## Treatise on Natural PhilosophyThis work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. |

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### Contents

Displacements of a Plane Figure in its 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 | 128 |

Integral CurvatureCurvatura integraHorographChange | 136 |

Deduction of the Equations of Motion of any SystemInde | 271 |

Moment of an Impact about an AxisBallistic Pendulum | 282 |

General Theorem of Fundamental Modes of infinitely small | 338 |

Kinetics of a perfect fuidEffect of a Rigid Plane on | 340 |

Characteristic FunctionCharacteristic Equation of Motion | 354 |

Slightly disturbed EquilibriumSimultaneous Transformation | 364 |

EXPERIENCE | 369 |

Infinitely small Motion of a Dissipative SystemCycloidal | 384 |

Equation of ContinuityIntegral Equation of Continuity | 148 |

Freedom and ConstraintOf a Pointof a Rigid BodyGeo | 154 |

APPENDIX Ag Expression in Generalized Coordinates for Poissons | 160 |

APPENDIX A Extension of Greens Theorem | 167 |

DYNAMICAL LAWS AND PRINCIPLES | 219 |

Conservation of Energy 278 279 | 251 |

Momental EllipsoidEquilibration of Centrifugal Forces | 264 |

mental Oscillations similarly dealt with by Solution | 408 |

Kinetic StabilityConservative disturbance of motionKi | 427 |

MEASURES AND INSTRUMENTS | 457 |

APPENDIX B CONTINUOUS CALCULATING MACHINES | 479 |

An Instrument for calculating Sų x + x dx the Integral of | 493 |

Mechanical Integration of the general Linear Differential Equation | 500 |

### Other editions - View all

Treatise on Natural Philosophy, Part 1 William Thomson,William Thomson, Peter Guthrie Tait No preview available - 2010 |

### Common terms and phrases

according action actual altered amount angle angular application axes axis becomes body called Cambridge centre circle co-ordinates coefficients complete component condition configuration consider constant corresponding course curvature curve denote described determined differential direction displacement distance equal equations equilibrium example expression finite fixed force freedom function give given harmonic Hence inertia infinitely small initial instant integral kinetic energy length less mass matter mean measured motion moving natural negative observations parallel particle particular path period perpendicular plane position present principal problem produced proved quantities ratio reference relative remain remarkable respectively resultant rigid rolling roots rotation round side simple solution space spherical stable strain suppose surface tangent tion turn unit values velocity whole