two sorts of curves. Fig. 3 shows three 

 "error curves" for observations of unequal précision ^). It 

 will be acknowledged that the similarity is very striking. 



Indeed in a great many cases the différences of the 

 frequency curves of nature with error curves are not greater 

 than can be readily explained by the remaining uncertainties 

 of the observations. Where, as in the case of our curve I, 

 the number of measures is very considérable, a drawing 

 on the scale of that of our figures almost fails to show 

 any différence at ail. 



It is for this reason that the Gaussian error curve has 

 come to the called the normal frequency curve. 



3» Ske"w curves. In the meanwhile it is certain that 

 we find in nature curves which diverge markedly from 

 this normal form. As a striking instance may be considered 

 the wealth-curve, that is the curve giving the frequency 

 of the différent amounts of property. I am not in the 

 possession of the direct data for such a curve, but every- 

 body realises that the most fréquent amount of property 

 is not very high. Let A be this most fréquent amount. 

 As the smallest amount is zéro, the greatest déviation from 

 the amount A on the one side is — A. On the other 

 side it is of course immensily higher. The frequency 

 curve therefore is small in extent on the lower side of 

 the maximum, very extensive on the other. It thus must 

 be a highly dissymmetrical curve. 



As a rough substitute for the wealth curve we may 

 perhaps use the frequency curve offered by the valuation 

 of house property (x) in England and Wales for the 

 years 1885 and 1886, as given by Pearson. Phil. Trans. 

 Vol. 186, p. 396. Owing to want of détail in the data. 



') In order to insure the greatest similarity with fig. 2, the modules 

 of précision were taken resp. 18.9; 5.96; 4.38. 



