133 



formed the observed scheme, we at once take out the 

 values of z from table 11 (4th col.). Then, having formed 

 the consécutive différences z of thèse z (in the 5th col.) 



tab. 12 furnishes the values of '— that is the ordinales 



z 



of the reaction curve. 



The following examples will serve to illustrate further 

 both the process of computation and the conclusions to 

 which this computation leads. The observed numbers and 

 full numerical treatment will be given in the Appendix; 

 the corresponding figures will be found at the end of the 

 paper. In ail the figures the frequency curve has been 

 represented by a line in short dashes; the z by line in 

 long dashes and the reaction curve by a continuous line. 

 The figure for Example I shows a fourth curve, which 

 is dotted, to represent the scheme. In order to get the 

 figures on a suitable scale I hâve sometimes multiplied 

 the numbers given in the Appendix for the frequency 



and the reaction curve I—, by some factor. For reasons 



that will appear further on such a procédure is not 

 allowable for the z, at least if this curve must serve for 

 the computation of the quartiles (see art. 17). 



In the treatment of the observations I hâve sometimes 

 thoroughly smoothed the frequency curve before using it 

 for further work (see the computation in the Appendix). 

 Of course the computer shall take good care not to smooth 

 any trait out that he thinks really indicated by the obser- 

 vations. It is only the quite accidentai irregularities that 

 ought to be got rid of in this way. Thèse irregularities 

 are simply the conséquence of an insufficiency in the 

 number of observations. Where this number is very con- 

 sidérable ail smoothing is rather to be avoided. The same 

 holds for cases (as in our 3d Example below) where, by 

 some inadequacy in the observed numbers, it is somewhat 



