The Cavendish Torsion Balance Experiment and Determination of the Gravitational Constant | 卡文迪许扭秤实验与引力常量测定

📚 The Cavendish Torsion Balance Experiment and Determination of the Gravitational Constant | 卡文迪许扭秤实验与引力常量测定

Nearly a century after Newton proposed his law of universal gravitation, the constant G remained unknown. It was Henry Cavendish’s torsion balance experiment in 1798 that first measured the tiny gravitational attraction between laboratory masses, allowing the density of Earth and, later, the gravitational constant to be determined. This experiment is a classic example of precise measurement with a delicate instrument and remains a key topic in physics examinations.

在牛顿提出万有引力定律近一个世纪后，引力常量 G 仍然是未知的。1798年，亨利·卡文迪许通过扭秤实验首次测量了实验室物体之间微小的引力，从而推算出地球密度，后来人们进一步由此计算引力常量。该实验是精巧仪器精确测量的经典范例，也是物理考试的重点内容。

1. Historical Background and Newton’s Law of Gravitation | 历史背景与牛顿引力定律

Newton’s law of universal gravitation states that two masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of their distance:

牛顿的万有引力定律指出：两个物体相互吸引，引力大小与质量乘积成正比，与距离平方成反比。

F = G m₁m₂ / r²

The symbol G is the gravitational constant. In Newton’s time its value was entirely unknown, because the gravitational force between ordinary laboratory masses is far too small to be felt directly. The same law that governs the orbits of planets must also act between two lead balls, but measuring that force required a uniquely sensitive instrument.

其中 G 为引力常量。在牛顿时代，G 的数值完全未知，因为普通实验室物体之间的引力极其微弱，无法直接感受。支配行星轨道的定律同样作用于两个铅球之间，但要测量这种力需要极其灵敏的仪器。

The original design of the torsion balance is credited to the Reverend John Michell. After Michell died, Cavendish obtained his apparatus, rebuilt it, and carried out a series of careful measurements that became known as the Cavendish experiment.

扭秤的最初设计归功于约翰·米歇尔牧师。米歇尔去世后，卡文迪许获得了他的装置，加以重建，并完成了一系列精细测量，这便是有名的卡文迪许实验。

2. The Torsion Balance: Apparatus and Core Principle | 扭秤装置与核心原理

The torsion balance consists of a light horizontal rod suspended at its centre by a thin wire or fibre. Two equal small lead spheres are fixed to the ends of the rod. Two large lead spheres are then brought near

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