The linearized Boltzmann equation for the hard‐sphere gas is analyzed by comparing the eigenvalues of its relaxation rate with those of the corresponding foreign gas equation. An analysis of the latter, carried out by reduction to a second‐order differential equation, exists elsewhere. It is shown for the angular indices 0 and 1 that the Boltzmann equation has an infinite set of eigenvalues each of which is smaller than the corresponding eigenvalue of the foreign gas equation. The basic theorem is also valid for the angular index 2. However, as the properties of the foreign gas equation have not yet been established for this case, only tentative conclusions can be drawn. The two equations share the same continuous spectrum; it covers all values larger than a positive minimum. The discrete series found are asymptotic to the minimum.