PROF. K PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 103 
Clearly there is only one positive root. This was found to be 
This gave 
whence I found 
Consequently the roots of 
X = 2-5868658. 
P 2 = 25-868,658, 
2 ^^ = 9-669,970. 
r — P}y + = 0 
were imaginary and no solution involving the diiference of two normal components 
was possible. 
The next stage was to find the negative roots. These were easily demonstrated to 
lie between 0 and 1, and then it was shown that the value of only changed sign 
twice between these values. Thus the nonic was proved, without calculating Sturm’s 
functions, to have only three real roots. The two negative roots are :— 
=- -154,481,14 
and 
X 3 = - -078,262,95. 
These roots lead to the following solutions :— 
(A.) First mlditive Solution for Carapace of Praivns. 
2h=— 1-544,8114, 
p^= 26-758,0108, 
y^= - -057,6086, 
= -997,856, 
1st Component. 
Cl = 995,860, 
— - -057,6086, 
0-1 = 3-5595, 
y^= 111-6142. 
ya = 26-815,6194, 
23 = -002,144. 
2nd Component. 
C 3 = 2-140, 
Z >3 = 26-815,6194, 
cTo^ 5-7626 
2/2 = imaginarj'. 
(B.) Second additive Solution for Carapace of Prawns. 
^2 = - -782,6295, 
Pi = 5-163,5907, 
yi =--147,3614, ya = 5-310,9521, 
= -973,0024, 2 a = -026,9976. 
