James Clerk Maxwell
In his paper "A Dynamical Theory of the Electromagnetic Field” (1865) Maxwell proposed a model of the ether, starting out with the original fluid ether and a force acting on it. This force trows the ether into whirls that Maxwell referred to as vortex cells. These vortex cells form a solid medium. Between these cells, there are tiny particles like the molecules of a gas.
The vortex cells are the ultimate cause of magnetism and these particles are the ultimate cause of electric effects.
This model eventually led to the now-famous Maxwell equations that he published in 1873, "A Treatise on Electricity & Magnetism“.
Nikola Tesla
In his lecture of Feb 3rd, 1892, “Experiments with Alternate Currents of High Potential and High Frequency”, Tesla says:
"But he [the experimenter] must remain in doubt as to whether the effects observed are due wholly to the molecules, or atoms, of the gas which chemical analysis discloses to us, or whether there enters into play another medium of a gaseous nature, comprising atoms, or molecules, immersed in a fluid pervading the space. Such a medium, surely must exist,"Tesla mentions the fluid ether and states that in it there must bu a gaseous medium causing electric effects. It is very easy to recognize a part of Maxwell's ether here. Though Tesla openly opposes Maxwell for his transverse electromagnetic waves he seems to agree on what causes electric effects; namely, a gaseous medium immersed in the fluid ether.
I think it would be appropriate to call this medium "electricity". And I would like to stress that these particles do not carry an electric charge. Instead, they cause electric charges.
Longitudinal vs transverse waves
It should now become clear that when Tesla was talking about longitudinal waves he was talking about something different from Maxwell's electromagnetic waves.
If electricity is a gaseous medium, it can only support longitudinal waves. But now we are talking about a medium that can cause electric effects but does not necessarily do so. The density of this medium can increase or decrease without producing any electrical effect. But when this medium does create an electrical effect, that effect would increase or decrease along with the density.
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