26 Mr. Francis Galton on 



the curve in the above figure* is, or at least tends to be, of as 

 definite a character as an ellipse or any other familiar curve ; that 

 it equally admits of mathematical definition, and that it possesses 

 peculiar properties of its own that are of the highest importance 

 to statistical inquirers. Just as an infinite variety of ellipses may 

 be drawn on the axis A B, differing from one another in their 

 extension above and below AB, but otherwise preserving the well- 

 known proportion of an ellipse ; so may an infinite variety of 

 curves of normal variability be drawn on the axis A B, differing 

 from one another only in the amount of their extension above or 

 below it, as measured conveniently by the length of Q. They will 

 all maintain the proportions shown in the table below, which refers 

 to the middle nine-tenths of the curve. The twentieth part at 

 either end is sure to become irregular. O A is supposed in the Table 

 to be divided into 50 parts, the division at counting as 0°, and that 

 at A at 50° ; then, when Q is taken equal to 100 units, the several 

 ordinates drawn from the principal divisions on the axis are of 

 the lengths shown in the table. For any other value of Q all 

 the tabular values must be changed in uniform proportion to the 

 new value of Q. 



As the curve is symmetrical the same measurements apply to 

 either half of it, but in the one half they are made from the axis 

 upwards, in the other half they are made downwards. 



If the curve derived from a series of measurements of any 

 variable characteristic is found on trial to conform fairly well with 

 these proportions, it may be assumed that the characteristics in 

 question vary "normally," that is to say, according to the recog- 

 nised laws of chance, which specify the relative frequency of runs 

 of luck of different lengths. Again, in so far as they vary 

 normally, all the properties of the laws of normal variation may 

 justly be assigned to them. It was by the use of these laws that 

 my deductions were made. 



* The curve actually used by these writers is of another kind and 

 has another signification, but for all that it is the basis of the 

 curve that I employ. 



