L. ISSERLIS 
51 
Tables XI, XII, XIII give the distributions of height and weight, height and 
age, and age and weight for the whole of the individuals in the preceding ten tables. 
They are summaries. The direct calculation of one of the three generalized //'s, 
say that of age on height and weight, requires the use of Tables I-X, while the 
various approximations given in the paper cited can be obtained from the 
summaries in Tables XI-XIII. 
I have calculated the correlation ratio of age on height and weight, and that 
of weight on age and height directly, and compared them with the values obtained 
as approximations from the summaries. 
The direct calculation is laborious and the results show that the various 
approximation formulae are in general sufficiently accurate to enable us to dispense 
with this heavy labour. 
Throughout the present paper, I denote the age by 'z' with an arbitrary origin 
at 10 years, the height by 'a-' with the origin at 49 inches and the weight by 'y' 
with origin at 56 lbs. 
2. With the arbitrary origin at 49 inches, the raw moments for the height 
frequencies are : 
X = = _ 0-511861*, 
p\,= 3-453699, 
/^.= - 4-938324, 
/^.= 30-678791. 
Thus the mean height is 49 - 3 (0-511861) = 47-46 inches. 
The moments referred to mean are given by the formulae : 
^9,. = /,.- (p'J^ = 3-191697, 
f^. = - 37>',./, + 2/,3 = 0-096908, 
p,, = p',,, - ip',.p', + 6p',.p'/ - 3p'./ = 25-7912. 
From these = = -0003, 
^ fx? 
= = 2-5318. 
Px- 
The standard deviation is ct^, = 1-78653 in 3 inch units, or 5-36 inches. 
For weights the arbitrary origin is at 56 lbs., and the raw moments are: 
y = p\ = - 0-205412, 
p'y. = 6-772096, 
p'y.= 5-979090, 
p'y>= 134-637146. 
* For the sake of uniformity the constants in all intermediate results are given to six places of decimals. 
4—2 
