CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
171 
organs. Let be the mean sizes of A and B, or,„ o-^ their standard deviations, 
r „4 tlieir coefficient of correlation, then the most [probable value of B for a given value 
of A is, 
B — (A — ma) 
or 
= C] + CoA...(i.) 
where Cj and c., are constants for the pair of organs under consideration. The 
probable error of such a determination is '67449 cr^ X \/il — 
Now there are several points to be noticed here. 
(i.) If be small, the probable error of reconstruction will be large, if the organ 
B is to be reconstructed for a single individual. No ingenuity in constructing other 
formulae can in the least get over this difficulty ; it is simply an exju'ession of the 
fact that races are variable. Any formula which professes to reconstruct individuals 
with extreme accuracy may at once be put aside as unscientific. On the other hand, 
if A be known for p individuals, the corresponding mean value of the unknown organ 
B may be found with a probable error of '67449 o-^ X \/{l — 't'lb)l\/p^ thus with 
increasing accuracy as p increases. 
(ii.) Anthropologists and anatomists have frequently assumed that the ratio of two 
organs, B/A, is the measure to be ascertained in a reconstruction problem. They 
were soon compelled to admit, however, that this varies wiidi A, and accordingly have 
tabulated the ratio B/A for three or four ranges of the organ A. Such a table, 
for example is given by M. ManouveiepA for the ratio of stature to the length of 
the six long bones. He gives the ratio for three values of each long bone. He also 
in a second table gives values of the ratios which are to be taken when the long 
bones exceed or fall short of certain values, i.e., in cases of what he terms macroskely 
and microskely. The regression formula shows us that ; 
B/A = Co + c,/A, 
and since Cj is never small as compared with A, this ratio can never be treated as 
constant. Accordingly, while a table can be constructed which will give quite good 
reconstruction values, by determining the mean value of B/A for each value of A, we 
see that it is theoretically an erroneous principle to start from ; no constancy of tlie 
ratio B/A ought to be expected. The theory of regression shows us that the most 
probable value of B is expressible, so long as the correlation is normal (or at least 
“linear ”), as a linear function of A.t 
* ‘ Memoires cle la Societe cTAntliropologie cle Paris,’ vol. 4, pp. 347-402. 
t Sir George Humphry gives a table of the ratio B/A for stature in his “ Treatise on the Human 
z 2 
