Airy points and Bessel points
Airy points are named after Sir George Airy who developed them. They represent points on a beam where gravity will not cause the ends to deflect if the beam sags from gravity. Or, in engineering speak, they induce zero slope at the ends. They are often used to support standard measures like a standard metre rule used for calibration. Surface plates, which are large and very dense blocks of granite or steel that are intended to be perfectly flat, also need precise support, and Airy points are often used. Airy points are intended to keep the ends perpendicular and square. They will also keep the edges square and flat. Bessel points are named after Friedrich Bessel and do something similar, but they will enable a beam to maintain its length. This is a better option for surface plates in that Bessel points will ensure that the surface stays relatively flat, which is the preferable condition. In practice there is very little between them and either will do. The diagrams show a very exaggerated version of the effects. The change in flatness due to gravity is more pronounced the larger the plate, and the effects are only measurable with some high-precision equipment. Professional surface plates are regularly checked and lapped if necessary to maintain their flatness.