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 takes place per second in a falling body, and abstract mathematics educes results from the equations so discovered, and obtains unknown quantities from known. ASTRONOMY. Astronomy may be defined as the science by which we discover the laws of the geometrical and mechanical phenomena presented by heavenly bodies. To discover these laws we can use only our sense of sight and our reasoning power, and reasoning bears a greater proportion to observation here than in any other science. Sight alone would never teach us the figure of the earth or the path of a planet, and only by the measurement of angles and computation of times can we discover astronomical laws. The observation of these invariable laws frees man from servitude to the theological and metaphysical conceptions of the universe. PHYSICS. Physics may be defined briefly as the study of the laws which regulate the general properties of bodies regarded _en masse_, their molecules remaining unaltered and usually in a state of aggregation. In the observations of physics all the senses are employed, and mathematical analysis and experiment assist observation. In the phenomena of astronomy human intervention was impossible; in the phenomena of physics man begins to modify natural phenomena. Physics includes the subdivisions statics, dynamics, thermology, acoustics, optics, and electrology. Physics is still handicapped by metaphysical conceptions of the primary causes of phenomena.