Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/19

CONTENTS.

xiii

Chapter V.

General Equations of Dynamics.

553. Lagrange's method furnishes appropriate ideas for the study of the higher dynamical sciences	184
554. These ideas must be translated from mathematical into dynamical language	184
555. Degrees of freedom of a connected system	185
556. Generalized meaning of velocity	186
557. Generalized meaning of force	186
558. Generalized meaning of momentum and impulse	186
559. Work done by a small impulse	187
560. Kinetic energy in terms of momenta, ($T_{p}$)	188
561. Hamilton's equations of motion	189
562. Kinetic energy in terms of the velocities and momenta, ($T_{p{\dot {q}}}$)	190
563. Kinetic energy in terms of velocities, ($T_{\dot {q}})$	191
564. Relations between $T_{p}$ and $T_{\dot {q}}$, $p$ and ${\dot {q}}$	191
565. Moments and products of inertia and mobility	192
566. Necessary conditions which these coefficients must satisfy	193
567. Relation between mathematical, dynamical, and electrical ideas	193

Chapter VI.

Application of Dynamics to Electromagnetism.

568. The electric current possesses energy	195
569. The current is a kinetic phenomenon	195
570. Work done by electromotive force	196
571. The most general expression for the kinetic energy of a system including electric currents	197
572. The electrical variables do not appear in this expression	198
573. Mechanical force acting on a conductor	198
574. The part depending on products of ordinary velocities and strengths of currents does not exist	200
575. Another experimental test	202
576. Discussion of the electromotive force	204
577. If terms involving products of velocities and currents existed they would introduce electromotive forces, which are not observed	204

Chapter VII.

Electrokinetics.

578. The electrokinetic energy of a system of linear circuits	206
579. Electromotive force in each circuit	207