Bernoulli, Daniel (1700–1782)
Daniel Bernoulli, the son of Johann Bernoulli, was born in Groningen while his father held a chair of mathematics at the university. He was born into a dynasty of mathematicians who were prone to bitter rivalry. His father tried to map out Daniel's life by selecting a wife and a career for him. By the time Daniel was thirteen, his father was reconciled to the fact that his son would never be a merchant, but absolutely refused to allow him to take up mathematics, decreeing that Daniel would become a doctor. Daniel gained his baccalaureate in 1715 and master's degree in 1716 at Basle University, but, while studying philosophy at Basle, he began learning about the calculus from his father and his older brother Nikolas. He studied medicine at Heidelberg in 1718, Strasbourg in 1719, and then returned to Basle in 1720 to complete his doctorate. About this time, he was attracted to the work of William Harvey, On the Movement of Heat and Blood in Animals, which combined his interests in mathematics and fluids. By 1720 his father had introduced him to what would later be called "conservation of energy," which he applied in his medical studies, writing his doctoral dissertation on the mechanics of breathing.
After completing his medical studies in 1721, he applied for a chair at Basle, but like his father before him, he lost out in a lottery. Disappointed with his lack of success, he accepted an invitation from Catherine I, Empress of Russia, to become Professor of Mathematics at the Imperial Academy in St. Petersburg in 1725. Catherine was so desperate to secure Daniel that she agreed to offer a second chair to his brother, Nikolas. Unfortunately, Nikolas died of tuberculosis shortly after arriving in Russia. Despondent over his death, Daniel thought of returning home, but stayed when his father suggested that one of his own students, Leonard Euler, would make an able assistant.
Bernoulli and Euler dominated the mechanics of flexible and elastic bodies for many years. They also investigated the flow of fluids. In particular, they wanted to know about the relationship between the speed at which blood flows and its pressure. Bernoulli experimented by puncturing the wall of a pipe with a small, open-ended straw, and noted that as the fluid passed through the tube the height to which the fluid rose up the straw was related to fluid's pressure. Soon physicians all over Europe were measuring patients' blood pressure by sticking pointed-ended glass tubes directly into their arteries. (It was not until 1896 that an Italian doctor discovered a less painful method that is still in widespreaduse.) However, Bernoulli's method of measuring air pressure is still used today to measure the airspeed of airplanes. Around the same time, he made yet another fundamental discovery when he showed that the movements of strings of musical instruments are composed of an infinite number of harmonic vibrations, all superimposed on the string.
Another major contribution that Bernoulli made while in Russia was the discovery that whereas a moving body traded its kinetic energy for potential energy when it gained height, a moving fluid traded its kinetic energy for pressure. In terms of mathematical symbols, the law of conservation of energy becomes:
where P is pressure, ρ is the density of the fluid and v is its velocity. A consequence of this law is that if the pressure falls, then the velocity or the density must increase, and conversely. This explains how an airplane wing can generate lift: the air above a wing travels faster than that below it, creating a pressure difference.
By 1730 Bernoulli longed to return to Basle, but despite numerous attempts, he lost out in ballots for academic positions until 1732. However, in 1734 the French Academy of Sciences awarded a joint prize to Daniel and his father in recognition of their work. Johann found it difficult to admit that his son was at least his equal, and once again the house of Bernoulli was divided.
Of all the work that Bernoulli carried out in Russia, perhaps the most important was in hydrodynamics, a draft account of which was completed in 1734. The final version appeared in 1738 with the frontispiece "Hydrodynamica, by Daniel Bernoulli, Son of Johann." It is thought that Daniel identified himself in this humble fashion in an attempt to mend the conflict between himself and his father. Hydrodynamica contains much discussion on the principle of conservation of energy, which he had studied with his father since 1720. In addition, it gives the basic laws for the theory of gases and gave, although not in full detail, the equation of state discovered by Johannes Van der Waals a century later. A year later, his father published his own work, Hydraulics, which appeared to have a lot in common with that of his son, and the talk was of blatant plagiarism.
Hydrodynamica marked the beginning of fluid dynamics—the study of the way fluids and gases behave. Each particle in a gas obeys Isaac Newton's laws of motion, but instead of simple planetary motion, a much richer variety of behavior can be observed. In the third century B.C.E., Archimedes of Syracuse studied fluids at rest, hydrostatics, but it was nearly 2,000 years before Daniel Bernoulli took the next step. Using calculus, he combined Archimedes' idea of pressure with Newton's laws of motion. Fluid dynamics is a vast area of study that can be used to describe many phenomena, from the study of simple fluids such as water, to the behavior of the plasma in the interior of stars, and even interstellar gases.
After the dispute with his father in 1734, Daniel Bernoulli lost much of his drive to study mathematics and turned his attention to medicine and physiology. Finally, in 1750, Daniel was appointed chair of physics at Basle, where he taught until his death on March 17, 1782.
Bibliography
Bell, E. T. (1965). Men of Mathematics. London: Penguin. Cannon, J. T., and Dostrovsky, S. (1981). The Evolution of Dynamics: Vibration Theory from 1687 to 1742. New York: Springes.
Fauvel, J., and Gray, J. (1987). The History of Mathematics. Houndmills, United Kingdom: Macmillan.
Hollingdale, S. (1983). Makers of Mathematics. London: Pelican.
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