126 



certain quantities x, the frequencies inserted in the second 

 column of table 2. 



Table 2. 



It will be convenient to start, not from the frequency 

 curve, but from the scheme. We therefore formed the 

 scheme in the 3d Col. It has been represented in fig. 8. 



Now the question a comes to this; can we find any 

 quantities z, which are normally distributed and wich at 

 the same time are pure functions of x, that is, are such 

 that to any given value of x we can assign the corres- 

 ponding value of 2? 



The solution of this question is extremely simple. And 

 first: I maintain that the functions z must be such that, 



a. they either continuously mcrease, 



b. or continuously c/ecrease, 

 for increasing x's. 



They cannot, for instance, begin by increasing and then 

 afterwards change their increase for a decrease. For this 

 would involve that, at the turning point, the z would not 

 change at ail for a certain change in x and, as will 

 presently appear, (art. 14, Remark III) this must be con- 

 sidered as being impossible in nature. 



