How to derive this formula??#End correction of meter bridge.

The major systematic errors in this experiment are due to the heating effect, end corrections introduced due to shift of the zero of the scale at A and B, and stray resistances in P and Q, and errors due to non-uniformly of the meter bridge wire.
 

Error Analysis

End corrections can be estimated by including known resistances P1and Q1 in the two ends and finding the null point:

  (where a and b are the end corrections).

When the resistance Q1 is placed in the left gap and P1 in the right gap,

which give two linear equation for finding a and b.

In order that aand b be measured accurately, P1 and Q1 should be as different from each other as possible.

For the actual balance point,

Errors due to non-uniformity of the meter bridge wire can be minimized by interchanging the resistances in the gaps P and Q.

Where d and d are the order of the least count of the scale.