190 . PROFESSOR KARL PE ARSON, MATHEMATICAL 
The first point with regard to these tables is to note how, even with only ten cases, 
the mean errors accord closely with their theoretical values. For example, the mean 
error of k is 2‘31 centims. for male and 2'35 centims. for female when deduced from 
the probable errors in Tables V. and VI.: the observed mean errors in the two cases 
are 2'4 centims. for male and 2'0 centims. for female. The mean of the mean errors 
is for male 2'57 centims., and for females 2'66 centims.; the observed values are 
2*46 centims. and 2'2 centims. for the two sets of ten cases respectively. We con¬ 
clude at once that our formulae, and therefore certainly any other linear formulae, will 
not give results with a probable error of less than 2 centims. for the individual 
stature. In our case the worst error is one of 8 centims. (about 3 inches) in the 
stature of a man of 47 years of age, who must have had a remarkably long trunk in 
proportion to his leg and arm-lengths. It would be impossible to have predicted 
his stature any closer without taking into account the correlation between stature 
and trunk. The preservation of the vertebral column is comparatively rare, and at 
present there are absolutely no statistics on the relationship between the dimensions 
of any part of it and living stature. We must therefore content ourselves with a 
probable error of 2 centims., and expect, but rarely, to make an error of as much as 
8 centims. in the reconstructing of the stature of an individual. 
We have placed in the above tables M. Maxouveier’s results as calculated from 
his ‘ Table-bareme.’ They give somewhat larger mean errors than our formula*, 
which would have been probably reduced somewhat if we had excluded, as he has 
done, the aged. We have seen, however (p. 179), that there seems no reason to 
exclude the aged women, and in the case of the seven men over 60, he actually in 
three cases under-estimates their stature. In other words, while in four cases his 
table might have given better results for adult stature, in three it would havm given 
worse results. If we allow a mean old-age shrinkage of 3 centims."—an amount 
hardly justified by averaging the adult and old-age portions of Rollet’s returns—we 
should find that Manouvriee’s method would have made a total error of 17 centims. 
in estimating the stature of these seven old men in youth, whereas it gives a total 
error of 16 centims. in estimating their old-age stature. Thus there might, perhaps, 
be a small, but it would not be a very sensible, reduction of the mean errors of the 
results given by Manouveier’s ‘ Table-bareme ’ had we excluded the old age cases. 
'What deserves special notice is that our formula [k] gives a better result than the 
mean of all the formulae (o)-(^), and a better result than the mean of the values 
obtained by Manouveiee’s method for the lour long bones. 
(9.) The next stage in our work is to so modify Tables IX. and X. that they will 
serve for the reconstruction of the living stature from bones ont of ivhich all the 
animal matter has disa 2 ipeared, and ivhich are dry and free of all cartilage. This 
* Tins value is that given by M. Maxodvrier himself, ‘ Memoires de la Societe d’Anthropologie de 
Paris,’ vol. 4, p. 366, 1892. 
