* Of the four Maxwell's equations, two — Faraday's law and Ampère's law — can be compactly expressed using curl.

In 1884 he recast Maxwell's mathematical analysis from its original cumbersome form ( they had already been recast as quaternions ) to its modern vector terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four differential equations in two unknowns we now know as Maxwell's equations.

The four re-formulated Maxwell's equations describe the nature of static and moving electric charges and magnetic dipoles, and the relationship between the two, namely electromagnetic induction.

Heaviside employed the curl and divergence operators of the vector calculus to reformulate 12 of these 20 equations into four equations in four variables ( B, E, J, and ρ ), the form by which they have been known ever since ( see Maxwell's equations ).

The motivation behind this approach began with the Kaluza-Klein theory in which it was noted that applying general relativity to a five dimensional universe ( with the usual four dimensions plus one small curled-up dimension ) yields the equivalent of the usual general relativity in four dimensions together with Maxwell's equations ( electromagnetism, also in four dimensions ).

Gauss's law for magnetism, which is one of the four Maxwell's equations, states that the total magnetic flux through a closed surface is equal to zero.

* Maxwell's equations ( sometimes called the Maxwell equations ) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter.

It is one of the four Maxwell's equations which form the basis of classical electrodynamics, the other three being Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's correction.

It is the paper in which the original set of four Maxwell's equations first appeared.

In part III of " A Dynamical Theory of the Electromagnetic Field ", which is entitled " General Equations of the Electromagnetic Field ", Maxwell formulated twenty equations which were to become known as Maxwell's equations, until this term became applied instead to a set of four vectorized equations selected in 1884 by Oliver Heaviside, which had all appeared in " On physical lines of force ".

Another of Heaviside's four equations is an amalgamation of Maxwell's law of total currents ( equation " A ") with Ampère's circuital law ( equation " C ").

The Maxwell – Faraday equation is one of the four Maxwell's equations, and therefore plays a fundamental role in the theory of classical electromagnetism.

This relation is known as Gauss ' law for electric field in its integral form and it is one of the four Maxwell's equations.

Over time, this work culminated in Maxwell's equations, a set of four equations that could be used to calculate the entirety of electromagnetism.

Starting from the first and second laws of thermodynamics, four equations called the " fundamental equations of Gibbs " can be derived.

From these four, a multitude of equations, relating the thermodynamic properties of the thermodynamic system can be derived using relatively simple mathematics.

The space M × C is compactified over the compact set C, and after Kaluza-Klein decomposition we have an effective field theory over M. A splitting of five-dimensional spacetime into the Einstein equations and Maxwell equations in four dimensions was first discovered by Gunnar Nordström in 1914, in the context of his theory of gravity, but subsequently forgotten.

with R < sub > AB </ sub > the five-dimensional Ricci curvature, may be re-expressed so that in four dimensions, these solutions satisfy Einstein's equations

) Of the four equations, two of them, Gauss's law and Gauss's law for magnetism, describe how the fields emanate from charges.

If they did exist, both Gauss's law for magnetism and Faraday's law would need to be modified, and the resulting four equations would be fully symmetric under the interchange of electric and magnetic fields ; see magnetic monopoles for details.

Except for special cases like the Lagrangian points, no method is known to solve the equations of motion for a system with four or more bodies.

Another important antecedent to spacetime was the work of James Clerk Maxwell as he used partial differential equations to develop electrodynamics with the four parameters.

The final blow against corpuscular theory came when James Clerk Maxwell discovered that he could combine four simple equations, which had been previously discovered, along with a slight modification to describe self propagating waves of oscillating electric and magnetic fields.

The maneuvers were held `` in secret '' after a regional seminar for the Minutemen, held in nearby Shiloh, Ill., had been broken up the previous day by deputy sheriffs, who had arrested regional leader Richard Lauchli of Collinsville, Ill., and seized four operative weapons, including a Browning machine gun, two Browning automatic rifles and an M-4 rifle.

The new interchange among the four Los Angeles freeways, including the grade-constructed accesses, occupies by itself no less than eighty acres of downtown land, one-eighth of a square mile, an area about the size of Rockefeller Center in New York.

Scherer also had a big night at bat with four hits in five trips including a double, Len Boehmer also was 4-for-5 with two doubles and Dave Ritchie had a home run and a triple.

There also were reports of a collection at the County Line Elementary School, 3505o Dequindre, which has been attended this year by four of the Kowalski children including Christine.

`` Le Theatre D'Art Du Ballet '', of Monte Carlo, will present a program of four ballets including `` Francesca Da Rimini ''.

Although only one of his four children survived to adulthood, Antoninus came to be ancestor to generations of prominent Roman statesmen and socialites, including at least one empress consort.

* 1692 – Salem witch trials: in Salem, Massachusetts, Province of Massachusetts Bay, five people, one woman and four men, including a clergyman, are executed after being convicted of witchcraft.

Mainly because the re-publication of The Tenant of Wildfell Hall was prevented by Charlotte Brontë after Anne's death, she is less known than her sisters Charlotte, author of four novels including Jane Eyre, and Emily, author of Wuthering Heights.

In 2011 the production received four Lucille Lortel Award nominations including Outstanding Musical, Outer Critics Circle and Drama League nominations, as well as five Drama Desk nominations including Outstanding Musical and won for Outstanding Ensemble Performance.

The term shmoo has also entered the lexicon, defining highly technical concepts in no less than four separate fields of science, including the variations shmooing ( a microbiological term for the " budding " process in yeast reproduction ), and shmoo plot ( a technical term in the field of electrical engineering ).

The blind form of the Mexican tetra is different from the surface-dwelling form in a number of ways, including having unpigmented skin, having a better olfactory sense by having taste buds all over its head, and by being able to store four times more energy as fat allowing it to deal with irregular food supplies more effectively.

In 2007, U. S. Department of Defense ’ s Telemedicine and Advanced Technologies Research Center ( TATRC ) began to study the antimicrobial properties of copper alloys, including four brasses ( C87610, C69300, C26000, C46400 ) in a multi-site clinical hospital trial conducted at the Memorial Sloan-Kettering Cancer Center ( New York City ), the Medical University of South Carolina, and the Ralph H. Johnson VA Medical Center ( South Carolina ).

The High Command meets to discuss all issues, including those of a political nature, and is responsible for drawing up the list of generals from which the president chooses those who will be promoted to four stars.

In byte-oriented systems ( i. e. most modern computers ), the term uncompressed BCD usually implies a full byte for each digit ( often including a sign ), whereas packed BCD typically encodes two decimal digits within a single byte by taking advantage of the fact that four bits are enough to represent the range 0 to 9.

The apple is said to be a bundle of properties including redness, being four inches ( 100 mm ) wide, and juiciness.

They played one extra match on this tour, making the total of 21 games, including four tests against South Africa, with the British Isles winning three of them.

" The charter required that the makeup of the board of 36 trustees include, 22 Baptists, five Friends, four Congregationalists, and five Church of England members, and by 12 Fellows, of whom eight, including the President, should be Baptists " and the rest indifferently of any or all denominations.

It has been awarded eight Pulitzer Prizes in its history, including four for editorial writing and three for photography before it was converted to tabloid format in 1981.

Biotechnology has applications in four major industrial areas, including health care ( medical ), crop production and agriculture, non food ( industrial ) uses of crops and other products ( e. g. biodegradable plastics, vegetable oil, biofuels ), and environmental uses.

In 2009, the North Carolina Department of Transportation began widening 1. 1 miles of U. S. 421 ( King Street ) to a four to six-lane divided highway with a raised concrete median from U. S. 321 ( Hardin Street ) to east of N. C. 194 ( Jefferson Road ), including a new entrance and exit to the new Watauga High School, at a cost of $ 16. 2 million.

The definition of rapid cycling most frequently cited in the literature ( including the DSM ) is that of Dunner and Fieve: at least four major depressive, manic, hypomanic or mixed episodes are required to have occurred during a 12-month period.

Together these four " foundation collections " included many of the most treasured books now in the British Library including the Lindisfarne Gospels and the sole surviving copy of Beowulf.

And, based on the findings of placebo-controlled studies, they do not recommend use of benzodiazepines beyond two to four weeks, as tolerance and physical dependence develop rapidly, with withdrawal symptoms including rebound anxiety occurring after six weeks or more of use.

Under the Cronquist system, the first four families ( including Begoniaceae, Cucurbitaceae, and Datiscaceae ), were placed in the order Violales, within the Dilleniidae, with the Tetramelaceae subsumed within the Datiscaceae.