MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 391 
Thus we have for the curve of Type I. 
zg \2'79291 i fi aes 
y = 1890°83 (1 a srs0) (\— Fo) 
where the centroid is ‘98643 unit from axis of y. 
The curve of Type III. is 
e -LOT1M5 32, 
a 3°673042 
y = 1894°57 (1 + ) 
3428094 
The centroid is in this case 933313 unit on the positive side of the origin and the 
skewness = °462594. 
It will be noticed that the curve of Type I. extends 2706 unit or 1°353 years, 
and the curve of Type III. °5676 unit or 2°838 years before birth. In both cases 
the chances of an “antenatal” death from enteric fever are very, very small. Curve 
of Type I. is in this respect better than the curve of Type III. The latter curve 
gives no maximum limit, the former a limit of about 77 units or 385 years. In both 
cases, however, the chances of a case of enteric fever with the subject over 100 years 
are vanishingly small. These statistics of enteric fever thus set a maximum limit to 
the duration of life, but it is a limit so high as to have little suggestiveness. 
In order to see what is the nature of the difference made, when we suppose the 
lability to enteric fever to commence with birth, I will treat these statistics as a 
case falling under § 16. 
If then p’), p’2, and p’, be the first three moments about the vertical through 
0 years we have 
Pi = 379382, yw'n = 1846362, 
y's = 108°53175, 
Xo = 1282813, x3 17549399, 
u = 030435, v= 321856, 
m,= 214296, My = 28°71414, 
b = 401206, Yo = 1878°39, 
@, = 2°78629, @y = $7°33481. 
whence we have for the curve 
Xv a 
y 2714206 28°71414 
ITY (1 us Tae) (1 = = 
Here the duration of life is 200 years about, and the maximum incidence of the 
disease is at 13°93 years. 
Lastly for the normal curve, we have the constants « = 2:01756 units = 10°0878 
years and y, = 1718°12. 
All the above four curves are drawn, Plate 12, fig. 9. 
