The measured variance is obtained as,

(33.5)

The equation shows that the contribution due to the thermal fluctuation decreases with the increase in number of modes n and that due to the

(33.6)

Measurement error also results in over estimation of the length of the filament. This overestimation too inserts slight bias in the estimation of the persistence length. If L' is as measured using equation 32.10, then we have

(33.7)

Averaging this expression over the N+1 independent and putting , and using lowest order in ,

(33.8)

Because we use  in equation 16, is overestimated by a factor .