  Lagrangian perturbation theory for cosmological fluid describes structure
formation in the quasi-nonlinear stage well. In a previous paper, we presented
a third-order perturbative equation for Lagrangian perturbation with pressure.
There we considered only the longitudinal modes for the first-order
perturbation. In this paper, we generalize the perturbation, i.e., we consider
both the longitudinal and the transverse modes for the first-order
perturbation. Then we derive third-order perturbative equations and solutions.
