88 PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
Discussion of first solution, — — •8‘757. pg was first calculated from (27) on 
p. 84, and then pj = pg/pa found. There resulted ; p^ = — 1’027. 
The quadratic for yo, wliich are here identical with h^, h .2 (the distances of the 
centroids of the component probability-curves from the centroid vertical of the 
frequency-curve), is ;— 
y- + f027y - 8 757 = 0, 
whence 
y^=— 3'517, ya 2-490. 
The values of,-:] and '..t were now found from (14) and (15) of p. 82. 
= -4145, Z.2 = -5855, 
thus the numljers of individuals in either group are respectively 
Cj = 414-5, Co = 585-5. 
The values of the standard-deviations, o-^ and cto, were now determined from 
(18) and (19), where, since h = 1, = cr^®, and At the same time the 
maximum ordinates of the component probability-curves, and po, were found from 
There resulted 
f ( 2 -^) 0-1 
cTj := 4-4685, 
p^ = 37-008, 
^3 
\/{’27t) cr„ 
cTa = 3-1154. 
Pa = 74-976. 
Thus the 1st solution may be summed up as follows :— 
2nd Component. 
Ca = 585-5. 
60 = 2-490. 
0 - 0 = 3-1154. 
Pa= 74-976. 
These two normal curves were now drawn by aid of the Table II., which was 
calculated afresh for this purpose from the exi^onential.'*’" These curves are plotted out 
in fig. 1, and their ordinates added together give the resultant curve. It will be seen that 
this curve is in remarkably close agreement with the original asymmetrical frequency- 
curve, an agreement quite as close as we could reasonably expect from the com- 
* I have always found it more convenient to work with the standard-deviation than with the probable 
error or the modulus, in terms of which the error-function is usually tabulated. 
1st Component. 
Cl = 414-5, 
61 = — 3-517, 
cTj = 4-4685, 
Pi = 37-008, 
