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In 1786, Coulomb announced his law that showed that the electromagnetic force between two charged sources followed an inverse square law.

Given that gravity followed a similar law, did anyone suggest a unified description?

It's worth noting that Priestley twenty years earlier, carrying out an experiment suggested by Benjamin Franklin, and on noting the absence of electrical influence inside a hollow charged sphere said:

May we infer from the experiment that the atteaction of electricity follows the same laws as that of gravity and is therefore according to the inverse square of the distances, since it is easily demonstrated if the earth is in the shape of a shell, a body inside it would not be attracted to one side of it more than the ither side.

However, Priestley wasn't saying that electricity and gravity had a unified description.

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    $\begingroup$ Mossotti, 1830:"if it be assumed that the attractive forces between particles of opposite electrical charge, slightly exceed the repulsive forces of the like particles, a universal tendency for attraction would result". Lorentz developed it quantitatively in 1900. But inverse square law for magnetic poles was known since 1750, and its repeated appearance does not mean much since it derives from a general conservation argument not specific to gravity. $\endgroup$ – Conifold Apr 17 at 20:48
  • $\begingroup$ @Conifold: It means a great deal more than you assume it dors - the argument you are referring to arose from theoretical considerations of the inverse square law. $\endgroup$ – Mozibur Ullah Apr 17 at 20:54
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Clifford 1876 conjectured all motion results from a curvature of space, in which the unification of the OP's two specific examples is implicit. I'll hereafter discuss subsequent attempts to mathematize the details of electromagnetism/gravity unification.

An attempt to explain inertial mass in terms of electromagnetism began in 1881. In 1900, it was suggested this could also cause gravity, with inertial mass equaling gravitational mass.

The earliest attempt to explain both forces from a common origin (rather than as one resulting from the other) was Nordström, Gunnar (1914). "On the possibility of unifying the gravitational and electromagnetic fields". Phys. Zeitschr. 15: 504.. You can find the original German version here, and a translation here. The latter provides context for modern readers, in the form of an abstract and a notation-modernizing appendix.

Nordström discusses no prior interest in unifying electromagnetism and gravity, prior suspicion such a unification is possible or should be attempted, or prior work to that end. What he does mention is work the previous year by him and Mie on a special relativistic (but pre-GR) theory of gravity, lacking unification with electromagnetism. Nor can I find any discussion of the history of such unification research that implies any work beyond Nordström's predates the much more famous, slightly more recent work of Kaluza & Klein.

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  • $\begingroup$ There is a wikipedia article on Electromagnetic mass: such views were not uncommon in the late 19th c. and some attempts at presenting mass as an effect of electric charge have been made (if I remember correctly Feynman mentions some). Why not count them as únifications"? $\endgroup$ – sand1 Apr 17 at 20:10
  • $\begingroup$ @sand1 Thanks! I've done my best to incorporate that into my answer, though I can't guarantee I've adequately explained it. I've kept the existing description of Nordström 1914, to contrast two notions of "unification". $\endgroup$ – J.G. Apr 17 at 20:27

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