Utility Of Quaternions In Physics

Introduction

General remarks on the place of Quaternions in Physics

Cartesian form of some of the results to follow

Definitions

Properties of ζ

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 -∇ (σ2)/2

Consideration of the term -∇ (σ2)/2