## Daniel Bernoulli

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## Bernoulli, Daniel (1700-1782)

# 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 widespread use.) 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.

*Douglas Quinney*

## 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.

## Daniel Bernoulli

# Daniel Bernoulli

**1700-1782**

**Swiss Mathematician and Physicist**

Daniel Bernoulli belongs to that rarefied upper echelon of mathematicians and scientists for whom distinctions between disciplines are largely academic. Trained as a mathematician, he is best known for the application of his ideas to physics as expressed in Bernoulli's principle, which concerns the inverse relationship of pressure and velocity in fluids. Numerous and groundbreaking as his contributions in the field of hydrodynamics were, however, these were far from the full range of the discoveries made by a genius whose work explored realms as diverse as probability, medicine, and music.

Throughout his life, Bernoulli would be locked in competition with his father Johann (1667-1748), professor of mathematics at the University of Groningen in the Netherlands when Bernoulli was born. As he became aware of his second son's great talents, Johann would become increasingly jealous; yet the Bernoulli family, whose native land was Switzerland, was filled with men of distinction. Johann's brother Jakob (1654-1705) held the chair of mathematics at the University of Basel, a position Johann took over when Daniel was five.

As he progressed with his education, Daniel demonstrated abilities that made him a standout even within the Bernoulli family. At age 16, he had already earned a master's degree, which so inflamed Johann's jealousy that he forbade his son from a career in the sciences. The closest Daniel could come to a scientific career was to study medicine, and there too he excelled. His first love was mathematics, however, and he continued to study the subject in Italy during the early 1720s. He gained his first fame in 1724, with the publication of *Exercitationes quaedam mathematicae, *which contained his first discussions in the areas of probability and fluid motion—areas in which he was destined to make his most lasting impact.

On the strength of this widely recognized publication, Bernoulli received an appointment to the St. Petersburg Academy in Russia, where he was joined by his brother Nikolaus (1695-1726). More honors were to follow, as in 1725 he won the first of nine prizes from the French Académie Royale des Sciences. While in St. Petersburg, Bernoulli produced important studies in the field of probability, and began a correspondence with his distinguished compatriot Leonhard Euler (1707-1783). Eventually he grew homesick, and in 1737 accepted a professorship in botany—a subject of limited interest to him—simply because it would give him an opportunity to return to Basel.

Back in Switzerland, Bernoulli devoted himself to a wide array of undertakings, the most notable of which was *Hydrodynamica,* published in 1738. (Ever jealous, Johann later published his own *Hydraulica,* which he retroactively dated to 1732 and in which he appropriated many of his son's discoveries as his own.) *Hydrodynamica *contains Bernoulli's principle, which states that the pressure of a fluid decreases as its velocity increases. Also in *Hydrodynamica,* Bernoulli confirmed Boyle's law on the inverse relationship of pressure and volume; and by relating the ideas of pressure, motion, and temperature, he laid the foundations for the kinetic theory of gases that would emerge in the following century.

Bernoulli became a professor of physiology in 1743, and seven years later was appointed to the chair of natural philosophy, or physics, in Basel. He remained in that position until his retirement in 1776, and during those years continued to develop his seminal ideas on kinetic energy—then called *vis viva,* or "living force." He also conducted a number of musical experiments, calculating frequencies and demonstrating the relationship between mathematics and music. Bernoulli died in Basel on March 17, 1782.

**JUDSON KNIGHT**

## Bernoulli, Daniel (1700-1782)

# Bernoulli, Daniel (1700-1782)

*Dutch-born Swiss physicist*

Daniel Bernoulli's work on fluids pioneered the sciences of hydrodynamics and **aerodynamics** . Born in the Netherlands and spending most of his life in Switzerland, Bernoulli was one of a large family of scientists and mathematicians that included his father, Jean Bernoulli, and uncle, Jacques Bernoulli.

Ignoring his family's pleas to enter the world of business, Bernoulli pursued a degree in medicine and then, after graduation, a career as a professor of mathematics. He began teaching in 1725 at a college in St. Petersburg, Russia, eventually returning to Switzerland in 1732. While a professor at the University of Basel, he became the first scientist outside of Great Britain to fully accept Newtonian **physics** . It was also here that Bernoulli performed the research on fluid behavior that would make him famous.

The 1738 publication *Hydrodynamica* developed the prominent theories of hydrodynamics, or the movement of **water** . Paramount among these was the fact that, as the velocity of a fluid increases, the pressure surrounding it will decrease. Called **Bernoulli's principle** , this pressure drop was also shown to occur in moving air, and it is the reason boats and planes experience lift as water or air passes around them. This effect is easily shown by blowing between two pieces of paper; the drop in pressure will cause the papers to bend toward each other. Bernoulli's research marked the first attempt to explain the connection pressure and **temperature** have with the behavior of gas and fluids.

Bernoulli's experiments with fluids caused him to devise a series of hypotheses about the nature of gases. He was certainly one of the first to formulate principles dealing with gases as groups of particles, which later became the basis for atomic theories. As groundbreaking as this work was, it was paid little attention by his peers, and subsequently it was nearly a century before the **atomic theory** rose again.

** See also ** Atmospheric pressure; Atomic theory; Hydrostatic pressure

## Daniel Bernoulli

# Daniel Bernoulli

The Swiss mathematician and physicist Daniel Bernoulli (1700-1782) is best known for his work on hydrodynamics, but he also did pioneering work on the kinetic theory of gases.

Daniel Bernoulli was born on Jan. 29, 1700, in Gröningen, Netherlands. He was the second son of Jean Bernoulli, a noted mathematician who began the use of "*g*" for the acceleration of gravity.

When Daniel was 11, he became the pupil of his 16-year-old brother, Nicholas. He continued his studies in Italy until he was 24 and received a doctorate in medicine. The following year he went to St. Petersburg, Russia, as a professor of mathematics. After 8 years he returned to Switzerland because of his health. He first taught anatomy and botany, then changed to experimental and speculative philosophy (or, in modern terminology, theoretical physics). He has been called the father of mathematical physics.

In 1738 Bernoulli published *Hydrodynamica.* In this treatise, which was far in advance of his time in many ways, is his famous equation governing the flow of fluids in terms of speed, pressure, and potential energy, upon which much modern technology is based, especially aerodynamics. Being interested in practical application as well as in theory, he devised a number of experiments which demonstrated the effects he predicted.

In this treatise is also found his remarkable treatment of gas pressure. Considering an enclosed gas as a swarm of moving particles in dynamic equilibrium, he derived the correct expression for the resulting pressure, thus anticipating the approach adopted about 100 years later.

Bernoulli won or shared 10 prizes of the Paris Academy of Sciences, a feat equaled by only one other person, his friend and rival Leonhard Euler. Because of a difference of opinion with Euler, Bernoulli became interested in sound phenomena and discovered that a closed organ pipe can produce only odd harmonics and that pressure determines the relative amplitudes of the harmonics. His last work involved the application of probability theory to various practical matters, such as inoculation and relative proportion of male and female births. He died in Basel on March 17, 1782.

## Further Reading

Information on Bernoulli in English is scarce. E. T. Bell, *Men of Mathematics* (1937) and *The Development of Mathematics* (1940; 2d ed. 1945), are valuable. See also Alfred Hooper, *Makers of Mathematics* (1948), and David E. Smith, *History of Mathematics,* vol. 1 (1951). □

## Bernoulli, Daniel

**Bernoulli, Daniel** (1700–82) A Swiss mathematician (one of 11 eminent mathematicians his family produced over four generations), whose most important work was in the field of hydrodynamics. In his book Hydrodynamica (1738), he showed that the pressure within a flowing fluid depends inversely on its velocity (the greater the velocity, the lower the pressure). This is now known as Bernoulli's principle (see BERNOULLI EQUATION). Bernoulli was born at Groningen, the Netherlands, and educated at Basel, Switzerland, where his father had been appointed professor of mathematics on the death of his brother (Daniel's uncle) who held the post previously. Daniel obtained his master's degree at the age of 16 and his doctorate, on the action of the lungs, at 21. In 1725 he was appointed professor of mathematics at St Petersburg Academy, Russia, but left Russia in 1732. In 1733 he became professor of anatomy and botany at the University of Basel; in 1750 he became professor of natural philosophy, a post he held until his retirement in 1777. He died in Basel.

## Bernoulli, Daniel

**Bernoulli, Daniel** (1700–82) Swiss mathematician and physicist. His work on hydrodynamics demonstrated that pressure in a fluid decreases as the velocity of fluid flow increases. This fact, which explains the lift of an aircraft, became known as Bernoulli's principle. Bernoulli also formulated Bernoulli's law and made the first statement of the kinetic theory of gases.