Balancing of sights means that:

1
the horizontal angles in the face left and face right conditions of theodolite should be same.
2
the distance corresponding to the fore sight and back sight in differential levelling should be equal.
3
the stadia intercepts corresponding to the upper and lower cross hairs with respect to the middle cross hairs in tachometry should be equal.
4
the error of the loop closure in traverse adjustment should be zero.

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