Abstract
The first electrostatics was for Maxwell but a mere blueprint; the second electrostatics, which we now explain, is, instead, a developed theory, to which its author returned on several occasions. More closely than the first theory, it is inspired by views of Faraday and especially Mossotti on the constitution of dielectrics.
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Notes
- 1.
M. Faraday , An Answer to D \({}^\textit{r}\) Hare’s Letter on Certain Theoretical Opinions (Sillimann’s Journal, vol. XXXIX, p. 108 à 120; 1840.— Faraday ’s Experimental Researches in Electricity, vol. II, p. 262).
- 2.
Mossotti , Recherches théoriques sur l’induction électrostatique envisagée d’après les idées de Faraday (Bibliothèque universelle, Archives, t. VI, p. 195, 1847).
- 3.
J. Clerk Maxwell , On Physical Lines of Force , Part III: The Theory of molecular Vortices applied to statical Electricity (Philosophical Magazine, January and February 1862.— Scientific Papers , vol. I, p. 491).
- 4.
The sign \(-\), in the second member of Eq. (4.1a), comes, as we shall see later, from a clerical error.
- 5.
[ibid., p. 492].
- 6.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 495. From equations
$$\begin{aligned} R=-2\pi m a(e+2f), \end{aligned}$$(100)$$\begin{aligned} h=\frac{a e}{2\pi }, \end{aligned}$$(103)Maxwell derives the equation
$$\begin{aligned} R=4\pi ^2m\frac{e+2f}{e}h. \end{aligned}$$(104)Moreover, this whole memoir of Maxwell is literally riddled with sign errors.
- 7.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 482.
- 8.
[ibid.].
- 9.
J. Clerk Maxwell , A Dynamical Theory of the Electromagnetic Field , read at the Royal Society of London on 8 December 1854 (Philosophical Transactions, vol. CLV.— Scientific Papers , vol. I, p. 526).
- 10.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 563.
- 11.
J. Clerk Maxwell, Ibid. , vol. I, p. 531.
- 12.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 558.
- 13.
Ibid., vol. 1, p. 561.
- 14.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 561, equality (G).
- 15.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 496.
- 16.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 497.
- 17.
Ibid., vol. I, p. 497, equality (115).
- 18.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 497.
- 19.
In this passage, Maxwell reasons always as if \(E^2\) had the same value throughout all of space; but one can easily free his reasonings from this hypothesis.
- 20.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 563.
- 21.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 568.
- 22.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 497, 498.
- 23.
The reader will easily avoid any confusion between the coefficient \(E^2\) and the surface density \(E\).
- 24.
- 25.
J. Clerk Maxwell , Scientific Papers , vol. I, pp. 566 Ã 568.
- 26.
Loc. cit., p. 568, equalities (D).
- 27.
In reality, Maxwell wrote
$$\begin{aligned} \varPsi _2=\frac{K}{4\pi }\frac{q_2}{r}, \end{aligned}$$[loc. cit., equality (43)]; but this sign error is offset by a sign error in equality (44).
- 28.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 500.
- 29.
J. Clerk Maxwell , Scientific Papers , vol. I, p. 572.
- 30.
Loc. cit., p. 572, equality (48).
- 31.
Loc. cit., p. 560, equalities (E).
- 32.
Loc. cit., p. 568.
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Duhem, P.M.M. (2015). The Second Electrostatics of Maxwell. In: The Electric Theories of J. Clerk Maxwell. Boston Studies in the Philosophy and History of Science, vol 314. Springer, Cham. https://doi.org/10.1007/978-3-319-18515-6_4
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