Airy points

Three or more support points will not share the load evenly (unless they are hinged in a non-rigid whiffle tree or similar).

A beam supported only in the middle will sag at the ends, making a similar shape but upside down.

Supporting a uniform beam at the Airy points produces zero angular deflection of the ends.

They are much less convenient to use than end standards[5][6] but, when the marks are placed on the neutral plane of the beam, allow greater accuracy.

To support a line standard, one wishes to minimise the linear, rather than angular, motion of the ends.

A uniform beam deflects based on where it is supported. (Vertical sag greatly exaggerated.)
A beam supported at its Airy points has parallel ends.
Vertical and angular deflection of a beam supported at its Airy points.
A beam supported at its Bessel points has maximum length.
One end of a prototype metre bar, an example of a line standard. A fine line marked on the polished section of the central rib marks one end.