232 
PROFESSOR KARL PEARSOJST, MATHEMATICAL 
for races of more than 155 centims. stature. The position and character of the 
instability is undefined and appears to be quite arbitrary. At the same time, I give 
the stature of the dwarf races with which I have dealt below on this hypothesis. In 
order to apply it, I add the additional data for the female stature and long bone ratios 
recjuired for this and Manouvrier’s method, putting in the Aino for comparison : — 
Data—Female. 
S/F. 
S/T. 
S/H. 
S/R. 
•50 normal French. 
3-73 
4-62 
5T9 
7T6 
Manouvrier ( “ Coefficients moyens ultimes,” 1 
[ stature <.140 . . . . J 
3-87 
4-85 
5-41 
7-44 
Aino,* stature = 147T. 
3-85 
4-75 
5-31 
6-98 
The reader must remember that Maxouvrier’s coefficients are for corpse stature 
and length of bones when the latter contain animal matter. Hence he first adds 
2 millims. to the length of the dead bone to get the bone with animal matter, and 
then 2 centims. are subtracted by him from the corpse length to get the living 
stature. In the case of the femur, however, he works with the bone in oblique 
position, or with a length about 3’2 millims. less in the normal individual than the 
maximum length. This probably does not amount to more than 2 millims. in the 
case of dwarf races. Hence, when the femur of the dwarf is given by its maximum 
length, we need not add or subtract anything before multiplying by the stature- 
femur coefficient. We have accordingly the following methods of estimating the 
stature of dwarf races from their long bones .— 
(i.) The lines of regression for a normal population, i.e., the formulae of p. 196 of this 
paper, or the heavy straight lines of our charts. As we have already seen, this over¬ 
estimates the stature of dwarfs as it underestimates that of giants. 
(ii.) The curves of regression given by the empirical formulae of p. 224, or by the 
heavy curves of our charts. In the case of female dwarfs the lengths of their long 
bones must first be reduced to male equivalents by the rule on p. 230, and the 
statures found again reconverted to their female equivalents. 
(iii.) The “Coefficients moyens ultimes ” of Makouvrter may be used. These 
arc given on pp. 231 and 232. Special attention must be paid to the reductions 
(discussed above) of bones and corpse length. 
(iv.) The stature and long bone ratios for the normal population may be used. 
The values of these ratios are given on pp. 231 and 232, but for most practical purposes 
it suffices to use the dotted lines of the chart. 
I shall refer to these methods as Pi_ Ihr, M, and Fh In the latter case, not 
* It will be noticed bow close these are to the male coefficients on p. 231, except in the case of the 
radins, a bone very irregular in pilmitive and dwaif races. 
