A PBS documentary Inside Einstein's Mind presents results of a time dilation measurement (at minute 39:10) when a pair of atomic clocks at MIT were calibrated to each other after which one was driven by car to the top of Mt Sunapee in New Hampshire. The Mt Sunapee clock stayed up at that higher Earth altitude for four days, after which it was driven back to MIT. The comparison between the two clocks showed the speeding up of the higher altitude clock (lower gravitational field at mountain top) relative to the slower clock held at sea level at MIT (stronger gravitational field). The meausured difference was 20 nanoseconds.
What follows is an attempt to theoretically calculate this 20 nanoseconds using General Relativity. The relevant theory needed for the time dilation calculations is described in a primer
These calculations are completed and their transfer to the web is ongoing and will be forthcoming.