Who contributed to Maxwell's Equations and how?

[aqwas]

The four equations carry the names of Gauss, Faraday and Ampere, however, I cannot seem to find any information regarding each's involvement in them. Are those names solely due to physical observations made by the person (in the case of Faraday for example) or have they contributed towards the actual mathematics behind them (which I would assume Gauss has)? Exactly what was Maxwell's contribution? As far as I am aware, the initial form of Maxwell's Equations consisted of 20 equations with Maxwell's main contribution being the second term in Ampere's law. Did he formulate the entire (or majority of) mathematics behind electromagnetism or did he simply link all of the previous equations into a single theory?

(Bear in mind, I am not trying to discredit Maxwell in any way)

 

[jtbell]

The Wikipedia pages about the individual equations have brief comments about their history. The footnotes of those pages also have some nuggets of information.

https://en.wikipedia.org/wiki/Gauss's_law
https://en.wikipedia.org/wiki/Gauss's_law_for_magnetism
https://en.wikipedia.org/wiki/Faraday's_law_of_induction
https://en.wikipedia.org/wiki/Ampère's_circuital_law