o far as we have observed, it is invariably verified, and
that calculations founded upon it enable us to bring a vast variety of
phenomena under a single rule, is quite enough to justify astronomical
calculation.

If, therefore, we could find a mathematical formula which was, as a
matter of fact, verifiable in economical problems about prices, and so
forth, we should rightly apply to mathematicians to help us with their
methods. But, not only do we not find any such simple relations, but we
can see conclusive reasons for being sure that we can never find them.
Take, for example, the case of the number of marriages under given
conditions. I need hardly say that it is impossible for the ablest
mathematician to calculate whether the individual A will marry the
individual B. But, by taking averages, and so eliminating individual
eccentricities, he might discover that, in a given country and at a
given time, a rise of prices will diminish marriages in certain
proportion. Our knowledge of human nature is sufficient to make that
highly probable. But our knowledge also shows that such a change will
act differently in different cases: there will be one formula for
France, and another for England; one for Lancashire, and another for
Cornwall; one for the rich, and another for the poor; and both the
total wealth of a country and its distribution will affect the rule.
Differences of national temperament, of political and social
constitution, of religion and ecclesiastical organisation, will all
have an effect; and, therefore, a formula true here and now must, in
all probability, fail altogether elsewhere. The formula is, in the
mathematical phrase, a function of so many independent variables, that
it must be complex beyond all conception, if it takes them all into
account; while it must yet be necessarily inaccurate if it does not take
them into account. But, besides this, the conditions upon which the law
obviously depends are not themselves capable of being accurately
defined, and still less of being numerically stated. Ingenious thinkers
have, indeed, tried to apply mathematical formulae to psychology; but
they have not got very far; and it may, I think, be assumed, without
further argument, that while you have to deal both with psychological
and sociological elements, with human desires, and with those desires
modified by social relations, it is impossible to find any data which
can be mathematically stated. There is no arithme