Daniel Bernoulli (1700-1772) is known for his masterpiece Hydrodynamica (1738), which presented the original formalism of "Bernoulli's Theorem," a fundamental law of fluid mechanics. Previous historical analyses have assumed that Daniel solely used the controversial principle of "conservation of vis viva" to introduce his theorem in this work. The "vis viva controversy" began in the 1680s between Cartesians, who defended the importance of momentum, and Leibnizians, who defended vis viva, as the basis of mechanics. In the 1720s, various Newtonians entered the dispute and sided with the crucial role of momentum. Since then, historians believed that 18th century natural philosophers regarded "vis viva" as incompatible with and opposed to Newtonian mechanics. This article argues that to introduce his theorem, Bernoulli not only used the principle of the conservation of vis viva but also the acceleration law, which originated in Newton's second law of motion. By looking at how eighteenth century scholars actually solved the challenging problems of their period instead of looking only at their philosophical claims, this paper shows the practice of mechanics at that time was far more pragmatic and dynamic than previously realized.
In 1916 Einstein considered a thermal equilibrium between blackbody radiation and gas molecules in a cavity. On this occasion he introduced probability coefficients A and B of spontaneous and induced transitions, respectively. Then, he derived the ratio A/B (Eq. (4) in the text). With respect to this, Planck, in the fourth edition of his book (1921), Lectures on the Heat Radiation, derived the individual equation of A (Eq. (13)). Furthermore, it is quite interesting that in the course of derivation Planck introduced the substitution of a difference quotient (Eq. (11)) for a differential one (Eq. (9)). Thus, it should be noted that Planck employed this mathematical manipulation earlier than Kramers. This paper also argues that Planck's idea of difference quotient stems from the energy fluctuation based on the Fokker equation (7).