an judge of the
frequency of the causes only through the medium of the empirical law,
which is based on the frequency of the effects), still then, too, the
inference really depends on causation alone. Thus, an actuary infers
from his tables that, of any hundred living persons under like
conditions, five will reach a given age, not simply because that
proportion have reached it in times past, but because that fact shows
the existence there of a particular proportion between the _causes_
which shorten and the causes which prolong life to the given extent.

CHAPTER XIX.

THE EXTENSION OF DERIVATIVE LAWS TO ADJACENT CASES.

Derivative laws are inferior to ultimate laws, both in the extent of the
propositions, and in their degree of certainty within that extent. In
particular, the uniformities of coexistence and sequence which obtain
between effects depending on different primaeval causes, vary along with
any variation in the collocation of these causes. Even when the
derivative uniformity is between different effects of the same cause, it
cannot be trusted to, since one or more of the effects may be producible
by another cause also. The effects, even, of derivative laws of
_causation_ (resulting, i.e. the laws, from the combination of several
causes) are not independent of collocations; for, though laws of
causation, whether ultimate or derivative, are themselves universal,
being fulfilled even when counteracted, the peculiar probability of the
latter kind of laws of causation being counteracted (as compared with
ultimate laws, which are liable to frustration only from one set of
counteracting causes) is fatal to the universality of the derivative
uniformities made up of the sequences or coexistences of their effects;
and, therefore, such derivative uniformities as the latter are to be
relied on only when the collocations are known not to have changed.

Derivative laws, not causative, may certainly be extended beyond the
limits of observation, but only to cases _adjacent_ in time. Thus, we
may not predict that the sun will rise this day 20,000 years, but we can
predict that it will rise to-morrow, on the ground that it has risen
every day for the last 5,000 years. The latter prediction is lawful,
_because_, while we know the causes on which its rising depends, we
know, also, that there has existed hitherto no perceptible cause to
counteract them; and that it is opposed to experience that a cause
imperceptible fo