XVL—NORMAL CORRELATION. 7 
the major and minor axes being 3:36 x ¢ and 1-91 x ¢ respectively. 
To find ¢ for any assigned value of the frequency y we have 
’ A 
Yig=1Y 1o¢ 
t= 2(log ¥'15 — log 715) 
log e : 
Supposing that we desire to draw the three contour-ellipses for 
y=95, 10 and 20, we find ¢=183, 1-40 and 0°76, or the following 
67 
to 
rj 
65 
66 
} 
Sf 67 
= 68 
= 69 
» ee... 
FP, 62 63 "oz NN WOU 6 63 69 70 TI 72 4% 7 
Stature of Father : inches 
Fic. 52.— Contour Lines for the Frequencies 5, 10 and 20 of the distribution 
of Table I11., Chap. IX., and corresponding Contour Ellipses of the fitted 
Normal Surface. P, P,, P, P,, principal axes: J, mean. 
values for the major and minor axes of the ellipses :—semi-major 
axes, 6°15, 4°70, 2°55: semi-minor axes, 3-50, 2:67, 1:45. The 
ellipses drawn with these axes are shown in fig. 52, very much 
392°