A. 0. POWYS 
49 
For men : 
y = 66'98419 - •056,559* - •001,458a;2 + •000,0608a;^ 
the origin being at 50 years of age, the unit of « a year and y being inches of 
stature. 
For women : 
y = 62-17403 - -046,309a; - -000,095a,'' + -000,003a^ 
the origin being also at 50 years of age, the unit of a; a year and y in inches of 
stature. 
But these will be found to give rather poor fits. To see if anything better 
could be done by taking a higher parabola one of the fourth order was fitted to 
the male statistics*. Its equation is 
y = 66-521,011 - 1-979,575 (j-^j + 2-814,332 (^^^ 
X 
+ 2-608,370 (^^j - 5-352,748 
with origin at 50 years, the unit of a; a year and y in inches of stature. 
This gave a fairly good fit from 27 to 85 yeai's, because the curve has both 
points of inflexion in this part, but again fitted badly from 15 to 27 years. In 
fact from the period of maximum fertility in either sex to the end of life a straight 
line gives quite as good a fit as it is possible to find. Either the curves selected 
must therefore be such that they have an asymptote parallel to this line, or we 
must express by different algebraic expressions the periods of growth and of deca- 
dence. In neither case is a parabola of any order whatever a suitable analytical 
expression. Mr Powys' data being for criminals do not go back sufficiently into 
childhood to enable us to get a suitable curve for the growth period f. 
Starting from the 25 — 30 group for both sexes we get the following best fitting 
straight lines for the period of decadence : 
For males : y = 68-33938 - -033,6664 X, 
for females: y = 63-61104 - -036,1345 Z, 
where y is the number of inches of stature at X years of age. 
It will be found that these lines give excellent results for all ages from 27 to 
85. We accordingly conclude that a man loses on the average -34" of stature and 
a woman -36" per ten years after 27 and 25 years of age respectively. Approxi- 
mately we may take this ^" per ten years. Hence if the stature of a man or 
woman be measured in adult life we can ascertain by a simple calculation their 
probable stature in their prime. It is to this stature that we really ought to refer 
our measurements as a standard : for example, in comparing the stature of parents 
and children for the purpose of measuring the intensity of inheritance. 
* I am responsible for the calculation of the constants of this curve and for those of the 
straight lines below. K. P. 
t I have found fairly good results for the curve of growth of the average child from a logarithmic 
curve, but my data are at present not sufficient for a good determination. K. P. 
Biometrika i 4 
