The paper by R. Peierls investigates when the free energy in quantum statistics can be calculated without knowledge of the system's stationary states. Using these methods, the paper examines the diamagnetic susceptibility of free electrons, their influence by collisions, and the magnetic behavior of bound electrons. It determines up to which field strengths the susceptibility is field-independent. The magnetic moment induced by a magnetic field in a collection of electrons consists of two components: the alignment of electron spins and the deflection of electrons from their straight-line motion. For conduction electrons, these effects can be treated separately in non-relativistic approximation and in weak magnetic fields. The first effect, responsible for paramagnetism, was studied by Pauli for free electrons. Bloch showed that the behavior of electrons in a periodic potential field is qualitatively similar to that of free electrons. Landau studied the influence of a magnetic field on the motion of a free electron gas. The present investigation extends Landau's theory. It is necessary to extend Landau's theory because the diamagnetism arises from the quantization of electron energy in a magnetic field, leading to periodic classical orbits. However, for electrons in a crystal lattice, this is not the case, and their magnetic behavior may differ qualitively. To resolve this, one would need to know the stationary states of electrons in a lattice and magnetic field. However, calculating these states leads to complex calculations. Therefore, a method to calculate susceptibility without knowing the stationary states is desired. Additionally, the periodicity of the orbit is lost when electrons are deflected by irregular disturbances, which are present in metals. The susceptibility is expected to depend on the field strength, but empirical results do not support this, except for some anomalies in bismuth, which are attributed to other causes. Therefore, it is concluded that the susceptibility can be calculated without explicit knowledge of the stationary states. The classical state integral is used to find the appropriate approach. The classical free energy is given by $ F = -kT \log S $, where $ S $ is the state integral.The paper by R. Peierls investigates when the free energy in quantum statistics can be calculated without knowledge of the system's stationary states. Using these methods, the paper examines the diamagnetic susceptibility of free electrons, their influence by collisions, and the magnetic behavior of bound electrons. It determines up to which field strengths the susceptibility is field-independent. The magnetic moment induced by a magnetic field in a collection of electrons consists of two components: the alignment of electron spins and the deflection of electrons from their straight-line motion. For conduction electrons, these effects can be treated separately in non-relativistic approximation and in weak magnetic fields. The first effect, responsible for paramagnetism, was studied by Pauli for free electrons. Bloch showed that the behavior of electrons in a periodic potential field is qualitatively similar to that of free electrons. Landau studied the influence of a magnetic field on the motion of a free electron gas. The present investigation extends Landau's theory. It is necessary to extend Landau's theory because the diamagnetism arises from the quantization of electron energy in a magnetic field, leading to periodic classical orbits. However, for electrons in a crystal lattice, this is not the case, and their magnetic behavior may differ qualitively. To resolve this, one would need to know the stationary states of electrons in a lattice and magnetic field. However, calculating these states leads to complex calculations. Therefore, a method to calculate susceptibility without knowing the stationary states is desired. Additionally, the periodicity of the orbit is lost when electrons are deflected by irregular disturbances, which are present in metals. The susceptibility is expected to depend on the field strength, but empirical results do not support this, except for some anomalies in bismuth, which are attributed to other causes. Therefore, it is concluded that the susceptibility can be calculated without explicit knowledge of the stationary states. The classical state integral is used to find the appropriate approach. The classical free energy is given by $ F = -kT \log S $, where $ S $ is the state integral.