170 
PROFESSOR KARL PEARSOK, MATHEMATICAL 
PAGE 
(20) Probable statiu'e of the Erencb of the Middle Ages.219 
(21) On the stature of giants and dwarfs. General considei’ations and regression curves . 220 
(22) Data for giant and dwarf statures.225 
(23) Dwarf races.228 
(24) Probable stature of Bushmen.233 
(25) Probable stature of Akkas.235 
■ (26) Probable stature of Andamanese.236 
(27) Probable stature of European Keolithic dwarfs ..238 
(28) Conclusion.240 
(29) Ta,ble of statures and sexual ratios for divers races.242 
(l.) The object of this paper is to show, by the use of a special case as illustration, 
the true limits within which it is possible to reconstruct the parts of an extinct race 
from a knowledge of the size of a few organs or bones, when complete measurements 
have been or can be made for an allied and still extant race. The illustration I 
have taken is one of considerable interest in itself, and has been considered from a 
variety of standpoints by a long series of investigators. But I wish it to be 
considered purely as an illustration of a general method. What is here done for 
stature from long bones is equally applicable to other organs in Man. We might 
reconstruct in the same manner the dimensions of the hand from a knowledge of any 
of the finger bones, or the bones of the upper limbs from a knowledge of the bones of 
the lower limbs. Further, we need not confine our attention to Man, but can 
predict, with what often amounts to a remarkable degree of accuracy, the dimensions 
of the organs of one local race of any species from a knowledge of a considerable number 
of organs in a second local race, and of only one or two organs of the first. The import¬ 
ance of this result for the reconstruction of fossil or prehistoric races will be obvious. 
What we need for any such reconstruction are the following data :— 
(a.) The mean sizes, the variabilities (standard-deviations), and the correlations of 
as many organs iq an extant allied race as it is possible conveniently to measure. 
When the correlations of the organs under consideration are high {e.g., the long- 
bones in Man), fifty to a hundred individuals may be sufficient; in other cases it is 
desirable that several hundred at least should be measured. 
(6.) The like sizes or characters for as many individual organs or bones of the 
extinct race should then be measured as it is possible to collect. It will be found 
always possible to reconstruct the mean racial tyj^e with greater accurac}' than to 
reconstruct a single individual. 
(c.) An appreciation must be made of the effect of time and climate in producing 
changes in the dimensions of the organs which have survived from the extinct race. 
(2.) Supposing the above data to exist in any particular instance, we have next to 
ask what is tlieoretically the best method of dealing with them. There cannot be a 
doubt about the answer to be given. If we know an organ A, then the most 
probable value of an organ B is that given by the regression formula for the two 
