104 PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
1st Component. 
Cl = 971-0564, 
6i = - -147,3614, 
0-1= 3-389,672, 
7/i = 114-28698. 
To these solutions we may add :— 
(C.) Parameters of Normal Curve deduced from entire group of ohservations. 
16-191,383, 
998, 
3-7572, 
105-968,04. 
2nd Component. 
Co = 26-9436, 
h,= 5-310,9521, 
0-2 = 8-932,996, 
^2 = 1-203,280. 
(D.) Parameters of Normal Curve deduced hy excluding two ‘‘giants'' from 
ohservations. 
d= 16-14357 (&= —-04781), 
c = 996, 
o- = 3-6051, 
y= 110-21786. 
The curves corresponding to (A), (B), (C), and (D) as well as the observation- 
curve are given in figs. 4 and 5. and I shall now proceed to discuss several important 
points with regard to them. 
(18.) The first point to be noted is the existence of the dwarf, carapace 27, and 
the giants, carapaces 65 and 69. 
The normal curve has a standard-deviation 3-7572, and the mean carapace being 
about 43, we have no less than three measurements deviating by more than four 
times the standard-deviation from the mean ; two of them, indeed, differ by nearly 
six times the standard-deviation from the mean. We might expect three such 
deviations of over four times the standard-deviation to occur in the measurement of 
50,000 Prawns, but they are extremely improbable in the measurement of 1000 
prawns. That two should occur in the measurement of 1000 Prawns, with a 
deviation six times the standard, is so improbable that it ought to lead us to reject 
the normal curve as a representation of the measurements. We are either dealing 
with a mixed population of Prawns, or possibly there are a few deformed individuals 
amid a normal population.""' 
There is another point, however, in which the normal curve, based on the total 
* I exclude the possibility of any serious error of measurement, having reason to believe in the great 
care with which the determinations were made. 
