The Mathematical Principles of Mechanical Philosophy and Their Application to Elementary Mechanics and Architecture: But Chiefly to the Theory of Universal GravitationJ. & J.J. Deighton, 1842 - 620 من الصفحات |
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طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
a₁ accelerating force angle angular velocity arch attraction axes axis beam calculate catenary centre of gravity co-ordinates coefficient conditions of equilibrium consequence constant cos² couple curve density determine direction distance disturbing force dt dt dx dy Earth ellipse equal equations of motion equilibrium extrados forces acting formulæ friction given Hence horizontal impulsive forces integration law of attraction magnitude mass measured Moon Moon's move orbit P₁ P₂ parallel particle perihelion perpendicular plane point of application position pressure principle PROB PROP pullies quantities radius ratio resolved resultant rigid body shew sin² space sphere spheroid suppose surface syzygy vertical Virtual Velocities vis viva voussoirs weight Y₁
مقاطع مشهورة
الصفحة 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.
الصفحة x - D'Alembert, was the Precession of the equinoxes and the Nutation of the earth's axis, according to the theory of gravitation.
الصفحة 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.
الصفحة 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...
الصفحة 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.
الصفحة 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.
الصفحة 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.
الصفحة 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...
الصفحة 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.
الصفحة 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...