THEORY OF STATISTICS. 
investigation of the motion of molecules”! have become part of 
the ordinary language of physicists. We find a work entitled 
“the principles of statistical mechanics”? and the Bakerian 
lecture for 1909, by Sir J. Larmor, was on “the statistical and 
thermodynamical relations of radiant energy.” 
7. It is unnecessary to multiply such instances to show that the 
words statistics,” “statistical,” no longer bear any necessary 
reference to “ matters of state.” They are applied indifferently in 
physics, biology, anthropology, and meteorology, as well as in the 
social sciences. Diverse though these cases are, there must be 
some community of character between them, or the same terms 
and the same methods would not be applied. What, then, is this 
common character ? 
8. Let us turn to social science, as the parent of the methods 
termed statistical,” for a moment, and consider its characteristics 
as compared, say, with physics or chemistry. One characteristic 
stands out so markedly that attention has been repeatedly 
directed to it by “statistical” writers as the source of the peculiar 
difficulties of their science—the observer of social Jacts cannot ex- 
pervment, but must deal with circumstances as they occur, apart 
Jrom his control. Now the object of experiment is to replace the 
complex systems of causation usually occurring in nature by 
simple systems in which only one causal circumstance is permitted 
to vary at a time. This simplification being impossible, the 
observer has, in general, to deal with highly complicated cases of 
multiple causation—cases in which a given result may be due to 
any one of a number of alternative causes or to a number of 
different causes acting conjointly. 
9. A little consideration will show, however, that this is also 
precisely the characteristic of the observations in other fields to 
which statistical methods are applied. The meteorologist, for 
example, is in almost precisely the same position as the student 
of social science. He can experiment on minor points, but the 
records of the barometer, thermometer, and rain gauge have to be 
treated as they stand. With the biologist, matters are in some- 
what better case. He can and does apply experimental methods 
to a very large extent, but frequently cannot approximate 
closely to the experimental ideal ; the internal circumstances of 
animals and plants too easily evade complete control. Hence a 
large field (notably the study of variation and heredity) is left, 
in which statistical methods have either to aid or to replace the 
methods of experiment. The physicist and chemist, finally, 
1 Clerk Maxwell, “Theory of Heat” (1871), and ‘‘On Boltzmann’s 
Theorem ” (1878), Camb. Phil. Trans., vol. xii. 
2 By J. Willard Gibbs (Macmillan, 1902), 
4