52 
On the Partial Congelation-Ratio 
So that the mean weight is 56 - 5 (0-205412) = 55-97 lbs., and the moments 
referred to the mean are : 
6-729902, 
Py,= 10-134965, 
p,. = 141-258877, 
giving ,,^1 = -3370, = 3-1189. 
The standard deviation is Oy = 2-594205 in 5 lb. units, or 12-97 lbs. 
With arbitrary origin at 10 years, the raw moments of the ages are: 
z = p\ = - 0-568617, 
= 6-402214, 
= - 9-423124, 
= 80-916710. 
The mean age is therefore 10 — 0-568617 = 9-43 years, and the moments about 
the mean age are : 
j9,:= 6-078889, 
29,.= 1-130401, 
23,4 = 71-591474, 
leading to = -0057, = 1-9374, 
while the standard deviation is a, = 2-47 years. 
3. The mixed moments p^y, Pxy-^, etc., can be found from the correlation tables 
XI-XIII. The values of the raw moments required are as follows : 
p'^y = 4-311017, p\, = 3-949042, 
p'^y^ = - 1-066245, = - 7-108065, 
p'^y^= 74-045335, p'ccz^= 50-313120, 
p\,^ = - 3-712880, p'^., = - 5-488842, 
p'^.y= 35-657353, p'^.,= 24-225619, 
p',y = 5-430241, p'^y, = 47-927956, p'^y, = - 4-341768, p\-2,2 = 37-510631. 
The corresponding moments about the mean are : 
l^xv = P'xy - ^-y = 4-205875, 
Py, = 5-313440, 
p,^ = 3-657989, 
Pxy^ = P'xy^ - ^P'xy " -''P' v'^ + 2^=F = 4-128088, 
Pxy' = p'xV - ^J/P'xy' + ^Yxy- ^^P' y' + ^'^W v"- = 79-144020, 
PxV- = P'x-y' - ^P'x'-y - '^^'P'xy- + V^P' x' + '^'^P' + ^J'ljP' xy - ^^^'f 
= 49-011115, 
Pxvz = P'xyz - - ^'Pyz " VPzx - zPxy = 1-580733. 
Similar formulae give : 
p,,.y = 1-302279, p^., = -219749, 
p^:y = 33-336761, p^., = 19-108627, 
p^,. = -328967, p^^^ = 42-785163. 
