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.

The four Maxwell's equations ( including the Maxwell – Faraday equation ), along with the Lorentz force law, are a sufficient foundation to derive everything in 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.

Though the four boys and two girls, the youngest nineteen years of age, the oldest twenty-four, came from varying backgrounds and had different professional and personal interests, there was surprising agreement among them.

The ideal home, they agreed, would be a small private house or a city apartment of four to five rooms, just enough for a family consisting of husband, wife, and two children.

'' The other important difference between the two Constitutions was that the President of the Confederacy held office for six ( instead of four ) years, and was limited to one term.

Tom had received four years of education at the University of North Carolina and two at Harvard, and Fred had been in and out of Georgia Tech and Carneigie Tech and part of the time had been a self-help student.

Blackman arrived a day or two early, and Lewis took him to a department store immediately and outfitted him, luggage and all, and then he took him to a party at the Woodwards that went on until four in the morning.

There were four from St. John's and four from Christ's, three from Pembroke, and two from each of the colleges, Jesus, Peterhouse, Queens', and Trinity, with Caius, Clare, King's, Magdalene, and Sidney supplying one each in the ordo senioritatis.

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.

There are forty-seven special district governments in Rhode Island ( excluding two regional school districts, four housing authorities, and the Kent County Water Authority ).

Five, four, three, two, one, fire!!

Take two three-inch-wide pieces and rip them down the center of the thickness to make the four.

It fell, February 6, 1827, carrying with it a horse and wagon, two men and four oxen.

We found that three men -- two carpenters and a helper -- can put up wall panels or trusses more economically than four men -- because four men don't make two teams ; ;

We found that wherever you can use two teams on a job, five men, not four, is the magic number ''.

Although there were only four fluids tested, it was apparent that there were two distinct types.

All samplers were operated for a period of two hours except one, which was operated for four hours.

After another two weeks, the first young emerge, four to eight small daughters that begin to play the role of worker bees, collecting pollen and nectar in the field and caring for the new young generation while the queen retires to a life of egg laying.

When now we count the frequency of the 71 items in the two language families appearing in the same column or grade, or one column or grade apart, or two or three or four, we find these differences: Af

This second conclusion, independently arrived at by independent study of material from two pairs of language families as different and remote from one another as these four are, cannot be ignored.

Between the ages of two and four years, negativism or resistance to adult authority is noticeable ; ;

For example, the BBB has reported it was receiving four times as many inquiries about quack devices and 10 times as many complaints compared with two years ago.