MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 407 
Professor Lexis has already suggested that the old age distribution of mortality 
is given by a normal curve.* Now, although the rougher French statistics give 
a fair approximation to a normal curve, this is not true for English males. The 
curve for old age is of Type I., but for all practical purposes it may be treated as one 
of Type III. Whatever be the chief causes of old age mortality, they extend very 
sensibly through middle life, and less sensibly through youth, only becoming inappre- 
ciable in childhood. Hence, if we speak of our first component as the “ mortality of 
old age,” the name is to be understood as referring to a group of causes especially 
active in old age mortality, but not excluded from other portions of life. The 
second and third components I found to be skew curves, but so nearly normal that to 
my degree of approximation no stress could be laid on the skewness obtained. The 
fourth component was a markedly skew curve, also closely given by a curve of 
Type III., and corresponding in general shape to the mortality curves of fevers 
peculiarly dangerous in childhood (e.g., diphtheria, scarlet fever, enteric fever, &c.). 
These three components I have termed respectively the mortality of middle life, of 
youth, and of childhood. I found it impossible to fit the remainder of the original 
mortality curve with any type of generalised curve, so long as I supposed the 
mortality frequency to commence with birth. Iwas therefore compelled to suppose 
the set of causes giving rise to “infantile mortality” extended into the period of 
gestation, and I obtained a satisfactory fit for the infantile mortality frequency, when 
the range of the curve started about *75 of a year before birth. The form taken by 
the curve is the extreme type in which the curve is asymptotic to the ordinate of 
maximum frequency (cf. Examples X.-XII.). The five fundamental components of 
the mortality curve for English males are the following, the numbers referring to 
1000 contemporaries, or persons born in same year :— 
(A.) Old Age Mortality. 
Total frequency = 484°1. 
Centroid-vertical at 67 years. 
Maximum mortality = 15°2 at 71°5 years. 
The equation ist 
: a NUT 2215 
y = 152 (1 — 35) ezlbe 
the axis of y being the maximum ordinate and the positive direction of « towards 
age. The skewness of the curve = ‘345, and its range concludes at 106°5 years. 
The corresponding French component = 411, but the maximum mortality (16°4) 
occurs at 72°5 years. 
* ‘Zur Theorie der Massenerscheinungen in der menschlichen Gesellschaft,’ § 46. Freiburg, 1877. 
+ Unit of c = 1 year, unit of y = 1 death per year. 
