736 Fluctuations 



for this purpose a point is chosen which lies 

 exactly half way between the average and the 

 extreme. Not however half way with respect to 

 the amplitude of the extreme deviation, for on 

 this ground it would partake of tlie uncertainty 

 of the extreme itself. It is the point on the 

 curve which is surpassed by half the number, 

 and not reached by the other half of the num- 

 ber of the observations included in the half of 

 the curve. This point corresponds to the im- 

 portant value called the probable error, and 

 was designated by Galton as the quartile. For 

 it is evident that the average and the two quar- 

 tiles divide the whole of the observations into 

 four equal parts. 



Choosing the quartiles as the basis for cal- 

 culations we are independent of all the second- 

 ary causes of error, which necessarily are in- 

 herent in the extremes. At a casual examina- 

 tion, or for demonstrative purposes, the ex- 

 tremes may be prominent, but for all further 

 considerations the quartiles are the real values 

 upon which to rest calculations. 



Moreover if the agreement with the law of 

 probability is once conceded, the whole curve is 

 defined by the average and the quartiles, and 

 the result of hundreds of measurements or 

 countings may be summed up in three, or, in 



