280 PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
Modern German (Bavarian Peasants*). 
Length of skull . 
, m 1 = 180*58, 
oq = 5*8441, 
v ] = 3*2363 
Breadth of skull . 
. m % = 1 50*47, 
(To = 5*8488, 
v 2 = 3*8871 
Cephalic index, B/L 
. M = 83*41, 
$ = 3*5794, 
V = 4*2913 
r = *2849. 
Modern French (Parisianst). 
Length of skull . 
nij = 181*85, 
cr 1 = 5*9420, 
v x = 3*2675 
Breadth of skull . 
ni 9 = 141*93, 
cTo = 5*2139, 
v. 2 = 3*5975 
Cephalic index, B/L 
. M = 79*82, 
t = 3*7865, 
Y = 4*7438 
r = *0474. 
The probable error of r in all three cases lies between *06 and *07. Now it is clear 
that had we only dealt with the race from Egypt and the Bavarians, we might easily 
have concluded that the coefficient of correlation was constant for local races of man, 
and had remained so for nearly 5,000 years. The French numbers completely upset 
this view". In order to test my French results I give another series from the 
Anthropological Collection at Munich ; the skulls are those of French soldiers who 
died at Munich during the Franco-German war. 
Modern French (Peasants). 
Length of skull . . . m 1 = 179'93, oy = 6*2987, v x = 3'5006 
Breadth of skull . . . m. 2 = 143*51, cr. : = 5*4208, v. 2 = 3*7772 
Cephalic index, B/L . M = 79*7857, t =3*8410, V = 4*8141 
r = *1265. 
This collection numbers only 57 crania, and the probable error of r is about *09, 
but clearly we have the same general features as in the previous French series. In 
particular the closeness in the line for the cephalic index constants is remarkable. 
The value of r might possibly be the same as for the Parisians; it is highly improb¬ 
able that it should agree with the value of r for the Germans or the race from 
Egypt. We are compelled to conclude, therefore, that it is very unlikely that 
“ Galton’s function ” is constant for all local races of man. 
* Calculated from measurements given by Professor J. Ranke : ‘ Beitrage zur pbysiscben Antliro- 
pologie der Bayern,’ Bd. 1, S. 88, Kapitel VI., I may take this opportunity of acknowledging tlie 
extreme kindness of Professor Ranke in helping me in a variety of ways. 
t Calculated from measurements extracted from the manuscripts of M. Paol Broca, which I owe 
to the courtesy of M. Manouyrier. He has responded to my request by forwarding to me copies of a 
great variety of measurements, which will be largely used in a paper on variation in man. 
