biology many abstract words such as "species," "generation," &c., may be employed, but the only thing which we can define is the concrete individual, and the ideas which the most accomplished biologist attaches to such words as "species" or "generation" have a very different degree of exactness from those which mathematicians associate, say, with the class or order of a surface, or with the umbilical generation of conicoids. Sciences of this kind are rich in facts, and will be well occupied for ages to come in the co-ordination of these facts, though their cultivators may be cheered in the meantime by the hope of the discovery of laws like those of the more abstract sciences, and may indulge their fancy in the contemplation of a state of scientific knowledge when maxims cast in the same mould as those which apply to our present ideas of dead matter will regulate all our thoughts about living things.
What is commonly called "physical science" occupies a position intermediate between the abstract sciences of arithmetic, algebra, and geometry and the morphological and biological sciences. The principal physical sciences are as follows.
A.The Fundamental Science of Dynamics, or the doctrine of the motion of bodies as affected by force.—The divisions of dynamics are the following. (1) Kinematics, or the investigation of the kinds of motion of which a body or system of bodies is capable, without reference to the cause of these motions. This science differs from ordinary geometry only in introducing the idea of motion, that is, change of position going on continuously in space and time. Kinematics includes, of course, geometry, but in every existing system of geometry the idea of motion is freely introduced to explain the tracing of lines, the sweeping out of surfaces, and the generation of solids. (2) Statics, or the investigation of the equilibrium of forces, that is to say, the conditions under which a system of forces may exist without producing motion of the body to which they are applied. Statics includes the discussion of systems of forces which are equivalent to each other. (3) Kinetics, or the relations between the motions of material bodies and the forces which act on them. Here the idea of matter as something capable of being set in motion by force, and requiring a certain force to generate a given motion, is first introduced into physical science. (4) Energetics, or the investigation of the force which acts between two bodies or parts of a body, as dependent on the conditions under which action takes place between one body or part of a body and another so as to transfer energy from one to the other.
The science of dynamics may be divided in a different manner with respect to the nature of the body whose motion is studied. This forms a cross division. (1) Dynamics of a particle; including its kinematics or the theory of the tracing of curves, its statics or the doctrine of forces acting at a point, its kinetics or the elementary equations of motion of a particle, and its energetics, including, as examples, the theory of collision and that of central forces. (2) Dynamics of a connected system, including the same subdivisions. This is the most important section in the whole of physical science, as every dynamical theory of natural phenomena must be founded on it. The sub-divisions of this, again, are—a. dynamics of a rigid system, or a body of invariable form; b. dynamics of a fluid, including the discussion (α) of its possible motion, (β) of the conditions of its equilibrium (hydrostatics), (γ) of the action of force in producing motion (hydrodynamics, not so unsatisfactory since Helmholtz, Stokes, and Thomson's investigations), and (δ) of the forces called into play by change of volume; c. dynamics of an elastic body; d. dynamics of a viscous body.
B.The Secondary Physical Sciences.—Each of these sciences consists of two divisions or stages. In the elementary stage it is occupied in deducing from the observed phenomena certain general laws, and then employing these laws in the calculation of all varieties of the phenomena. In the dynamical stage the general laws already discovered are analysed and shown to be equivalent to certain forms of the dynamical relations of a connected system (A, 2), and the attempt is made to discover the nature of the dynamical system of which the observed phenomena are the motions. This dynamical stage includes, of course, several other stages rising one above the other; for we may successfully account for a certain phenomenon, say the turning of a weathercock towards the direction of the wind, by assuming the existence of a force having a particular direction and tending to turn the tail of the cock in that direction. In this way we may account not only for the setting of the weathercock but for its oscillations about its final position. This, therefore, is entitled to rank as a dynamical theory. But we may go on and discover a new fact, that the air exerts a pressure and that there is a greater pressure on that side of the cock on which the wind blows. This is a further development of the theory, as it tends to account for the force already discovered. We may go on and explain the dynamical connexion between this inequality of pressure and the motion of the air regarded as a fluid. Finally, we may explain the pressure of the air on the hypothesis that the air consists of molecules in motion, which strike against each other and against the surface of any body exposed to the air. The dynamical theories of the different physical sciences are in very different stages of development, and in almost all of them a sound knowledge of the subject is best acquired by adopting, at least at first, the method which we have called "elementary,"—that is to say, the study of the connexion of the phenomena peculiar to the science without reference to any dynamical explanations or hypotheses. Thus we have—
(1) Theory of gravitation, with discussion of the weight and motion of bodies near the earth, of the whole of physical astronomy, and of the figure of the earth. There is a great deal of dynamics here, but we can hardly say that there is even a beginning of a dynamical theory of the method by which bodies gravitate towards each other.
(2) Theory of the action of pressure and heat in changing the dimensions and state of bodies. This is a very large subject and might be divided into two parts, one treating of the action of pressure and the other of heat. But it is much more instructive to study the action of both causes together, because they produce effects of the same kind, and therefore mutually influence each other. Hence the term "thermodynamics" might be extended to the whole subject were it not that it is already restricted to a very important department relating to the transformation of energy from the thermal to the mechanical form and the reverse. The divisions of the subject are seven, (a) Physical states of a substance,—gaseous, liquid, and solid; elasticity of volume in all three states; elasticity of figure in the solid state; viscosity in all three states; plasticity in the solid state; surface-tension, or capillarity; tenacity of solids; cohesion of liquids; adhesion of gases to liquids and solids, (b) Effects of heat in raising temperature, altering size and form, changing physical state, (c) Thermometry. (d) Calorimetry. (e) Thermodynamics, or the mutual convertibility of heat and work. (f) Dissipation of energy by diffusion of matter by mixture, diffusion of motion by internal friction of fluids, diffusion of heat by conduction, (g) Theory of propagation of sound, vibrations of strings, rods, and other bodies.
(3) Theory of radiance. (a) Geometrical optics; theory of conjugate foci and of instruments. (b) Velocity
