I'm going to have to dig further into the attribution of the Telegraphers' Equation to Weber and Kirchhoff in 1857. Prof. Assis has a nice paper on the subject, here:
Assis cites Whittaker as an authority [vol. 1 pp. 230-232]. But by Whittaker's account [pp. 228-229], "...we have an equation first obtained by Oliver Heaviside (1850-1925), namely ... which is known as the equation of telegraphy." Whittaker goes on to describe how Kirchhoff derived a wave equation complete with the speed of light (which may be related to the inductance and capacitance or equivalently the permeability and permittivity), but Kirchhoff's wave equation looks to be a special case that doesn't appear to take into account resistance as in Heaviside's more complete treatment.
I'll see if I can hunt down the other references when I have more time.
It seems to me that there are two different theories of action-at-a-distance here - Newton's with his invisible hand of gravity theory, and Fresnel's with his interference theory. Newton's equation has the big G, while the following equations seem to be converging on something that actually causes that big G. I'm going to go with Fresnel's.
Hi Tim, this is an interesting perspective, vis-à-vis Faraday and Clerk Maxwell, that I will examine in the coming months.
Nevertheless, it was clear during the exchanges between Faraday and Ampère around 1822 that there were serious divergences between the two. This can be seen in multiple parts of AKT Assis and JPMC Chaib, Ampere's Electrodynamics, Montreal: Apeiron, 2015. The passages cited below all come from that book.
Savary and Ampère, 1822:
If M. Faraday, in this passage, considered only that the attractions and repulsions between electric currents are complicated facts due to the fact that they result from an infinity of actions between all infinitely small parts of these currents, then he was in agreement with M. Ampère. However, he [Faraday] considered them complicated from another point of view, as he considered as a primitive fact the rotational action and shows quite well that these attractions and repulsions can be reduced to it. But we have just seen that by considering, on the contrary, as primitive facts the attractions and repulsions between the small portions of electric currents, according to the laws given by M. Ampère, one deduces immediately the circular motions of the conducting wires and magnets around each other. [p.252]
Ampère to Faraday, 1822:
A fundamental and obvious principle of physics is that, the action always being equal to the reaction, it is impossible that a rigid system be put in motion in any way by a mutual action between two of its particles, as this action produces on the two particles two equal and opposite forces which tend to move the body in opposite senses. It then follows that, when the particles of a magnet traversed by an electric current which puts them in the same state of the conducting wire act on the pole or on any other part of the magnet, no motion in this body can result from this action, [...]
From this observation, the rotation of a floating magnet around its axis can only be explained as I did in the memoir included in the May issue of the Annales de Chimie et de Physique, which I sent to you recently. [p.271]
"A speculation touching Electric Conduction and the Nature of Matter" is footnote 5. I gave the initial publication, rather than the reprint in his collected works.
I'm going to have to dig further into the attribution of the Telegraphers' Equation to Weber and Kirchhoff in 1857. Prof. Assis has a nice paper on the subject, here:
https://www.researchgate.net/publication/3452171_Telegraphy_equation_from_Weber's_electrodynamics
Assis cites Whittaker as an authority [vol. 1 pp. 230-232]. But by Whittaker's account [pp. 228-229], "...we have an equation first obtained by Oliver Heaviside (1850-1925), namely ... which is known as the equation of telegraphy." Whittaker goes on to describe how Kirchhoff derived a wave equation complete with the speed of light (which may be related to the inductance and capacitance or equivalently the permeability and permittivity), but Kirchhoff's wave equation looks to be a special case that doesn't appear to take into account resistance as in Heaviside's more complete treatment.
I'll see if I can hunt down the other references when I have more time.
It seems to me that there are two different theories of action-at-a-distance here - Newton's with his invisible hand of gravity theory, and Fresnel's with his interference theory. Newton's equation has the big G, while the following equations seem to be converging on something that actually causes that big G. I'm going to go with Fresnel's.
Fresnel's theory is not based on action-at-a-distance, but, rather, local action.
Thanks John, that makes more sense.
Hi Tim, this is an interesting perspective, vis-à-vis Faraday and Clerk Maxwell, that I will examine in the coming months.
Nevertheless, it was clear during the exchanges between Faraday and Ampère around 1822 that there were serious divergences between the two. This can be seen in multiple parts of AKT Assis and JPMC Chaib, Ampere's Electrodynamics, Montreal: Apeiron, 2015. The passages cited below all come from that book.
Savary and Ampère, 1822:
If M. Faraday, in this passage, considered only that the attractions and repulsions between electric currents are complicated facts due to the fact that they result from an infinity of actions between all infinitely small parts of these currents, then he was in agreement with M. Ampère. However, he [Faraday] considered them complicated from another point of view, as he considered as a primitive fact the rotational action and shows quite well that these attractions and repulsions can be reduced to it. But we have just seen that by considering, on the contrary, as primitive facts the attractions and repulsions between the small portions of electric currents, according to the laws given by M. Ampère, one deduces immediately the circular motions of the conducting wires and magnets around each other. [p.252]
Ampère to Faraday, 1822:
A fundamental and obvious principle of physics is that, the action always being equal to the reaction, it is impossible that a rigid system be put in motion in any way by a mutual action between two of its particles, as this action produces on the two particles two equal and opposite forces which tend to move the body in opposite senses. It then follows that, when the particles of a magnet traversed by an electric current which puts them in the same state of the conducting wire act on the pole or on any other part of the magnet, no motion in this body can result from this action, [...]
From this observation, the rotation of a floating magnet around its axis can only be explained as I did in the memoir included in the May issue of the Annales de Chimie et de Physique, which I sent to you recently. [p.271]
Hi Tim, are you referring to the following papers?
A speculation touching Electric Conduction and the Nature of Matter, Lond. and Edinb. Phil. Mag., 1844, vol. xxiv. .p 136.
On new magnetic actions, and on the magnetic condition of all matter-continued...., Philosophical Transactions, 1846, p. 41.
"A speculation touching Electric Conduction and the Nature of Matter" is footnote 5. I gave the initial publication, rather than the reprint in his collected works.
Michael Faraday, Experimental Researches in Electricity, 3 volumes (1839, 1844, 1855).