128 



the schetne be drawn for any normally distributed quan- 

 tifies z. According to what has been said just now, if 

 thèse quantifies z are pure functions of x, those values 

 of z and x must correspond, which hâve equal ordinates. 

 Therefore, if ÀB is a line parallel to the jc-axis, we must 

 take the quantifies 



2 - OK and jc = OH 

 as corresponding quantifies. 



This solves the first post (a) of our problem. For we see 



Ist that the z are normally spread quantifies. In fact 

 we took for them normally distributed quantifies. 



2nd they are pure functions of the x, for to each x 

 we can assign ifs corresponding z. Our présent example 

 has been purposely so chosen that thèse quantifies z are 

 very simply algebraically expressible. If will be found 

 (see lasf col. but one in table 2) that they are in reaUty 

 equal to y'ôJC® — 1.50. In the présent case therefore we 

 are led to the conclusion that thèse quantifies, therefore 

 also the quantifies x^, are normally spread. 



Suppose that the observed quantifies x, (which are not 

 normally spread) represent diameters of certain berries. 

 We would thus be led to the conclusion that had not 

 the diameters been measured, but the weights, we would 

 very probably hâve found at least approximately a normal 

 distribution. . 



') We can now at once see the truth of what was maintained above 

 that: we are exclusively led to functions z increasing continuously far 

 increasing values of x. For as the frequency of any quantity from its 

 lowest value up to any limit is higher, the higher this limit, the ordinates 

 both of the observed and of the normal scheme necessarily increased 

 with the abscissa. Therefore (see fig. 8) if OH that is x, grows, AH 

 and consequently KB grows. But if BK grows z grows. We conclude 

 that the x and the z grow at the same time. For the rest it is évident 

 that if the z are normally spread, the — z (which cfecrease with increasing 

 x) will also be normally spread. 



