The perturbation formula of Usachev-Gandini for a ratio of reaction rates is newly explained by (a) a formal functional treatment of perturbation theory and (b) the variational principle. At the outset a time-dependent problem is considered, and a perturbation formula of a reaction number ratio is obtained. In a static problem this formula directly turns to a formula of a reaction rate ratio which reduces to the Usachev-Gandini formula when an adiabatic approximation is introduced. It is shown that there is no need to solve iterative equations of successive neutron generations.