410 MRK. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
It would thus appear that there are 4 to 5 per cent. of still-births, thus leaving 
2‘7 to 8°7 per cent. of deaths to be accounted for—if there is any validity in our 
analysis—by. deaths of children born before their proper time and dying before 
their proper birthdays. Such deaths would not appear in the category of still-born 
children in the returns of the maternity charities, nor in any true proportion in the 
census returns. 
Thus, while it is impossible to assert any validity for the antenatal part of our 
curve of infantile mortality, while, indeed, the constants of that curve, and con- 
sequently the percentages of antenatal deaths, might be considerably modified had 
we surer data of the actual deaths in the first year of life; still there appears to be 
nothing wildly impossible in the results obtained, and they may at any rate be 
suggestive, if only as to the nature of those statistics of “antenatal” deaths, which 
it would be of the greatest interest to procure. 
The absolute necessity of skew curves in all questions of vital statistics is sufficiently 
evidenced in this resolution of the general mortality curve. A complete picture of the 
resolution into components of the mortality curve is given (Plate 16, fig. 18), with 
a separate figure on an enlarged scale of infantile mortality. ; 
(36.) In conclusion, there are several points on which it seems worth while to insist. 
The normal curve of errors connotes three equally important principles : 
(i.) An indefinitely great number of “ contributory ” causes. 
(ii.) Each contributory cause is in itself equally likely to give rise to a deviation of 
the same magnitude in excess and defect. 
(ii.) The contributory causes are independent. 
The frequency of each possible number of heads in repeatedly throwing several 
hundred coins in a group together, practically fulfils all the above three conditions. 
Condition (ii.) is not, however, fulfilled if a number of dice be thrown or a number 
of teetotums of the same kind be spun together. Condition (iii.) is still fulfilled. 
Condition (ii.) is not fulfilled if p cards be drawn out of a pack of n7 cards containing 
r equal suits, supposing the p cards to be drawn at one time. Now, it appears to 
me that we cannot say @ priori whether the example of tossing, of teetotum- 
spinning, or of card-drawing is more likely to fit the proceedings of nature. There 
is, I think, now sufficient evidence to show that the conditions (i.) to (ii.) are not 
fulfilled, or not exactly fulfilled, in many cases—in economic, in physical, in 
zoometric, and botanical statistics. We are, therefore, justified in seeing what results 
we shall obtain by supposing one or more of the above conditions which lead to the 
normal curve to be suspended. The analogy of teetotums and cards leads us to a 
system of skew frequency curves which in this paper have been shown to give a very 
close approximation to observed frequency in a wide number of cases——an approxi- 
mation quite as close as the writer has himself obtained between theory and 
experiment in very wide experiments in tossing, card-drawing, ball-drawing, and 
