111 



there is a slight difïiculty in drawing the curve quite 

 empirically very near the value zéro. For this neighbourhood 

 I hâve taken the représentation resulting from the discussion 

 of this case in Example 3 i^see farther on, art. 15). Fig. 



4, dotted Une, shows this curve. 



Another good example is ofFered by Heymans' obser- 

 vations of the threshold of sensation. It is shown in fîg. 



5. 120 déterminations were made of the minimum weight 

 which still produces a sensation of pressure. The various 

 déterminations fall in the curve represented by the figure. 



Hère too it is évident à priori, that if p is the real 

 value of the threshold, déviations on the négative side 

 cannot exceed p, whereas on the other side there is no 

 such limitation. Dissymmety of the curve seems therefore 

 a priori probable. 



4. Origin of normal curves, Coming back to the 

 normal curves which, not-withstanding such cases as those 

 just now considered, seem to dominate in nature, we are 

 naturally led to the question; what is the reason of the 

 widespread occurrence of just this curve? 



In elucidation of this question I will quote in fuU the 

 reasoning of the V^ paper ^). 



Take the foUowing example: 



Suppose we hâve measured the diameters of a great 

 number of ripe berries; that we hâve determined the 

 frequency of diameters between 2.0 and 2.1; between 2.1 

 and 2.2 millimètres, and so on from the smallest of ail the 

 diameters to the largest one. 



Suppose further that thèse frequencies arrange them- 

 selves practically in a normal curve. 



1) The t'ollowing pages (down to the end of art. 12) are practically 

 litterally quoted from the l^t paper. My purpose in inserting so unusually 

 long a quotation has been to make the présent popular exposition 

 complète in itself, so that the reader who wishes to acquaint himself 

 with the method may find ail he wants together. 



Recueil des trav. bot. Néerl. Vol. XIII. 1916. 8 



