Utility Of Quaternions In Physics

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Introduction General remarks on the place of Quaternions in Physics Cartesian form of some of the results to follow Definitions Properties of ¿ Fundamental Property of D Theorems in Integration Potentials Brief recapitulation of previous work in this branch Strain, Stress-force, Stress-couple Stress in terms of strain The equations of equilibrium Variation of temperature Small strains Isotropic Bodies Particular integral of the equation of equilibrium Orthogonal coordinates Saint-Venant's torsion problem Wires Electrostatics-general problem The force in particular cases Nature of the stress Magnetism-magnetic potential, force, induction Magnetic solenoids and shells Electro-magnetism-general theory Electro-magnetic stress Preliminary Notation Euler's equations The Lagrangian equations Cauchy's integrals of these equations Flow, circulation, vortex-motion Irrotational Motion Motion of a solid through a liquid The velocity in terms of the convergences and spins Viscosity Preliminary Statement of Sir Wm. Thomson's and Prof. Hicks's theories General considerations concerning these theories Description of the method here adopted Acceleration in terms of the convergences, their time-fluxes, and the spins Sir Wm. Thomson's theory Prof. Hicks's theory Consideration of all the terms except ¿¿ (¿2)/2 Consideration of the term ¿¿ (¿2)/2