## Treatise on Natural Philosophy |

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### Contents

PRELIMINARY | 1 |

Displacements of a Plane Figure in ita PlaneComposition | 78 |

Most general Motion of a Rigid Body 102 | 102 |

Free rotation of a Body kinetically symmetrical about an axis | 108 |

StrainDefinition of Homogeneous StrainProperties of | 118 |

TwistEstimation of Integral Twist in a Plane Curve | 119 |

Surface rolling on Surface without spinning | 125 |

Displacement of a Body rigid or not one point of which | 127 |

Resolution of ForcesEffective Component of a Force 227 | 227 |

Geometrical Theorem preliminary to Definition of Centre | 233 |

Newtons Laws of MotionFirst LawRestTimeEx | 242 |

Conservation of Energy 278 279 | 251 |

Momenta EllipsoidEquilibration of Centrifugal Forces | 264 |

EquilibriumPrinciple of Virtual VelocitiesNeutral Equi | 289 |

Moment of an Impact about an AxisBallistic Pendulum | 307 |

General Theorem ol Fundamental Modes of infinitely small | 338 |

Analogy between Lines and Surfaces as regards Curvature | 138 |

Equation of ContinuityIntegral Equation of Continuity | 148 |

Freedom and ConstraintOf a PointOf a Rigid BodyGeo | 154 |

ArrENmx A Expression in Generalized Coordinates for Poissons | 160 |

ArrENDix A Extension of Groens Theorem | 171 |

ForceSpecification of a ForcePlace of ApplicationDirec | 217 |

Kinetics of a perfect fluidEffect of a Rigid Plane on | 346 |

Characteristic FunctionCharacteristic Equation of Motion | 354 |

Slightly disturbed EquilibriumSimultaneous Transformation | 364 |

Infinitely Bmall Motion of a Dissipative SystemCycloidal | 384 |

Kinetic StabilityConservative disturbance of motionKi | 427 |

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### Common terms and phrases

acceleration action altered angular velocity anticlastic application Cambridge centre of inertia change of direction circle circular co-ordinates coefficients condition cone configuration constant corresponding course curvature curve cycloid cylinder degrees of freedom denote described determined diagram differential equation direction cosines distance ellipse ellipsoid elongation equal equations of motion equilibrium expression finite fixed point fluid force formula function geodetic geometrical given Hence hodograph infinitely small initial instant instantaneous axis integral kinetic energy length linear notation osculating plane parallel parallelepiped particle path period perpendicular polygon position principal axes quadratic function quantities radius radius-vector ratio rectangular relative resultant right angles rigid body rolling roots rotation round shear simple harmonic motions solution space spherical harmonic spherical surface St John's College straight line strain suppose synclastic tangent plane tangential displacement theorem tion trace twist values variable whole