Daniel Bernoulli FRS (German pronunciation: [bɛʁˈnʊli];
8 February 1700 – 17 March 1782) was a Swiss
mathematician and physicist and was one of the many prominent
mathematicians in the Bernoulli family. He is particularly remembered
for his applications of mathematics to mechanics, especially fluid
mechanics, and for his pioneering work in probability and statistics.
His name is commemorated in the Bernoulli's principle, a particular
example of the conservation of energy, which describes the mathematics
of the mechanism underlying the operation of two important
technologies of the 20th century: the carburetor and the airplane
1 Early life
2 Mathematical work
3 Economics and statistics
5 See also
6.2 Works cited
7 External links
Daniel Bernoulli was born in Groningen, in the Netherlands, into a
family of distinguished mathematicians. The
Bernoulli family came
originally from Antwerp, at that time in the Spanish Netherlands, but
emigrated to escape the Spanish persecution of the Huguenots. After a
brief period in Frankfurt the family moved to Basel, in Switzerland.
Daniel was a son of
Johann Bernoulli (one of the "early developers" of
calculus) and a nephew of
Jacob Bernoulli (who "was the first to
discover the theory of probability"). He had two brothers, Niklaus
and Johann II.
Daniel Bernoulli was described by
W. W. Rouse Ball
W. W. Rouse Ball as
"by far the ablest of the younger Bernoullis". He is said to have
had a bad relationship with his father. Upon both of them entering and
tying for first place in a scientific contest at the University of
Paris, Johann, unable to bear the "shame" of being compared Daniel's
equal, banned Daniel from his house.
Johann Bernoulli also plagiarized
some key ideas from Daniel's book
Hydrodynamica in his own book
Hydraulica which he backdated to before Hydrodynamica. Despite
Daniel's attempts at reconciliation, his father carried the grudge
until his death.
Around schooling age, his father, Johann, encouraged him to study
business, there being poor rewards awaiting a mathematician. However,
Daniel refused, because he wanted to study mathematics. He later gave
in to his father's wish and studied business. His father then asked
him to study in medicine, and Daniel agreed under the condition that
his father would teach him mathematics privately, which they continued
for some time. Daniel studied medicine at Basel, Heidelberg, and
Strasbourg, and earned a PhD in anatomy and botany in 1721.
He was a contemporary and close friend of Leonhard Euler. He went to
St. Petersburg in 1724 as professor of mathematics, but was very
unhappy there, and a temporary illness in 1733 gave him an excuse for
leaving St. Petersburg. He returned to the University of Basel,
where he successively held the chairs of medicine, metaphysics, and
natural philosophy until his death.
In May, 1750 he was elected a Fellow of the Royal Society.
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His earliest mathematical work was the Exercitationes (Mathematical
Exercises), published in 1724 with the help of Goldbach. Two years
later he pointed out for the first time the frequent desirability of
resolving a compound motion into motions of translation and motion of
rotation. His chief work is Hydrodynamica, published in 1738; it
resembles Joseph Louis Lagrange's Mécanique Analytique in being
arranged so that all the results are consequences of a single
principle, namely, conservation of energy. This was followed by a
memoir on the theory of the tides, to which, conjointly with the
memoirs by Euler and Colin Maclaurin, a prize was awarded by the
French Academy: these three memoirs contain all that was done on this
subject between the publication of Isaac Newton's Philosophiae
Naturalis Principia Mathematica and the investigations of Pierre-Simon
Laplace. Bernoulli also wrote a large number of papers on various
mechanical questions, especially on problems connected with vibrating
strings, and the solutions given by
Brook Taylor and by Jean le Rond
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
Soon physicians all over Europe were measuring patients' 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
displaystyle tfrac 1 2 rho u^ 2 +P= text constant
where P is pressure, ρ 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 above its surface where the air
velocity increases. The pressure in this area is lower than that under
the wing, so the wing is pushed upwards by the relatively higher
pressure under the wing.
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
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
Daniel Bernoulli in 1753: "The general motion of a vibrating
system is given by a superposition of its proper vibrations."
Euler-Bernoulli beam equation
St. Petersburg paradox
^ Mangold, Max (1990) Duden — Das Aussprachewörterbuch. 3. Auflage.
^ a b Rothbard, Murray.
Daniel Bernoulli and the Founding of
Mises Institute (excerpted from An Austrian
Perspective on the History of Economic Thought)
^ a b c Rouse Ball, W. W. (2003) . "The Bernoullis". A Short
Account of the History of Mathematics (4th ed.). Dover.
^ a b c O'Connor, John J.; Robertson, Edmund F., "Daniel Bernoulli",
MacTutor History of Mathematics archive, University of St
Andrews . (1998)
^ Anderson, John David (1997). A History of
Aerodynamics and its
Impact on Flying Machines. New York, NY: Cambridge University Press.
^ a b [Anon.] (2001) "Daniel Bernoulli", Encyclopædia Britannica
^ "Library and Archive Catalogue". Royal Society. Retrieved 13
December 2010. [permanent dead link]
^ The Turner Collection, Keele University, includes Bernoulli's
diagram to illustrate how pressure is measured. See also part of
Bernoulli's original Latin explanation.
^ English translation in Bernoulli, D. (1954). "Exposition of a New
Theory on the Measurement of Risk" (PDF). Econometrica. 22 (1):
23–36. doi:10.2307/1909829. JSTOR 1909829.
^ Stanford Encyclopedia of Philosophy: "The St. Petersburg Paradox by
R. M. Martin
^ Cooter & Ulen (2016), pp. 44–45.
^ reprinted in Blower, S; Bernoulli, D (2004). "An attempt at a new
analysis of the mortality caused by smallpox and of the advantages of
inoculation to prevent it" (PDF). Reviews in medical virology. 14 (5):
275–88. doi:10.1002/rmv.443. PMID 15334536. Archived from the
original (PDF) on 27 September 2007.
^ Timoshenko, S. P. (1983) . History of Strength of Materials.
New York: Dover. ISBN 0-486-61187-6.
^ Brillouin, L. (1946). Wave propagation in Periodic Structures:
Electric Filters and Crystal Lattices, McGraw–Hill, New York, p. 2.
(Original entry based on the public domain Rouse History of
[Anon.] (1911) "Bernoulli, Encyclopædia Britannica
Cardwell, D.S.L. (1971). From Watt to Clausius: The Rise of
Thermodynamics in the Early Industrial Age. Heinemann: London.
Cooter, Robert; Ulen, Thomas (2016). Law & Economics. Berkeley Law
Books (6th ed.). Berkeley: Addison-Wesley.
Mikhailov, G.K. (2005). "Hydrodynamica". In Grattan-Guinness, Ivor.
Landmark Writings in Western Mathematics 1640–1940. Elsevier.
pp. 131–42. ISBN 978-0-08-045744-4.
Pacey, A.J.; Fisher, S.J. (December 1967). "
Daniel Bernoulli and the
vis viva of compressed air". British Journal for the History of
Science. 3: 388–392. doi:10.1017/S0007087400002934.
Straub, Hans (1970). "Bernoulli, Daniel". Dictionary of Scientific
Biography. 2. New York: Charles Scribner's Sons. pp. 36–46.
Wikimedia Commons has media related to Daniel Bernoulli.
"Bernoulli Daniel". Mathematik.ch. Retrieved 2007-09-07.
Daniel Bernoulli and the Founding of Mathematical
Mises Institute (excerpted from An Austrian Perspective on
the History of Economic Thought)
Weisstein, Eric Wolfgang (ed.). "Bernoulli, Daniel (1700–1782)".
Daniel Bernoulli at Project Gutenberg
Works by or about
Daniel Bernoulli at Internet Archive
Bernoulli family tree
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Nicolaus I Bernoulli
Nicolaus II Bernoulli
Johann II Bernoulli
Johann III Bernoulli
Daniel II Bernoulli
Nicolaus IV Bernoulli
Jakob II Bernoulli
Hans Benno Bernoulli
Family tree of the Bernoulli family
ISNI: 0000 0000 9018 961X
BNF: cb122991859 (data)