AvGeusST 27, 1897. ] 
make them larger, then theoretically the de- 
viations from the mean will be distributed in a 
certain symmetrical fashion, and measurements 
show that such a distribution does in fact ap- 
proximately obtain. According to the Darwin- 
ian theory such chance variations as proved 
useful have by natural selection been preserved, 
and have given rise to new species and to or- 
ganic evolution. The quantitative study of 
these variations, especially in their relations to 
heredity, is, I believe, the most pressing prob- 
lem of biological science. The small amount 
of work hitherto accomplished has been chiefly 
carried out in England by Mr. Galton, Mr. 
Weldon, Mr. Bateson and Mr. Pearson. Mr. 
Galton has assumed the validity of the theo- 
retical distribution. Mr. Pearson has shown 
that the distribution may be complex and non- 
symmetrical, and has subjected it to mathe- 
matical analyses. 
Turning now to the essays in this book, which 
are of special value because the scientific papers 
of the author are of such a technical character, as 
to make them unintelligible to many naturalists, 
we find the first to be on ‘The Chances of 
Death.’ Mr. Pearson explains the theory of 
deviations from the mean, and shows how mor- 
tality statistics may be analyzed into five ‘skew’ 
eurves. Thus ‘old age’ mortality includes 
about one-half of alldeaths. The maximum of 
the curve is at about 71 years, but it has a 
‘skewness’ toward youth of 0.345. The mean 
isat about 65 years, with a ‘standard devia- 
tion’ of about 13.5 years and a limit on the 
old age side of 106.5 years. Components are 
then found representing the mortality of middle 
age, of youth, of childhood and of infancy. In 
the last case Mr. Pearson found that to secure 
a frequency curve it was necessary to take ac- 
count of antenatal mortality, and that the 
curve discovered corresponds fairly well with 
the facts. 
It is quite evident that the regular frequency 
curve does not represent mortality statistics or, 
indeed, most social and vital statistics. I have 
in several publications claimed that the ordi- 
nary frequency curve can in all actual cases be 
but an approximation. Mr. Pearson’s skew 
curves allow us to express the facts with greater 
approximation, just as the orbits of planets are 
SCIENCE. 
329 
more nearly ellipses than circles. But, in fact, 
the orbits of the planets are endlessly complex, 
and so are the distributions of errors or devia- 
tions. Mr. Pearson claims to give a simple 
curve for infancy, but the material is not homo- 
geneous. Antenatal mortality is due to causes 
different from those of infant mortality. The 
mortality of infants of the two sexes, of differ- 
ent races, of different classes, of those born at 
different seasons of the year, of those legitimate 
and those illegitimate, of those nursed by the 
mother and those brought up by hand, etc., has 
each a different distribution. In antenatal mor- 
tality there is a maximum at each four weeks, a 
greater maximum in the second and third 
months, etc. The curve for infancy would, in 
my opinion, need to be further broken up, quite 
beyond the possibility of mathematical analysis, 
in order to express the facts. 
The second essay analyzes certain alleged 
results of Monte Carlo Roulette, and shows that 
they are deficient in short runs to an almost 
impossible degree. Presumably the published 
figures do not represent the actual falls of the 
ball, or it would be easy to ‘break the bank.’ 
The author does not give this explanation, and 
apparently does not notice that in one case the 
zeros (where the money goes to the bank ) are 
only 499 instead of a most probable 840, a re- 
turn perhaps intended to encourage the gam- 
bler. I must admit that I do not think that 
Mr. Pearson has made the best possible use of his 
time in tossing shillings 25,000 times, ete., in 
order to test the laws of probability. He 
might as well measure the sides of 25,000 right- 
angled triangles in order to see whether the 
square of the hypotheneuse is really equal to 
the sum of the squares of the other two sides. 
The third essay, entitled ‘Reproductive Se- 
lection,’ is concerned with a statistical study of 
the size of families. The material is of much 
theoretical interest and of the greatest practical 
importance. If there is a complete correlation 
between fertility of parent and offspring, we 
might expect those having large families to 
supplant quickly all others, whereas it is not 
commonly supposed that those most fertile are 
those most fit forsociety. From 4,390 families, 
mostly of middle and upper Anglo-Saxon stock, 
Mr. Pearson finds that the most frequent 
