The linear free-energy relation \[\log _{10}k_{\rm{N}} = \log _{10}k_{0}+N_{\rm{+}}\] applied to the reactions between nucleophiles and certain large and relatively stable organic cations, e.g. arenediazonium, triarylmethyl and aryltropylium cations in various solvents. \(k_{\rm{N}}\) is the rate constant for reaction of a given cation with a given nucleophilic system (i.e. given nucleophile in a given solvent). \(k_{0}\) is the rate constant for the same cation with water in water, and \(N_{\rm{+}}\) is a parameter which is characteristic of the nucleophilic system and independent of the cation. A surprising feature of the equation is the absence of a coefficient of \(N_{\rm{+}}\), characteristic of the substrate (cf. the \(s\) in the Swain–Scott equation), even though values of \(N_{\rm{+}}\) vary over 13 log units. The equation thus involves a gigantic breakdown of the reactivity–selectivity principle. The equation has been extended both in form and in range of application.