L. ISSBRLIS 57 
With the above values of xv^'^z ^i^d xijR^z> the right-hand side of Blakeman's 
formula reduces to 13-47, so that on this assumption ^.yH'^^ — xyR^z is 13 or 
14 times greater than its probable error. 
If we examine the regression of weight on height and age, we find in the same 
way that: 
,xH% = -8634, ,xHy = -9292, 
= .8427, ,xRy = -9180, 
,,^r2^-,,/^^, = •0207. 
In this case too the regression is significantly non-planar, Blakeman's formula 
reducing to 11-43 so that ^^.//"y — zxR'^u is more than 11 times greater than its 
probable error. 
Physically ^^Hy is more interesting than ^u^z- ^ knowledge of the former 
enables us to construct by means of equation (53) of my Part I, a formula 
predicting the mean weight of a group of boys of given age and height. Such 
a formula would be an alternative solution to the one given by Table a on 
p. 300 of the paper by Miss Elderton referred to above. 
6. We may consider now equation (70) of Part I which gives the approximate 
age of xvH% — xyR^z ill terms of constants all derivable from Tables XI, XII, XIII, 
i.e. constants whose determination does not require a detailed knowledge of the 
distribution. The equation is : 
Xxv'"'- s xy-^'' zl „ „2 
'^xy^x-y ^xy- '^yz '^xz^xy 
1 - r2 
I '^xy^xy''- 1x-y xz yz ^ xy 
ixy^'^yz ^x^y'^xz ^ xy 
I ^2 _ ,.2 \ _ ( 2 „ ..2 \ 
\y'l z ' zyl I -I 2 / V?/'/ x ' xy) 
\ 1 ' xy ^ 
2 1.2 \ l^yz ^xz^xy\ / 2 „.2 \ 
xTz - > zx) - —ri.v2 — ) (^"^ " ~ 
^ ' xy ^ 
.(70). 
When x^i, A* are very small and y-rjx, xVy ^'^^ '*'xy are nearly equal, we use 
instead of (70) the following equations : 
U2 _ P2 ^ <hV^Zj^xy / 2 _ ,,.2 \ /yi \ 
xy^-"- z xy*-^ z „ i \y'i z ' zu) V'^/? 
IxV — 1 
xy'-'- z xy'-*' z 
or approximately 
ZJ2 _ m = '1^" ( yfi _ \ in-2\ 
xy"- z xy'-'' z „ -i \x'i z ' zxl \'^h 
Qx-y^ — J- 
1 + f2 
-'I xy 
xyH^z xy-R^z ~ l^yZ^ ixV^z * zx) C^^) - 
xy 
J./?! is used to denote the of the frequencies of the x character. 
