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I’ve just put up a copy of my presentation on Cavendish, Maxwell, and the inverse square law of electrostatic repulsion, given at the Making of Measurement Conference in Cambridge last week.

This poses the question of what Maxwell and his student Donald MacAlister, get out of repeating Cavendish’s null experiment on the inverse square law.  The abstract read,

Traditionally, the foundation of the theory of electrostatics has been taken to be Coulomb’s 1785 torsion balance experiments, reified as “Coulomb’s Law”. However, Coulomb’s results, and interpretation, were frequently challenged, notably by Volta and Simon and, as late as 1836, by William Snow Harris.

In the first edition of the Treatise on Electricity and Magnetism (1873), Maxwell acknowledges Coulomb’s experiments as establishing the inverse square law, merely to dismiss them again as demonstrating it only to a rough approximation. Instead he cites the observation that a charged body, touched to the inside of a conducting vessel, transfers all its charge to the outside surface of the vessel, as ‘far more conclusive than any measurements of electrical forces can be’ (#74). This assertion was based on mathematical proof that an exact inverse square law was a necessary condition for electricity to rest in equilibrium on the surface of a conductor.

The following year Maxwell acquired the hitherto unpublished electrical researches of Henry Cavendish, and found that around 1771 Cavendish had conducted a (fairly) rigorous test of the mathematically predicted null result concluding that the negative exponent in the force law could not differ from 2 by more than about 1/50. Maxwell and a research student, Donald McAlister, created their own version of Cavendish’s experiment, achieving a claimed sensitivity of 1/21600. By the second edition of the Treatise (1881) his previous, ‘…far more conclusive than any measurements…’ has become ‘… a far more accurate verification of the law of force [than Coulomb’s]’ (#74). In his draft for the Cambridge Philosophical Society, Maxwell wrote, ‘Cavendish thus established the law of electrical repulsion by an experiment in which the thing to be observed was the absence of charge on an insulated conductor. No actual measurement of force was required. No better method of testing the accuracy of the received law of force has ever been devised’ (my emphasis).

 More recently, Dorling (1974) has explored the sense in which it was rational for Cavendish and Maxwell to generate an entire law from a single (null) data point, while Laymon (1994) has pointed out the circularity of Maxwell’s argument and located the actual measurement in the testing of the sensitivity of the electrometer.

 Taking Laymon’s and Dorling’s critiques on board, and drawing on works and papers by Maxwell, Kelvin, Tait and Harris, this paper will examine how Maxwell and his contemporaries understood what Cavendish had done, what they thought the null method achieved, and the value to them of recreating the experiment.

References

Dorling, Jon. ‘Henry Cavendish’s Deduction of the Electrostatic Inverse Square Law from the Result of a Single Experiment’. Studies in History and Philosophy of Science Part A 4, (1974): 327–48.

Laymon, Ronald. ‘Demonstrative Induction, Old and New Evidence and the Accuracy of the Electrostatic Inverse Square Law’. Synthese 99, (1994): 23–58.

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