title: Blown Away (TV series)

text: The contestants on the show are 10 glassblowers. Katherine Gray, an artist and associate professor at California State University, San Bernardino, is the chief judge, and Nick Uhas, a former "Big Brother USA" contestant and science YouTuber, hosts the show. The winner receives a prize package worth the equivalent of $60,000, including an artist residency at the Corning Museum of Glass. The first season was filmed in a converted warehouse in Hamilton, Ontario, a facility that was "custom-built to accommodate 10 glass blowers working simultaneously". Industry experts from the Craft and Design Glass Studio at Sheridan College, Pilchuck Glass School, and the Corning Museum of Glass consulted the producers during the construction of the facility and provide advice and evaluation to the contestants each round.


title: Blown Away (TV series)

text: "Blown Away" received a positive review from Joel Keller of Decider who compared it to "Top Chef" and "The Great British Bake Off". "The Fader" praised the series as rising above other competition shows and being educational.


title: Fubini's theorem

text: In mathematical analysis Fubini's theorem is a result that gives conditions under which it is possible to compute a double integral by using an iterated integral, introduced by Guido Fubini in 1907. One may switch the order of integration if the double integral yields a finite answer when the integrand is replaced by its absolute value.


title: Fubini's theorem

text: Fubini's theorem implies that two iterated integrals are equal to the corresponding double integral across its integrands. Tonelli's theorem, introduced by Leonida Tonelli in 1909, is similar, but applies to a non-negative measurable function rather than one integrable over their domains.


title: Fubini's theorem

text: A related theorem is often called Fubini's theorem for infinite series, which states that if formula_2 is a doubly-indexed sequence of real numbers, and if formula_3 is absolutely convergent, then


title: Fubini's theorem

text: Although Fubini's theorem for infinite series is a special case of the more general Fubini's theorem, it is not appropriate to characterize it as a logical consequence of Fubini's theorem. This is because some properties of measures, in particular sub-additivity, are often proved using Fubini's theorem for infinite series. In this case, Fubini's general theorem is a logical consequence of Fubini's theorem for infinite series.


title: Fubini's theorem

text: The special case of Fubini's theorem for continuous functions on a product of closed bounded subsets of real vector spaces was known to Leonhard Euler in the 18th century. extended this to bounded measurable functions on a product of intervals. conjectured that the theorem could be extended to functions that were integrable rather than bounded, and this was proved by . gave a variation of Fubini's theorem that applies to non-negative functions rather than integrable functions.


title: Fubini's theorem

text: If "X" and "Y" are measure spaces with measures, there are several natural ways to define a product measure on their product.


title: Fubini's theorem

text: The product "X" × "Y" of measure spaces (in the sense of category theory) has as its measurable sets the σ-algebra generated by the products "A" × "B" of measurable subsets of "X" and "Y".


title: Fubini's theorem

text: A measure "μ" on "X" × "Y" is called a product measure if "μ"("A" × "B") = "μ"("A")"μ"("B") for measurable subsets "A" ⊂ "X" and "B" ⊂ "Y" and measures "µ" on "X" and "µ" on "Y". In general there may be many different product measures on "X" × "Y". Fubini's theorem and Tonelli's theorem both need technical conditions to avoid this complication; the most common way is to assume all measure spaces are σ-finite, in which case there is a unique product measure on "X"×"Y". There is always a unique maximal product measure on "X" × "Y", where the measure of a measurable set is the inf of the measures of sets containing it that are countable unions of products of measurable sets. The maximal product measure can be constructed by applying Carathéodory's extension theorem to the additive function μ such that "μ"("A" × "B") = "μ"("A")"μ"("B") on the ring of sets generated by products of measurable sets. (Carathéodory's extension theorem gives a measure on a measure space that in general contains more measurable sets than the measure space "X" × "Y", so strictly speaking the measure should be restricted to the σ-algebra generated by the products "A" × "B" of measurable subsets of "X" and "Y".)


title: Fubini's theorem

text: The product of two complete measure spaces is not usually complete. For example, the product of the Lebesgue measure on the unit interval "I" with itself is not the Lebesgue measure on the square "I" × "I". There is a variation of Fubini's theorem for complete measures, which uses the completion of the product of measures rather than the uncompleted product.


title: Fubini's theorem

text: Suppose "X" and "Y" are σ-finite measure spaces, and suppose that "X" × "Y" is given the product measure (which is unique as "X" and "Y" are σ-finite). Fubini's theorem states that if "f" is "X" × "Y" integrable, meaning that "f" is a measurable function and


title: Fubini's theorem

text: The first two integrals are iterated integrals with respect to two measures, respectively, and the third is an integral with respect to the product measure. The partial integrals formula_7 and formula_8 need not be defined everywhere, but this does not matter as the points where they are not defined form a set of measure 0.


title: Fubini's theorem

text: If the above integral of the absolute value is not finite, then the two iterated integrals may have different values. See below for an illustration of this possibility.


title: Fubini's theorem

text: The condition that "X" and "Y" are σ-finite is usually harmless because in practice almost all measure spaces one wishes to use Fubini's theorem for are σ-finite.


title: Fubini's theorem

text: Fubini's theorem has some rather technical extensions to the case when "X" and "Y" are not assumed to be σ-finite . The main extra complication in this case is that there may be more than one product measure on "X"×"Y". Fubini's theorem continues to hold for the maximal product measure, but can fail for other product measures. For example, there is a product measure and a non-negative measurable function "f" for which the double integral of |"f"| is zero but the two iterated integrals have different values; see the section on counterexamples below for an example of this. Tonelli's theorem and the Fubini–Tonelli theorem (stated below) can fail on non σ-finite spaces even for the maximal product measure.


title: Fubini's theorem

text: Tonelli's theorem (named after Leonida Tonelli) is a successor of Fubini's theorem. The conclusion of Tonelli's theorem is identical to that of Fubini's theorem, but the assumption that formula_9 has a finite integral is replaced by the assumption that formula_10 is a non-negative measurable function.


title: Fubini's theorem

text: Tonelli's theorem states that if ("X", "A", μ) and ("Y", "B", ν) are σ-finite measure spaces, while "f" from "X"×"Y" to [0,∞] is non-negative measurable function, then


title: Fubini's theorem

text: A special case of Tonelli's theorem is in the interchange of the summations, as in formula_12, where formula_13 are non-negative for all "x" and "y". The crux of the theorem is that the interchange of order of summation holds even if the series diverges. In effect, the only way a change in order of summation can change the sum is when there exist some subsequences that diverge to formula_14 and others diverging to formula_15. With all elements non-negative, this does not happen in the stated example.


title: Fubini's theorem

text: Without the condition that the measure spaces are σ-finite it is possible for all three of these integrals to have different values.


title: Fubini's theorem

text: Some authors give generalizations of Tonelli's theorem to some measure spaces that are not σ-finite but these generalizations often add conditions that immediately reduce the problem to the σ-finite case. For example, one could take the σ-algebra on "A"×"B" to be that generated by the product of subsets of finite measure, rather than that generated by all products of measurable subsets, though this has the undesirable consequence that the projections from the product to its factors "A" and "B" are not measurable. Another way is to add the condition that the support of "f" is contained in a countable union of products of sets of finite measure. gives some rather technical extensions of Tonelli's theorem to some non σ-finite spaces. None of these generalizations have found any significant applications outside abstract measure theory, largely because almost all measure spaces of practical interest are σ-finite.


title: Fubini's theorem

text: the Fubini–Tonelli theorem (often just called Fubini's theorem), which states that if formula_16 and formula_17 are σ-finite measure spaces, and if formula_10 is a measurable function, then


title: Fubini's theorem

text: The absolute value of formula_10 in the conditions above can be replaced by either the positive or the negative part of formula_10; these forms include Tonelli's theorem as a special case as the negative part of a non-negative function is zero and so has finite integral. Informally all these conditions say that the double integral of formula_10 is well defined, though possibly infinite.


title: Fubini's theorem

text: The advantage of the Fubini–Tonelli over Fubini's theorem is that the repeated integrals of formula_9 may be easier to study than the double integral. As in Fubini's theorem, the single integrals may fail to be defined on a measure 0 set.


title: Fubini's theorem

text: The versions of Fubini's and Tonelli's theorems above do not apply to integration on the product of the real line formula_25 with itself with Lebesgue measure. The problem is that Lebesgue measure on formula_26 is not the product of Lebesgue measure on formula_25 with itself, but rather the completion of this: a product of two complete measure spaces formula_16 and formula_17 is not in general complete. For this reason one sometimes uses versions of Fubini's theorem for complete measures: roughly speaking one just replaces all measures by their completions. The various versions of Fubini's theorem are similar to the versions above, with the following minor differences:


title: Fubini's theorem

text: Proofs of the Fubini and Tonelli theorems are necessarily somewhat technical, as they have to use a hypothesis related to σ-finiteness. Most proofs involve building up to the full theorems by proving them for increasingly complicated functions with the steps as follows.


title: Fubini's theorem

text: For Riemann integrals, Fubini's theorem is proven by refining the partitions along the x-axis and y-axis as to create a joint partition of the form formula_36, which is a partition over formula_30. This is used to show that the double integrals of either order are equal to the integral over formula_30.


title: Fubini's theorem

text: The following examples show how Fubini's theorem and Tonelli's theorem can fail if any of their hypotheses are omitted.


title: Fubini's theorem

text: Suppose that "X" is the unit interval with the Lebesgue measurable sets and Lebesgue measure, and "Y" is the unit interval with all subsets measurable and the counting measure, so that "Y" is not σ-finite. If "f" is the characteristic function of the diagonal of "X"×"Y", then integrating "f" along "X" gives the 0 function on "Y", but integrating "f" along "Y" gives the function 1 on "X". So the two iterated integrals are different. This shows that Tonelli's theorem can fail for spaces that are not σ-finite no matter what product measure is chosen. The measures are both decomposable, showing that Tonelli's theorem fails for decomposable measures (which are slightly more general than σ-finite measures).


title: Fubini's theorem

text: Fubini's theorem holds for spaces even if they are not assumed to be σ-finite provided one uses the maximal product measure.


title: Fubini's theorem

text: In the example above, for the maximal product measure, the diagonal has infinite measure so the double integral of |"f"| is infinite, and Fubini's theorem holds vacuously.


title: Fubini's theorem

text: However, if we give "X"×"Y" the product measure such that the measure of a set is the sum of the Lebesgue measures of its horizontal sections, then the double integral of |"f"| is zero, but the two iterated integrals still have different values. This gives an example of a product measure where Fubini's theorem fails.


title: Fubini's theorem

text: This gives an example of two different product measures on the same product of two measure spaces. For products of two σ-finite measure spaces, there is only one product measure.


title: Fubini's theorem

text: Suppose that "X" is the first uncountable ordinal, with the finite measure where the measurable sets are either countable (with measure 0) or the sets of countable complement (with measure 1). The (non-measurable) subset "E" of "X"×"X" given by pairs ("x","y") with "x"<"y" is countable on every horizontal line and has countable complement on every vertical line. If "f" is the characteristic function of "E" then the two iterated integrals of "f" are defined and have different values 1 and 0. The function "f" is not measurable. This shows that Tonelli's theorem can fail for non-measurable functions.


title: Fubini's theorem

text: A variation of the example above shows that Fubini's theorem can fail for non-measurable functions even if |"f"| is integrable and both repeated integrals are well defined: if we take "f" to be 1 on "E" and –1 on the complement of "E", then |"f"| is integrable on the product with integral 1, and both repeated integrals are well defined, but have different values 1 and –1.


title: Fubini's theorem

text: Assuming the continuum hypothesis, one can identify "X" with the unit interval "I", so there is a bounded non-negative function on "I"×"I" whose two iterated integrals (using Lebesgue measure) are both defined but unequal. This example was found by .


title: Fubini's theorem

text: The stronger versions of Fubini's theorem on a product of two unit intervals with Lebesgue measure, where the function is no longer assumed to be measurable but merely that the two iterated integrals are well defined and exist, are independent of the standard Zermelo–Fraenkel axioms of set theory. The continuum hypothesis and Martin's axiom both imply that there exists a function on the unit square whose iterated integrals are not equal, while showed that it is consistent with ZFC that a strong Fubini-type theorem for [0, 1] does hold, and whenever the two iterated integrals exist they are equal. See List of statements undecidable in ZFC.


title: Fubini's theorem

text: Fubini's theorem tells us that (for measurable functions on a product of σ-finite measure spaces) if the integral of the absolute value is finite, then the order of integration does not matter; if we integrate first with respect to "x" and then with respect to "y", we get the same result as if we integrate first with respect to "y" and then with respect to "x". The assumption that the integral of the absolute value is finite is "Lebesgue integrability", and without it the two repeated integrals can have different values.


title: Fubini's theorem

text: A simple example to show that the repeated integrals can be different in general is to take the two measure spaces to be the positive integers, and to take the function "f"("x","y") to be 1 if "x" = "y", −1 if "x" = "y" + 1, and 0 otherwise. Then the two repeated integrals have different values 0 and 1.


title: Fubini's theorem

text: have different values. The corresponding double integral does not converge absolutely (in other words the integral of the absolute value is not finite):


title: Giant house spider

text: The giant house spider has been treated as either one species, under the name Eratigena atrica, or as three species, "E. atrica", E. duellica and E. saeva. , the three species view was accepted by the World Spider Catalog. They are among the largest spiders of Central and Northern Europe. They were previously placed in the genus "Tegenaria". In 2013, they were moved to the new genus "Eratigena" as the single species "Eratigena atrica". In 2018, the three separate species were restored. The bite of these species does not pose a threat to humans or pets, and they are generally reluctant to bite, preferring instead to hide or escape.


title: Giant house spider

text: The two sexes do not differ in coloration or markings. Its coloration is mainly dark brown. On its sternum is a lighter marking, with three light spots on each side that form an arrow-like shape pointing toward the head of the spider. The opisthosoma features a lighter middle line with six "spots" on each side. The giant house spider has the same coloration as the domestic house spider, "Tegenaria domestica"; it has earthy tones of brown and muddy red or yellow. They also have conspicuously hairy legs, palps and abdomen. The female body size can reach in length, with males having a slightly smaller body at around in length. The female leg span is typically around . The leg span of the male is highly variable, with spans between being common.


title: Giant house spider

text: Its eight eyes are of equal size and are arranged in two rows. As the eyes contain fewer than 400 visual cells, "E. atrica" can probably only distinguish light and dark.


title: Giant house spider

text: The first description of a spider now assigned to this species was by Carl Ludwig Koch in 1843, under the name "Tegenaria atrica". Other supposedly different species were described later, including "Tegenaria saeva" by John Blackwall in 1844, "Tegenaria duellica" by Eugène Simon in 1875 and "Tegenaria gigantea" by Ralph Vary Chamberlin and Wilton Ivie in 1935. "T. gigantea" was synonymized with "T. duellica" in 1978. The three remaining taxa have been regarded as distinct species, particularly in Britain. Thus Roberts (1995) provides distinguishing characters for "T. atrica", "T. duellica" and "T. saeva", as does Oxford (2008) for "T. duellica" (as "T. gigantea") and "T. saeva". Others consider these three as part of a single morphologically variable species, for which the oldest name, and hence the senior synonym, is "T. atrica".


title: Giant house spider

text: A phylogenetic study in 2013 concluded that "Tegenaria", as then defined, was not monophyletic, and split off some species, including "T. atrica", into the newly created segregate genus "Eratigena". The study also consolidated the various giant house spider species into one species, "E. atrica". A subsequent genetic study of "E. atrica" specimens determined that there were three distinct morphological groups, leading to the restoration of three separate species: "E. atrica", "E. duellica", and "E. saeva".


title: Giant house spider

text: "E. atrica" is found in Europe, Central Asia and Northern Africa. It was unwittingly introduced to the Pacific Northwest of North America circa 1900 due to human activity and has strongly increased in numbers for the last century.


title: Giant house spider

text: In the last few years the spider has been found in several European countries in which it was previously not recorded, like Estonia, Latvia and Lithuania. It is recorded in the checklist of Danish spider species, and is also found in Iceland.


title: Giant house spider

text: The giant house spider's original habitat consists mostly of caves, or dry forests where it is found under rocks, but it is a common spider in people's homes.


title: Giant house spider

text: The webs built by the giant house spider are flat and messy with a funnel at one end. They do not contain sticky threads. The spider lurks in the funnel until a small invertebrate happens to get trapped in the web, at which point the spider runs out and attacks it. They usually build their webs in corners (on both the floor and ceiling), between boxes in basements, behind cupboards, in attics, or any other area that is rarely disturbed by large animals or humans. They are also often found near window openings.


title: Giant house spider

text: "E. atrica" normally lives for two or three years, but lifetimes of up to six years have been observed. While the female only leaves its nest to feed, males can often be seen wandering around houses during the late summer and early autumn looking for a mate. Males can be found from July to October, adult females occur all year.


title: Giant house spider

text: At least 60 spiderlings emerge from an egg sac. Unusual for spiders, they are subsocial at this stage: they remain together for about a month, but do not cooperate in prey capture. The amount of cannibalism correlates with the amount of available food. "E. atrica" molts seven or eight times before reaching the immature adult state, and after a final molt reaches maturity.


title: Giant house spider

text: Like most spiders, the spider possesses venom to subdue its prey. Since "E. atrica" bites can penetrate human skin on occasion, the effects of agatoxin might be felt by bite victims, though these spiders will not bite unless provoked.


title: Giant house spider

text: With speeds clocked at , the giant house spider held the Guinness Book of World Records for top spider speed until 1987 when it was displaced by solifugids, although the latter are not true spiders.


title: Giant house spider

text: A population of giant house spiders is popularly thought to be a deterrent to the establishment of "Eratigena agrestis", known in North America as the "hobo spider", and considered by some to be more likely to bite humans. Giant house spiders may compete with hobo spiders for the same resources.


title: Giant house spider

text: Hobo spiders grow no more than a body size of long whereas the larger female giant house spider can have a body size of , but has proportionately much longer legs.


title: Giant house spider

text: Humorist David Sedaris has written about his relationship with "E. atrica". His essay "April in Paris" documents his growing affection toward and domestic association with giant house spiders, particularly one named April. The essay can be found in the collection "When You Are Engulfed in Flames".


title: Aztlán

text: Aztlán (from , ) is the ancestral home of the Aztec peoples. "Astekah" is the Nahuatl word for "people from Aztlan". Aztlan is mentioned in several ethnohistorical sources dating from the colonial period, and while they each cite varying lists of the different tribal groups who participated in the migration from Aztlan to central Mexico, the Mexica who went on to found Mexico-Tenochtitlan are mentioned in all of the accounts.


title: Aztlán

text: Historians have speculated about the possible location of Aztlan and tend to place it either in northwestern Mexico or the Southwestern United States, although there are doubts about whether the place is purely mythical or represents a historical reality.


title: Aztlán

text: Nahuatl histories relate that seven tribes lived in Chicomoztoc, or "the place of the seven caves". Each cave represented a different Nahua group: the Xochimilca, Tlahuica, Acolhua, Tlaxcalteca, Tepaneca, Chalca, and Mexica. Along with these people, the Olmec-Xicalanca and Xaltocamecas are also said to come from Aztlan. Because of their common linguistic origin, those groups are called collectively "Nahualteca" (Nahua people). These tribes subsequently left the caves and settled "near" Aztlán.


title: Aztlán

text: The various descriptions of Aztlán apparently contradict each other. While some legends describe Aztlán as a paradise, the Codex Aubin says that the Aztecs were subject to a tyrannical elite called the Azteca Chicomoztoca. Guided by their priest, the Aztec fled. On the road, their god Huitzilopochtli forbade them to call themselves "Azteca", telling them that they should be known as "Mexica". Scholars of the 19th century—in particular Alexander von Humboldt and William H. Prescott—translated the word Azteca, as is shown in the Aubin Codex, to Aztec.


title: Aztlán

text: Some say that the southward migration began on May 24, 1064, CE, after the Crab Nebula events from May to July 1054. Each of the seven groups is credited with founding a different major city-state in Central Mexico.


title: Aztlán

text: A 2004 translation of the Anales de Tlatelolco gives the only known date related to the exit from Aztlan; day-sign "4 Cuauhtli" (Four Eagle) of the year "1 Tecpatl" (Knife) or 1064–1065, and correlated to January 4, 1065.


title: Aztlán

text: Cristobal del Castillo mentions in his book "Fragmentos de la Obra General Sobre Historia de los Mexicanos", that the lake around the Aztlan island was called Metztliapan or "Lake of the moon." Another version reads:One day a man heard a bird calling to him, saying, "Go now, go now." When the man told the chief about the bird, the chief was relieved. He had known his people must find a new land, their own land, but had waited for a sign. So the people gathered and began a long march. They followed an idol of Huitzilopochtli that the priests carried. As they went, Huitzilopochtli spoke through the priests and prepared the people for the greatness of their empire to come. He explained that they should travel until they came to a large lake; there, they should look for another sign—an eagle in a cactus.


title: Aztlán

text: The journey took 200 years, and the people settled for a while in the Toltec capital of Tollan. Some people stayed in Tollan and some moved on. From time to time, Huitzilopochtli changed himself into a white eagle to inspire the people, and they traveled until they came to Lake Texcoco and saw a great eagle sitting on a cactus, holding a serpent. There they built Tenochtitlán, the city that became the capital and center of the Aztec empire.


title: Aztlán

text: Although in present-day it is known that people, prior to Mexico-Tenochtitlan build, came to its location from the city-state of Tula, where was ultimately expelled, as from many other city-states, in the past was many attempts to find the "potential" mythological site of "Aztlán". Friar Diego Durán (c. 1537–1588), who chronicled the history of the Aztecs, wrote of Aztec emperor Moctezuma I's attempt to recover the history of the Mexica by congregating warriors and wise men on an expedition to locate Aztlán. According to Durán, the expedition was successful in finding a place that offered characteristics unique to Aztlán. However, his accounts were written shortly after the conquest of Tenochtitlan and before an accurate mapping of the American continent was made; therefore, he was unable to provide a precise location.


title: Aztlán

text: During the 1960s, Mexican intellectuals began to seriously speculate about the possibility that Mexcaltitán de Uribe was the mythical city of Aztlán. One of the first to consider Aztlán being linked to the Nayaritian island was historian Alfredo Chavero towards the end of the 19th century. Historical investigators after his death tested his proposition and considered it valid, among them Wigberto Jiménez Moreno. This hypothesis is still up for debate.


title: Aztlán

text: The meaning of the name "Aztlan" is uncertain. One suggested meaning is "place of Herons" or "place of egrets"—the explanation given in the "Crónica Mexicáyotl"—but this is not possible under Nahuatl morphology: "place of egrets" is "Aztatlan". Other proposed derivations include "place of whiteness" and "at the place in the vicinity of tools", sharing the "āz-" element of words such as "teponāztli", "drum" (from "tepontli", "log").


title: Aztlán

text: The concept of Aztlán as the place of origin of the pre-Columbian Mexican civilization has become a symbol for various Mexican nationalist and indigenous movements.


title: Aztlán

text: In 1969 the notion of Aztlan was introduced by the poet Alurista (Alberto Baltazar Urista Heredia) at the National Chicano Youth Liberation Conference held in Denver, Colorado by the Crusade for Justice. There he read a poem, which has come to be known as the preamble to El Plan de Aztlan or as "El Plan Espiritual de Aztlan" due to its poetic aesthetic. For some Chicanos, Aztlan refers to the Mexican territories annexed by the United States as a result of the Mexican–American War of 1846–1848. Aztlán became a symbol for activists who believe they have a legal and primordial right to the land. In order to exercise this right, some members of the Chicano movement propose that a new nation be created, a República del Norte.


title: Aztlán

text: "Aztlán" is also the name of the Chicano studies journal published out of the UCLA Chicano Studies Research Center.


title: Aztlán

text: "Aztlán" has been used as the name of speculative fictional future states that emerge in the southwestern United States or Mexico after their governments suffer a collapse or major setback; examples appear in such works as the novels "Heart of Aztlán" (1976), by Rudolfo Anaya; "Warday" (1984), by Whitley Strieber and James Kunetka; "The Peace War" (1984), by Vernor Vinge; "The House of the Scorpion" (2002), by Nancy Farmer; and "World War Z" (2006), by Max Brooks; as well as the role-playing game "Shadowrun", in which the Mexican government was usurped by the "Aztechnology" Corporation (1989). In Gary Jennings' novel "Aztec" (1980), the protagonist resides in Aztlán for a while, later facilitating contact between Aztlán and the Aztec Triple Alliance just before Hernán Cortés' arrival.


title: Aztlán

text: "Strange Rumblings in Aztlan" is an article written by Hunter S. Thompson that appeared in the April 29, 1971 issue of "Rolling Stone". The article is about the death of civil rights activist Ruben Salazar in East Los Angeles during a Vietnam War protest.


title: Aztlán

text: In the grand strategy computer wargame "Hearts of Iron IV", the Man the Guns expansion revamps thoroughly Mexico's national focus tree, and gives it the focus "Redeem Aztlan", which grants it cores on 7 US states that used to be a part of Mexico. If the United States are already a subject (puppet, satellite, etc.) of Mexico, they will also be fully annexed.


title: Phreaking

text: Phreaking is a slang term coined to describe the activity of a culture of people who study, experiment with, or explore telecommunication systems, such as equipment and systems connected to public telephone networks. The term "phreak" is a sensational spelling of the word "freak" with the "ph-" from "phone", and may also refer to the use of various audio frequencies to manipulate a phone system. "Phreak", "phreaker", or "phone phreak" are names used for and by individuals who participate in phreaking.


title: Phreaking

text: The term first referred to groups who had reverse engineered the system of tones used to route long-distance calls. By re-creating these tones, phreaks could switch calls from the phone handset, allowing free calls to be made around the world. To ease the creation of these tones, electronic tone generators known as blue boxes became a staple of the phreaker community. This community included future Apple Inc. cofounders Steve Jobs and Steve Wozniak.


title: Phreaking

text: The blue box era came to an end with the ever-increasing use of computerized phone systems which allowed telecommunication companies to discontinue the use of in-band signaling for call routing purposes. Instead, dialing information was sent on a separate channel which was inaccessible to the telecom customer. By the 1980s, most of the public switched telephone network (PSTN) in the US and Western Europe had adopted the SS7 system which uses out-of-band signaling for call control (and which is still in use to this day). Phreaking has since become closely linked with computer hacking.


title: Phreaking

text: Phone phreaking got its start in the late 1950s in the United States and become prominent in the 1960s and early 1970s. Phone phreaks spent a lot of time dialing around the telephone network to understand how the phone system worked, engaging in activities such as listening to the pattern of tones to figure out how calls were routed, reading obscure telephone company technical journals, learning how to impersonate operators and other telephone company personnel, digging through telephone company trash bins to find "secret" documents, sneaking into telephone company buildings at night and wiring up their own telephones, building electronic devices called blue boxes, black boxes, and red boxes to help them explore the network and make free phone calls, hanging out on early conference call circuits and "loop arounds" to communicate with one another and writing their own newsletters to spread information.


title: Phreaking

text: Before 1984, long-distance telephone calls were a premium item in the United States, with strict regulations. In some locations, calling across the street counted as long distance. To report that a phone call was long-distance meant an elevated importance because the calling party is paying by the minute to speak to the called party.


title: Phreaking

text: Phreaking consists of techniques to evade long-distance charges. This evasion is illegal; the crime is called "toll fraud". In 1990, the pager cloning technique arose and was used by law enforcement.


title: Phreaking

text: In the UK the situation was rather different due to the difference in technology between the American and British systems, the main difference being the absence of tone dialing and signaling, particularly in the 1950s and 1960s.


title: Phreaking

text: The tone system in the United States has been almost entirely replaced, but in some countries, in addition to new systems, the tone system is still available, for example in Italy.


title: Phreaking

text: Possibly one of the first phreaking methods was switch-hooking, which allows placing calls from a phone where the rotary dial or keypad has been disabled by a key lock or other means to prevent unauthorized calls from that phone. It is done by rapidly pressing and releasing the switch hook to open and close the subscriber circuit, simulating the pulses generated by the rotary dial. Even most current telephone exchanges support this method, as they need to be backward compatible with old subscriber hardware.


title: Phreaking

text: By rapidly clicking the hook for a variable number of times at roughly 5 to 10 clicks per second, separated by intervals of roughly one second, the caller can dial numbers as if they were using the rotary dial. The pulse counter in the exchange counts the pulses or clicks and interprets them in two possible ways. Depending on continent and country, one click with a following interval can be either "one" or "zero" and subsequent clicks before the interval are additively counted. This renders ten consecutive clicks being either "zero" or "nine", respectively. Some exchanges allow using additional clicks for special controls, but numbers 0-9 now fall in one of these two standards. One special code, "flash", is a very short single click, possible but hard to simulate. Back in the day of rotary dial, technically identical phone sets were marketed in multiple areas of the world, only with plugs matched by country and the dials being bezeled with the local standard numbers.


title: Phreaking

text: Such key-locked telephones, if wired to a modern DTMF capable exchange, can also be exploited by a tone dialer that generates the DTMF tones used by modern keypad units. These signals are now very uniformly standardized worldwide. It is notable that the two methods can be combined: Even if the exchange does not support DTMF, the key lock can be circumvented by switch-hooking, and the tone dialer can be then used to operate automated DTMF controlled services that can not be used with rotary dial.


title: Phreaking

text: The origins of phone phreaking trace back at least to AT&T's implementation of fully automatic switches. These switches used tone dialing, a form of in-band signaling, and included some tones which were for internal telephone company use. One internal-use tone is a tone of 2600 Hz which causes a telephone switch to think the call had ended, leaving an open carrier line, which can be exploited to provide free long-distance, and international calls. At that time, long-distance calls were more expensive.


title: Phreaking

text: The tone was discovered in approximately 1957, by Joe Engressia, a blind seven-year-old boy. Engressia had perfect pitch, and discovered that whistling the fourth E above middle C (a frequency of 2637.02 Hz) would stop a dialed phone recording. Unaware of what he had done, Engressia called the phone company and asked why the recordings had stopped. Joe Engressia is considered to be the father of phreaking.


title: Phreaking

text: Other early phreaks, such as "Bill from New York" (William "Bill" Acker 1953-2015), began to develop a rudimentary understanding of how phone networks worked. Bill discovered that a recorder he owned could also play the tone at 2600 Hz with the same effect. John Draper discovered through his friendship with Engressia that the free whistles given out in Cap'n Crunch cereal boxes also produced a 2600 Hz tone when blown (providing his nickname, "Captain Crunch"). This allows control of phone systems that work on single frequency (SF) controls. One can sound a long whistle to reset the line, followed by groups of whistles (a short tone for a "1", two for a "2", etc.) to dial numbers.


title: Phreaking

text: While single-frequency worked on certain phone routes, the most common signaling on the then long-distance network was multi-frequency (MF) controls. The slang term for these tones and their use was "Marty Freeman". The specific frequencies required were unknown to the general public until 1954, when the Bell System published the information in the "Bell System Technical Journal" in an article describing the methods and frequencies used for inter-office signalling. The journal was intended for the company's engineers; however, it found its way to various college campuses across the United States. With this one article, the Bell System accidentally gave away the "keys to the kingdom", and the intricacies of the phone system were at the disposal of people with a knowledge of electronics.


title: Phreaking

text: The second generation of phreaks arose at this time, including New Yorkers "Evan Doorbell", "Ben Decibel" and Neil R. Bell and Californians Mark Bernay, Chris Bernay, and "Alan from Canada". Each conducted their own independent exploration and experimentation of the telephone network, initially on an individual basis, and later within groups as they discovered each other in their travels. "Evan Doorbell", "Ben" and "Neil" formed a group of phreaks, known as "Group Bell". Bernay initiated a similar group named the "Mark Bernay Society". Both Bernay and Evan received fame amongst today's phone phreakers for internet publications of their collection of telephone exploration recordings. These recordings, conducted in the 1960s, 1970s, and early 1980s are available at Mark's website "Phone Trips".


title: Phreaking

text: In October 1971, phreaking was introduced to the masses when "Esquire" magazine published a story called "Secrets of the Little Blue Box" by Ron Rosenbaum. This article featured Engressia and John Draper prominently, synonymising their names with phreaking. The article also attracted the interest of other soon-to-be phreaks, such as Steve Wozniak and Steve Jobs, who went on to found Apple Computer.


title: Phreaking

text: 1971 also saw the beginnings of "YIPL" ("Youth International Party Line"), a publication started by Abbie Hoffman and Al Bell to provide information to Yippies on how to "beat the man", mostly involving telephones. In the first issue of "YIPL", writers included a "shout-out" to all of the phreakers who provided technological information for the newsletter: "We at YIPL would like to offer thanks to all you phreaks out there." In the last issue, YIPL stated:


title: Phreaking

text: YIPL believes that education alone cannot affect the System, but education can be an invaluable tool for those willing to use it. Specifically, YIPL will show you why something must be done immediately in regard, of course, to the improper control of the communication in this country by none other than bell telephone company.


title: Phreaking

text: Al Bell was denied opening a bank account under the name of "Technological American Party", since he was not a political party, so he changed the name to "Technological Assistance Program" to get a bank account.<ref name="malicious.life/3/50/YIPL"></ref>


title: Phreaking

text: TAP developed into a major source for subversive technical information among phreaks and hackers all over the world. TAP ran from 1973 to 1984, with Al Bell handing over the magazine to "Tom Edison" in the late 1970s. TAP ended publication in 1984 due mostly to a break-in and arson at Tom Edison's residence in 1983. Cheshire Catalyst then took over running the magazine for its final (1984) year.


title: Phreaking

text: A controversially suppressed article "Regulating the Phone Company In Your Home" in "Ramparts" magazine (June 1972) increased interest in phreaking. This article published simple schematic plans of a "black box" used to make free long-distance phone calls, and included a very short parts list that could be used to construct one. AT&T forced "Ramparts" to pull all copies from shelves, but not before numerous copies were sold and many regular subscribers received them.


title: Phreaking

text: In the 1980s, the revolution of the personal computer and the popularity of computer bulletin board systems (BBSes) (accessed via modem) created an influx of tech-savvy users. These BBSes became popular for computer hackers and others interested in the technology, and served as a medium for previously scattered independent phone phreaks to share their discoveries and experiments. This not only led to unprecedented collaboration between phone phreaks, but also spread the notion of phreaking to others who took it upon themselves to study, experiment with, or exploit the telephone system. This was also at a time when the telephone company was a popular subject of discussion in the US, as the monopoly of AT&T Corporation was forced into divestiture. During this time, exploration of telephone networks diminished, and phreaking focused more on toll fraud. Computer hackers began to use phreaking methods to find the telephone numbers for modems belonging to businesses, which they could exploit later. Groups then formed around the BBS hacker/phreaking (H/P) community such as the famous Masters of Deception (Phiber Optik) and Legion of Doom (Erik Bloodaxe) groups. In 1985, an underground e-zine called "Phrack" (a combination of the words phreak and hack) began circulation among BBSes, and focused on hacking, phreaking, and other related technological subjects.


title: Phreaking

text: In the early 1990s, groups like Masters of Deception and Legion of Doom were shut down by the US Secret Service's Operation Sundevil. Phreaking as a subculture saw a brief dispersion in fear of criminal prosecution in the 1990s, before the popularity of the internet initiated a reemergence of phreaking as a subculture in the US and spread phreaking to international levels.


title: Phreaking

text: Into the turn of the 21st century, phreaks began to focus on the exploration and playing with the network, and the concept of toll fraud became widely frowned on among serious phreakers, primarily under the influence of the website Phone Trips, put up by second generation phreaks Mark Bernay and Evan Doorbell.


title: Phreaking

text: The 1984 AT&T breakup gave rise to many small companies intent upon competing in the long-distance market. These included the then-fledgling Sprint and MCI, both of whom had only recently entered the marketplace. At the time, there was no way to switch a phone line to have calls automatically carried by non-AT&T companies. Customers of these small long-distance operations would be required to dial a local access number, enter their calling card number, and finally enter the area code and phone number they wish to call. Because of the relatively lengthy process for customers to complete a call, the companies kept the calling card numbers short – usually 6 or 7 digits. This opened up a huge vulnerability to phone phreaks with a computer.


title: Phreaking

text: 6-digit calling card numbers only offer 1 million combinations. 7-digit numbers offer just 10 million. If a company had 10,000 customers, a person attempting to "guess" a card number would have a good chance of doing so correctly once every 100 tries for a 6-digit card and once every 1000 tries for a 7-digit card. While this is almost easy enough for people to do manually, computers made the task far easier. "Code hack" programs were developed for computers with modems. The modems would dial the long-distance access number, enter a random calling card number (of the proper number of digits), and attempt to complete a call to a computer bulletin board system (BBS). If the computer connected successfully to the BBS, it proved that it had found a working card number, and it saved that number to disk. If it did not connect to the BBS in a specified amount of time (usually 30 or 60 seconds), it would hang up and try a different code. Using this method, code hacking programs would turn up hundreds (or in some cases thousands) of working calling card numbers per day. These would subsequently be shared amongst fellow phreakers.


title: Phreaking

text: There was no way for these small phone companies to identify the culprits of these hacks. They had no access to local phone company records of calls into their access numbers, and even if they had access, obtaining such records would be prohibitively expensive and time-consuming. While there was some advancement in tracking down these code hackers in the early 1990s, the problem did not completely disappear until most long-distance companies were able to offer standard 1+ dialing without the use of an access number.


title: Phreaking

text: Another method of obtaining free phone calls involves the use of "diverters". Call forwarding was not an available feature for many business phone lines in the late 1980s and early 1990s, so they were forced to buy equipment that could do the job manually between two phone lines. When the business would close, they would program the call diverting equipment to answer all calls, pick up another phone line, call their answering service, and bridge the two lines together. This gave the appearance to the caller that they were directly forwarded to the company's answering service. The switching equipment would typically reset the line after the call had hung up and timed out back to dial tone, so the caller could simply wait after the answering service had disconnected, and would eventually get a usable dial tone from the second line. Phreakers recognized the opportunity this provided, and they would spend hours manually dialing businesses after hours, attempting to identify faulty diverters. Once a phreaker had access to one of these lines, they could use it for one of many purposes. In addition to completing phone calls anywhere in the world at the businesses' expense, they could also dial 1-900 phone sex/entertainment numbers, as well as use the line to harass their enemies without fear of being traced. Victimized small businesses were usually required to foot the bill for the long-distance calls, as it was their own private equipment (not phone company security flaws) that allowed such fraud to occur. By 1993, call forwarding was offered to nearly every business line subscriber, making these diverters obsolete. As a result, hackers stopped searching for the few remaining ones, and this method of toll fraud died. Many (different type) of diverters still exist and are actively "phreaked" in the United States as of 2020, It is rare to find a diverter solely used for Answering Service forwarding anymore, but the many other types such as phone-company test numbers and remote PBX DISAs are still used as diverters.


title: Phreaking

text: Before the BBS era of the 1980s phone phreaking was more of a solitary venture as it was difficult for phreaks to connect with one another. In addition to communicating over BBSs phone phreaks discover voice mail boxes and party lines as ways to network and keep in touch over the telephone. They usually appropriate unused boxes that are part of business or cellular phone systems. Once a vulnerable mailbox system is discovered, word would spread around the phreak community, and scores of them would take residence on the system. They use these systems as a "home base" for communication with one another until the rightful owners would discover the intrusion and wipe them off. Voice mailboxes also provide a safe phone number for phreaks to give out to one another as home phone numbers and personal cellular numbers would allow the phreak's identity (and home address) to be discovered. This is especially important given that phone phreaks are breaking the law.


title: Phreaking

text: Phreakers also use "bridges" to communicate live with one another. The term "bridge" originally referred to a group of telephone company test lines that were bridged together giving the effect of a party-line. Eventually, all party-lines, whether bridges or not, came to be known as bridges if primarily populated by hackers and/or phreakers.


title: Phreaking

text: The popularity of the Internet in the mid-1990s, along with the better awareness of voice mail by business and cell phone owners, made the practice of stealing voice mailboxes less popular. To this day bridges are still very popular with phreakers yet, with the advent of VoIP, the use of telephone company owned bridges has decreased slightly in favor of phreaker-owned conferences.


title: Phreaking

text: By the late 1990s, the fraudulent aspect of phreaking all but vanished. In the United States most mobile phones offered unlimited domestic long-distance calling for the price of standard airtime (often totally unlimited on weekends), and flat-rate long-distance plans appeared offering unlimited home phone long-distance for as little as $25 per month. Rates for international telephone calls had also decreased significantly and by the 2000s, the advent of applications offering OTT voice calls over the internet provided no-cost alternatives for international calls. Between the much higher risk of being caught (due to advances in technology) and the much lower gain of making free phone calls, toll fraud started to become a concept associated very little with phreaking.


title: Phreaking

text: The end of multi-frequency (MF) phreaking in the lower 48 United States occurred on June 15, 2006, when the last exchange in the contiguous United States to use a "phreakable" MF-signalled trunk replaced the aging (yet still well kept) N2 carrier with a T1 carrier. This exchange, located in Wawina Township, Minnesota, was run by the Northern Telephone Company of Minnesota.


title: Phreaking

text: Recent notable instances of phreaking involve hacking of VOIP systems. In 2011, the government of the Philippines and the FBI arrested four hackers for phone phreaking through PBX hacking. In 2015, Pakistani officials arrested a prominent phreaker who had amassed more than $50 million from PBX hacking activities.


title: Battle of Long Island

text: The Battle of Long Island, also known as the Battle of Brooklyn and the Battle of Brooklyn Heights, was an action of the American Revolutionary War fought on August 27, 1776, at the western edge of Long Island in present-day Brooklyn, New York. The British defeated the Americans and gained access to the strategically important Port of New York, which they held for the rest of the war. It was the first major battle to take place after the United States declared its independence on July 4, and in troop deployment and combat, it was the largest battle of the war.


title: Battle of Long Island

text: After defeating the British in the siege of Boston on March 17, commander-in-chief George Washington relocated the Continental Army to defend the port city of New York, located at the southern end of Manhattan Island. Washington understood that the city's harbor would provide an excellent base for the Royal Navy, so he established defenses there and waited for the British to attack. In July, the British, under the command of General William Howe, landed a few miles across the harbor on the sparsely populated Staten Island, where they were reinforced by a fleet of ships in Lower New York Bay over the next month and a half, bringing their total force to 32,000 troops. Washington knew the difficulty in holding the city with the British fleet in control of the entrance to the harbor at the Narrows, and accordingly moved the bulk of his forces to Manhattan, believing that it would be the first target.


title: Battle of Long Island

text: On August 21, the British landed on the shores of Gravesend Bay in southwest Kings County, across the Narrows from Staten Island and more than a dozen miles south of the established East River crossings to Manhattan. After five days of waiting, the British attacked the American defenses on the Guan Heights. Unknown to the Americans, however, Howe had brought his main army around their rear and attacked their flank soon after. The Americans panicked, resulting in twenty percent losses through casualties and capture, although a stand by 400 Maryland and Delaware troops prevented greater losses. The remainder of the army retreated to the main defenses on Brooklyn Heights. The British dug in for a siege, but on the night of August 29–30, Washington evacuated the entire army to Manhattan without the loss of supplies or a single life. The Continental Army was driven out of Manhattan entirely after several more defeats and was forced to retreat through New Jersey to Pennsylvania.


title: Battle of Long Island

text: In the first stage of the war, the British Army was trapped in the peninsular city of Boston and were forced to abandon it on March 17, sailing to Halifax, Nova Scotia, to await reinforcements. Washington then began to transfer regiments to New York City, which he believed the British would attack next because of the port's strategic importance. He had sent his second-in-command, Charles Lee, ahead to New York the previous February to establish the city's defenses. Washington left Boston on April 4, arrived in New York on April 13, and established headquarters at the former home of Archibald Kennedy on Broadway facing Bowling Green.


title: Battle of Long Island

text: Lee remained in New York City until March when the Continental Congress sent him to South Carolina; construction of the city's defenses was left to General William Alexander (Lord Stirling). Troops were in limited supply, so Washington found the defenses incomplete, but Lee had concluded that in any case, it would be impossible to hold the city with the British commanding the sea. He reasoned that the defenses should be located with the ability to inflict heavy casualties upon the British if any move was made to take and hold ground. Barricades and redoubts were established in and around the city, and the bastion of Fort Stirling was built across the East River in Brooklyn Heights, facing the city. Lee had also seen to it that the immediate area was cleared of Loyalists.


title: Battle of Long Island

text: Washington began moving troops to Brooklyn in early May, and there were several thousand of them there in a short time. Three more forts were under construction on the eastern side of the East River to support Fort Stirling, which stood to the west of the hamlet of Brooklyn Heights. These new fortifications were Fort Putnam, Fort Greene, and Fort Box (named for Major Daniel Box). They lay from north to south, with Fort Putnam farthest to the north, Greene slightly to the southwest, and Box slightly farther southwest. Each of these defensive structures was surrounded by a large ditch, all connected by a line of entrenchments and a total of 36 cannons.


title: Battle of Long Island

text: Fort Defiance was also being constructed at this time, located farther southwest, past Fort Box, near present-day Red Hook. In addition to these new forts, a mounted battery was established on Governors Island, on Manhattan, cannons were placed at Fort George facing Bowling Green, and more cannons were placed at the Whitehall Dock, which sat on the East River. Hulks were sunk at strategic locations to deter the British from entering the East River and other waterways.


title: Battle of Long Island

text: Washington had been authorized by Congress to recruit an army of up to 28,501 troops, but he had only 19,000 when he reached New York. Military discipline was inadequate; routine orders were not carried out, muskets were fired in camp, flints was ruined, bayonets were used as knives to cut food, and firearm readiness was lax. Petty internal conflict was common under the strain of a large number of people from different regional cultures and temperaments living in relatively close proximity.


title: Battle of Long Island

text: Commander of the artillery Henry Knox persuaded Washington to transfer 400 to 500 soldiers, who lacked muskets or guns, to crew the artillery. In early June, Knox and General Nathanael Greene inspected the land at the north end of Manhattan and decided to establish Fort Washington. Fort Constitution, later renamed Fort Lee, was planned opposite Fort Washington on the Hudson River. The forts were intended to discourage the British ships from sailing up the Hudson River.


title: Battle of Long Island

text: On June 28, Washington learned that the British fleet had set sail from Halifax on June 9 and was heading toward New York. On June 29, signals were sent from men stationed on Staten Island, indicating that the British fleet had appeared. Within a few hours, 45 British ships dropped anchor in Lower New York Bay. The population of New York went into a panic at the sight of the British ships; alarms went off and troops immediately rushed to their posts. On July 2, British troops began to land on Staten Island. The Continental regulars on the island took a few shots at them before fleeing, and the citizens' militia switched over to the British side. Less than a week later, there were 130 ships off Staten Island under the command of Richard Howe, the brother of General Howe.


title: Battle of Long Island

text: On July 6, news reached New York that Congress had voted for independence four days earlier. On Tuesday, July 9, at 18:00, Washington had several brigades march onto the commons of the city to hear the "Declaration of Independence" read. After the end of the reading, a mob ran down to Bowling Green with ropes and bars, where they tore down the gilded lead equestrian statue of George III of Great Britain. In their fury, the crowd cut off the statue's head, severed the nose, mounted what remained of the head on a spike outside a tavern, and the rest of the statue was dragged to Connecticut and melted down into musket balls.


title: Battle of Long Island

text: On July 12, the British ships "Phoenix" and " Rose" sailed up the harbor toward the mouth of the Hudson. The American batteries opened fire from the harbor defenses of Fort George, Fort Defiance, and Governors Island, but the British returned fire into the city. The ships sailed along the New Jersey shore and continued up the Hudson, sailing past Fort Washington and arriving by nightfall at Tarrytown, the widest part of the Hudson. The goals of the British ships were to cut off American supplies from New England and the north and to encourage Loyalist support. The only casualties of the day were six Americans who were killed when their own cannon blew up.


title: Battle of Long Island

text: The next day, July 13, Howe attempted to open negotiations with the Americans. He sent a letter to Washington delivered by Lieutenant Philip Brown, who arrived under a flag of truce. The letter was addressed to "George Washington, Esq." Brown was met by Joseph Reed, who had hurried to the waterfront on Washington's orders, accompanied by Henry Knox and Samuel Webb. Washington asked his officers whether it should be received or not, as it did not recognize his rank as general, and they unanimously said no. Reed told Brown that there was no one in the army with that address. On July 16, Howe tried again, this time with the address "George Washington, Esq., etc., etc.", but it was again declined. The next day, Howe sent Captain Nisbet Balfour to ask if Washington would meet with Howe's adjutant face to face, and a meeting was scheduled for July 20. Howe's adjutant was Colonel James Patterson. Patterson told Washington that Howe had come with powers to grant pardons, but Washington said, "Those who have committed no fault want no pardon." Patterson departed soon after. Washington's performance during the meeting was praised in many parts of the country.


title: Battle of Long Island

text: Meanwhile, British ships continued to arrive. On August 1, 45 ships arrived with generals Henry Clinton and Charles Cornwallis, along with 3,000 troops. By August 12, 3,000 more British troops and another 8,000 Hessians had arrived. At this point, the British fleet numbered over 400 ships, including 73 warships, and 32,000 troops were camped on Staten Island. Faced with this large force, Washington was unsure as to where the British would attack. Both Greene and Reed thought that the British would attack Long Island, but Washington felt that a British attack on Long Island might be a diversion for the main attack on Manhattan. He broke his army in half, stationing half of it on Manhattan, and the other half on Long Island; the army on Long Island was commanded by Greene. On August 20, Greene became ill and was forced to move to a house in Manhattan where he rested to recover. John Sullivan was placed in command until Greene was well enough to resume command.


title: Battle of Long Island

text: At 05:10 on August 22, an advance guard of 4,000 British troops left Staten Island under the command of Clinton and Cornwallis to land on Long Island. At 08:00, all 4,000 troops landed unopposed on the shore of Gravesend Bay. Colonel Edward Hand's Pennsylvanian riflemen had been stationed on the shore, but they did not oppose the landings and fell back, killing cattle and burning farmhouses on the way. By noon, 15,000 troops had landed on shore along with 40 pieces of artillery, as hundreds of Loyalists came to greet the British troops. Cornwallis pushed on with the advance guard, advancing six miles onto the island and establishing a camp at the village of Flatbush. He was given orders to advance no further.


title: Battle of Long Island

text: Washington received word of the landings the same day but was informed that the number was 8,000 to 9,000 troops. This convinced him that it was the feint that he had predicted and therefore he only sent 1,500 more troops to Brooklyn, bringing the total number of troops on Long Island to 6,000. On August 24, Washington replaced Sullivan with Israel Putnam who commanded the troops on Long Island. Putnam arrived on Long Island the next day along with six battalions. Also that day, the British troops on Long Island received 5,000 Hessian reinforcements, bringing their total to 20,000. There was little fighting on the days immediately after the landing, although some small skirmishes did take place with American marksmen armed with rifles picking off British troops from time to time.


title: Battle of Long Island

text: The American plan was for Putnam to direct the defenses from Brooklyn Heights, while Sullivan and Stirling and their troops would be stationed forward on the Guan Heights. The Guan (hills) were up to 150 feet high and blocked the most direct route to Brooklyn Heights. Washington believed that, by stationing men on the heights, heavy casualties could be inflicted on the British before the troops fell back to the main defenses at Brooklyn Heights. There were three main passes through the heights; the Gowanus Road farthest to the west, the Flatbush Road slightly farther to the east, in the center of the American line where it was expected that the British would attack, and the Bedford Pass even further to the east. Stirling was responsible for defending the Gowanus Road with 500 men, and Sullivan was to defend the Flatbush and Bedford roads where there were 1,000 and 800 men respectively. Six-thousand troops were to remain behind at Brooklyn Heights. There was one lesser-known path through the heights called the Jamaica Pass, farthest to the east, which was patrolled by just five militia officers on horseback.


title: Battle of Long Island

text: On the British side, General Clinton learned of the almost undefended Jamaica Pass from local Loyalists. He drew up a plan and gave it to William Erskine to propose to Howe. Clinton's plan had the main army making a night march and going through the Jamaica Pass to turn the American flank, while other troops would keep the Americans busy in front. On August 26, Clinton received word from Howe that the plan would be used, and that Clinton was to command the advance guard of the main army of 10,000 men on the march through the Jamaica Pass. While they made the night march, General James Grant's British troops along with some Hessians, a total of 4,000 men, were to attack the Americans in front to distract them from the main army coming on their flank. Howe told Clinton to be ready to move out that night, August 26.


title: Battle of Long Island

text: At 21:00, the British moved out. No one except the commanders knew of the plan. Clinton led a crack brigade of light infantry with fixed bayonets in front, followed by Cornwallis who had eight battalions and 14 artillery pieces. Cornwallis was followed by Howe and Hugh Percy with six battalions, more artillery, and baggage. The column consisted of 10,000 men who stretched out over two miles. Three Loyalist farmers led the column toward the Jamaica Pass. The British had left their campfires burning to deceive the Americans into thinking that nothing was happening. The column headed northeast until it reached what later became the village of New Lots, when it headed directly north toward the heights.


title: Battle of Long Island

text: The column had yet to run into any American troops when they reached Howard's Tavern (also known as "Howard's Half-Way House"), just a few hundred yards from the Jamaica Pass. Tavern keeper William Howard and his son William Jr. were forced to act as guides to show the British the way to the Rockaway Foot Path, an old Indian trail that skirted the Jamaica Pass to the west (located today in the Cemetery of the Evergreens). William Howard Jr. describes meeting Howe:


title: Battle of Long Island

text: It was about two in the morning of August 27 that I was awakened by seeing a soldier at the side of my bed. I got up and dressed and went down to the barroom, where I saw my father standing in one corner with three British soldiers before him with muskets and bayonets fixed. The army was then lying in the field in front of the house... General Howe and another officer were in the barroom. General Howe wore a camlet cloak over his regimentals. After asking for a glass of liquor from the bar, which was given him, he entered into familiar conversation with my father, and among other things said, "I must have some one of you to show me over the Rockaway Path around the pass." My father replied, "We belong to the other side, General, and can’t serve you against our duty." General Howe replied, "That is alright; stick to your country, or stick to your principles, but Howard, you are my prisoner and must guide my men over the hill." My father made some further objection, but was silenced by the general, who said, "You have no alternative. If you refuse I shall shoot you through the head.


title: Battle of Long Island

text: Five minutes after leaving the tavern, the five American militia officers stationed at the pass were captured without a shot fired, as they thought that the British were Americans. Clinton interrogated the men and they informed him that they were the only troops guarding the pass. By dawn, the British were through the pass and stopped so that the troops could rest. At 09:00, they fired two heavy cannons to signal the Hessian troops below Battle Pass to begin their frontal assault against Sullivan's men deployed on the two hills flanking the pass, while Clinton's troops simultaneously flanked the American positions from the east.


title: Battle of Long Island

text: At about 23:00 on August 26, the first shots were fired in the Battle of Long Island, near the Red Lion Inn (near present-day 39th Street and 4th Avenue). American pickets from Samuel John Atlee's Pennsylvania regiment fired upon two British soldiers who were foraging in a watermelon patch near the inn.


title: Battle of Long Island

text: Around 01:00 on August 27, the British approached the vicinity of the Red Lion with 200–300 troops. The American troops fired upon the British; after approximately two fusillades, they fled up the Gowanus Road toward the Vechte–Cortelyou House. Major Edward Burd had been in command, but he was captured along with a lieutenant and 15 privates. This first engagement was fought in the vicinity of 38th and 39th streets between 2nd and 3rd avenues near a swamp located adjacent to the Gowanus Road.


title: Battle of Long Island

text: Brigadier General Samuel Holden Parsons and Colonel Atlee were stationed farther north on the Gowanus Road. Parsons was a lawyer from Connecticut who had recently secured a commission in the Continental Army; Atlee was a veteran of the French and Indian War in command of the First Regiment of Pennsylvania Musketry. Putnam had been awakened by a guard at 03:00 and told that the British were attacking through the Gowanus Pass. He lit signals to Washington, who was on Manhattan, and then rode south to warn Stirling of the attack.


title: Battle of Long Island

text: Stirling led two units of Colonel John Haslet's 1st Delaware Regiment under the immediate command of Major Thomas Macdonough, and Colonel William Smallwood's 1st Maryland Infantry under the immediate command of Major Mordecai Gist; both Haslet and Smallwood were on courts-martial duty in Manhattan. Following close behind was Parson's Connecticut regiment with 251 men. Stirling led this combined force to reinforce Parsons and Atlee and stop the British advance. Stirling had a total of 1,600 troops at his command.


title: Battle of Long Island

text: Stirling placed Atlee's men in an apple orchard owned by Wynant Bennett on the south side of the Gowanus Road near present-day 3rd Avenue and 18th Street. Upon the approach of the British, the Americans:


title: Battle of Long Island

text: Stirling took up positions with the Delaware and Maryland regiments just to the north of Atlee's men on the slopes of a rise of land between 18th and 20th streets. Some of the Maryland troops were positioned on a small hill near today's 23rd Street, which the local Dutch called ""Blokje Berg"" (Dutch for cube or block hill). At the base of this hill, the Gowanus Road crossed a small bridge over a ditch which drained a marshy area. When the British advanced up the Gowanus Road, the American troops fired upon them from positions on the north side of the ditch. To their left was Colonel Peter Kachline's Pennsylvania regiment.


title: Battle of Long Island

text: Just to the southeast of "Blokje Berg" were a few hills; amongst them was a hill which is the highest point in King's County at 220 feet which came to be known as "Battle Hill," in what is today Greenwood Cemetery by the cemetery's boundary of 23rd Street and 7th Avenue. The British attempted to outflank the American positions by taking this hill. The Americans tried to prevent the British move, sending troops under Parsons and Atlee to take the hill. The British got there first but the Americans were able to dislodge them in fierce fighting. Battle Hill was the site of especially brutal fighting, with the Americans inflicting the highest number of casualties against the British troops during the entire Battle of Long Island. Among those killed was British Colonel James Grant, which led the Americans to believe that they had killed "General" James Grant. He was alleged to have been shot by a Pennsylvanian rifleman who had been sniping at the British from up in a tree. Among the American dead was Pennsylvania Colonel Caleb Parry, who was killed while rallying his troops.


title: Battle of Long Island

text: The Americans were still unaware that this was not the main British attack, in part due to the ferocity of the fighting and the number of British troops engaged.


title: Battle of Long Island

text: The Hessians, in the center under the command of General von Heister, began to bombard the American lines stationed at Battle Pass under the command of General John Sullivan. The Hessian brigades did not attack, as they were waiting for the pre-arranged signal from the British, who were in the process of outflanking the American lines at that time. The Americans were still under the assumption that Grant's attack up the Gowanus Road was the main thrust, and Sullivan sent four hundred of his men to reinforce Stirling.


title: Battle of Long Island

text: Howe fired his signal guns at 09:00 and the Hessians began to attack up Battle Pass, while the main army came at Sullivan from the rear. Sullivan left his advance guard to hold off the Hessians while he turned the rest of his force around to fight the British. Heavy casualties mounted between the Americans and the British, and men on both sides fled out of fear. Sullivan attempted to calm his men and tried to lead a retreat. By this point, the Hessians had overrun the advance guard on the heights and the American left had completely collapsed. Hand-to-hand fighting followed, with the Americans swinging their muskets and rifles like clubs to save their own lives. It was later claimed, Americans who surrendered were bayoneted by the Hessians. Sullivan, despite the chaos, managed to evacuate most of his men to Brooklyn Heights though he himself was captured.


title: Battle of Long Island

text: At 09:00, Washington arrived from Manhattan. He realized that he had been wrong about a feint on Long Island and he ordered more troops to Brooklyn from Manhattan. His location on the battlefield is not known because accounts differ, but most likely he was at Brooklyn Heights where he could view the battle.


title: Battle of Long Island

text: Stirling still held the line against Grant on the American right, to the west. He held on for four hours, still unaware of the British flanking maneuver, and some of his own troops thought that they were winning the day because the British had been unable to take their position. However, Grant was reinforced by 2,000 marines, and he hit Stirling's center by 11:00, and Stirling was attacked on his left by the Hessians. Stirling pulled back, but British troops were coming at him from the rear, from the south up the Gowanus Road. The only escape route left was across Brouwer's millpond on the Gowanus Creek which was 80 yards wide, where the American defenses on Brooklyn Heights lay on the other side.


title: Battle of Long Island

text: Stirling ordered all of his troops to cross the creek, except a contingent of Maryland troops under the command of Gist. This group became known to history as the "Maryland 400", although they numbered about 260–270 men. Stirling and Gist led the troops in a rear-guard action against the overwhelming numbers of British troops, which surpassed 2,000 supported by two cannons. Stirling and Gist led the Marylanders in two attacks against the British, who were in fixed positions inside and in front of the Vechte–Cortelyou House (known today as the "Old Stone House"). After the last assault, the remaining troops retreated across the Gowanus Creek. Some of the men who tried to cross the marsh were bogged down in the mud and under musket fire, and others who could not swim were captured. Stirling was surrounded and, unwilling to surrender to the British, broke through their lines to von Heister's Hessians and surrendered to them. Two hundred fifty six Maryland troops were killed in the assaults in front of the Old Stone House, and fewer than a dozen made it back to the American lines. Washington watched from a redoubt on nearby Cobble Hill (intersection of today's Court Street and Atlantic Avenue) and reportedly said, "Good God, what brave fellows I must this day lose."


title: Battle of Long Island

text: The American troops who were not killed or captured escaped behind the fortified American positions centered on Brooklyn Heights. Howe then ordered all of his troops to halt the attack, despite the protests of many officers in his command who believed that they should push on to Brooklyn Heights. Howe had decided against a direct frontal assault on the entrenched American positions, choosing instead to begin a siege and setting up lines of circumvallation around the American positions. He believed the Americans to be essentially trapped, with his troops blocking escape by land and the Royal Navy in control of the East River, which they would have to cross to reach Manhattan Island.


title: Battle of Long Island

text: Howe's failure to press the attack and the reasons for it have been disputed. He may have wished to avoid the casualties that his army suffered when attacking the Continentals under similar circumstances at the Battle of Bunker Hill. He may also have been giving Washington an opportunity to conclude that his position was hopeless and surrender, in the European gentleman-officer tradition. Howe told Parliament in 1779 that his essential duty was to avoid excessive British casualties for insufficient purpose, and capturing Brooklyn Heights would likely not have meant capturing the entire American army. "The most essential duty I had to observe was, not wantonly to commit his majesty's troops, where the object was inadequate. I knew well that any considerable loss sustained by the army could not speedily, nor easily, be repaired. . . . The loss of 1,000, or perhaps 1,500 British troops, in carrying those lines, would have been but ill repaid by double that number of the enemy, could it have been supposed they would have suffered in that proportion."


title: Battle of Long Island

text: Washington and the army were surrounded on Brooklyn Heights with the East River to their backs. As the day went on, the British began to dig trenches, slowly coming closer to the American defenses. By doing this, the British would not have to cross over open ground to assault the American defenses as they did in Boston the year before. Despite this perilous situation, Washington ordered 1,200 more men from Manhattan to Brooklyn on August 28. The men that came over were two Pennsylvania regiments and Colonel John Glover's regiment from Marblehead, Massachusetts. In command of the Pennsylvanian troops was Thomas Mifflin who, after arriving, volunteered to inspect the outer defenses and report back to Washington. In these outer defenses, small skirmishes were still taking place. On the afternoon of August 28, it began to rain and Washington had his cannons bombard the British well into the night.


title: Battle of Long Island

text: As the rain continued, George Washington sent a letter instructing General William Heath, who was at Kings Bridge over the Harlem River between Manhattan and what is now the Bronx, to send every flat-bottomed boat and sloop without delay, in case battalions of infantry from New Jersey came to reinforce their position. At 16:00, on August 29, Washington held a meeting with his generals. Mifflin advised Washington to retreat to Manhattan while Mifflin and his Pennsylvania regiments made up the rear guard, holding the line until the rest of the army had withdrawn. The generals agreed unanimously with Mifflin that retreat was the best option and Washington had orders go out by the evening.


title: Battle of Long Island

text: The troops were told that they were to gather up all their ammunition and baggage and prepare for a night attack. By 21:00, the sick and wounded began to move to the Brooklyn Ferry in preparation for evacuation. At 23:00, Glover and his Massachusetts men, who were sailors and fishermen, began to evacuate the troops.


title: Battle of Long Island

text: As more troops were evacuated, more were ordered to withdraw from the lines and march to the ferry landing. Wagon wheels were muffled, and men were forbidden to talk. Mifflin's rear guard was tending campfires to deceive the British. At 04:00, on August 30, Mifflin was informed that it was his unit's turn to evacuate. Mifflin told the man who had been sent to order him to leave, Major Alexander Scammell, that he must be mistaken, but Scammell insisted that he was not and Mifflin ordered his troops to move out. When Mifflin's troops were within a half mile of the ferry landing, Washington rode up and demanded to know why they were not at their defenses. Edward Hand, who was leading the troops, tried to explain what had happened, but Mifflin arrived shortly. Washington exclaimed "Good God. General Mifflin, I am afraid you have ruined us." Mifflin explained that he had been told that it was his turn to evacuate by Scammell; Washington told him it had been a mistake. Mifflin then led his troops back to the outer defenses.


title: Battle of Long Island

text: Artillery, supplies, and troops were all being evacuated across the river at this time but it was not going as fast as Washington had anticipated and daybreak soon came. A fog settled in and concealed the evacuation from the British. British patrols noticed that there did not seem to be any American pickets and thus began to search the area. While they were doing this, Washington, the last man left, stepped onto the last boat. At 07:00, the last American troops landed in Manhattan. All 9,000 troops had been evacuated with no loss of life.


title: Battle of Long Island

text: The British were stunned to find that Washington and the army had escaped. Later in the day, August 30, the British troops occupied the American fortifications. When news of the battle reached London, it caused many festivities to take place. Bells were rung across the city, candles were lit in windows and King George III gave Howe the Order of the Bath.


title: Battle of Long Island

text: Washington's defeat, in the opinions of some, revealed his deficiencies as a strategist, because of how he split his forces. His inexperienced generals misunderstood the situation, and his raw troops fled in disorder at the first shots. However, his daring nighttime retreat has been seen by some historians as one of his greatest military feats. Other historians concentrate on the failure of British naval forces to prevent the withdrawal.


title: Battle of Long Island

text: Howe remained inactive for the next half month, not attacking until September 15 when he landed a force at Kip's Bay. The British quickly occupied the city. Although American troops delivered an unexpected check to the British at Harlem Heights in mid-September, Howe defeated Washington in battle again at White Plains and then again at Fort Washington. Because of these defeats, Washington and the army retreated across New Jersey and into Pennsylvania. On September 21, a fire of uncertain origin destroyed a quarter of New York City. In the immediate aftermath of the fire Nathan Hale was executed for spying.


title: Battle of Long Island

text: At the time, it was by far the largest battle ever fought in North America. If the Royal Navy is included, over 40,000 men took part in the battle. Howe reported his losses as 59 killed, 268 wounded and 31 missing. The Hessian casualties were 5 killed and 26 wounded. The Americans suffered much heavier losses. About 300 had been killed and over 1,000 captured. As few as half of the prisoners survived. Kept on prison ships in Wallabout Bay, then transferred to locations such as the Middle Dutch Church, they were starved and denied medical attention. In their weakened condition, many succumbed to smallpox.


title: Battle of Long Island

text: Historians believe that as many as 256 soldiers of the First Maryland Regiment under Colonel William Smallwood fell in the battle, about two-thirds of the regiment. It is known that they were buried in a mass-grave, but the grave's exact location has been a mystery for 240 years.


title: Battle of Long Island

text: The most significant legacy of the Battle of Long Island was that it showed there would be no easy victory, and that the war would be long and bloody. The British took control of the strategically vital harbor and put New York City under military occupation until the treaty ending the war was signed. With the British military command in residence the city became the focal point for espionage and intelligence gathering. The area surrounding the city and the harbor remained in a near-constant state of conflict as a forage-war harassed the surrounding communities.


title: Battle of Long Island

text: There are only thirty currently existing units in the U.S. Army with lineages that go back to the colonial and revolutionary eras. Five Army National Guard units (101st Eng Bn, 125th MP Co, 175th Inf, 181st Inf and 198th Sig Bn) and one Regular Army Field Artillery battalion (1–5th FA) are derived from American units that participated in the Battle of Long Island.


title: Nickel–cadmium battery

text: The nickel–cadmium battery (Ni–Cd battery or NiCad battery) is a type of rechargeable battery using nickel oxide hydroxide and metallic cadmium as electrodes. The abbreviation "Ni-Cd" is derived from the chemical symbols of nickel (Ni) and cadmium (Cd): the abbreviation "NiCad" is a registered trademark of SAFT Corporation, although this brand name is commonly used to describe all Ni–Cd batteries.


title: Nickel–cadmium battery

text: Wet-cell nickel-cadmium batteries were invented in 1899. A Ni-Cd battery has a terminal voltage during discharge of around 1.2 volts which decreases little until nearly the end of discharge. The maximum electromotive force offered by a Ni-Cd cell is 1.3V. Ni-Cd batteries are made in a wide range of sizes and capacities, from portable sealed types interchangeable with carbon-zinc dry cells, to large ventilated cells used for standby power and motive power. Compared with other types of rechargeable cells they offer good cycle life and performance at low temperatures with a fair capacity but their significant advantage is the ability to deliver practically their full rated capacity at high discharge rates (discharging in one hour or less). However, the materials are more costly than that of the lead–acid battery, and the cells have high self-discharge rates.


title: Nickel–cadmium battery

text: Sealed Ni-Cd cells were at one time widely used in portable power tools, photography equipment, flashlights, emergency lighting, hobby RC, and portable electronic devices. The superior capacity of nickel–metal hydride batteries, and recent lower cost, has largely supplanted Ni-Cd use. Further, the environmental impact of the disposal of the toxic metal cadmium has contributed considerably to the reduction in their use. Within the European Union, Ni-Cd batteries can now only be supplied for replacement purposes or for certain types of new equipment such as medical devices.


title: Nickel–cadmium battery

text: Larger ventilated wet cell Ni-Cd batteries are used in emergency lighting, standby power, and uninterruptible power supplies and other applications.


title: Nickel–cadmium battery

text: The first Ni–Cd battery was created by Waldemar Jungner of Sweden in 1899. At that time, the only direct competitor was the lead–acid battery, which was less physically and chemically robust. With minor improvements to the first prototypes, energy density rapidly increased to about half of that of primary batteries, and significantly greater than lead–acid batteries. Jungner experimented with substituting iron for the cadmium in varying quantities, but found the iron formulations to be wanting. Jungner's work was largely unknown in the United States. Thomas Edison patented a nickel– or cobalt–cadmium battery in 1902, and adapted the battery design when he introduced the nickel–iron battery to the US two years after Jungner had built one. In 1906, Jungner established a factory close to Oskarshamn, Sweden to produce flooded design Ni–Cd batteries.


title: Nickel–cadmium battery

text: In 1932 active materials were deposited inside a porous nickel-plated electrode and fifteen years later work began on a sealed nickel-cadmium battery.


title: Nickel–cadmium battery

text: The first production in the United States began in 1946. Up to this point, the batteries were "pocket type," constructed of nickel-plated steel pockets containing nickel and cadmium active materials. Around the middle of the twentieth century, sintered-plate Ni–Cd batteries became increasingly popular. Fusing nickel powder at a temperature well below its melting point using high pressures creates sintered plates. The plates thus formed are highly porous, about 80 percent by volume. Positive and negative plates are produced by soaking the nickel plates in nickel- and cadmium-active materials, respectively. Sintered plates are usually much thinner than the pocket type, resulting in greater surface area per volume and higher currents. In general, the greater amount of reactive material surface area in a battery, the lower its internal resistance.


title: Nickel–cadmium battery

text: The maximum discharge rate for a Ni–Cd battery varies by size. For a common AA-size cell, the maximum discharge rate is approximately 1.8 amperes; for a D size battery the discharge rate can be as high as 3.5 amperes.


title: Nickel–cadmium battery

text: Model-aircraft or -boat builders often take much larger currents of up to a hundred amps or so from specially constructed Ni–Cd batteries, which are used to drive main motors. 5–6 minutes of model operation is easily achievable from quite small batteries, so a reasonably high power-to-weight figure is achieved, comparable to internal combustion motors, though of lesser duration. In this, however, they have been largely superseded by lithium polymer (Lipo) and lithium iron phosphate (LiFe) batteries, which can provide even higher energy densities.


title: Nickel–cadmium battery

text: Ni–Cd cells have a nominal cell potential of 1.2 volts (V). This is lower than the 1.5 V of alkaline and zinc–carbon primary cells, and consequently they are not appropriate as a replacement in all applications. However, the 1.5 V of a primary alkaline cell refers to its initial, rather than average, voltage. Unlike alkaline and zinc–carbon primary cells, a Ni–Cd cell's terminal voltage only changes a little as it discharges. Because many electronic devices are designed to work with primary cells that may discharge to as low as 0.90 to 1.0 V per cell, the relatively steady 1.2 V of a Ni–Cd cell is enough to allow operation. Some would consider the near-constant voltage a drawback as it makes it difficult to detect when the battery charge is low.


title: Nickel–cadmium battery

text: Ni–Cd batteries used to replace 9 V batteries usually only have six cells, for a terminal voltage of 7.2 volts. While most pocket radios will operate satisfactorily at this voltage, some manufacturers such as Varta made 8.4 volt batteries with seven cells for more critical applications.


title: Nickel–cadmium battery

text: Ni–Cd batteries can be charged at several different rates, depending on how the cell was manufactured. The charge rate is measured based on the percentage of the amp-hour capacity the battery is fed as a steady current over the duration of the charge. Regardless of the charge speed, more energy must be supplied to the battery than its actual capacity, to account for energy loss during charging, with faster charges being more efficient. For example, an "overnight" charge, might consist of supplying a current equal to one tenth the ampere-hour rating (C/10) for 14–16 hours; that is, a 100 mAh battery takes 10 mA for 14 hours, for a total of 140 mAh to charge at this rate. At the rapid-charge rate, done at 100% of the rated capacity of the battery in 1 hour (1C), the battery holds roughly 80% of the charge, so a 100 mAh battery takes 125 mAh to charge (that is, approximately 1 hour and fifteen minutes). Some specialized batteries can be charged in as little as 10–15 minutes at a 4C or 6C charge rate, but this is very uncommon. It also greatly increases the risk of the cells overheating and venting due to an internal over-pressure condition: the cell's rate of temperature rise is governed by its internal resistance and the square of the charging rate. At a 4C rate, the amount of heat generated in the cell is sixteen times higher than the heat at the 1C rate. The downside to faster charging is the higher risk of overcharging, which can damage the battery. and the increased temperatures the cell has to endure (which potentially shortens its life).


title: Nickel–cadmium battery

text: The safe temperature range when in use is between −20 °C and 45 °C. During charging, the battery temperature typically stays low, around the same as the ambient temperature (the charging reaction absorbs energy), but as the battery nears full charge the temperature will rise to 45–50 °C. Some battery chargers detect this temperature increase to cut off charging and prevent over-charging.


title: Nickel–cadmium battery

text: When not under load or charge, a Ni–Cd battery will self-discharge approximately 10% per month at 20 °C, ranging up to 20% per month at higher temperatures. Note; year 2022, the preceding sentence was certainly true when NiCad was introduced and even 50 years ago. However continued improvements seen around 40 years ago lead to 5% per month and today the NiCad batteries have substantially lower self-discharge, on the order of 1% or 2% per month. It is possible to perform a trickle charge at current levels just high enough to offset this discharge rate; to keep a battery fully charged. However, if the battery is going to be stored unused for a long period of time, it should be discharged down to at most 40% of capacity (some manufacturers recommend fully discharging and even short-circuiting once fully discharged), and stored in a cool, dry environment.


title: Nickel–cadmium battery

text: Sealed Ni–Cd cells consist of a pressure vessel that is supposed to contain any generation of oxygen and hydrogen gases until they can recombine back to water. Such generation typically occurs during rapid charge and discharge, and exceedingly at overcharge condition. If the pressure exceeds the limit of the safety valve, water in the form of gas is lost. Since the vessel is designed to contain an exact amount of electrolyte this loss will rapidly affect the capacity of the cell and its ability to receive and deliver current. To detect all conditions of overcharge demands great sophistication from the charging circuit and a cheap charger will eventually damage even the best quality cells.


title: Nickel–cadmium battery

text: Ni-Cd batteries usually have a metal case with a sealing plate equipped with a self-sealing safety valve. The positive and negative electrode plates, isolated from each other by the separator, are rolled in a spiral shape inside the case. This is known as the jelly-roll design and allows a Ni–Cd cell to deliver a much higher maximum current than an equivalent size alkaline cell. Alkaline cells have a bobbin construction where the cell casing is filled with electrolyte and contains a graphite rod which acts as the positive electrode. As a relatively small area of the electrode is in contact with the electrolyte (as opposed to the jelly-roll design), the internal resistance for an equivalent sized alkaline cell is higher which limits the maximum current that can be delivered.


title: Nickel–cadmium battery

text: During recharge, the reactions go from right to left. The alkaline electrolyte (commonly KOH) is not consumed in this reaction and therefore its specific gravity, unlike in lead–acid batteries, is not a guide to its state of charge.


title: Nickel–cadmium battery

text: When Jungner built the first Ni-Cd batteries, he used nickel oxide in the positive electrode, and iron and cadmium materials in the negative. It was not until later that pure cadmium metal and nickel hydroxide were used. Until about 1960, the chemical reaction was not completely understood. There were several speculations as to the reaction products. The debate was finally resolved by infrared spectroscopy, which revealed cadmium hydroxide and nickel hydroxide.


title: Nickel–cadmium battery

text: Another historically important variation on the basic Ni-Cd cell is the addition of lithium hydroxide to the potassium hydroxide electrolyte. This was believed to prolong the service life by making the cell more resistant to electrical abuse. The Ni–Cd battery in its modern form is extremely resistant to electrical abuse anyway, so this practice has been discontinued.


title: Nickel–cadmium battery

text: "Vented cell" ("wet cell", "flooded cell") NiCd batteries are used when large capacities and high discharge rates are required. Traditional NiCd batteries are of the sealed type, which means that charge gas is normally recombined and they release no gas unless severely overcharged or a fault develops. Unlike typical NiCd cells, which are sealed, vented cells have a vent or low pressure release valve that releases any generated oxygen and hydrogen gases when overcharged or discharged rapidly. Since the battery is not a pressure vessel, it is safer, weighs less, and has a simpler and more economical structure. This also means the battery is not normally damaged by excessive rates of overcharge, discharge or even negative charge.


title: Nickel–cadmium battery

text: They are used in aviation, rail and mass transit, backup power for telecoms, engine starting for backup turbines etc. Using vented cell NiCd batteries results in reduction in size, weight and maintenance requirements over other types of batteries. Vented cell NiCd batteries have long lives (up to 20 years or more, depending on type) and operate at extreme temperatures (from −40 to 70 °C).