The limit of length of the offset is below 15 and should not increase 15 m if its direction is set simply by eye or by tape.

**However, the length of offset mainly depends upon:**

(i) The scale of the plan

(ii) The accuracy desired

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(iii) The maximum permissible error in eye judgement in laying out the direction of the offset and

(iv) The error in chaining.

In fig. 3.5 let AB be the chain line and P the point upto which the offset is to be measured. D is the correct position of the foot of the perpendicular from P and PD is the correct length of the offset. But while laying, CP is considered to be the direction of the α^{0}. C being the foot of the perpendicular CP is the measured length of offset (say l).

While plotting, the measured length of the offset (l), is set out at right angles to AB at C, so that the point P is displaced to P’ and the amount of displacement PP’ is approximately equal l sin α to I sin α on the ground and on the paper, where s m to 1 cm is the scale of the paper. The length of the offset should be limited to such an amount that this displacement should not be appreciable on the paper. It is assumed that the smallest distance on the paper which can be distinguished while plotting is 0.025 cm.

= 0.025 cm (Eqn. 3.1)

**The displacement of the point in a direction perpendicular to the chain line: **

= CP’ – PD = I-I cos α

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=l (1- cos α) on the ground

This is very small and hence negligible.

Putting the values of α (the angular error) and s (the scale) in the above equations, the limiting length of the offset (l) can be found out.

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**Errors in Length and Direction Combined: **

Sometimes the error in measuring the length of the offset also occurs. In that case, referring to the Fig. 3.6.

If CP= the true length of the offset

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CP’=I= the measured length of the offset.

CP’’=I= the length of the offset as plotted on paper

α= the angular error in direction

Putting the value of n, α and s, the limiting length of the offset (I) can be found out.