energy when it gains height. Daniel realised that in a similar way, a moving fluid exchanges its specific kinetic energy for pressure, the former being the kinetic energy per unit volume. Mathematically this law is now written: where P is pressure, ρ is the density of the fluid and u is its velocity. Economics and statistics In his 1738 book Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), Bernoulli offered a solution to the St. Petersburg paradox as the basis of the economic theory of risk aversion, risk premium, and utility. Bernoulli often noticed that when making decisions that involved some uncertainty, people did not always try to maximize their possible monetary gain, but rather tried to maximize "utility", an economic term encompassing their personal satisfaction and benefit. Bernoulli realized that for humans, there is a direct relationship between money gained and utility, but that it diminishes as the money gained increases. For example, to a person whose income is $10,000 per year, an additional $100 in income will provide more utility than it would to a person whose income is $50,000 per year. One of the earliest attempts to analyze a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of inoculation. Physics In Hydrodynamica (1738) he laid the basis for the kinetic theory of gases, and applied the idea to explain Boyle's law. He worked with Euler on elasticity and the development of the Euler–Bernoulli beam equation. Bernoulli's principle is of critical use in aerodynamics. According to Léon Brillouin, the principle of superposition was first stated by Daniel Bernoulli in 1753: "The general motion of a vibrating system is given by a superposition of its proper vibrations." Works Legacy In 2002, Bernoulli was inducted into the International Air & Space Hall of Fame at the San Diego Air & Space Museum. See also Bernoulli's principle Euler–Bernoulli beam equation St. Petersburg paradox Hydrodynamica References Footnotes Works cited (Original entry based on the public domain Rouse History of Mathematics) External links Rothbard, Murray. Daniel Bernoulli and the Founding of Mathematical Economics, Mises Institute (excerpted from An Austrian Perspective on the History of Economic Thought'') 1700 births 1782 deaths Daniel Heidelberg University alumni 18th-century Swiss physicists 18th-century Latin-language writers 18th-century male writers 18th-century Swiss mathematicians Swiss Calvinist and Reformed Christians Mathematical analysts Fluid