Didn't see the reply this late, hopefully you will see mine. He did indeed use quaternions but it's not easy to find: https://archive.org/details/atreatiseonel

Didn't see the reply this late, hopefully you will see mine. He did indeed use quaternions but it's not easy to find: https://archive.org/details/atreatiseonelec02maxwgoog/page/257/mode/2up https://archive.org/details/atreatiseonelec02maxwgoog/page/2... Unfortunately these equations are not quite without mistakes (I remember a missing dot for a time derivative) compared to the component form. They're correct in the wikipedia article: https://en.wikipedia.org/wiki/History_of_Maxwell's_equations#A_Treatise_on_Electricity_and_Magnetism https://en.wikipedia.org/wiki/History_of_Maxwell's_equations... If you replace S.∇ with ∇· and V.∇ with ∇× you essentially get the vector calculus version of the equations. Thank you for extracting the core ideas out of this lengthy text. But I'm still wondering where this very concise present-day formulation with just 4 equations was first written down, even if you can somehow find them scattered around in the book. I found something about Hertz but didn't try to follow up on it, i think he may have only considered a vacuum.