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Reblogged by cstanhope@social.coop ("Your friendly 'net denizen"):
niconiconi@mk.absturztau.be wrote:
#TIL Kirchhoff already derived the original transmission line equation in 1857, nearly 20 years before Heaviside. Kirchhoff found a wave equation that makes a signal travel like heat (per Kelvin) but it also reflects at boundaries like a vibrating string, and this wavefront moves at the speed of light. Time to start calling transmission lines "Kirchhoff's third law"? It's mostly forgotten today because of its use of pre-Maxwell E&M based on Newtonian forces without fields (today called "Weber's electrodynamics" and remain on the fringe of research) https://www.ifi.unicamp.br/~assis/Apeiron-V19-p19-25(1994).pdf https://thepilyfe.wordpress.com/wp-content/uploads/2020/07/1.2238887.pdf #electronics
Attachments:
- Eliminating i, one obtains: dE / dT = (8γl)/r (d^2 E) / (dx^2) which is an equation of the same form as the one which determines the conduction of heat in the conductor. Therefore, in the case considered here, the electricity propagates through the metal like heat does. With the assumptions made with regard to the resistance r' in equations (16) and (17), it is easily proved "a posteriori" that (16) and (17) are real solutions of (14) and (15). It is possible to convince oneself without difficulty that (4 / c^2)(di/dt) is infinitely small compared with dE/dx when i and E are taken from (17) and (16). The case in which the ends of the wire are separated from each other, and are subject to two potential values, can be treated in a similar manner as the case where the wire forms a closed loop. In the open circuit, and provided the resistance of the wire is large enough, one finds the same analogy between the conduction of electrity and heat. With Jacobi's resistance standard, a copper wire of 7.62 m length, 0.333 mm diameter, as shown in the previous paper, is: 32γ / (π sqrt(2)) = 2070 For a wire of the same material, the same cross-section, and a length of 100 km this quantity is 0.034, By way of an approximation, it can be treated as infinitely large in the first case, and as infinitely small in the second case. In the first case the electricity propagates like a wave in a taught string, and in the second case it travels like heat. Thomson has examined the motion of el (remote)
- III. THE RATIO OF UNITS AND THE SPEED OF LIGHT During the 1850s and 1860s Weber, Kirchhoff, and Ludwig Lorenz used the constant c_w and found situations in which electromagnetic effects propagate with the speed c_w / sqrt(2). In 1857, Kirchhoff studied electric currents in thin wires and extended media. He found that in media with vanishing resistance, electric currents propagate with speed c_w / sqrt(2). From the value of c_w, determined experimentally by Weber and Kohlrausch in 1856, Kirchhoff recognized that c_w / sqrt(2) is equal to the speed of light. Weber did similar studies and drew the same conclusion at about the same time but independently of Kirchhoff. However, his work was not published until 1864. Kirchhoff and Weber were not studying electromagnetic waves but electric currents in conductors. But it is interesting that, several years before Maxwell, they found electromagnetic effects that propagate with the speed of light. (remote)
