No, it doesn't matter which direction the cities are from each other. The calculations assume that the earth is spherical so the calculations work because a gr

No, it doesn't matter which direction the cities are from each other. The calculations assume that the earth is spherical so the calculations work because a great circle will pass between the cities even if they lie at the same latitude. The calculations also assume that the well and the pole lie on a radius of the earth, that is, that they are straight up and down; this can be determined with a simple plumb line. The calculations also assume that the shadow cast by the pole lies on the line between the two cities, but this is always true if the well is pointing straight at the sun. Note that the well in the first city is pointing straight at the sun at a particular time (noon on the summer solstice). Why is this time important? Because it can be accurately determined in the second city without clocks, with accurate clocks (or communication to synchronize the observations) this measurement could be made between any cities at any time as long as the sun was shining straight down the well of one of the cities at that time.