We extend previous work on the algebraic first-order moments of polarization profiles of hydrogen lines in the presence of external fields, to include the effect of configuration mixing induced by the applied fields. An algebraic formula for hydrogen line shifts due to the quadratic Stark effect is derived, under the assumption that the applied electric field is weak enough that line quenching induced by field ionization can be neglected. The derivation of such a formula is made possible by an aimed use of standard techniques of projection-operator algebra and of the fundamental implications of the spectral theorem. The results of this paper should help in decreasing the amount of numerical work needed in the calculation of line shifts of hydrogen lines induced by the presence of electric fields, as the preliminary numerical calculation of the Hamiltonian eigenvalues and eigenvectors is avoided, thus making calculations tractable for lines of higher hydrogen series than considered so far, e.g., in applications of pressure-broadening theory. (C) 1998 American Institute of Physics.