The data from the position grid study are used to examine how the BPM sum signal depends on the beam position. This effect is studied as a function of the beam position along the measured coordinate and also as a function of the beam position transverse to the measured coordinate. The behavior along the measured coordinate is approximately quadratic and the minimum of the parabola can be found to a precision of less than 100~$\mu$m. The position of this minimum depends on the beam position in the direction orthogonal to the measured coordinate. If the orthogonal coordinate is unknown, this contributes an error of order 200~$\mu$m to the position of the minimum. This last conclusion is a little uncertain because there are some outlier data points which have yet to be explained.