PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 255 
biologists and medical men have yet fully appreciated that he has really shown how 
many of the problems which perplex them may receive at any rate a partial answer. 
A considerable portion of the present memoir will be devoted to the expansion and 
fuller development of Mr. Galton’s ideas, particularly their application to the problem 
of bi-pa,rental inheritance. At the same time I shall endeavour to point out how the 
results apply to some current biological and medical problems. In the first place, we 
must definitely free our minds, in the present state of our knowledge of the mechanism 
of inheritance and reproduction, of any hope of reaching a mathematical relation express¬ 
ing the degree of correlation between individual parent and individual offspring.* The 
causes in any individual case of inheritance are far too complex to admit of exact 
treatment ; and up to the present the classification of the circumstances under which 
greater or less degrees of correlation between special groups of parents and offspring 
may be expected has made but little progress. This is largely owing to a certain 
prevalence of almost metaphysical speculation as to the causes of heredity, which 
has usurped the place of that careful collection and elaborate experiment by which 
alone sufficient data might have been accumulated, with a view to ultimately narrow¬ 
ing and specialising the circumstances under which correlation was measured. We 
must proceed from inheritance in the mass to inheritance in narrower and narrwoer 
classes, rather than attempt to build up general rules on the observation of individual 
instances. Shortly, we must proceed by the method of statistics, rather than by the 
consideration of typical cases. It may seem discouraging to the medical practitioner, 
with the problem before him of inheritance in a particular family, to be told that 
nothing but averages, means, and probabilities with regard to large classes can as 
yet be scientifically dealt with ; but the very nature of the distribution of variation, 
whether healthy or morbid, seems to indicate that we are dealing with that sphere of 
indefinitely numerous small causes, which in so many other instances has shown itself 
only amenable to the calculus of chance, and not to any analysis of the individual 
instance. On the other hand, the mathematical theory will be of assistance to the 
medical man by answering, inter alia, in its discussion of regression the problem as 
to the average effect upon the offspring of given degrees of morbid variation in the 
parents, It may enable the physician, in many cases, to state a belief based on a 
high degree of probability, if it offers no ground for dogma in individual cases. 
One of the most noteworthy results of Mr. Francis Gai, ton’s researches is his 
discovery of the mode in which a population actually reproduces itself by regression 
and fraternal variation. It is with some expansion and fuller mathematical treatment 
of these ideas that this memoir commences. 
* The physical and arithmetical statements of Weismann’s “ Theory of Germ Plasm ” offer, so far as I 
have been able to interpret them, no sound basis for a quantitative theory of heredity in the mathemati¬ 
cian’s sense. 
