In a series of elementary reactions, the changes in Gibbs activation energies are often found to be proportional to the changes in Gibbs energies for the overall reaction.\[\updelta \Delta^{\ddagger}G = \alpha \Delta_{\rm{r}}G^{\circ}\] This relation was interpreted in terms of the simple assumption that a small change in any transition-state property \(P_{\ddagger}\) is a linear combination of changes in reactant- and product-state properties, \(P_{\ce{R}}\) and \(P_{\ce{P}}\). \[\updelta P_{\ddagger} = \alpha \updelta P_{\ce{P}} + (1-\alpha)\updelta P_{\ce{R}}\] Within the limits of this assumption, the parameter \(\alpha\) is an approximate measure of the fractional displacement of the transition state along the minimum-energy reaction path from reactants to products.