392 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
We see at once that the normal curve is perfectly incapable of expressing statistical 
results like these. It gives an average error in the ordinate of 25:8 per cent. and no 
less than 260 antenatal deaths ! 
For the remaining three curves we have the following results :— 

Percentage error 
g Antenatal cases. 
in ordinate. enatal case 


Curve of Type I. (closest fit) . . . 5°75 3 
S 3 (starting at birth) . 73 0 
Curve of Type III. . of irate ih 5:98 g) 



The percentage errors here are well within those usually passed by statisticians. 
If they are slightly larger than what we have found in previous cases the source of 
the error is not far to seek. We have combined both male and female cases, but the 
distributions of enteric fever for both sexes are not the same. ‘The fever curves for 
either sex differ in some cases markedly, although less for enteric fever than for 
diphtheria, for example. We have thus, in reality, a compound curve. I have found 
for about 700 male cases only a percentage error of about 5.* 
Another point needing notice is the question of antenatal cases, which may at first 
strike the reader as absurd. The closest fitting curve of Type I. runs, as we have seen, 
1°35 years about before birth, and gives three antenatal cases. Three antenatal cases 
(or, indeed, 9 in the case of the curve of Type III.) is a very small percentage of 
8689 cases, and not of importance from the statistician’s standpoint. But the fact 
that a curve starting before birth gives a better fit than one starting at birth, is 
significant, and there is every probability that a curve starting from about — ‘75 year 
would give a still less percentage error than one from 1°35 year or from birth.t 
In dealing with mortality curves for infancy I have found it impossible to get good 
fitting theoretical curves, without carrying these curves backward to a limit of 
something less than a year. The “ theoretical” statistics thus obtained of antenatal 
deaths seem to be fairly well in accordance with the actual statistics of maternity 
charities. In vital statistics therefore we must be prepared in most diseases for small 
percentages of antenatal cases and antenatal deaths, and it is just possible that theory 
in this matter will be able to indicate lines of profitable inquiry to the medical 
statistician. 
(27.) Example VII—As an example of the method of Section 15, I take the 
following statistics of guessing a tint. Nine mixtures of black and white were taken, 
* T prepose on another occasion to deal with the age distribution of fever cases. My object at present 
is only to give typical illustrations of the method of calculating skew curves. 
+ In fact the case of a pregnant woman with enteric fever is to be considered as a case also of 
antenatal enteric fever. 
