The rigorously solvable (quadratic in Fermi creation and annihilation opreators) part of the Hamiltonian of the 1D Ising model ( S = $) with an infinite radius of interaction is studied in a transversal magnetic field H . After diagonalization of the Hamiltonian, an analytical and numerical investigation is made for the spectrum and some basic thermodynamic quantities a t two longrange interaction laws. The spectrum has some peculiarities; the energy gap vanishes only in the centre of the zone at H = H,, which leads t o singularities in some quantities and is reflected in the phase transition in the model considered. Some dependences of the thermodynamic quantities on H and on the coupling constants are obtained from the numerical data. PaccMoTpeHa Tom0 peruaeMaR (KBanpaTHsHaR no cDepMH onepaTopaM pomneamzr