The _Pure_ Mathematical Sciences can hardly be called _Inductive_ Sciences. Their principles are not obtained by Induction from Facts, but are necessarily assumed in reasoning upon the subject matter which those sciences involve. The Astronomy of the Ancients aimed only at explaining the motions of the heavenly bodies, as a _mechanism_. Modern Astronomy, explains these motions on the principles of Mechanics. The term _Physics_, when confined to a peculiar class of Sciences, is usually understood to exclude the Mechanical Sciences on the one side, and Chemistry on the other; and thus embraces the Secondary Mechanical and Analytico-Mechanical Sciences. But the adjective _Physical_ applied to any science and opposed to _Formal_, as in Astronomy and Optics, implies those speculations in which we consider not only the Laws of Phenomena but their Causes; and generally, as in those cases, their Mechanical Causes. The term _Metaphysics_ is applied to subjects in which the Facts examined are emotions, thoughts and mental conditions; subjects not included in our present survey. {140} Fundamental Ideas or Sciences. Classification. Conceptions. Space Geometry ) Time ) Pure Mathematical _Number_ Arithmetic } Sign Algebra ) Sciences. Limit Differentials ) _Motion_ Pure Mechanism } Pure Motional Formal Astronomy } Sciences. Cause _Force_ Statics ) _Matter_ Dynamics ) Mechanical _Inertia _ Hydrostatics } _Fluid Pressure_ Hydrodynamics ) Sciences. Physical Astronomy ) Outness Medium _of Sensation_ Acoustics ) Intensity _of Qualities_ Formal Optics ) Secondary _Scales of Qualities_ Physical Optics } Mechanical Thermotics ) Sciences. Atmology ) (_Physics_.) Polarity Electricity ) Analytico-Mecha- Magnetism } nical Sciences. Galvanism ) (_Physics_.)