is 



c. V. L. Chavlier. 



The agreement is as perfect as can be wished. Tlie diiïerence for n = 0 

 and n = \ will diminnish, if a curve of type B be used. I have not considered this 

 necessary in this case, as the curve of type A also gives a very good agreement. 

 In example 8 I have in addition given a comparison of the same material with a 

 curve of type B. 



In constructing the curve of frequency I have not directly used the above 

 values of the frequency. It is namely useful and instructive to reproduce the dif- 

 ferent frequency curves all in the same scale. For this purpose the standard devia- 

 tion a is taken as unit for the abscisste and the numbers expressing the frequency 

 are all multiplied by a : [j.^. As we have 



-^nr) = 'f„(,0 + ß3'f3 + ß.^, + ••• 

 ro 



we thus obtain for all frequency curves with the same values of ßj and iden- 

 tically the same form. The construction of the curves of frequency is very simple, 

 if the table I is used. The abscissœ of the observed values are obtained by means 

 of the expression 



X — h 



where ./■ denotes the value of the character in question referred to the provisional 

 origin. The comparison between theory and observation may conveniently be made 

 with the help of the curve. 



For the position of the mean, mode and median we obtain the values: 



Mode: a:' = 3.07.^, 

 Median : = 3.359, 

 Mean: re = 3.501. 



Second Example. Distribution oj frequeney of stigmatic bands of 1001 samples 

 of Papaver. 



All the flowers were gathered in the same garden in Arild (Skåne) and counted 

 by me the 27 July 1905. 



Number of bands 4 5 (3 7 8 9 10 11 12 



Frequency 3 8 68 257 344 236 70 14 1 



An easy calculation gives us, taking the provisional origin at 8, 



H-o = 1Ö01, 

 ^ = — 0.007, 

 a = -f 1.142, 



ßg = — 0.0006, 



ß^ = + 0.0093. 



The curve is nearly normal, with the mode, mean and median at 8, a standard 

 deviation equal to 1.142 and a small positive excess. In fig. 7 the observed fre- 

 quencies are compared with a normal-curve (without excess). 



