134 



uncertain, a priori, how we ought really to draw the 

 frequency curve. 



À moment ago (prec. art. Remark II) we drew atten- 

 tion to the relatively great uncertainties, consequently 

 irregularities, we hâve to expect in the reaction curve, 

 especially towards the hmits of the curve. Thèse irregu- 

 larities would come out smaller if the intervais in the x 

 were taken greater. Such extension of the intervais being 

 generally objectionable on the grounds mentioned above in 

 remark I, the best way to act seems to be to smooth 

 the reaction curve, graphically or otherwise. In the figures 

 accompanying the following examples I hâve drawn such 

 smoothed curves, but hâve left visible the points obtained 

 directly from the computation. In fact, I simply drew a 

 somewhat smooth curve passing as nearly as possible 

 through the whole of thèse points, taking into account of 

 course the very great uncertainty of the extrême points. 



Example L Stature of 8585 men (tab. 4 Fig. 1). 



The fig. shows that the reaction curve is a straight 

 Une parallel to the x-axis. We conclude at once that the 

 distribution is a normal one (for it means that the reac- 

 tion, that is the déviations, are independent of the size jc). 



As must be always the case in the circumstances, the 

 curve of the z is also a straight Une, which however 

 is inclined. 



Example IL Threshold of sensation (tab. 5, fig. 5) 

 taken from Ith paper p. 25. The observations are those 

 of Prof. G. Heymans of the minimum weight which 

 still produces a sensation of pressure. From the figure 

 we see that the reaction curve is an inclined straight line, 

 passing through the origin. The reaction is thus found 

 to be proportional to the dimension x, that is in the 

 présent case: if under the influence of certain causes the 

 threshold is high, a furher cause will hâve a greater 

 eflfect than in the case that the momentary threshold were 



