Editing History of physics (section)

===Mechanics===
[[File:ETH-BIB-Bernoulli, Daniel (1700-1782)-Portrait-Portr 10971.tif (cropped).jpg|thumb|upright|left|[[Daniel Bernoulli]] (1700–1782)]]
In 1714, [[Brook Taylor]] derived the [[fundamental frequency]] of a stretched vibrating string in terms of its tension and mass per unit length by solving a [[differential equation]]. The Swiss mathematician [[Daniel Bernoulli]] (1700–1782) made important mathematical studies of the behavior of gases, anticipating the kinetic theory of gases developed more than a century later, and has been referred to as the first mathematical physicist.<ref>{{Harvtxt|Darrigol|2005}}</ref> In 1733, [[Daniel Bernoulli]] derived the fundamental frequency and [[harmonic]]s of a hanging chain by solving a differential equation. In 1734, Bernoulli solved the differential equation for the vibrations of an elastic bar clamped at one end. Bernoulli's treatment of [[fluid dynamics]] and his examination of [[fluid]] flow was introduced in his 1738 work ''[[Hydrodynamica]]''.

Rational mechanics dealt primarily with the development of elaborate mathematical treatments of observed motions, using Newtonian principles as a basis, and emphasized improving the tractability of complex calculations and developing of legitimate means of analytical approximation. A representative contemporary textbook was published by [[Johann Baptiste Horvath]]. By the end of the century analytical treatments were rigorous enough to verify the stability of the Solar System solely on the basis of Newton's laws without reference to divine intervention&nbsp;– even as deterministic treatments of systems as simple as the [[n-body problem|three body problem]] in gravitation remained intractable.<ref>{{Harvtxt|Bos|1980}}</ref> In 1705, [[Edmond Halley]] predicted the periodicity of [[Halley's Comet]], [[William Herschel]] discovered [[Uranus]] in 1781, and [[Henry Cavendish]] measured the [[gravitational constant]] and determined the mass of the Earth in 1798. In 1783, [[John Michell]] suggested that some objects might be so massive that not even light could escape from them.

In 1739, [[Leonhard Euler]] solved the ordinary differential equation for a forced harmonic oscillator and noticed the resonance phenomenon. In 1742, [[Colin Maclaurin]] discovered his [[Maclaurin spheroid|uniformly rotating self-gravitating spheroids]]. In 1742, Benjamin Robins published his ''New Principles in Gunnery'', establishing the science of aerodynamics. British work, carried on by mathematicians such as Taylor and Maclaurin, fell behind Continental developments as the century progressed. Meanwhile, work flourished at scientific academies on the Continent, led by such mathematicians as Bernoulli and Euler, as well as [[Joseph-Louis Lagrange]], [[Pierre-Simon Laplace]], and [[Adrien-Marie Legendre]]. In 1743, [[Jean le Rond d'Alembert]] published his ''Traité de dynamique'', in which he introduced the concept of generalized forces for accelerating systems and systems with constraints, and applied the new idea of [[virtual work]] to solve dynamical problem, now known as [[D'Alembert's principle]], as a rival to Newton's second law of motion. In 1747, [[Pierre Louis Maupertuis]] applied minimum principles to mechanics. In 1759, Euler solved the partial differential equation for the vibration of a rectangular drum. In 1764, Euler examined the partial differential equation for the vibration of a circular drum and found one of the Bessel function solutions. In 1776, [[John Smeaton]] published a paper on experiments relating power, [[work (physics)|work]], [[momentum]] and [[kinetic energy]], and supporting the [[conservation of energy]]. In 1788, Lagrange presented his [[Lagrangian mechanics|equations of motion]] in ''[[Mécanique analytique]]'', in which the whole of mechanics was organized around the principle of virtual work. In 1789, [[Antoine Lavoisier]] stated the law of [[conservation of mass]]. The rational mechanics developed in the 18th century received expositions in both Lagrange's ''Mécanique analytique'' and Laplace's ''[[Traité de mécanique céleste]]'' (1799–1825).