# On Physical Lines of Force: elasticity, density and the speed of light

## Main Question or Discussion Point

Maxwell: -"The ratio of m to mu varies in different substances; but in a medium whose elasticity depend entirely upon forces acting between pairs of particles, this ratio is that of 6 to 5, and in this case E^2= Pi*m"

Q1: What is this 6:5 ratio and how did he make that conclusion?

Q2: What is the importance of "depend entirely... pairs of particles"?

Maxwell: -"To find the rate of propagation of transverse vibrations through the elastic medium, on the supposition that its elasticity is due entirely to forces acting between pairs of particles

[PLAIN]https://www.physicsforums.com/latex_images/26/2647530-2.png [Broken]

where 'm' is the coefficient of transverse elasticity, and 'p' is the density."

Q3: Again this "entirely due to pairs of particles", what is he talking about, is he saying photons are made of particle pairs, or is he describing aether as something like Dirac Sea made of electron-positron pairs, or what?

Q4: Where did he get numerical values for this elasticity 'm' and density 'p', are those two the same numbers as electric and magnetic constant in modern equations?

Q5: Did anyone notice his original "wave equation" is nothing else but the 'wave equation for vibrating string': -"The speed of propagation of a wave in a string (v) is proportional to the square root of the tension of the string (T) and inversely proportional to the square root of the linear mass (μ) of the string:

[PLAIN]https://www.physicsforums.com/latex_images/26/2647530-3.png [Broken]

". - http://en.wikipedia.org/wiki/Vibrating_string

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What are the E and m in the E^2 = pi*m?

"Pairs of particles." The wave equation is often derived using the model of a chain of particles all connected to their neighbors using springs. When he says connected as paris of particles he probably is referring to the fact that the equation assumes a rather pedestrian situation like this (as opposed to something that may have different symmetries of springiness in different direction, etc...)

Did anyone notice his original "wave equation" is nothing else but the 'wave equation for vibrating string
Yep, the derivations are extremely similar. One case you look at particles vertically displaced from their neighbours (restoring force in the small oscillation limit of T*theta) and in the other case you look at particles horizontally displaced from their neighbours (restoring force of k*x)

Hope that was of help. The parts I didn't respond to I don't know how to.

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