This paper shows that Max Planck changed the usage of the Boltzmann principle S = k log W from its original way, in which he applied the entropy expression directly into a thermodynamic relation while Boltzmann did not. The originality of my claim is based on the aspect that it focuses on the difference in the usage of the principle between the two, while the former literature has mainly emphasized on the conceptual difference. The main support for my claim is the analysis of the structure of Boltzmann's famous 1877 paper and that of Planck's investigations on black-body radiation.

In Boltzmann's writings, there are three examples in which he referred to the Boltzmann principle. First, he proposed the relation between S and W to derive the Maxwell distribution for gases in 1877, where W means ways of distributing energy into each molecule in a gas. The state with the largest value of W corresponds to the one in thermal equilibrium. By taking the continuous limit of kinetic energy, he obtained the continuous limit of S. The maximization of the limit had been already known by Boltzmann and led to the Maxwell distribution for gases. Later, in his Lectures on gas theory (1896), he used the principle similarly. Another example is found in the paper published in 1883, in which he applied the principle to maximize the total number of possible combinations of dissociated and undissociated molecules.

In contrast to Boltzmann, Planck adopted the strategy to combine Boltzmann's new expression of entropy with the thermodynamic relation 1/θ = dS/dU without maximizing it. Planck had mastered thermodynamic methods from the very beginning of his career. It can be assumed that this experience helped him to apply the Boltzmann principle to the thermodynamic relation. For instance, in his paper ``On the theory of the laws of the energy distribution in the normal spectrum'' (1901), the definition of W was the number of ways to distribute energy into resoantors in equilibrium, in which the unit of energy epsilon was introduced as an essential trick. The entropy determined was then substituted into the relation 1/θ = dS/dU, where U is the energy of resonators and led to the Planck radiation law. This method, which is in contrast to Boltzmann's original usage of the principle, can also be found in his Lectures on the theory of thermal radiation (1906) and other papers.