PROF. K. PE4RS0X ON THE MATHEMATICAL THEORY OF EVOLUTION. 87 
Put Pz— and divide by 10® we then have for the fundamental nonic the 
following equation, where only three decimal places are retained :— 
X®+ •994x^ + 4-354x® - 42-370x" - 37-029x^+ 119-299x® -f 123-24ix® 
- 9-571X- 24-452 = 0. 
After a somewhat laborious calculation, the values of Sturm’s functions ./’(x)^ 
fi ixl f-2 {x\ /a (x)> /4(x)> f-. (x)> A (xl fi (x)= A (x). /o (x) were ascertained and gave 
the following results :— 
/(“) = 
/(- 
) = — 
/l ( “ ) = 
+ 
/i( 
= + 
/2(°°) = 
— 
/3( 
/s ( «= ) = 
— 
= — 
/4(-) = 
— 
fd^) 
= + 
/5(-) = 
+ 
fd^) 
= + 
/6(°°) = 
+ 
A{^) 
= — 
A{^) = 
+ 
/? ( °° ) 
= + 
/s ( ) = 
— 
/s ( ) 
= + 
/g ( ^ ) = 
— 
A{^) 
= — 
3 changes. 6 changes. 
Thus there are 6 — 3 = 3 real roots. 
These three real roots were then localized as follows :— 
Two roots between 0 and — 1, Xi and xo. 
One root between 0 and 1, xs* 
As successive approximations, I found :— 
To xi : 
- 1, 
— -89, 
- -870, 
- *8757, 
X2 : 
- -5, 
— -65, 
- *670, 
- -6724, 
Xa : 
*5, 
•40, 
-422, 
•4170. 
With sufficient accuracy we may then take for the values of p .^:— 
1st solution, P2 = ~ 8-757. 
2 nd ,, P2 = — 6-724. 
3 rd ,, P2 — 4 * 170 . 
