The telegraph model of Weber-Gauss, relying on Weber's electrodynamics, modeled instantaneous action at a distance of the electric scalar potential (Coulomb potential) manifesting as propagation of signals in a resistanceless wire, through the collective forces of charge carriers in the wire.
Despite seeing many allusions to the notion that there was work on modeling wireless transmission of signals with Weber's electrodynamics I have been unable to locate such a model even for a simple Hertzian dipole acting on a remote test charge. Does such a wireless signaling model exist?
Some relevant background: Maxwell cited Weber's model in a positive light and objected to it because of a faulty critique by Helmholtz to the effect that it necessarily violated conservation of energy. Weber debunked this critique and later Maxwell retracted his critique but, presumably due to the absence of a way to describe electromagnetic energy propagation through space, he left it at that. This is most ironic not only because the speed of light was first described in Weber's work, but also because the vector potential originated with Weber's colleague, Kirchhoff. And that, presumably, contributed to Maxwell's development of his equations.