What does height really mean? Part III: Height Systems

This is the third paper in a four-part series considering the fundamental question, "what does the word "height" really mean?" The first paper reviewed reference ellipsoids and mean sea level datums. The second paper reviewed the physics of heights culminating in a simple development of the geoid and explained why mean sea level stations are not all at the same orthometric height. This third paper develops the principle notions of height, namely measured, differentially deduced changes in elevation, orthometric heights, Helmert orthometric heights, normal orthometric heights, dynamic heights, and geopotential numbers. We conclude with a more in-depth discussion of current thoughts regarding the geoid.