109 



curves, by lines in the scheme. This is what gives the 

 scheme a great advantage in many cases. 



The same regularity which we hère fînd in the distribution 

 of the frequencies of the différent heights of men, we find 

 back in numberless cases presented by nature. In order 

 to see this regularity in its true Hght it is important to 

 express the sizes of the measured property in fractions of 

 the average amount, as was done in the second part of 

 the preceding table. 



Fig. 2 represents threc of such cases ail expressed in 

 this way: 



I. (Highest curve). Represents the same case as that 

 of fig. 1 (stature of men). 



II. Length of the lowest fruit on the main stem of 

 568 spécimens of Oenothera Lamarckiana (H. de Vries, 

 Ber. der Deutsch-Bot. Gesellsch., 1 894. Bd. 1 2, Heft 7, p. 200). 



III. (Lowest curve). Strength of pull of 519 maies 

 aged 23—26. (Gai ton, Natural Inheritance p. 199.) 



The figure shows that in ail thèse cases we get curves 

 having the same characteristics. 



a. They reach their maximum for the average value of .r ; 



b. they are symmetrical with regard to this maximum; 



c. from the maximum the curves very gradually and 

 without intermission slope down to zéro; 



d. they meet the x axis tangentially. 



In the meanwhile the several curves are still very 

 distinct especially in the fact that the whole range of the 

 déviations from the average value is very différent. 



Ail thèse characteristics remind us very strongly of the 

 frequency curves of accidentai observation errors. Gauss 

 and others hâve derived the mathematical form of thèse 

 "error curves". They show ail the characteristics a, b, c, 

 d, and, like our curves, are only différent in range, the 

 range of the errors being of course smallest in the case 

 of the best observations. 



