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°