Bessel points Airy points

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a beam supported @ bessel points has maximum length.



one end of prototype metre bar, example of line standard. fine line marked on polished section of central rib marks 1 end.


line standards measured between lines marked on surfaces. less convenient use end standards but, when marks placed on neutral plane of beam, allow greater accuracy.


to support line standard, 1 wishes minimise linear, rather angular, motion of ends. bessel points (after friedrich bessel) points @ length of beam maximized. because maximum, effect of small positioning error proportional square of error, smaller amount.


the bessel points located 0.5594 of length of rod apart, closer airy points.


because line standards invariably extend beyond lines marked on them, optimal support points depend on both overall length , length measured. latter quantity maximized, requiring more complex calculation. example, 1927–1960 definition of metre specified international prototype metre bar measured while supported on 2 cylinders of @ least 1 centimetre diameter, symmetrically placed in same horizontal plane @ distance of 571 mm each other. bessel points of beam 1020 mm long.








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