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. x ; and that at 75°, Q. 2 , 

 then the unit by which every Scheme will be defined 

 is its value of g(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 1} 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 ^ ; those 

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



q% 



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. 



