Green the Giant

What should I write about during the off season? I am deep into Classic Jackson and some Quantum problems with little time for fun reading like the burst I had during break. Maybe I will complain about how my sometimes favorite internet radio source, WMUC at University of Maryland, has seemed to be down for two days. I miss my Modest Mouse, Jens Lechman, and the occasional Dylan Hour.
I'm learning a lot of fun things about Green's Theorem and his first identity. Jackson presents this in the "look what happens when I do this" sort of framework. He just puts down a collection of scalar fields and their gradients and laplacians. He says its all based on the divergance theorem, which I believe. However why define the vector in that theorem as a scalar field times the divergance of another scalar field?
I was quietly awed by the Green's accomplishment. His identity and some clever manipulations give us this elegant form for the static potential from any charge distribution with simple support for Dirichlet or Neumann boundary conditions. A simple choice of guage in the Kernel/Green's function eliminates the unknown boundary condition. I wonder what they did for continous charge distributions before they figured this out.