Military schools and courses of instruction in the science and art of war, / in France, Prussia, Austria, Russia, Sweden, Switzerland, Sardinia, England, and the United States. Drawn from recent official reports and documents. Revised Edition

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General Theorems.

These theorems, four in number, are founded upon the principle of the equality of action and reaction applied to internal forces. They may be deduced from the preceding rule, but the three last are obtained more simply by extending to a system of material points analogous theorems established for isolated material points.

General theorem of the motion of the center of gravity of a system. Particular case called principle of the conservation of the motion of the center of gravity.

General theorem on the quantities of motion and impulsions of exterior forces projected on any axis.

General theorems of moments of quantities of motion and impulsions of exterior forces, projected on any axis whatever.

General theorems of the moments of quantities of motion and impulsions of exterior forces about any axis. Analogy of these two theorems with the equations of the equilibrium of a solid, in which the forces are replaced by impulsions and quantities of motion.

Composition of impulsions, of quantities of motion, or the areas which represent them. All the equations which can be obtained by the application of the two theorems relative to quantities of motion and impulsions, reduce themselves to six distinct equations. Particular case called principle of the conservation of areas. Fixed plane of the resulting moment of the quantities of motion called plane of maximum areas.

General theorem of work and vis viva. Part which appertains to the interior forces in this theorem. Particular case called principle of the conservation of vires vivæ, where the sum of the elements of work done by the exterior and interior forces is the differential of a function of the co-ordinates of different points of the system. Application of the theorem of work to the stability of the equilibrium of heavy systems.

Extension of the preceding theorems to the case of relative motions. Particular case of relative equilibrium. Motion of any material system relative to axes always passing through the center of gravity, and moving parallel to themselves. Invariable plane of Laplace. Relation between the absolute vis viva of a material system, and that which would be due to its motion, referred to the system of movable axes above indicated.

Examples and Applications.