William Thomson, 1st Baron Kelvin in the context of "Thermodynamics"

Treatise on Natural Philosophy was an 1867 text book by William Thomson (later Lord Kelvin) and Peter Guthrie Tait, published by Oxford University Press.

The Treatise was often referred to as ${\displaystyle T}$ and ${\displaystyle T^{1}}$, as explained by Alexander Macfarlane:

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics, which convey a quantitative description using measurable macroscopic physical quantities but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to various topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering, and mechanical engineering, as well as other complex fields such as meteorology.

Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a concise definition of thermodynamics in 1854 which stated, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency." German physicist and mathematician Rudolf Clausius restated Carnot's principle known as the Carnot cycle and gave the theory of heat a truer and sounder basis. His most important paper, "On the Moving Force of Heat", published in 1850, first stated the second law of thermodynamics. In 1865 he introduced the concept of entropy. In 1870 he introduced the virial theorem, which applied to heat.

Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook Treatise on Natural Philosophy, which he co-wrote with Lord Kelvin, and his early investigations into knot theory.

His work on knot theory contributed to the eventual formation of topology as a mathematical discipline. His name is known in graph theory mainly for Tait's conjecture on cubic graphs. He is also one of the namesakes of the Tait–Kneser theorem on osculating circles.

Peterhouse is a constituent college of the University of Cambridge in England, founded in 1284 by Hugh de Balsham, Bishop of Ely. Peterhouse has around 300 undergraduate and 175 graduate students, and 54 fellows.

Peterhouse alumni are notably eminent within the natural sciences, including scientists Lord Kelvin, Henry Cavendish, Charles Babbage, James Clerk Maxwell, James Dewar, Frank Whittle, and five Nobel prize winners in science: Sir John Kendrew, Sir Aaron Klug, Archer Martin, Max Perutz, and Michael Levitt. Peterhouse alumni also include Lord Chancellors, Lord Chief Justices, important poets such as Thomas Gray, the first Anglican Bishop of New York Samuel Provoost, the first British Fields Medallist Klaus Roth, Oscar-winning film director Sam Mendes and comedian David Mitchell. British Prime Minister Augustus FitzRoy, 3rd Duke of Grafton, and Elijah Mudenda, second prime minister of Zambia, also studied at the college.

William John Macquorn Rankine FRSE FRS (/ˈræŋkɪn/; 5 July 1820 – 24 December 1872) was a Scottish mathematician and physicist. He was a founding contributor, with Rudolf Clausius and William Thomson (Lord Kelvin), to the science of thermodynamics, particularly focusing on its First Law. He developed the Rankine scale, a Fahrenheit-based equivalent to the Celsius-based Kelvin scale of temperature.

Rankine developed a complete theory of the steam engine and indeed of all heat engines. His manuals of engineering science and practice were used for many decades after their publication in the 1850s and 1860s. He published several hundred papers and notes on science and engineering topics, from 1840 onwards, and his interests were extremely varied, including, in his youth, botany, music theory and number theory, and, in his mature years, most major branches of science, mathematics and engineering.

In electromagnetism, permeability is the measure of magnetization produced in a material in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter μ. It is the ratio of the magnetic induction ${\displaystyle B}$ to the magnetizing field ${\displaystyle H}$ in a material. The term was coined by William Thomson, 1st Baron Kelvin in 1872, and used alongside permittivity by Oliver Heaviside in 1885. The reciprocal of permeability is magnetic reluctivity.

In SI units, permeability is measured in henries per meter (H/m), or equivalently in newtons per ampere squared (N/A). The permeability constant μ₀, also known as the magnetic constant or the permeability of free space, is the proportionality between magnetic induction and magnetizing force when forming a magnetic field in a classical vacuum.