DANIEL BERNOULLI FRS (/bərˈnuːli/ ; Swiss ; 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 wing .
CONTENTS
* 1 Early life
* 2 Mathematical work
* 3
Statistics
Statistics
* 4 Physics
* 5 See also
* 6 References
* 7 Bibliography
* 8 External links
EARLY LIFE
Frontpage of
Hydrodynamica (1738)
Daniel Bernoulli
Daniel Bernoulli was born in Groningen , in the
Netherlands
Netherlands , into a
family of distinguished mathematicians. The
Bernoulli family came
originally from Antwerp, at that time in the Spanish
Netherlands
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 the son of
Johann Bernoulli
Johann Bernoulli (one of the "early developers"
of calculus ), nephew of
Jacob Bernoulli (who "was the first to
discover the theory of probability "). He had two brothers, Niklaus
and Johann II .
Daniel Bernoulli
Daniel Bernoulli was described by
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 as
Daniel's equal, banned Daniel from his house.
Johann Bernoulli
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
Basel , Heidelberg , and
Strasbourg , and earned a PhD in anatomy and botany in 1721.
He was a contemporary and close friend of
Leonhard Euler
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. Petersberg. He returned to the University of
Basel
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
Fellow of the Royal Society .
MATHEMATICAL WORK
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
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
d\'Alembert .
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 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
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 u 2 + P = constant {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.
STATISTICS
Daniel Bernoulli
Daniel Bernoulli was also the author in 1738 of Specimen theoriae
novae de mensura sortis (Exposition of a New Theory on the Measurement
of Risk), in which the
St. Petersburg paradox was the base of the
economic theory of risk aversion , risk premium and utility .
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
vaccination .
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
Léon Brillouin , the principle of superposition was
first stated by
Daniel Bernoulli
Daniel Bernoulli in 1753: "The general motion of a
vibrating system is given by a superposition of its proper
vibrations."
SEE ALSO
* Bernoulli\'s principle
*
Euler-Bernoulli beam equation
*
St. Petersburg paradox
REFERENCES
* ^ Mangold, Max (1990) Duden — Das Aussprachewörterbuch. 3.
Auflage. Mannheim/Wien/Zürich, Dudenverlag.
* ^ A B C Rothbard, Murray .
Daniel Bernoulli
Daniel Bernoulli and the Founding of
Mathematical Economics,
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. ISBN
0-486-20630-0 .
* ^ 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.
ISBN 0-521-45435-2 .
* ^ A B (2001) "Daniel Bernoulli",
Encyclopædia Britannica
Encyclopædia Britannica
* ^ "Library and Archive Catalogue". Royal Society. Retrieved 13
December 2010.
* ^ 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.
JSTOR
JSTOR 1909829 . doi :10.2307/1909829 .
* ^
Stanford Encyclopedia of Philosophy : "The St. Petersburg
Paradox by R. M. Martin
* ^ 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. PMID 15334536 . doi :10.1002/rmv.443 .
* ^ 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.
BIBLIOGRAPHY
Original entry based on the public domain Rouse History of
Mathematics
-------------------------
* (1911) "Bernoulli,
Encyclopædia Britannica
Encyclopædia Britannica
* Cardwell, D.S.L. (1971). From Watt to Clausius: The Rise of
Thermodynamics in the Early Industrial Age. Heinemann: London. ISBN
0-435-54150-1 .
* 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
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. ISBN
0-684-10114-9 .
EXTERNAL LINKS