98 PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
the coefficients were— 
= 26-47295. 
«3 == 18-11448. 
= 325-54964639. 
a.= 1604-777825,114 
= 977-342,6614. 
a^= — 3154-2006888. 
ftg = — 4412-284,2437. 
Og = - 1761-180374. 
Writing p.y, = ~ X’ have for the nonic /(x) and its first derived function*/j (x) 
the following expressions—• 
fix) = X^ + 26-472,95x^ - 18-114,48x® 
+ 325-549,646x® - 1604-777,825^^ 
+ 977-342,661x® + 3154-200,689x' - 4412-284,244x 
+ 1761-180,374 = 0, 
id 
/i (x) = X' + 20-590,07 x' - 12-076,32x' 
+ 180-860,915x^ “ 713-234,589x^ 
+ 325-780,887x^ + 700-933,486x 
— 490-253,805. 
The Sturm’s functions were now formed, and with the following results— 
X = 00 . 
x = o. 
X 1= - CO 
/(x)= • 
+ 
+ 
— 
/i (x) = • 
+ 
— 
+ 
f (x) = • 
— 
— 
+ 
f (x) = • 
+ 
+ 
.4 (x) = • 
• • • -f 
— 
— 
f (x) = • 
. . . + 
— 
Mx)= • 
. . . + 
— 
— 
/7(x)- • 
— 
— 
— 
/8(x)= • 
— 
+ 
A- 
/g (x) = • 
. . . + 
+ 
+ 
Totals 
4 changes 
4 changes 
5 changes. 
Thus the nonic has one root of x between 0 and — co, and no roots between 
0 and + 00 . In other words it has 8 imaginary roots and only 1 real one. 
* Divided by the factor 9. 
