d by supernatural beings. In the metaphysical stage
it seeks an explanation in abstract forces. In the scientific, or
positive, stage it applies itself to the study of the relation of
phenomena to each other.

Different sciences have passed through these stages at different rates.
Astronomy reached the positive stage first, then terrestrial physics,
then chemistry, then physiology, while sociology has not even yet
reached it. To put social phenomena upon a positive basis is the main
object of this work; its secondary object is to show that all branches
of knowledge spring from the same trunk. An integration of the sciences
on a positive basis should lead to the discovery of the laws which rule
the intellect in the investigation of facts, should regenerate science
and reorganise society. At present the theological, the metaphysical,
and the positive conflict, and cause intellectual disorder and
confusion.

The first step to be taken in forming a positive philosophy is to
classify the sciences. The first great division we notice in natural
phenomena is the division into inorganic and organic phenomena. Under
the inorganic we may include the sciences astronomy, physics, chemistry;
and under the organic we include the sciences physiology and sociology.
These five sciences, astronomy, physics, chemistry, physiology, and
sociology, we may consider the five fundamental sciences. This
classification follows the order of the development of the sciences, and
indicates their social relation and relative perfection. In order to
reach effective knowledge, the sciences must be studied in the order
named; sociology cannot be understood without knowledge of the anterior
sciences.

Behind and before all these sciences, however, lies the great science of
mathematics--the most powerful instrument the mind can employ in the
investigation of natural law--and the science of mathematics must be
divided into abstract mathematics or the calculus, and concrete
mathematics embracing general geometry and rational mechanics. We have
thus really six great sciences.

MATHEMATICS. Mathematics may be defined briefly as the indirect
measurement of magnitudes and the determination of magnitudes by each
other. It is the business of concrete mathematics to discover the
_equations_ of phenomena; it is the business of abstract mathematics to
educe results from the equations. Thus concrete mathematics discovers by
actual experiment the acceleration which