
First was Newton. He published his "Philosophiæ Naturalis Principia Mathematica" in 1687. This established a law of gravity for the first time.
Next came Coulomb. He established a very similar looking equation for his law of force between two charges.
Then came Ampère. He took the static force law Coulomb had developed and by experimentation added velocity terms to it. This lead to Ampère's law.
Weber then took Ampère's work and advanced, using his experimentation, it to include accelerations.
This is how electrodynamics was born.
Any good theory, especially if it is derived from experiment, can be tested from it's predictions. Here are the predictions from Weber: