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Eli Whitney

Eli Whitney Jr. (December 8, 1765 – January 8, 1825) was an American inventor, widely known for inventing the cotton gin in 1793, one of the key inventions of the Industrial Revolution that shaped the economy of the Antebellum South.

Whitney's invention made upland short cotton into a profitable crop, which strengthened the economic foundation of slavery in the United States and prolonged the institution. Despite the social and economic impact of his invention, Whitney lost much of his profits in legal battles over patent infringement for the cotton gin. Thereafter, he turned his attention to securing contracts with the government in the manufacture of muskets for the newly formed United States Army. He continued making arms and inventing until his death in 1825.

Early life and education
Whitney was born in Westborough, Massachusetts, on December 8, 1765, the eldest child of Eli Whitney Sr., a prosperous farmer, and his wife Elizabeth Fay, also of Westborough.

The younger Eli was famous during his lifetime and after his death by the name "Eli Whitney", though he was technically Eli Whitney Jr. His son, born in 1820, also named Eli, was known during his lifetime and afterward by the name "Eli Whitney Jr."

Whitney's mother, Elizabeth Fay, died in 1777, when he was 11. At age 14 he operated a profitable nail manufacturing operation in his father's workshop during the Revolutionary War.

Because his stepmother opposed his wish to attend college, Whitney worked as a farm laborer and school teacher to save money. He prepared for Yale at Leicester Academy (now Becker College) and under the tutelage of Rev. Elizur Goodrich of Durham, Connecticut, he entered in the fall of 1789 and graduated Phi Beta Kappa in 1792. Whitney expected to study law but, finding himself short of funds, accepted an offer to go to South Carolina as a private tutor.

Instead of reaching his destination, he was convinced to visit Georgia. In the closing years of the 18th century, Georgia was a magnet for New Englanders seeking their fortunes (its Revolutionary-era governor had been Lyman Hall, a migrant from Connecticut). When he initially sailed for South Carolina, among his shipmates were the widow (Catherine Littlefield Greene) and family of the Revolutionary hero Gen. Nathanael Greene of Rhode Island. Mrs. Greene invited Whitney to visit her Georgia plantation, Mulberry Grove. Her plantation manager and husband-to-be was Phineas Miller, another Connecticut migrant and Yale graduate (class of 1785), who would become Whitney's business partner.

Career
Whitney is most famous for two innovations which came to have significant impacts on the United States in the mid-19th century: the cotton gin (1793) and his advocacy of interchangeable parts. In the South, the cotton gin revolutionized the way cotton was harvested and reinvigorated slavery. Conversely, in the North the adoption of interchangeable parts revolutionized the manufacturing industry, contributing greatly to the U.S. victory in the Civil War.

Cotton gin

The cotton gin is a mechanical device that removes the seeds from cotton, a process that had previously been extremely labor-intensive. The word gin is short for engine. While staying at Mulberry Grove, Whitney constructed several ingenious household devices which led Mrs Greene to introduce him to some businessmen who were discussing the desirability of a machine to separate the short staple upland cotton from its seeds, work that was then done by hand at the rate of a pound of lint a day. In a few weeks Whitney produced a model. The cotton gin was a wooden drum stuck with hooks that pulled the cotton fibers through a mesh. The cotton seeds would not fit through the mesh and fell outside. Whitney occasionally told a story wherein he was pondering an improved method of seeding the cotton when he was inspired by observing a cat attempting to pull a chicken through a fence, and able to only pull through some of the feathers.

A single cotton gin could generate up to 55 lb of cleaned cotton daily. This contributed to the economic development of the Southern United States, a prime cotton growing area; some historians believe that this invention allowed for the African slavery system in the Southern United States to become more sustainable at a critical point in its development.

Whitney applied for the patent for his cotton gin on October 28, 1793, and received the patent (later numbered as X72) on March 14, 1794, but it was not validated until 1807. Whitney and his partner, Miller, did not intend to sell the gins. Rather, like the proprietors of grist and sawmills, they expected to charge farmers for cleaning their cotton – two-fifths of the value, paid in cotton. Resentment at this scheme, the mechanical simplicity of the device and the primitive state of patent law, made infringement inevitable. Whitney and Miller could not build enough gins to meet demand, so gins from other makers found ready sale. Ultimately, patent infringement lawsuits consumed the profits (one patent, later annulled, was granted in 1796 to Hogden Holmes for a gin which substituted circular saws for the spikes) and their cotton gin company went out of business in 1797. One oft-overlooked point is that there were drawbacks to Whitney's first design. There is significant evidence that the design flaws were solved by his sponsor, Mrs. Greene, but Whitney gave her no public credit or recognition.

After validation of the patent, the legislature of South Carolina voted $50,000 for the rights for that state, while North Carolina levied a license tax for five years, from which about $30,000 was realized. There is a claim that Tennessee paid about $10,000.

While the cotton gin did not earn Whitney the fortune he had hoped for, it did give him fame. It has been argued by some historians that Whitney's cotton gin was an important if unintended cause of the American Civil War. After Whitney's invention, the plantation slavery industry was rejuvenated, eventually culminating in the Civil War.

The cotton gin transformed Southern agriculture and the national economy. Southern cotton found ready markets in Europe and in the burgeoning textile mills of New England. Cotton exports from the U.S. boomed after the cotton gin's appearance – from less than 500000 lb in 1793 to 93 e6lb by 1810. Cotton was a staple that could be stored for long periods and shipped long distances, unlike most agricultural products. It became the U.S.'s chief export, representing over half the value of U.S. exports from 1820 to 1860.

Whitney believed that his cotton gin would reduce the demand for enslaved labor and would help hasten the end of southern slavery. Paradoxically, the cotton gin, a labor-saving device, helped preserve and prolong slavery in the United States for another 70 years. Before the 1790s, slave labor was primarily employed in growing rice, tobacco, and indigo, none of which were especially profitable anymore. Neither was cotton, due to the difficulty of seed removal. But with the invention of the gin, growing cotton with slave labor became highly profitable – the chief source of wealth in the American South, and the basis of frontier settlement from Georgia to Texas. "King Cotton" became a dominant economic force, and slavery was sustained as a key institution of Southern society.

Interchangeable parts
Eli Whitney has often been incorrectly credited with inventing the idea of interchangeable parts, which he championed for years as a maker of muskets; however, the idea predated Whitney, and Whitney's role in it was one of promotion and popularizing, not invention. Successful implementation of the idea eluded Whitney until near the end of his life, occurring first in others' armories.

Attempts at interchangeability of parts can be traced back as far as the Punic Wars through both archaeological remains of boats now in Museo Archeologico Baglio Anselmi and contemporary written accounts. In modern times the idea developed over decades among many people. An early leader was Jean-Baptiste Vaquette de Gribeauval, an 18th-century French artillerist who created a fair amount of standardization of artillery pieces, although not true interchangeability of parts. He inspired others, including Honoré Blanc and Louis de Tousard, to work further on the idea, and on shoulder weapons as well as artillery. In the 19th century these efforts produced the "armory system," or American system of manufacturing. Certain other New Englanders, including Captain John H. Hall and Simeon North, arrived at successful interchangeability before Whitney's armory did. The Whitney armory finally succeeded not long after his death in 1825.

The motives behind Whitney's acceptance of a contract to manufacture muskets in 1798 were mostly monetary. By the late 1790s, Whitney was on the verge of bankruptcy and the cotton gin litigation had left him deeply in debt. His New Haven cotton gin factory had burned to the ground, and litigation sapped his remaining resources. The French Revolution had ignited new conflicts between Great Britain, France, and the United States. The new American government, realizing the need to prepare for war, began to rearm. The War Department issued contracts for the manufacture of 10,000 muskets. Whitney, who had never made a gun in his life, obtained a contract in January 1798 to deliver 10,000 to 15,000 muskets in 1800. He had not mentioned interchangeable parts at that time. Ten months later, the Treasury Secretary, Oliver Wolcott Jr., sent him a "foreign pamphlet on arms manufacturing techniques," possibly one of Honoré Blanc's reports, after which Whitney first began to talk about interchangeability.

In May 1798, Congress voted for legislation that would use 800,000 dollars in order to pay for small arms and cannons in case war with France erupted. It offered a 5,000 dollar incentive with an additional 5,000 dollars once that money was exhausted for the person that was able to accurately produce arms for the government. Because the cotton gin had not brought Whitney the rewards he believed it promised, he accepted the offer. Although the contract was for one year, Whitney did not deliver the arms until 1809, using multiple excuses for the delay. Recently, historians have found that during 1801–1806, Whitney took the money and headed into South Carolina in order to profit from the cotton gin.

Although Whitney's demonstration of 1801 appeared to show the feasibility of creating interchangeable parts, Merritt Roe Smith concludes that it was "staged" and "duped government authorities" into believing that he had been successful. The charade gained him time and resources toward achieving that goal.

When the government complained that Whitney's price per musket compared unfavorably with those produced in government armories, he was able to calculate an actual price per musket by including fixed costs such as insurance and machinery, which the government had not accounted for. He thus made early contributions to both the concepts of cost accounting, and economic efficiency in manufacturing.

Milling machine
Machine tool historian Joseph W. Roe credited Whitney with inventing the first milling machine circa 1818. Subsequent work by other historians (Woodbury; Smith; Muir; Battison [cited by Baida ]) suggests that Whitney was among a group of contemporaries all developing milling machines at about the same time (1814 to 1818), and that the others were more important to the innovation than Whitney was. (The machine that excited Roe may not have been built until 1825, after Whitney's death.) Therefore, no one person can properly be described as the inventor of the milling machine.

Later life and legacy

Despite his humble origins, Whitney was keenly aware of the value of social and political connections. In building his arms business, he took full advantage of the access that his status as a Yale alumnus gave him to other well-placed graduates, such as Oliver Wolcott Jr., Secretary of the Treasury (class of 1778), and James Hillhouse, a New Haven developer and political leader.

His 1817 marriage to Henrietta Edwards, granddaughter of the famed evangelist Jonathan Edwards, daughter of Pierpont Edwards, head of the Democratic Party in Connecticut, and first cousin of Yale's president, Timothy Dwight, the state's leading Federalist, further tied him to Connecticut's ruling elite. In a business dependent on government contracts, such connections were essential to success.

Whitney died of prostate cancer on January 8, 1825, in New Haven, Connecticut, just a month after his 59th birthday. He left a widow and his four children behind. One of his offspring, Eli Whitney III (known as Eli Whitney Jr.), was instrumental in building New Haven, Connecticut's waterworks. During the course of his illness, he reportedly invented and constructed several devices to mechanically ease his pain.

The Eli Whitney Students Program, Yale University's admissions program for non-traditional students, is named in honor of Whitney, who not only began his studies there when he was 23, but also went on to graduate Phi Beta Kappa in just three years.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Eli Whitney


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Talk:List of extinct bird species since 1500

Structure of page
I'm beginning to wonder how to structure this page. The original idea was to list the species by date of extinction, but they are often not sure. Would a geographical sorting be better? PàğaĿ.
 * Sort them by family, that's what the books do. FunkMonk (talk) 15:24, 16 December 2014 (UTC)

Structure of entries
Also, is it a good idea to put brief texts about the species on the listing page, or should I drop them and keep all the information on the separate bird pages? I'm beginning to lean towards the later approach. --Pinkunicorn

 * I'd favor the following approach: a brief statement of area of occurrence and date of extinction for every taxon, followed by an indent for subspecies. Additional explanations could go here initially (but briefly, a few lines at max - see Bay Thrush and Rodrigues Starling for taxa which demand longer explanations), but with actual species/subspecies pages becoming available, they should be merged into these ASAP (see Labrador Duck for a species where only the Location and Date info needs to be here really). Trivial information should not be put on this page either way; explanatory notes should be reserved for remarks on taxonomy
 * A problem is that the verification of an extinction usually takes decades (the 50-year-caveat), so many of the taxa I listed today are not officially extinct, but the only reason for that is that nobody has gone looking yet. -- Dysmorodrepanis 19:16, 10 February 2006 (UTC)

Dodo
Was the dodo really hunted to extinction? Surely not for food. The Dutch name was walgvogel. Walg=loathing vogel=bird. Even after days of kooking the beast was inedible and the saylors refused to eat its flesh. Jcwf
 * Dodo had no enemies on the island. With human traffic, it was gone within 80 years.  The forests it lived in were destroyed and the animals settlers brought with them, pigs, rats, and cats, destroyed the dodo's nests.  Will add something.  Ortolan88

Hawaiʻi
I believe there used to be a giant flightless goose in Hawaii, but I don't know if this became extinct after 1600. I suspect probably before. Mintguy 22:20 Dec 12, 2002 (UTC)

 * The nene isn't particularly giant, to my knowledge, but it is flightless and endangered. It's the state bird. - Montréalais

 * There was a greater nene (nene-nui), a giant nene (unnamed as of yet, but listed), 4 species of moa-nalo (goose-like oversized ducks of the mallard kind) and at least 2 more goose species with undetermined affiliation. They are found on the page on Recent prehistoric extinctions as all became extinct before 1600. -- Dysmorodrepanis 18:20, 10 February 2006 (UTC)

Why is Hawaii listed as the hardest-hit area, when Guam (according to the next sentence) has had a higher rate of extinction? Tokerboy

 * I think what it's saying is that 30% of all bird extinctions ever occurred in Hawaii. Although 60% of Guam's species were lost, they were probably a smaller percentage of all extinctions ever.  -- Zoe

 * Ever? That seems very unlikely. 60% of extinctions due to man sounds more like it -- stewacide 16:55, 17 Dec 2003 (UTC)

 * aaah, a closer reading reveals you are probably right, and I have fixed it to make this distinction more clear. Tokerboy

 * Probably needs some updating though. I'd rather say 60% of human-induced bird extinctions in the Late Quarternary were in the Pacific, generally. 2000 species of rails alone are often cited, but this is an estimate based on what has been dug up (literally) to date. The 60% Hawaii figure dates from the mid-80s when this was the only major area of the Pacific reasonably well explored. -- Dysmorodrepanis 19:16, 10 February 2006 (UTC)

Rename article...
Shouldnt the name of this article be List of extinct birds? -AnonIs this article for all extinct birds, or only recently extinct ones? As written the page should probable be called Historically extinct birds or something like that, since it seems to be exclusively on extinctions caused by man. -- stewacide 17:00, 17 Dec 2003 (UTC)

 * I think that you are right about the nature of the content, but I'm not sure that the name change is necessary. If I wanted to look for info on extinct birds, I would look under this title. Although strictly speaking prehistoric birds are also extinct, you would expect to find Archaeopteryx under Fossil birds or prehistoric birds rather than this article.

 * The book of the same name, incidently, contained exactly what I would expect it to, excluding fossil species. jimfbleak 17:12, 17 Dec 2003 (UTC)

 * If that's the intent of this page then I think it does need a name change. I can't think of any reason, for example, that something like Teratornis shouldn't be included in a list of Extinct birds, although clearly it doesn't fit with the page (since they went extinct a few million years ago with no help from man).

 * IMHO this page should be renamed to Historically extinct birds, with Extince birds either serving as a catch-all or a pointer to Historically extinct birds and Prehistorically extince birds. List of historically extinct birds might be even better. -- stewacide 17:28, 17 Dec 2003 (UTC)

 * there are 14 links directly to this page. No-one has thought it necessary to create a link as you describe. I'm especially wary of List of..., sicne sooner or later some idiot will wonder why it isn't alphabetical (believe me, it happens. Jim

 * Well, I've been over the Prehistoric Birds list. It was not bad as it was very comprehensive (I would not have had the passion to copy everything relevant from the FMNH list...) but the layout was somewhat messed up. I will do some finetuning, remove the redlinks etc, but the Prehistorics page can't stand as it is. It's far too large now I included all the late-Quarternary-pre-1500 extinctions I could lay my hands on. It has to be split into 2 sections: pre-Late Quarternary birds and Late Quarternary prehistoric extinctions - the former being without human "aid" and most of the latter will be. Technically, the split will be along the lines of "Fossil" and "Prehistoric" as per the Wikipedia categories for taxon classification ("Fossil" and "Subfossil" in scientific lingo).
 * But I cannot think of good unambiguous names - "Fossil" is misleading perhaps, as Wikipedia as of now does not distinguish between subfossils and fossils. "Prehistoric" is a catchall term for both. The easiest bit is this here page - it should be renamed "Historically Extinct Birds" or such - technically, the appropriate term would be "Recent", but "Recently Extinct Birds" would be both misleading and wrong the; correctly it would be "Birds Extinct in Recent times". Then, the unelegant way would be a disambig for "Extinct Birds" listing the 3 categories (unelegant because most ppl will think of the dod or the IBW when hearing "Extinct Birds", and not of Confuciusornis). The elegant way would be a a redirect from "Extinct Birds" to this "Historically..." and disambig line or two at the head of this page.
 * So, any good suggestions for how to name the 2 non-Recent extinction pages? "Fossil Birds" and "Later Quarternary Prehistoric Birds" are the least awkward solutions that I can think of. -- Dysmorodrepanis 19:16, 10 February 2006 (UTC)

Ivory-billed Woodpecker
Since the ivory bills have been spotted in the wild, shouldn't they be removed from this article?

Record ist still controversial, but I changed the Ivorybill bit to reflect upon this. -- Dysmorodrepanis 19:16, 10 February 2006 (UTC)

Prehistoric Birds
I've found there is an article for Prehistoric bird. While it needs some work, I'm going to add a link to it on this page for ease of use (as it stands, I don't see any way to access a list of fossil birds from here). Dinoguy2 18:49, 11 December 2005 (UTC)

See above for renaming discussion for more on that -- Dysmorodrepanis 19:16, 10 February 2006 (UTC)

Extinct since 1600, earlier extinctions not included?
Are birds that became extinct before AD 1600 not included? The IUCN Red List and the Committee on Recently Extinct Organisms (CREO) use both AD 1500 as starting date. What is the reason for using AD 1600? Pmaas 18:22, 8 February 2006 (UTC)

Yo Peter, good to see you here! I've changed the figure to 1500; since the list already included the Saint Helena taxa it really was that way already except that one number in the intro section. -- Dysmorodrepanis 22:20, 11 February 2006 (UTC)

Extinction Dates
Extinction dates are a matter of contention. Rarely one can say when exactly a taxon has gone extinct. For many 18th century Polynesian extinctions, visits by scientists were so irregular and Norway rats probably jumped ship on every one of them that there is a 100-year-plus uncertainty period. I suggest reading this, especially Criterion 3; there should be a unified way what extinction date to give and how precise or vague it should be. I tend towards a more vague approach that could be refined using the "Dodo algorithm" published in Nature 426:245; even without that, narrowing it down to about 30 years or so is generally possible. See the entry on the Virgin Islands Screech Owl for a taxon that was shown to be extinct in 1995, but which may actually have disappeared as soon as 1865 (simply because nobody cared to look for a badly documented, unappealing and obscure taxon). Similarly, the Thick-billed Ground Pigeon (the latest officially confirmed extinction) has probably been gone since the 1940s at least. -- Dysmorodrepanis 19:16, 10 February 2006 (UTC)

Birds of prey subspecies
Hi, not to mean any offense, but I an unable to find any taxonomic reference confirming that these subspecies: are still considered valid. The HBW does not list them, neither does the AOU, Birds of North America/of the Westenr Palaearctic etc. See also here for what reference works are considered the default basis for bird taxonomy on Wikipedia. I am not aware of any new paper reestablishing these populations as valid subspecies; if there is one, please let me know. Thanks. Dysmorodrepanis 01:19, 1 September 2006 (UTC)
 * Korean Falcon, Falco peregrinus pelax (Korea, 1967)
 * Little Peregrine Falcon, Falco peregrinus pygmeaus (England, 1866)
 * Mexican Californian Condor, Gymnogyps californianus californianus, (Mexico, [[1909)
 * Nevada'sCalifornian Condor Gymnogyps californianus barberus
 * Mongolian Golden Eagle, Aquila chrysaetos mongoliae (Mongolia,1944)

One Sentence-Stubs
Noone will take notice of such articles (e.g. Amsterdam Island Duck) if you don't enter these stubs into the lists of the WikiProject Extinction or the Portal Extinction. Thanks. --Melly42 13:05, 27 July 2007 (UTC)

Which taxa should list here
It is possible to make a consensus for which taxa should list here and which not. Many species are not listed in the IUCN Redlist but where not seen for decades (should we left out this taxa?) and others seems to be doubtful though there is no official treatment (e.g. SACC, Clements Checklist) which shows how to deal with them. --Melly42 (talk) 10:56, 24 July 2009 (UTC)

External links modified
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Late Quaternary Page Vs. This Page
At what point does the page List of Late Quaternary prehistoric bird species overlap with this? Several birds that have gone extinct before Western documentation, such as upland moa and Tyto pollens, are included despite the fact that specimens were never officially collected by European taxonomists? — Preceding unsigned comment added by AidenD (talk • contribs) 01:39, 18 April 2019 (UTC)

Merge from List of bird extinctions by year
Both lists can be accommodated on a single page by making a table that has (at least) two sortable columns, for year and taxon. -- Beland (talk) 02:20, 4 October 2021 (UTC)
 * I feel like yes, we should merge both pages considering both are about extinct birds and because List of bird extinctions by year is lacking references. Also, it would add more detail to this page, so it says what year that type of bird went extinct. ValeAliz 21:37, 21 January 2022 (UTC)
 * Oppose, given that each page serves a different function, and merging without an enormous amount of work would make the combined page very long. Klbrain (talk) 20:41, 4 April 2022 (UTC)
 * Closing, given the uncontested objection with stale discussion. Klbrain (talk) 09:51, 6 November 2022 (UTC)


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The American Prisoner

The American Prisoner is a British novel written by Eden Phillpotts and published in 1904 and adapted into a film by the same name in 1929. The story concerns an English woman who lives at Fox Tor farm, and an American captured during the American War of Independence and held at the prison at Princetown on Dartmoor.

In the novel Malherb is a miscreant who destroys Childe's tomb and beats his servant. He is depicted as a victim of his own bad temper rather than a sadist.

Malherb is introduced as the younger son of a noble family and he builds the Fox Tor house to be the impressive gentleman's residence suggested by William Crossing rather than the humble cottage which it actually is.

title: The American Prisoner


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Electromagnetic field

An electromagnetic field (also EM field) is a physical field, mathematical functions of position and time, representing the influences on and due to electric charges. The field at any point in space and time can be regarded as a combination of an electric field and a magnetic field. Because of the interrelationship between the fields, a disturbance in the electric field can create a disturbance in the magnetic field which in turn affects the electric field, leading to an oscillation that propagates through space, known as an electromagnetic wave.

The way in which charges and currents (i.e. streams of charges) interact with the electromagnetic field is described by Maxwell's equations and the Lorentz force law. Maxwell's equations detail how the electric field converges towards or diverges away from electric charges, how the magnetic field curls around electrical currents, and how changes in the electric and magnetic fields influence each other. The Lorentz force law states that a charge subject to an electric field feels a force along the direction of the field, and a charge moving through a magnetic field feels a force that is perpendicular both to the magnetic field and to its direction of motion.

The electromagnetic field is described by classical electrodynamics, an example of a classical field theory. This theory describes many macroscopic physical phenomena accurately. However, it was unable to explain the photoelectric effect and atomic absorption spectroscopy, experiments at the atomic scale. That required the use of quantum mechanics, specifically the quantization of the electromagnetic field and the development of quantum electrodynamics.

History
The empirical investigation of electromagnetism is at least as old as the ancient Greek philosopher, mathematician and scientist Thales of Miletus, who around 600 BCE described his experiments rubbing fur of animals on various materials such as amber creating static electricity. By the 18th century, it was understood that objects can carry positive or negative electric charge, that two objects carrying charge of the same sign repel each other, that two objects carrying charges of opposite sign attract one another, and that the strength of this force falls off as the square of the distance between them. Michael Faraday visualized this in terms of the charges interacting via the electric field. An electric field is produced when the charge is stationary with respect to an observer measuring the properties of the charge, and a magnetic field as well as an electric field are produced when the charge moves, creating an electric current with respect to this observer. Over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole—the electromagnetic field. In 1820, Hans Christian Ørsted showed that an electric current can deflect a nearby compass needle, establishing that electricity and magnetism are closely related phenomena. Faraday then made the seminal observation that time-varying magnetic fields could induce electric currents in 1831.

In 1861, James Clerk Maxwell synthesized all the work to date on electrical and magnetic phenomena into a single mathematical theory, from which he then deduced that light is an electromagnetic wave. Maxwell's continuous field theory was very successful until evidence supporting the atomic model of matter emerged. Beginning in 1877, Hendrik Lorentz developed an atomic model of electromagnetism and in 1897 J. J. Thomson completed experiments that defined the electron. The Lorentz theory works for free charges in electromagnetic fields, but fails to predict the energy spectrum for bound charges in atoms and molecules. For that problem, quantum mechanics is needed, ultimately leading to the theory of quantum electrodynamics.

Practical applications of the new understanding of electromagnetic fields emerged in the late 1800s. The electrical generator and motor were invented using only the empirical findings like Faraday's and Ampere's laws combined with practical experience.

Mathematical description
There are different mathematical ways of representing the electromagnetic field. The first one views the electric and magnetic fields as three-dimensional vector fields. These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates. As such, they are often written as $E(x, y, z, t)$ (electric field) and $B(x, y, z, t)$ (magnetic field).

If only the electric field ($E$) is non-zero, and is constant in time, the field is said to be an electrostatic field. Similarly, if only the magnetic field ($B$) is non-zero and is constant in time, the field is said to be a magnetostatic field. However, if either the electric or magnetic field has a time-dependence, then both fields must be considered together as a coupled electromagnetic field using Maxwell's equations.

With the advent of special relativity, physical laws became amenable to the formalism of tensors. Maxwell's equations can be written in tensor form, generally viewed by physicists as a more elegant means of expressing physical laws.

The behavior of electric and magnetic fields, whether in cases of electrostatics, magnetostatics, or electrodynamics (electromagnetic fields), is governed by Maxwell's equations. In the vector field formalism, these are:

where $$\rho$$ is the charge density, which is a function of time and position, $$\varepsilon_0$$ is the vacuum permittivity, $$\mu_0$$ is the vacuum permeability, and $J$ is the current density vector, also a function of time and position. Inside a linear material, Maxwell's equations change by switching the permeability and permittivity of free space with the permeability and permittivity of the linear material in question. Inside other materials which possess more complex responses to electromagnetic fields, these terms are often represented by complex numbers, or tensors.
 * Gauss's law : $$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$$
 * Gauss's law for magnetism : $$\nabla \cdot \mathbf{B} = 0$$
 * Faraday's law : $$\nabla \times \mathbf{E} = -\frac {\partial \mathbf{B}}{\partial t}$$
 * Ampère–Maxwell law : $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0\varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$

The Lorentz force law governs the interaction of the electromagnetic field with charged matter.

When a field travels across to different media, the behavior of the field changes according to the properties of the media.

Electrostatics and magnetostatics
The Maxwell equations simplify when the charge density at each point in space does not change over time and all electric currents likewise remain constant. All of the time derivatives vanish from the equations, leaving two expressions that involve the electric field, $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$ and $$\nabla\times\mathbf{E} = 0,$$ along with two formulae that involve the magnetic field: $$\nabla \cdot \mathbf{B} = 0$$ and $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J}.$$ These expressions are the basic equations of electrostatics, which focuses on situations where electrical charges do not move, and magnetostatics, the corresponding area of magnetic phenomena.

Transformations of electromagnetic fields
Whether a physical effect is attributable to an electric field or to a magnetic field is dependent upon the observer, in a way that special relativity makes mathematically precise. For example, suppose that a laboratory contains a long straight wire that carries an electrical current. In the frame of reference where the laboratory is at rest, the wire is motionless and electrically neutral: the current, composed of negatively charged electrons, moves against a background of positively charged ions, and the densities of positive and negative charges cancel each other out. A test charge near the wire would feel no electrical force from the wire. However, if the test charge is in motion parallel to the current, the situation changes. In the rest frame of the test charge, the positive and negative charges in the wire are moving at different speeds, and so the positive and negative charge distributions are Lorentz-contracted by different amounts. Consequently, the wire has a nonzero net charge density, and the test charge must experience a nonzero electric field and thus a nonzero force. In the rest frame of the laboratory, there is no electric field to explain the test charge being pulled towards or pushed away from the wire. So, an observer in the laboratory rest frame concludes that a field must be present.

In general, a situation that one observer describes using only an electric field will be described by an observer in a different inertial frame using a combination of electric and magnetic fields. Analogously, a phenomenon that one observer describes using only a magnetic field will be, in a relatively moving reference frame, described by a combination of fields. The rules for relating the fields required in different reference frames are the Lorentz transformations of the fields.

Thus, electrostatics and magnetostatics are now seen as studies of the static EM field when a particular frame has been selected to suppress the other type of field, and since an EM field with both electric and magnetic will appear in any other frame, these "simpler" effects are merely a consequence of different frames of measurement. The fact that the two field variations can be reproduced just by changing the motion of the observer is further evidence that there is only a single actual field involved which is simply being observed differently.

Reciprocal behavior of electric and magnetic fields
The two Maxwell equations, Faraday's Law and the Ampère–Maxwell Law, illustrate a very practical feature of the electromagnetic field. Faraday's Law may be stated roughly as "a changing magnetic field inside a loop creates an electric voltage around the loop". This is the principle behind the electric generator.

Ampere's Law roughly states that "an electrical current around a loop creates a magnetic field through the loop". Thus, this law can be applied to generate a magnetic field and run an electric motor.

Behavior of the fields in the absence of charges or currents
Maxwell's equations can be combined to derive wave equations. The solutions of these equations take the form of an electromagnetic wave. In a volume of space not containing charges or currents (free space) – that is, where $$\rho$$ and $E$ are zero, the electric and magnetic fields satisfy these electromagnetic wave equations:
 * $$ \left( \nabla^2 - { 1 \over {c}^2 } {\partial^2 \over \partial t^2} \right) \mathbf{E} \ \ = \ \ 0$$
 * $$ \left( \nabla^2 - { 1 \over {c}^2 } {\partial^2 \over \partial t^2} \right) \mathbf{B} \ \ = \ \ 0$$

James Clerk Maxwell was the first to obtain this relationship by his completion of Maxwell's equations with the addition of a displacement current term to Ampere's circuital law. This unified the physical understanding of electricity, magnetism, and light: visible light is but one portion of the full range of electromagnetic waves, the electromagnetic spectrum.

Time-varying EM fields in Maxwell's equations
An electromagnetic field very far from currents and charges (sources) is called electromagnetic radiation (EMR) since it radiates from the charges and currents in the source. Such radiation can occur across a wide range of frequencies called the electromagnetic spectrum, including radio waves, microwave, infrared, visible light, ultraviolet light, X-rays, and gamma rays. The many commercial applications of these radiations are discussed in the named and linked articles.

A notable application of visible light is that this type of energy from the Sun powers all life on Earth that either makes or uses oxygen.

A changing electromagnetic field which is physically close to currents and charges (see near and far field for a definition of "close") will have a dipole characteristic that is dominated by either a changing electric dipole, or a changing magnetic dipole. This type of dipole field near sources is called an electromagnetic near-field.

Changing dipole fields, as such, are used commercially as near-fields mainly as a source of dielectric heating. Otherwise, they appear parasitically around conductors which absorb EMR, and around antennas which have the purpose of generating EMR at greater distances.

Changing dipole fields (i.e., magnetic near-fields) are used commercially for many types of magnetic induction devices. These include motors and electrical transformers at low frequencies, and devices such as RFID tags, metal detectors, and MRI scanner coils at higher frequencies.

Health and safety
The potential effects of electromagnetic fields on human health vary widely depending on the frequency, intensity of the fields, and the length of the exposure. Low frequency, low intensity, and short duration exposure to electromagnetic radiation is generally considered safe. On the other hand, radiation from other parts of the electromagnetic spectrum, such as ultraviolet light and gamma rays, are known to cause significant harm in some circumstances.

title: Electromagnetic field