Surveying
The difference between a level line and a horizontal line is that

level line is a curved line while hori-zontal line is a straight line
horizontal line is normal to plumb line while level line may not be normal to the plumb line
level line is normal to plumb line while horizontal line may not be normal to plumb line at the tangent point to level line
both are same

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Surveying
Normal tension is that pull which

makes the correction due to pull equal to zero
makes the correction due to sag equal to zero
is used at the time of standardising the tape
neutralizes the effect due to pull and sag

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