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.
I remember reading a great answer [1] from Stack Exchange, that claims:
> the 1873 treatise used a pre-Heavisde form of vector calculus cannnibalized from Hamilton's quaternions ... only sparingly, to present the equations in capsule summary form.
Thanks for the reply. From your link, I now understand what does "vector calculus cannnibalized from Hamilton's quaternions ... only sparingly" means.
He did indeed use quaternions but it's not easy to find: 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...
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.