48 



Mr. F. Galton. 



[Jan. 21, 



in column B in Table VI. The percentage values of these, taking the 

 total number of observations as 100, are written in column C. A series 

 is there obtained which shows how many per cent, of the statures fall 

 short of the parting value that separates each pair of adjacent grades. 

 Thus if n per cent, of the statures fall within the first r grades, that 

 is to say, are less than the value of the rth parting line, then 100 — n 

 per cent, of them will exceed that value. Consequently, if the observa- 

 tions are read off and recorded to the utmost nicety, r will be the value 

 of the ordinate representing the stature which has to be erected on a 

 base line at n per cent, of its length from one of its ends. In short, 

 a base line of any convenient length has to be divided into 100 parts, 

 and an ordinate of a length proportionate to r erected at the division n. 

 As observations are never read off and recorded with perfect accuracy, 

 a correction has here to be applied according to the circumstances of 

 the particular case, whenever we are drawing a stature -scheme, and 

 not merely an ogive. If the records are kept to the nearest mth 

 part of an inch, the phrase " exceeding r inches " would really mean 

 exceeding r— 1/m inches." This then is the true parting value corre- 

 sponding to the nominal r. In drawing ogives, and not stature- 

 schemes, this correction may of course be disregarded. Having 

 erected ordinates corresponding to each value of r, their tops are 

 connected by straight lines forming a polygonal boundary that 

 approximates to the curvature of an ogive, and would become one if 

 it were corrected with a free hand, or otherwise smoothed. The 

 centre of the ogive lies at the intersection of the curve with the 

 ordinate drawn from the base at the fiftieth division, and the hori- 

 zontal axis of the ogive runs through that point of intersection (see 

 fig. 3). 



A half- ogive, whose ordinates are the mean lengths of the symme- 

 trically disposed ordinates of the complete ogive, is constructed on the 

 same general principles, but more simply, because the base from 

 which it is plotted coincides with the axis of the ogive, and the 

 graduations run alike, viz., from 0° to 50°. 



In Table VII, the entries in the first lines of each of the three 

 groups it contains, are the lengths of the ordinates that have been 

 measured from the bases of ogives constructed from the data in 

 Table VI. The abscissae corresponding to the measured ordinates, 

 are in every case the same fractional lengths of the bases. The 

 entries in the second lines are the differences between these several 

 ordinates and the median ordinate ; they are, therefore, the deviates. 

 The entries in the third lines are the negative deviates written under 

 the corresponding positive ones. The entries in the fourth' lines are 

 the means of the values of the positive and negative deviates, dis- 

 regarding their signs. 



Comparison of Ogives. — The ogive being drawn according to the 



