Surveying
The correction applied to the measured base of length ‘L’ is

Sag = L³w²/24P² where w is the weight of tape/m
All of these
Slope = (h²/2L) + (h⁴/8L³) where h is height difference of end supports
Tension = (P - Ps)L/AE

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Surveying
The rise and fall method

is not suitable for levelling with tilting levels
is less accurate than height of instrument method
quicker and less tedious for large number of intermediate sights
provides a check on the reduction of intermediate point levels

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