A modification of the Bunnett–Olsen equation of the form: \[\log_{10}(\frac{[\ce{SH^{+}}]}{[\ce{S}]}) - \log_{10}[\ce{H^{+}}] = m^{*}X + \pu{p}K_{\ce{SH}^{+}}\] is the activity function \[\log_{10}(\frac{\gamma_{\rm{S}}\ \gamma_{\rm{H}^{+}}}{\gamma_{\rm{SH}^{+}}})\] for an arbitrary reference base. The function \(X\) is called the excess acidity because it gives a measure of the difference between the acidity of a solution and that of an ideal solution of the same concentration. In practice \[X = -(\rm{H}_{0} + \log_{10}[\rm{H}^{+}])\] and \[m^{*} = 1 - \mathit{\Phi}\]