222 
PROFESSOR KARL PEARSON, MATHEMATICAL 
often be repeated that the idea that there is in any sense a constant proportion 
between stature and any long bone is misleading. Manouvrier makes this ratio 
decrease from dwarf to giant, and this is correct so long as we suppose the regression 
formula linear, for example, S/F = a -\- hjY. But this ratio really begins to decrease 
again as we go from short people to actual dwarfs, and to increase again as we 
go from tall people to actual giants. 
For example, we have the following results for the ratios of long bones and 
stature :— 
Data. 
S/F. 
S/T. 
S/H. 
SR. 
•50 normal Erenchnien . 
3-71 
4-54 
5-06 
6-S3 
-^r f “ Coefficients moyens nltimes,” 1 
JliKOUTHIKK, 1 ^ ^ ; 1 
3-53 
4-32 
4-93 
6-70 
Topinaed, 22 case.s, stature 7> 175. 
3-61 
4-46 
5'05 
6-94 
Pearson, 12 cases, stature > 200 . 
3-73 
4-41 
o'Ol 
7-07 
It will be at once obvious that Manouvrier’s “ Coefficients moyens ultimes” are 
by no means ultimate, but that in the case of giants the coefficients actually tend to 
return to their values for the mean population. This will be sufficient to show that 
it is quite impossible to consider any method of determining stature from a presumed 
constant ratio to femur as satisfactory. 
But this table shows an important principle, namely, that as the ratio of stature 
to long bone first decreases as the bone increases and then begins to increase, it is 
impossible to consider the regression curve as a straight line when we extend it so 
far as the region of dwarfs and giants. 
Now this is, a priori, what might have been expected, for all distributions of 
zoometric frequency that I have come across seem to possess sensible skewness, and 
in skew correlation the regression curve is not a straight line. Its actual form is of 
a somewhat complicated nature,* -and it would be purely idle to attempt to deter¬ 
mine the constants of it from the data for dwmrfs and giants which are at present 
available. Accordingly it seemed to me desirable to select some empirical curve 
which would, so far as possible, represent the available material and give results in 
harmony with certain general principles. The considerations Avhich led me to the 
choice of this curve were of the followdng character ;— 
(rt.) It must sensibly coincide with the line of regression already found between 
statures of 155 centims. to 175 centims. It must accordingly have a point of inflexion 
at the mean stature, at wdiich the tangent should be the already determined line of 
regression. Beferred to this tangent and its perpendicular, the form of the curve in 
the neighbourhood of the origin must be y = r.rt Away from the origin, c may 
become a sensible function of x and y, one or both. 
* 1 hope to ret □.I’ll to this point in a paper on skew correlation. 
