The zeroth, first and second order perturbed Schrödinger equations for the helium atom in an external electric field have been solved to high accuracy through the variation principle. A ground-state energy, differing by only about 1 part in 10⁹ from Pekeris's extrapolated figure, was obtained with a wave function ϕ₀ containing 181 adjustable parameters (compared to Pekeris's 1078). The first-order wave function ϕ₁, and hence the second-order energy and polarizability of the atom, was obtained with up to 84 adjustable parameters in ϕ₁. The polarizability α is 1.38319 a.u. = 0.204956 × 10^–24 cm³= 0.228044 × 10^–40 C²m² J^–1. The dipole shielding factor differs from its exact value of unity by a few parts in 10⁵. The second-order wave function ϕ₂, and hence the fourth-order energy and hyperpolarizability γ, were obtained for various wave functions ϕ₀ and ϕ₁, and with up to 106 adjustable parameters in ϕ₂. Smooth convergence was obtained, yielding γ= 43.10 a.u. = 2.171 × 10^–38 e.s.u. = 2.688 × 10^–63 C⁴m⁴J^–3. However, an extension to ϕ₁ may be needed before an accurate value of γ can be computed. Accurate values have also been obtained for the δ-values of the unperturbed atom and for the quadrupole and octopole polarizabilities.