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| 1820 |
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| André-Marie Ampère (1775–1836) repeated Oersted's experiments (1820) and reported his discovery that two current-carrying wires exercise a reciprocal action upon one another. He later established a mathematical theory of known electrical phenomena and experimentally demonstrated the principles of the electrodynamics of adjacent current-carrying conductors. | 1 |
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| 1821–59 |
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| Michael Faraday (1791–1867) demonstrated electromagnetic rotation (1821) and discovered electromagnetic induction (1831). He independently discovered self-induced currents (1834), found two years earlier by Joseph Henry (1797–1878). He propounded the laws of electrochemical decomposition and conduction, and established a general theory of electrolysis. He also introduced the concept of field into physics. These and other investigations were collected in his Experimental Researches in Electricity (1839–55) and in his Experimental Researches in Chemistry and Physics (1859). | 2 |
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| 1821–23 |
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| Augustin-Louis Cauchy (1789–1857) gave the first essentially correct definition of limit in Cours d'analyse (1821). This work also contained the first systematic study of convergence of series and general tests for it, and the first theory of functions of a complex variable. He defined the derivative and integral in terms of limit and obtained the fundamental theorem of calculus (1823). | 3 |
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| 1822 |
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| Joseph Fourier (1768–1830) published Théorie analytique de la chaleur, giving a mathematical theory of heat conduction. He introduced trigonometric series, Fourier series of arbitrary, piecewise, continuous functions, thus extending the notion of function. | 4 |
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| 1824 |
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| Niels Abel (1802–29) proved that the general quintic cannot be solved by radicals. | 5 |
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| 1824 |
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| Nicolas Sadi Carnot (1796–1832) published Réflexions sur la puissance motrice du feu. Here he showed that the transformation of heat into motive power depends on the quantity of heat (“caloric”) and the temperature difference between the source and sink of heat. He also introduced the reversible cycle of a heat engine—now called the Carnot cycle. | 6 |
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| 1827–29 |
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| Niels Abel and Karl Jacobi (1804–51) independently founded the theory of elliptic (doubly periodic) functions. | 7 |
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| 1827 |
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| Georg S. Ohm (1789–1854) found that the ratio of electromotive force to the current, in an electric circuit, is a constant (Ohm's Law) and called this constant the resistance of the circuit. | 8 |
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| 1829–32 |
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| Nikolai Lobachevskii (1793–1856) and János Bólyai (1802–60) independently developed the first non-Euclidean geometries. | 9 |
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| 1831 |
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| The foundation of the British Association for the Advancement of Science, dedicated to the promotion and professionalization of British science. The B.A.A.S. was based on a German model, Gesellschaft deutscher Naturforscher, and served as an example for the American Association for the Advancement of Science (1848). | 10 |
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| 1832 |
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| Evariste Galois (1811–32) left posthumous papers showing the use of group theory to give necessary and sufficient conditions for the solution of equations by radicals. He emphasized the importance of the invariant, or normal, subgroup. | 11 |
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| 1833 |
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| Charles Babbage (1792–1871) conceived an “analytical engine” (a large-scale digital calculator). In 1822, he had made a working model of a smaller “difference engine” to calculate tables of functions by finite difference methods. | 12 |
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