General Theorem of Fundamental Modes of infinitely small
Motion about a Configuration of Equilibrium-Normal
Displacements from Equilibrium-Theorem of Kinetic
Energy-Of Potential Energy-Infinitesimal Motions in
neighbourhood of Configuration of Unstable Equilibrium
Case of Equality among Periods-Graphic Representation—
Dissipative Systems-Views of Stokes on Resistance to a
Solid moving through a Liquid-Friction of Solids-
Resistances varying as Velocities-Effect of Resistance
varying as Velocity in a simple Motion
Infinitely small Motion of a Dissipative System-Cycloidal
System defined-Positional and Motional Forces-Differ-
ential Equations of Complex Cycloidal Motion-Their
Solution-Algebra of Linear Equations-Minors of a De-
terminant-Relations among the Minors of an Evanescent
Determinant-Case of Equal Roots-Case of Equal Roots
and Evanescent Minors-Routh's Theorem-Case of no
Motional Forces-Conservative Positional, and no Mo-
tional, Forces-Equation of Energy in Realized General
Solution
Artificial or Ideal Accumulative System-Criterion of Sta-
bility-Cycloidal System with Conservative Positional
Forces and Unrestricted Motional Forces-Dissipativity
defined-Lord Rayleigh's Theorem of Dissipativity-In-
tegral Equation of Energy-Real part of every Root of
Determinantal Equation proved negative when Potential
Energy is positive for all real Co-ordinates; positive for
some Roots when Potential Energy has negative values;
but always negative for some Roots-Non-oscillatory sub-
sidence to Stable Equilibrium, or falling away from Un-
stable-Oscillatory subsidence to Stable Equilibrium, or
falling away from Unstable-Falling away from wholly
Unstable Equilibrium is essentially non-oscillatory if
Motional Forces wholly viscous-Stability of Dissipative
System-Various origins of Gyroscopic Terms-Equation
of Energy-Gyrostatic Conservative System-simplifica-
tion of its Equations-Determinant of Gyrostatic Conser-
vative System-Square Roots of Skew Symmetric De-
terminants-Gyrostatic System with Two Freedoms-Gy.
rostatic Influence dominant-Gyrostatic Stability--Ordi-
nary Gyrostats-Gyrostats, on gimbals; on universal
flexure-joint in place of gimbals; on stilts; bifilarly slung in
four ways-Gyrostatic System with Three Freedoms-Re-
duced to a mere rotating System-Quadruply free Gyro-
static System without force-Excepted case of failing gy-
rostatic predominance-Quadruply free Cycloidal System,
gyrostatically dominated-Four Irrotational Stabilities
confirmed, four Irrotational Instabilities rendered stable,