> I don't have a globe handy, but would somebody check and see if a line drawn from New Hampshire through the center of the earth, would come out close to New Zealand?

Well, it depends on your idea of "close"... :)

No, it will come out somewere between Australia and the Antarctic continent.
Also a map can show it: if you consider the position of NH and NZ and their relative distance from equator and the Greenwich meridiane, it's the same as having NH in the second quadrant and NZ in the fourth quadrant of a Cartesian coordinate system.

AP.