CONTEIBUTIONS TO THE THEORY OF EVOLETIOH. 
185 
It is shown in the memoir on selection to which I have previously referred, that 
this expression remains the same for all local races, and equal to its value in 
the original stock under precisely the same conditions (stated on p. 177) as the 
regression coefficients themselves remain constant. Hence we have the same degree 
of justification in applying our whole stature reconstruction formula from one race to 
a second, as in applying the regression coefficients. 
(7.) Re-examining Tables Y. and VI. with a view to drawing one or two general 
conclusions before we proceed further, we notice ; 
(i.) The probable error of the reconstruction of the stature of a single individual is 
never sensibly less than two centimetres, and if we have only the radius to predict 
from may amount to 2f centims. 
Hence no attempt to reconstruct the stature of an individual from the four chief 
long bones can possibly exceed this degree of accuracy on the average, at any rate no 
linear formula.^ No other linear formulse will give a better, or indeed as good a 
result as the above. 
The reconstruction of racial stature is naturally more accurate, since if we recon¬ 
struct the mean from p bones of one type, the probable error is reduced by the 
multiplier ijs/p. At the same time we must bear in mind that possibly a definite, 
if small amount of direct, selection by stature has actually taken place in the differen¬ 
tiation of human races, and accordingly the values of e given in Tables Y. and YI. 
are not absolutely true measures of the probable error of racial reconstruction, even 
when one or more of the long bones have not been directly selected. A direct selection 
of the long bones is usually evidenced by one or more of the formulfe giving discordant 
results. When, as will be seen later to be usually the case, several of the formulm give 
results well in accordance with each other, then we may assume that 2/\/y) centims. 
is an approxlmatet measure of the probable error of the reconstructed stature. 
(ii.) The four long bones give for males the least probable error, but with sensibly 
equal accuracy and less arithmetic we may use F & H, F -f- T or F & T ; then follow 
fairly close together H & R, F or H alone ; T alone is sensibly worse, and R is worst 
ot‘ all. It is noteworthy that H is better than T, and the H & R is sensibly as 
good as F alone. 
Turning to female stature reconstruction, we notice that the order of probable 
errors is considerably altered. Tibia and radius now play a more inqDortant part in 
the determination of stature. The four long bones still give the best result; F & T, 
and F -{- T follow closely ; then come F & H, and F alone ; followed at some 
distance by H & R, and H alone, but both these are now worse than T alone; last of 
* I stall return to the question of tlie lineai'ity of the formula, when dealing later with the stature of 
giants and dwarfs, see p. 222. 
t It must be remembered that we have, as a rule, a number of long bones which in part do not even 
belong to the same skeletons. This result accordingly is the probable error of a group to whom one 
kind of long bones belonged, rather than the probable error of the racial stature as reconstructed. 
VOL. CXCII.—A. 2 B 
