As the Great Northern War was beginning, Daniel Bernoulli had just entered the world. Born on January 29, 1700, he entered a long line of mathematicians. His father Johann Bernoulli held the chair of mathematics at Groningen University in the Netherlands and his uncle Jakob Bernoulli was also an accomplished mathematician, as was his oldest brother Nicolaus (II) Bernoulli. Living with such established Dutch citizens, Daniel was brought into a family where there was unfortunate rivalry, jealousy and bitterness.
This sense of rivalry had its roots deep in his father’s family. When, at the age of five, Daniel’s family decided to return to their native city of Basel in Switzerland, they faced the effects of the jealousy they had left behind. Some years earlier Johann had applied to become professor of mathematics at Basel University, but this was denied him because his elder brother, Jakob had deliberately schemed to prevent him getting the post. Later Jakob got the professorship. En route to Basel, however, Johann learned that Jakob had just died of tuberculosis. He set about lobbying for the vacant position and in less than two months, he was the successor of his late brother’s job.
Daniel’s father was extremely controlling. By selecting a wife for him and trying to force him into a business career, Johann tried to map out Daniel's life, despite Daniel’s obvious resistance. Although, while the Peace of Utrecht was ending the Spanish succession, Daniel was sent to Basel University to study philosophy and logic. He obtained his baccalaureate examinations in 1715 and went on to obtain his master’s degree in 1716. Daniel also spent considerable amounts of time with his father and learned much about the secrets of the calculus. Johann was eventually reconciled to the fact that his son would never be a merchant but absolutely refused to allow him to take up mathematics as a profession, as there was little or no money in it. He instead decreed that Daniel would become a doctor, and so Daniel was sent back to Basel University to study medicine. He ended up spending time studying medicine at Heidelberg in 1718 and in Strasbourg in 1719. He completed his doctorate in medicine in 1720, a year before the Great Northern War ended.
Despite his work in the medicinal field, in time it became apparent that Daniel's interest in Mathematics was no passing fancy, so his father relented and tutored him. Among the many topics they talked about, one was to have a substantial influence on Daniel's future discoveries. It was called the "Law of Vis Viva Conservation" which is commonly referred to today as the "Law of Conservation of Energy". The young Bernoulli found a kindred spirit in the English physician William Harvey who wrote in his book On the Movement of Heat and Blood in Animals that the heart was like a pump which forced blood to flow like a fluid through our arteries. Daniel was attracted to Harvey's work since it combined his two loves of mathematics and fluids while also earning the medical degree his father expected of him.
After completing his medical studies, he wished to embark on an academic career like his father. He sought two academic chairs at Basel in anatomy and botany. These posts were awarded by lot, and unfortunately for Daniel, he lost out both times. The next chair to fall vacant at Basel was the chair of logic, but again the final selection went against him.
Having failed to obtain an academic post, Daniel went to Padua, Italy to study practical medicine at the age of 23. While in Italy he fell ill and ended up staying in Venice for longer than expected. He took advantage of his time there and worked on his mathematics, publishing (with the help of friend Christian Goldbach) his first mathematical work Mathematical Exercises in 1724. This book consisted of four parts being four separate topics that had attracted his interest.
The first part described Daniel’s understanding of probability in relation to the popular game faro. The second part was on the flow of water from a hole in a container and discussed Newton’s theories (which were later proved incorrect). Although Daniel had not solved the problem of pressure by this time, the work shows that his interest in was moving in this direction. His interest in fluid flow may also have stemmed from his medicinal work on the flow of blood and pressure. The third part of Mathematical Exercises was on the Riccati differential equation, while the final part was on a geometry question concerning figures by two arcs of a circle.
He eventually arrived in Padua, where he designed an hourglass for a ship, which would produce a reliable trickle of sand even in stormy weather. He submitted his design to the Paris Academy in 1725 and took first prize.
He returned home to Basel that same year to find a letter from Empress Catherine I of Russia awaiting him, inviting him to become professor of mathematics at the Imperial Academy in St. Petersburg. At first Daniel was not keen to travel to such a distant land, but his elder brother Nicolaus offered to go with him. Catherine was so keen to secure Daniel that she agreed to offer a second chair to Nicolaus! So the two brothers travelled to St. Petersburg. Unfortunately, within eight months, Nikolas died of tuberculosis. Daniel was greatly saddened at the loss of his brother and thought of returning home. He wrote home to his father telling him how unhappy he was. However, he decided to stay when his father suggested that one of his own students, a certain Leonard Euler would make an able assistant for Daniel in his research. Euler arrived in St. Petersburg during the year 1727 and this period, from 1727 to 1733 (when Daniel left St. Petersburg) is thought to be his most productive time.
Daniel and Euler first focused on the mechanics of flexible and elastic bodies, and derived the equilibrium curves for these bodies. One of his most famous discoveries though was when he defined the simple nodes and the frequencies of oscillation of a system. He showed that the movements of strings of musical instruments are composed of and infinite number of harmonic vibrations all superimposed on the string.
A second important work which Daniel produced while in St. Petersburg was one on probability and political economy. Daniel assumes that the moral value of the increase in a person's wealth is inversely proportional to the amount of that wealth. He then assigns probabilities to the various means that a person has to make money and deduces an expectation of increase in moral expectation.
Together Bernoulli and Euler tried to discover more about the flow of fluids. In particular, they wanted to know about the relationship between the speed at which blood flows and its pressure. To investigate this, Daniel experimented by puncturing the wall of a pipe with a small open ended straw and noted that the height to which the fluid rose up the straw was related to fluid's pressure in the pipe. Soon physicians all over Europe were measuring patient’s blood pressure by sticking point-ended glass tubes directly into their arteries. It was not until about 170 years later, in 1896 that an Italian doctor discovered a less painful method, which is still in use today. However, Bernoulli's method of measuring pressure is still used today in modern aircraft to measure the speed of the air passing the plane; that is its air speed.
Taking his discoveries further, Daniel Bernoulli now returned to his earlier work on Conservation of Energy. It was known that a moving body exchanges its kinetic energy for potential energy when it gains height. Daniel realised that in a similar way, a moving fluid exchanges its kinetic energy for pressure. Mathematically this law is now written:
1/2*rho*u^2 + p = constant
where p is pressure, rho is the density of the fluid and u is its velocity. A consequence of this law is that if the velocity increases then the pressure falls. This is exploited by the wing of an aeroplane which is designed to create an area of fast flowing air above its surface. The pressure of this area is lower and so the wing is sucked upwards.
Undoubtedly the most important of his works was on hydrodynamics. Even the term itself is based on the title of the work which he produced called Hydrodynamica and, before he left St Petersburg, Daniel left a draft copy of the book with a printer. However the work was not published until 1738 and although he revised it considerably between 1734 and 1738, it is more the presentation that he changed rather then the substance.
This work contains for the first time the correct analysis of water flowing from a hole in a container. This was based on the principle of conservation of energy which he had studied with his father in 1720. Daniel also discussed pumps and other machines to raise water. One remarkable discovery appears in Chapter 10 of Hydrodynamica where Daniel discussed the basis for the kinetic theory of gases. He was able to give the basic laws for the theory of gases and gave, although not in full detail, the equation of state discovered by Van der Waals a century later.
Despite the obvious scientific advantage of working with Euler, Daniel Bernoulli was not happy in St. Petersburg. By 1731 he was applying for posts in Basel but probability seemed to work against him and he would lose out in the ballot for the post. The post was neither one in mathematics nor physics but Daniel would rather return to Basel and give lectures on botany rather than remain in St. Petersburg. By this time his younger brother Johann (II) Bernoulli was also with him in St Petersburg and they left St Petersburg in 1733, making visits to Danzig, Hamburg, Holland and Paris before returning to Basel in 1734.
Daniel Bernoulli submitted an entry for the Grand Prize of the Paris Academy for 1734 giving an application of his ideas to astronomy. This had unfortunate consequences since Daniel's father, Johann Bernoulli, also entered for the prize and their entries were declared joint winners of the Grand Prize. The result of this episode of the prize of the Paris Academy had unhappy consequences for Daniel. His father was furious to think that his son had been rated as his equal and this resulted in a breakdown in relationships between the two. The outcome was that Daniel found himself back in Basel but banned from his father's house.
Although Daniel had left St Petersburg, he began an immediate correspondence with Euler and the two exchanged many ideas on vibrating systems. Euler used his great analytical skills to put many of Daniel's physical insights into a rigorous mathematical form. Daniel continued to work on polishing his masterpiece Hydrodynamica for publication and added a chapter on the force of reaction of a jet of fluid and the force of a jet of water on an inclined plane. In this chapter, he also discussed applications to the propulsion of ships.
The 1737 prize of the Paris Academy also had a nautical theme, the best shape for a ship's anchor, and Daniel Bernoulli was again the joint winner of this prize, this time winning jointly with Poleni. Hydrodynamica was published in 1738 but, in the following year, Johann Bernoulli published Hydraulica which is largely based on his son's work But Johann tried to make it look as if Daniel had based Hydrodynamica on Hydraulica by predating the date of publication on his book to 1732 instead of its real date which is probably 1739. This was a disgraceful attempt by Johann to gain credit for work which was not his and at the same time to discredit his own son.
Daniel Bernoulli did produce other excellent scientific work during these many years back in Basel. In total he won the Grand Prize of the Paris Academy 10 times, for topics in astronomy and nautical topics. He won in 1740 (jointly with Euler) for work on Newton's theory of the tides; in 1743 and 1746 for essays on magnetism; in 1747 for a method to determine time at sea; in 1751 for an essay on ocean currents; in 1753 for the effects of forces on ships; and in 1757 for proposals to reduce the pitching and tossing of a ship in high seas.
Another important aspect of Daniel Bernoulli's work that proved important in the development of mathematical physics was his acceptance of many of Newton's theories and his use of these together with the tolls coming from the more powerful calculus of Leibniz. Daniel worked on mechanics and again used the principle of conservation of energy which gave an integral of Newton's basic equations. He also studied the movement of bodies in a resisting medium using Newton's methods.
Daniel Bernoulli was much honoured in his own lifetime. He was elected to most of he leading scientific societies of his day including those in Bologna, St Petersburg, Berlin, Paris, London, Bern, Turin, Zurich and Mannheim. He remained in Basel and died there on March 17th, 1782 at the age of 82.
This sense of rivalry had its roots deep in his father’s family. When, at the age of five, Daniel’s family decided to return to their native city of Basel in Switzerland, they faced the effects of the jealousy they had left behind. Some years earlier Johann had applied to become professor of mathematics at Basel University, but this was denied him because his elder brother, Jakob had deliberately schemed to prevent him getting the post. Later Jakob got the professorship. En route to Basel, however, Johann learned that Jakob had just died of tuberculosis. He set about lobbying for the vacant position and in less than two months, he was the successor of his late brother’s job.
Daniel’s father was extremely controlling. By selecting a wife for him and trying to force him into a business career, Johann tried to map out Daniel's life, despite Daniel’s obvious resistance. Although, while the Peace of Utrecht was ending the Spanish succession, Daniel was sent to Basel University to study philosophy and logic. He obtained his baccalaureate examinations in 1715 and went on to obtain his master’s degree in 1716. Daniel also spent considerable amounts of time with his father and learned much about the secrets of the calculus. Johann was eventually reconciled to the fact that his son would never be a merchant but absolutely refused to allow him to take up mathematics as a profession, as there was little or no money in it. He instead decreed that Daniel would become a doctor, and so Daniel was sent back to Basel University to study medicine. He ended up spending time studying medicine at Heidelberg in 1718 and in Strasbourg in 1719. He completed his doctorate in medicine in 1720, a year before the Great Northern War ended.
Despite his work in the medicinal field, in time it became apparent that Daniel's interest in Mathematics was no passing fancy, so his father relented and tutored him. Among the many topics they talked about, one was to have a substantial influence on Daniel's future discoveries. It was called the "Law of Vis Viva Conservation" which is commonly referred to today as the "Law of Conservation of Energy". The young Bernoulli found a kindred spirit in the English physician William Harvey who wrote in his book On the Movement of Heat and Blood in Animals that the heart was like a pump which forced blood to flow like a fluid through our arteries. Daniel was attracted to Harvey's work since it combined his two loves of mathematics and fluids while also earning the medical degree his father expected of him.
After completing his medical studies, he wished to embark on an academic career like his father. He sought two academic chairs at Basel in anatomy and botany. These posts were awarded by lot, and unfortunately for Daniel, he lost out both times. The next chair to fall vacant at Basel was the chair of logic, but again the final selection went against him.
Having failed to obtain an academic post, Daniel went to Padua, Italy to study practical medicine at the age of 23. While in Italy he fell ill and ended up staying in Venice for longer than expected. He took advantage of his time there and worked on his mathematics, publishing (with the help of friend Christian Goldbach) his first mathematical work Mathematical Exercises in 1724. This book consisted of four parts being four separate topics that had attracted his interest.
The first part described Daniel’s understanding of probability in relation to the popular game faro. The second part was on the flow of water from a hole in a container and discussed Newton’s theories (which were later proved incorrect). Although Daniel had not solved the problem of pressure by this time, the work shows that his interest in was moving in this direction. His interest in fluid flow may also have stemmed from his medicinal work on the flow of blood and pressure. The third part of Mathematical Exercises was on the Riccati differential equation, while the final part was on a geometry question concerning figures by two arcs of a circle.
He eventually arrived in Padua, where he designed an hourglass for a ship, which would produce a reliable trickle of sand even in stormy weather. He submitted his design to the Paris Academy in 1725 and took first prize.
He returned home to Basel that same year to find a letter from Empress Catherine I of Russia awaiting him, inviting him to become professor of mathematics at the Imperial Academy in St. Petersburg. At first Daniel was not keen to travel to such a distant land, but his elder brother Nicolaus offered to go with him. Catherine was so keen to secure Daniel that she agreed to offer a second chair to Nicolaus! So the two brothers travelled to St. Petersburg. Unfortunately, within eight months, Nikolas died of tuberculosis. Daniel was greatly saddened at the loss of his brother and thought of returning home. He wrote home to his father telling him how unhappy he was. However, he decided to stay when his father suggested that one of his own students, a certain Leonard Euler would make an able assistant for Daniel in his research. Euler arrived in St. Petersburg during the year 1727 and this period, from 1727 to 1733 (when Daniel left St. Petersburg) is thought to be his most productive time.
Daniel and Euler first focused on the mechanics of flexible and elastic bodies, and derived the equilibrium curves for these bodies. One of his most famous discoveries though was when he defined the simple nodes and the frequencies of oscillation of a system. He showed that the movements of strings of musical instruments are composed of and infinite number of harmonic vibrations all superimposed on the string.
A second important work which Daniel produced while in St. Petersburg was one on probability and political economy. Daniel assumes that the moral value of the increase in a person's wealth is inversely proportional to the amount of that wealth. He then assigns probabilities to the various means that a person has to make money and deduces an expectation of increase in moral expectation.
Together Bernoulli and Euler tried to discover more about the flow of fluids. In particular, they wanted to know about the relationship between the speed at which blood flows and its pressure. To investigate this, Daniel experimented by puncturing the wall of a pipe with a small open ended straw and noted that the height to which the fluid rose up the straw was related to fluid's pressure in the pipe. Soon physicians all over Europe were measuring patient’s blood pressure by sticking point-ended glass tubes directly into their arteries. It was not until about 170 years later, in 1896 that an Italian doctor discovered a less painful method, which is still in use today. However, Bernoulli's method of measuring pressure is still used today in modern aircraft to measure the speed of the air passing the plane; that is its air speed.
Taking his discoveries further, Daniel Bernoulli now returned to his earlier work on Conservation of Energy. It was known that a moving body exchanges its kinetic energy for potential energy when it gains height. Daniel realised that in a similar way, a moving fluid exchanges its kinetic energy for pressure. Mathematically this law is now written:
1/2*rho*u^2 + p = constant
where p is pressure, rho is the density of the fluid and u is its velocity. A consequence of this law is that if the velocity increases then the pressure falls. This is exploited by the wing of an aeroplane which is designed to create an area of fast flowing air above its surface. The pressure of this area is lower and so the wing is sucked upwards.
Undoubtedly the most important of his works was on hydrodynamics. Even the term itself is based on the title of the work which he produced called Hydrodynamica and, before he left St Petersburg, Daniel left a draft copy of the book with a printer. However the work was not published until 1738 and although he revised it considerably between 1734 and 1738, it is more the presentation that he changed rather then the substance.
This work contains for the first time the correct analysis of water flowing from a hole in a container. This was based on the principle of conservation of energy which he had studied with his father in 1720. Daniel also discussed pumps and other machines to raise water. One remarkable discovery appears in Chapter 10 of Hydrodynamica where Daniel discussed the basis for the kinetic theory of gases. He was able to give the basic laws for the theory of gases and gave, although not in full detail, the equation of state discovered by Van der Waals a century later.
Despite the obvious scientific advantage of working with Euler, Daniel Bernoulli was not happy in St. Petersburg. By 1731 he was applying for posts in Basel but probability seemed to work against him and he would lose out in the ballot for the post. The post was neither one in mathematics nor physics but Daniel would rather return to Basel and give lectures on botany rather than remain in St. Petersburg. By this time his younger brother Johann (II) Bernoulli was also with him in St Petersburg and they left St Petersburg in 1733, making visits to Danzig, Hamburg, Holland and Paris before returning to Basel in 1734.
Daniel Bernoulli submitted an entry for the Grand Prize of the Paris Academy for 1734 giving an application of his ideas to astronomy. This had unfortunate consequences since Daniel's father, Johann Bernoulli, also entered for the prize and their entries were declared joint winners of the Grand Prize. The result of this episode of the prize of the Paris Academy had unhappy consequences for Daniel. His father was furious to think that his son had been rated as his equal and this resulted in a breakdown in relationships between the two. The outcome was that Daniel found himself back in Basel but banned from his father's house.
Although Daniel had left St Petersburg, he began an immediate correspondence with Euler and the two exchanged many ideas on vibrating systems. Euler used his great analytical skills to put many of Daniel's physical insights into a rigorous mathematical form. Daniel continued to work on polishing his masterpiece Hydrodynamica for publication and added a chapter on the force of reaction of a jet of fluid and the force of a jet of water on an inclined plane. In this chapter, he also discussed applications to the propulsion of ships.
The 1737 prize of the Paris Academy also had a nautical theme, the best shape for a ship's anchor, and Daniel Bernoulli was again the joint winner of this prize, this time winning jointly with Poleni. Hydrodynamica was published in 1738 but, in the following year, Johann Bernoulli published Hydraulica which is largely based on his son's work But Johann tried to make it look as if Daniel had based Hydrodynamica on Hydraulica by predating the date of publication on his book to 1732 instead of its real date which is probably 1739. This was a disgraceful attempt by Johann to gain credit for work which was not his and at the same time to discredit his own son.
Daniel Bernoulli did produce other excellent scientific work during these many years back in Basel. In total he won the Grand Prize of the Paris Academy 10 times, for topics in astronomy and nautical topics. He won in 1740 (jointly with Euler) for work on Newton's theory of the tides; in 1743 and 1746 for essays on magnetism; in 1747 for a method to determine time at sea; in 1751 for an essay on ocean currents; in 1753 for the effects of forces on ships; and in 1757 for proposals to reduce the pitching and tossing of a ship in high seas.
Another important aspect of Daniel Bernoulli's work that proved important in the development of mathematical physics was his acceptance of many of Newton's theories and his use of these together with the tolls coming from the more powerful calculus of Leibniz. Daniel worked on mechanics and again used the principle of conservation of energy which gave an integral of Newton's basic equations. He also studied the movement of bodies in a resisting medium using Newton's methods.
Daniel Bernoulli was much honoured in his own lifetime. He was elected to most of he leading scientific societies of his day including those in Bologna, St Petersburg, Berlin, Paris, London, Bern, Turin, Zurich and Mannheim. He remained in Basel and died there on March 17th, 1782 at the age of 82.
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