I noticed there are two varieties of Maxwell's equations and although I am not sure which form Maxwell originally worked with and perhaps the differential form came much latter, I was wondering if he made use of Green's Theorem. I ask because after reading about Green , I got the impression he was motivated to develop his theorem for trying to understand electrical behavior. I looked at Wiki and James Clerk Maxwell lived from 1831 to 1879 and George Green from 1793 to 1841. Certainly Maxwell was old enough to have read about Green's work before Green passed away.