## The Mathematical Principles of Mechanical Philosophy and Their Application to Elementary Mechanics and Architecture: But Chiefly to the Theory of Universal Gravitation |

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### Common terms and phrases

acting action angle application arch attraction axes axis beam becomes body calculate called cause centre of gravity Chapter co-ordinates coefficient consequence constant couple curve density described determine differential direction distance disturbing dt dt Earth effect ellipse equal equations equilibrium expression extremity figure fixed fluid forces forces acting function given gives greater Hence horizontal impulsive inclination integration length limits magnitude manner mass mean measured Moon motion move nearly neglect observed obtain orbit origin parallel particle passing perpendicular plane portion position pressure principle PROP prove quantities radius ratio resolved respect rest resultant shew space sphere square suppose surface uniform varies velocity vertical weight

### Popular passages

Page 505 - A uniform ladder, 10 feet long, rests with one end against a smooth vertical wall and the other on the ground, the coefficient of friction between the ladder and the ground being J.

Page x - D'Alembert, was the Precession of the equinoxes and the Nutation of the earth's axis, according to the theory of gravitation.

Page 238 - Gravitation is, that every particle of matter attracts every other particle with a force which varies directly as the mass of the attracting particle, and inversely as the square of the distance.

Page 4 - ... to be statical. But if the force be estimated by the magnitude of the motion generated in a body which it causes to move, the estimate is dynamical. 10. Weight is the name given to the pressure which the attraction of the Earth causes a body to exert on another with which it is in contact. Since the gravitation of bodies downwards is unceasing, weight becomes a very useful means of estimating all statical forces. Thus the force of a constrained spring, may be measured by the weight which will...

Page 85 - P act vertically, e - ^ir - a, P - W. 114. The fifth Mechanical Power is the Wedge. This is a triangular prism, and is used to separate obstacles by introducing its edge between them and then thrusting the wedge forward. This is effected by the blow of a hammer or other such means, which produces a violent pressure for a short time, sufficient to overcome the greatest forces.

Page 71 - A Lever is an inflexible rod moveable only about a fixed axis, which is called the fulcrum. The portions of the lever into which the fulcrum divides it are called the arms of the lever : when the arms are in the same straight line, it is called a straight lever, and in other cases a bent lever.

Page 523 - Let us express a in terms of the ratio of the centrifugal force at the equator to the equatorial gravity. Call this ratio m, which is small in the case of the earth, being of the same order as g.

Page 231 - Put 9 = 0 and r = R in the value of - : r By referring to Art. 234, we see that the velocity of a body falling from an infinite distance to a distance R from a centre of force — is equal to \/ —. Hence the orbit described about this centre of force will be an ellipse, parabola, or hyperbola according as the velocity is less than, equal to, or greater than that from infinity. 253. We might make use of the equation to discover the law of force when the orbit is given. Thus if the orbit be a conic...

Page 192 - Mr. Hodgkinson proceeds to describe the methods by which his experiments were made, and derives from them the following nonelusions : 1. All rigid bodies are possessed of some degree of elasticity, and among bodies of the same nature the hardest are generally the most elastic.

Page 385 - A body moves in a groove under the action of two centres of force each varying inversely as the distance, and of equal intensity at the same distance; the body is projected from the mid-point between the centres: prove that if the velocity be uniform the form of the groove is a lemniscate. PROB. 32. A body attracted to two centres of force varying inversely as the square of the distance moves in a hyperbolic groove, of which the foci are the centres of force : required to find the pressure on the...