v.] NORMAL VARIABILITY. 53 



selected Grades will be always those of 25 and 75. 

 They stand at the first and third quarterly divisions of 

 the base, and are therefore easily found by a pair of 

 compasses. They are also well placed to afford a fair 

 criterion of the general slope of the Curve. If we call 

 the perpendicular at 25, Q.! ; and that at 75, Q. 2 , 

 then the unit by which every Scheme will be defined 

 is its value of i(Q. 2 -Q.i), and will be called its 

 Q. As the M measures the Average Height of the 

 curved boundary of a Scheme, so the Q measures its 

 general slope. When we wish to transform many differ- 

 ent Schemes, numbered I., II., III., &c., whose respective 

 values of Q are q l} q 2 , q 3 , &c., to others whose values of Q 

 are in each case equal to q , then all the data from which 



Scheme I. was drawn, must be multiplied by 9.2 ; those 



<?i 



from which Scheme II. was drawn, by ^, and so on, and 



92 



new Schemes have to be constructed from these trans- 

 muted values. 



Our Q has the further merit of being practically the 

 same as the value which mathematicians call the 

 " Probable Error," of which we shall speak further on. 



Want of space in Table 2 prevented the insertion of 

 the measures at the Grades 25 and 75, but those at 

 20 and 30 are given on the one hand, and those at 70 

 and 80 on the other, whose respective averages differ 

 but little from the values at 25 and 75. I therefore 

 will use those four measures to obtain a value. for our 

 unit, which we will call Q', to distinguish it from Q. 



