# 4.8. Calculation of the Difference Between F Pillar and Absolute Pillar

If \(F_v\) is the magnetude of the magnetic vector at the primary absolute pillar, and \(p = F_v-F_s\) is the constant magnetic vector difference between the primary pillar and auxiliary pillar used to measure scalar F, then:

If we set \(F_s = F_s^0 + \delta\) , where \(F_s^0\) is constant typical value and the \(\delta\) is time-dependent variation

\(F_v-F_s\) is the scalar pier difference at any moment in time. The variable terms are \((F_v+F_s)\) and \(2\delta.p\). In some situations, such as auroral observatories on highly-magnetic volcanic rock, \(\delta\) and/or p may be large, and \(F_v-F_s\) may show a measureable variation. In this case a simple scalar pier correction is not sufficient. This can be tested by measuring the total field at both locations for some time with some variation in \(\delta\). If there is no variation in \(F_v-F_s\) outside the measurement noise then a simple scalar correction is acceptable. Otherwise a vector pier correction needs to be determined and applied. The simplest determination of p is by direct vector measurement using variometer corrections. If this is not possible or convenient, then it may be possible to determine p by a multi-linear regression of \((F_v^2 - F_s^2)\) against \(\delta\) as measured by a variometer.

The application of this vector pier correction then requires reasonably calibrated variometer data to remove the first order changes in \(F_v-F_s\).