ADDITIONAL TABLES AND DIAGEAM FOR THE DETER- 
MINATION OF THE ERRORS OF TYPE OF FREQUENCY 
DISTRIBUTIONS. 
SECOND PAPER. 
By a. RHIND, B.Sc. 
In Bioynetrika, Vol. vil. page 131, a diagram was given to determine the type 
to which an observed frequency distribution belongs for given values of /Sj and /Sa- 
The probable errors of /3i and /Sg define a region within which the most 
probable values lie. 
Since, however, ySj and are highly correlated this area is not a rectangle but 
an ellipse ; a contour of the surface 
2 1 - iJ2 
'P, "P2 " ft) 
1 1X2 
2 |Si2 + S?l (A). 
or, referred to principal axes, 
= -^-^ 
The semi-axes of an elliptic cylinder, with section similar to a contour of (A), 
and containing half the frequency, are I'lTTSj and l*177So. 
These are inclined to the axis of ^2 at angles $ given by 
tan 26 = ^^^^^■•l'^^^^^-^ = R^^^^ tan 2(^, where tan 0 = (r^Ja^,^. 
The directions were calculated from this formula and Diagram C (p. 389), 
constructed in such manner that the tangent and normal to one of the broken- 
line curves at any point are the major and minor axes respectively. The major 
axis is inclined to the axis of /9o at angles given by Table IX. 
