184 
PROFESSOR KARL PEARSOK, MATHEilATICAL 
Thus the regression coefficient is not changed more than ‘55 per cent, for males and 
1'7 per cent, for females, even in this case where the difference between the maximum 
and oblique lengths of the femur has been much insisted upon as very significant 
with regard to stature. Putting in the lengths of the means as found on the corpse, 
we have : 
Male S = 81-147 + 1-894 F'" 
Y .(i.). 
Female S = 7-2-406 + 1-9/ 9 F' 
The corresponding formulm for the stature in terms of the maximum length of 
femur are, as we shall see later : 
Male S = 81-231 + 1-880 F 
Female S = 73-163 + 1-945 F 
The extreme oblique femur lengths are for males 39'6 and 49-8, and for females 37-4 
and 48-0. Let us calculate the stature of these individuals directly from (i.) and 
indirectly from (ii.), by putting F = F' + '32 for males and F' + -33 for females. 
We find 
(t) 
(it) 
IMale min. 
156-15 
156-21 
Female min. 
146-42 
146-53 
Male max. 
175-47 
175-46 
Female max. 
167-40 
167-17 
The differences here in these extreme cases are absolutely unimportant for the 
determination of stature. In other words, the changes in the regression equation are 
insignificant, when we even make such a change as from oblique to maximum femur 
length. Accordingly we have the rule, if the oblique length of femur be given, 
the equations for the maximum length can always be safely used if we add -32 for the 
male and "33 for female to the oblique length in centimetres before using equations of 
type (ii.). 
So farw^e have generalised Tables Y. and YI., having regard to the nature and con¬ 
dition of the organs when measured. AYe see that the regression coefficients will remain 
sensibly constant. Our general considerations on pp. 177 and 178 indicate the limits 
under which these regression coefficients may be considered constant for different local 
races. But the constancy of the regression coefficients is not sufficient to preserve the 
constancy of the linear reconstruction formulas for stature. It would be of no service 
if Ms, Mp, Mh, Mt, Me varied from local race to local race absolutely independently. 
Now if niQ be the mean of a not directly selected organ, and mi, m 2 , m^ . . . the means 
of any other organs, the constant part in a reconstruction formula will wnth the 
notation of p. 172, be : 
b(i'> 
R 
n« 
O-n 
