This paper, authored by R. Peierls and submitted to the Zentralblatt für Physik on December 8, 1932, explores the theory of diamagnetism in free electrons. The author investigates under what conditions the free energy can be calculated without knowledge of the stationary states of the system. Using the methods developed, Peierls examines the diamagnetic susceptibility of free electrons, its influence from collisions, and the magnetic behavior of bound electrons. The paper also determines the field strengths at which the susceptibility is field-independent. The problem is approached by considering the magnetic moment induced by a magnetic field in a collection of electrons, which consists of two parts: aligning the spins of the electrons and deflecting them from their straight-line motion. For non-relativistic electrons in weak magnetic fields, these effects can be treated separately. Pauli and Bloch studied the first effect for free electrons, while Landau studied the second effect on the motion of a Fermi gas of free electrons. Peierls' work extends Landau's theory, aiming to determine the magnetic behavior of electrons in a periodic potential field, which is more complex than in a free electron gas. The paper highlights the importance of understanding the susceptibility without explicitly knowing the stationary states, as the periodicity of the electron's orbit is lost when electrons are perturbed by irregularities in the lattice, such as thermal motion and impurities. Despite these perturbations, the empirical evidence suggests that the susceptibility is field-independent, indicating that the formation of stationary states may not be necessary for diamagnetism. The author suggests that an approach similar to the classical treatment of the state integral can simplify the problem.This paper, authored by R. Peierls and submitted to the Zentralblatt für Physik on December 8, 1932, explores the theory of diamagnetism in free electrons. The author investigates under what conditions the free energy can be calculated without knowledge of the stationary states of the system. Using the methods developed, Peierls examines the diamagnetic susceptibility of free electrons, its influence from collisions, and the magnetic behavior of bound electrons. The paper also determines the field strengths at which the susceptibility is field-independent. The problem is approached by considering the magnetic moment induced by a magnetic field in a collection of electrons, which consists of two parts: aligning the spins of the electrons and deflecting them from their straight-line motion. For non-relativistic electrons in weak magnetic fields, these effects can be treated separately. Pauli and Bloch studied the first effect for free electrons, while Landau studied the second effect on the motion of a Fermi gas of free electrons. Peierls' work extends Landau's theory, aiming to determine the magnetic behavior of electrons in a periodic potential field, which is more complex than in a free electron gas. The paper highlights the importance of understanding the susceptibility without explicitly knowing the stationary states, as the periodicity of the electron's orbit is lost when electrons are perturbed by irregularities in the lattice, such as thermal motion and impurities. Despite these perturbations, the empirical evidence suggests that the susceptibility is field-independent, indicating that the formation of stationary states may not be necessary for diamagnetism. The author suggests that an approach similar to the classical treatment of the state integral can simplify the problem.