# Physics

## Nineteenth Century

The development of physics during the nineteenth century can be seen as both a culmination of what went before and as preparing the stage for the revolutions in relativity and quantum theory that were to follow. The work of the Irish mathematician and astronomer William Rowan Hamilton (1805–1865) built on Laplace's revision of Newtonian dynamics to establish a thoroughly abstract and mathematical approach to physical problems. Originally motivated by his work in optics, Hamilton developed a new principle of least action. Instead of using Lagrange's integral of kinetic energy, Hamilton chose to minimize the integral of the difference between the kinetic and the potential energies. In applying this principle in mechanics, Hamilton reproduced the results of Euler and Lagrange, and showed that it applied to a broader range of problems. After his work was published, as two essays in 1833 and 1834, it was critiqued and improved upon by the German mathematician Carl Gustav Jacob Jacobi (1804–1851). The resulting Hamilton-Jacobi formalism was applied in many fields of physics, including hydrodynamics, optics, acoustics, the kinetic theory of gases, and electrodynamics. However, it did not achieve its full significance until the twentieth century, when it was used to buttress the foundations of quantum mechanics.

Work on magnetism was encouraged by Alessandro Volta's (1745–1827) development, in 1800, of the voltaic pile (an early battery), which, unlike the Leyden jar, was able to produce
a steady source of electric current. Inspired by the German philosophical movement of *Naturphilosophie,* which espoused that the forces of nature were all interrelated in a higher unity, the Danish physicist Hans Christian Ørsted (1777–1851) sought a magnetic effect from the electric current of Volta's battery. Ørsted's announcement of his success, in 1820, brought a flurry of activity, including the work of Jean-Baptiste Biot and Félix Savart, on the force law between a current and a magnet, and the work of André-Marie Ampère, on the force law between two currents. The magnetic force was found to depend on the inverse square of the distance but was more complex due to the subtle vector relations between the currents and distances. For the analysis of inverse-square force laws, the German mathematician Carl Friedrich Gauss (1777–1855) introduced, in 1839, the concept of "potential," which could be applied with great generality to both electrostatics and magnetism. This work grew from Gauss's efforts in measuring and understanding the earth's magnetic field, which he undertook with his compatriot Wilhelm Eduard Weber (d. 1891).

The most significant work in magnetism was done by Michael Faraday (1791–1861) at the Royal Institution of London. By 1831, Faraday had characterized a kind of reverse Ørsted effect, in which a change in magnetism gave rise to a current. For example, he showed that this "electromagnetic induction" occurred between two electric circuits that communicated magnetism through a shared iron ring but, otherwise, were electrically insulated from one another (an early version of the transformer). Faraday made the first measurements of magnetic materials, characterizing diamagnetic, paramagnetic, and ferromagnetic effects (though this terminology is

due to the English mathematician William Whewell). Finally, Faraday pioneered the concept of the field, coining the term "magnetic field" in 1845. He saw the "lines of force" of magnetic or electric fields as being physically real and as filling space (in opposition to the idea of action at a distance).

One of the pinnacles of nineteenth-century physics is the theory of electromagnetism developed by the Scottish physicist James Clerk Maxwell (1831–1879). Maxwell brought together the work of Coulomb, Ampère, and Faraday, and made the crucial addition of the "displacement current," which acknowledged that a magnetic field can be produced not only by a current but also by a changing electric field. These efforts resulted in a set of four equations that Maxwell used to derive wave equations for the electric and magnetic fields. This led to the astonishing prediction that light was an electromagnetic wave. In developing and interpreting his results, Maxwell sought to build a mechanical model of electromagnetic radiation. Influenced by Faraday's rejection of action at a distance, Maxwell attempted to see electromagnetic waves as vortices in an ether medium, interspersed with small particles that acted as idle wheels to connect the vortices. Maxwell discarded this mechanical model in later years, in favor of a dynamical perspective. This latter attitude was taken by the German experimentalist Heinrich Rudolph Hertz (1857–1894), who, in 1886, first demonstrated the propagation of electromagnetic waves in the laboratory, using a spark-gap device as a transmitter.

During the eighteenth century, most researchers saw the flow of heat as the flow of the imponderable fluid caloric. Despite developments, such as Benjamin Thompson's cannon-boring experiments, which suggested that heat involved some sort of microscopic motion, caloric provided a heuristic model that aided in the quantification of experimental results and in the creation of mathematical models. For example, the French engineer Sadi Carnot (1837–1894) did empirical work on steam engines which led to the theory of the thermodynamic cycle, as reported in his *Reflections on the Motive Power of Fire* (1824). A purely mathematical approach was developed by Jean-Baptiste-Joseph Fourier, who analyzed heat conduction with the method of partial differential equations in his *Analytical Theory of Heat* (1822).

Carnot's opinion that caloric was conserved during the running of a steam engine was proved wrong by the development of the first law of thermodynamics. Similar conceptions of the conservation of energy (or "force," as energy was still referred to) were identified by at least three different people during the 1840s, including the German physician Julius Robert von Mayer (1814–1878), who was interested in the human body's ability to convert the chemical energy of food to other forms of energy, and the German theoretical physicist Hermann Ludwig Ferdinand von Helmholtz (1821–1894), who gave a mathematical treatment of different types of energy and showed that the different conservation laws could be traced back to the conservation of *vis viva* in mechanics. The British physicist James Prescott Joule (1818–1889) did an experiment that measured the mechanical equivalent of heat with a system of falling weights and a paddlewheel that stirred water within an insulated vessel (see Fig. 4).

In his *Hydrodynamica,* Bernoulli had proposed the first kinetic theory of gases, by suggesting that pressure was due to the motion and impact of atoms as they struck the sides of their containment vessel. The work of the chemists John Dalton (1766–1844) and Amedeo Avogadro (1776–1856) indirectly lent support to such a kinetic theory by casting doubt upon the Newtonian program of understanding chemistry in terms of force laws between atoms. After John Herapath's work on the kinetic theory, in 1820, was largely ignored, Rudolf
Clausius published two papers, in 1857 and 1858, in which he sought to derive the specific heats of a gas and introduced the concept of the mean free path between atomic collisions. James Clerk Maxwell added the idea that the atomic collisions would result in a range of velocities, not an average velocity as Clausius thought, and that this would necessitate the use of a statistical approach. In a number of papers published from 1860 to 1862, Maxwell completed the foundations of the kinetic theory and introduced the equipartition theorem, the idea that each degree of freedom (translational or rotational) contributed the same average energy, which was proportional to the temperature of the gas. Clausius and Maxwell's work in kinetic theory was tied to their crucial contributions to developing the second law of thermodynamics (see sidebar, "Second Law of Thermodynamics").

## Additional topics

- Physics - Causes Of Motion: Medieval Understandings
- Physics - Eighteenth Century
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Science EncyclopediaScience & Philosophy: *Philosophy of Mind - Early Ideas* to *Planck length*Physics - Middle Ages, Sixteenth And Seventeenth Centuries, Eighteenth Century, Nineteenth Century, Causes Of Motion: Medieval Understandings