details is definitely made out, and each particular truth can be
recognized as a case of the operation of wider laws. This point of
progress, at which the study passes from the preliminary state of mere
preparation, into a science, cannot be reached by the more complex
studies until it has been attained by the simpler ones. A certain
regularity of recurrence in the celestial appearances was ascertained
empirically before much progress had been made in geometry; but
astronomy could no more be a science until geometry was a highly
advanced one, than the rule of three could have been practised before
addition and subtraction. The truths of the simpler sciences are a part
of the laws to which the phaenomena of the more complex sciences
conform: and are not only a necessary element in their explanation, but
must be so well understood as to be traceable through complex
combinations, before the special laws which co-exist and co-operate with
them can be brought to light. This is all that M. Comte affirms, and
enough for his purpose.[5] He no doubt occasionally indulges in more
unqualified expressions than can be completely justified, regarding the
logical perfection of the construction of his series, and its exact
correspondence with the historical evolution of the sciences;
exaggerations confined to language, and which the details of his
exposition often correct. But he is sufficiently near the truth, in both
respects, for every practical purpose.[6] Minor inaccuracies must often
be forgiven even to great thinkers. Mr Spencer, in the very-writings in
which he criticises M. Comte, affords signal instances of them.[7]

Combining the doctrines, that every science is in a less advanced state
as it occupies a higher place in the ascending scale, and that all the
sciences pass through the three stages, theological, metaphysical, and
positive, it follows that the more special a science is, the tardier is
it in effecting each transition, so that a completely positive state of