Planck's Law and the Light Quantum Hypothesis. By Bose (Dacca University, India). (Received on July 2, 1924.) The phase space of a light quantum with respect to a given volume is divided into cells of size $ h^3 $. The number of possible distributions of light quanta of a macroscopically defined radiation into these cells provides the entropy and thus all thermodynamic properties of the radiation. Planck's formula for the distribution of energy in blackbody radiation serves as the starting point for quantum theory, which has developed over the past 20 years and has yielded rich results in all areas of physics. Since its publication in 1901, many derivations of this law have been proposed. It is widely accepted that the fundamental assumptions of quantum theory are incompatible with the laws of classical electrodynamics. All previous derivations use the relation $ \mathbf{q}_{\mathbf{r}}d\nu = \frac{8\pi\mathbf{v}^{2}d\mathbf{v}}{c^{3}}E $, which relates the radiation density to the average energy of an oscillator, and make assumptions about the number of degrees of freedom of the aether, as reflected in the first factor of the right-hand side of the equation. This factor could only be derived from classical theory, which is the unsatisfactory point in all derivations. It is not surprising that efforts have been made to provide a derivation free from this logical error. Einstein provided a remarkably elegant derivation. He recognized the logical flaw in all previous derivations and attempted to deduce the formula independently of classical theory. Starting from simple assumptions about the energy exchange between molecules and radiation field, he derived the relation $ \varrho_{\nu} = \frac{\alpha_{mn}}{\frac{\varepsilon_{m}-\varepsilon_{n}}{e^{\frac{k T}{k T}}-1}} $. However, to reconcile this formula with Planck's, he had to use Wien's displacement law and Bohr's correspondence principle. Wien's law is based on classical theory, and the correspondence principle assumes that quantum theory agrees with classical theory in certain limiting cases. In all cases, I find the derivations insufficiently logically justified. In contrast, the light quantum hypothesis combined with statistical mechanics (as adjusted by Planck to meet the needs of quantum theory) seems sufficient for deriving the law independently of classical theory. In the following, I will briefly sketch the method. The radiation is confined to a volume V, and its total energy E is given. There are different types of quanta with respective numbers $ N_s $ and energies $ h\nu_s $. The total energy E is then $ E = \sum_{\varepsilon} N_{\varepsilon} h \nu_{\varepsilon} =Planck's Law and the Light Quantum Hypothesis. By Bose (Dacca University, India). (Received on July 2, 1924.) The phase space of a light quantum with respect to a given volume is divided into cells of size $ h^3 $. The number of possible distributions of light quanta of a macroscopically defined radiation into these cells provides the entropy and thus all thermodynamic properties of the radiation. Planck's formula for the distribution of energy in blackbody radiation serves as the starting point for quantum theory, which has developed over the past 20 years and has yielded rich results in all areas of physics. Since its publication in 1901, many derivations of this law have been proposed. It is widely accepted that the fundamental assumptions of quantum theory are incompatible with the laws of classical electrodynamics. All previous derivations use the relation $ \mathbf{q}_{\mathbf{r}}d\nu = \frac{8\pi\mathbf{v}^{2}d\mathbf{v}}{c^{3}}E $, which relates the radiation density to the average energy of an oscillator, and make assumptions about the number of degrees of freedom of the aether, as reflected in the first factor of the right-hand side of the equation. This factor could only be derived from classical theory, which is the unsatisfactory point in all derivations. It is not surprising that efforts have been made to provide a derivation free from this logical error. Einstein provided a remarkably elegant derivation. He recognized the logical flaw in all previous derivations and attempted to deduce the formula independently of classical theory. Starting from simple assumptions about the energy exchange between molecules and radiation field, he derived the relation $ \varrho_{\nu} = \frac{\alpha_{mn}}{\frac{\varepsilon_{m}-\varepsilon_{n}}{e^{\frac{k T}{k T}}-1}} $. However, to reconcile this formula with Planck's, he had to use Wien's displacement law and Bohr's correspondence principle. Wien's law is based on classical theory, and the correspondence principle assumes that quantum theory agrees with classical theory in certain limiting cases. In all cases, I find the derivations insufficiently logically justified. In contrast, the light quantum hypothesis combined with statistical mechanics (as adjusted by Planck to meet the needs of quantum theory) seems sufficient for deriving the law independently of classical theory. In the following, I will briefly sketch the method. The radiation is confined to a volume V, and its total energy E is given. There are different types of quanta with respective numbers $ N_s $ and energies $ h\nu_s $. The total energy E is then $ E = \sum_{\varepsilon} N_{\varepsilon} h \nu_{\varepsilon} =