title: Gel

text: Nanocomposite hydrogels or hybrid hydrogels, are highly hydrated polymeric networks, either physically or covalently crosslinked with each other and/or with nanoparticles or nanostructures. Nanocomposite hydrogels can mimic native tissue properties, structure and microenvironment due to their hydrated and interconnected porous structure. A wide range of nanoparticles, such as carbon-based, polymeric, ceramic, and metallic nanomaterials can be incorporated within the hydrogel structure to obtain nanocomposites with tailored functionality. Nanocomposite hydrogels can be engineered to possess superior physical, chemical, electrical, thermal, and biological properties.


title: Gel

text: By replacing the liquid with gas it is possible to prepare aerogels, materials with exceptional properties including very low density, high specific surface areas, and excellent thermal insulation properties.


title: Gel

text: A gel is in essence the mixture of a polymer network and a solvent phase. Upon stretching, the network crosslinks are moved further apart from each other. Due to the polymer strands between crosslinks act as entropic springs, gels demonstrate elasticity like rubber (which is just a polymer network, without solvent). This is so because the free energy penalty to stretch an ideal polymer segment formula_1 monomers of size formula_2 between crosslinks to an end-to-end distance formula_3 is approximately given by


title: Gel

text: This is the origin of both gel and rubber elasticity. But one key difference is that gel contains an additional solvent phase and hence is capable of having significant volume changes under deformation by taking in and out solvent. For example, a gel could swell to several times its initial volume after being immersed in a solvent after equilibrium is reached. This is the phenomenon of gel swelling. On the contrary, if we take the swelled gel out and allow the solvent to evaporate, the gel would shrink to roughly its original size. This gel volume change can alternatively be introduced by applying external forces. If a uniaxial compressive stress is applied to a gel, some solvent contained in the gel would be squeezed out and the gel shrinks in the applied-stress direction. To study the gel mechanical state in equilibrium, a good starting point is to consider a cubic gel of volume formula_5 that is stretched by factors formula_6, formula_7 and formula_8 in the three orthogonal directions during swelling after being immersed in a solvent phase of initial volume formula_9. The final deformed volume of gel is then formula_10 and the total volume of the system is formula_11 that is assumed constant during the swelling process for simplicity of treatment. The swelled state of the gel is now completely characterized by stretch factors formula_6, formula_7 and formula_8 and hence it is of interest to derive the deformation free energy as a function of them, denoted as formula_15. For analogy to the historical treatment of rubber elasticity and mixing free energy, formula_15 is most often defined as the free energy difference after and before the swelling normalized by the initial gel volume formula_5, that is, a free energy difference density. The form of formula_15 naturally assumes two contributions of radically different physical origins, one is associated with the elastic deformation of the polymer network, and the other with the mixing of the network with the solvent. Hence, we write


title: Gel

text: We now consider the two contributions separately. The polymer elastic deformation term is independent of the solvent phase and has the same expression as a rubber, as derived in the Kuhn's theory of rubber elasticity:


title: Gel

text: where formula_21 denotes the shear modulus of the initial state. On the other hand, the mixing term formula_22 is usually treated by the Flory-Huggins free energy of concentrated polymer solutions formula_23, where formula_24 is polymer volume fraction. Suppose the initial gel has a polymer volume fraction of formula_25, the polymer volume fraction after swelling would be formula_26 since the number of monomers remains the same while the gel volume has increased by a factor of formula_27. As the polymer volume fraction decreases from formula_25 to formula_24, a polymer solution of concentration formula_25 and volume formula_5 is mixed with a pure solvent of volume formula_32 to become a solution with polymer concentration formula_24 and volume formula_10. The free energy density change in this mixing step is given as


title: Gel

text: where on the right hand side, the first term is the Flory-Huggins energy density of the final swelled gel, the second is associated with the initial gel and the third is of the pure solvent prior to mixing. Substitution of formula_26 leads to


title: Gel

text: Note that the second term is independent of the stretching factors formula_6, formula_7 and formula_8 and hence can be dropped in subsequent analysis. Now we make use of the Flory-Huggins free energy for a polymer-solvent solution that reads


title: Gel

text: where formula_42 is monomer volume, formula_1 is polymer strand length and formula_44 is the Flory-Huggins energy parameter. Because in a network, the polymer length is effectively infinite, we can take the limit formula_45 and formula_23 reduces to


title: Gel

text: This provides the starting point to examining the swelling equilibrium of a gel network immersed in solvent. It can be shown that gel swelling is the competition between two forces, one is the osmotic pressure of the polymer solution that favors the take in of solvent and expansion, the other is the restoring force of the polymer network elasticity that favors shrinkage. At equilibrium, the two effects exactly cancel each other in principle and the associated formula_6, formula_7 and formula_8 define the equilibrium gel volume. In solving the force balance equation, graphical solutions are often preferred.


title: Gel

text: In an alternative, scaling approach, suppose an isotropic gel is stretch by a factor of formula_53 in all three directions. Under the affine network approximation, the mean-square end-to-end distance in the gel increases from initial formula_54 to formula_55 and the elastic energy of one stand can be written as


title: Gel

text: where formula_57 is the mean-square fluctuation in end-to-end distance of one strand. The modulus of the gel is then this single-strand elastic energy multiplied by strand number density formula_58 to give


title: Gel

text: This modulus can then be equated to osmotic pressure (through differentiation of the free energy) to give the same equation as we found above.


title: Gel

text: Consider a hydrogel made of polyelectrolytes decorated with weak acid groups that can ionize according to the reaction


title: Gel

text: is immersed in a salt solution of physiological concentration. The degree of ionization of the polyelectrolytes is then controlled by the formula_61 and due to the charged nature of formula_62 and formula_63, electrostatic interactions with other ions in the systems. This is effectively a reacting system governed by acid-base equilibrium modulated by electrostatic effects, and is relevant in drug delivery, sea water desalination and dialysis technologies. Due to the elastic nature of the gel, the dispersion of formula_63 in the system is constrained and hence, there will be a partitioning of salts ions and formula_62 inside and outside the gel, which is intimately coupled to the polyelectrolyte degree of ionization. This ion partitioning inside and outside the gel is analogous to the partitioning of ions across a semipemerable membrane in classical Donnan theory, but a membrane is not needed here because the gel volume constraint imposed by network elasticity effectively acts its role, in preventing the macroions to pass through the fictitious membrane while allowing ions to pass.


title: Gel

text: The coupling between the ion partitioning and polyelectrolyte ionization degree is only partially by the classical Donnan theory. As a starting point we can neglect the electrostatic interactions among ions. Then at equilibrium, some of the weak acid sites in the gel would dissociate to form formula_63that electrostatically attracts positive charged formula_62 and salt cations leading to a relatively high concentration of formula_62 and salt cations inside the gel. But because the concentration of formula_62 is locally higher, it suppresses the further ionization of the acid sites. This phenomenon is the prediction of the classical Donnan theory. However, with electrostatic interactions, there are further complications to the picture. Consider the case of two adjacent, initially uncharged acid sites formula_70 are both dissociated to form formula_63. Since the two sites are both negatively charged, there will be a charge-charge repulsion along the backbone of the polymer than tends to stretch the chain. This energy cost is high both elastically and electrostatically and hence suppress ionization. Even though this ionization suppression is qualitatively similar to that of Donnan prediction, it is absent without electrostatic consideration and present irrespective of ion partitioning. The combination of both effects as well as gel elasticity determines the volume of the gel at equilibrium. Due to the complexity of the coupled acid-base equilibrium, electrostatics and network elasticity, only recently has such system been correctly recreated in computer simulations.


title: Gel

text: Some species secrete gels that are effective in parasite control. For example, the long-finned pilot whale secretes an enzymatic gel that rests on the outer surface of this animal and helps prevent other organisms from establishing colonies on the surface of these whales' bodies.


title: Gel

text: Hydrogels existing naturally in the body include mucus, the vitreous humor of the eye, cartilage, tendons and blood clots. Their viscoelastic nature results in the soft tissue component of the body, disparate from the mineral-based hard tissue of the skeletal system. Researchers are actively developing synthetically derived tissue replacement technologies derived from hydrogels, for both temporary implants (degradable) and permanent implants (non-degradable). A review article on the subject discusses the use of hydrogels for nucleus pulposus replacement, cartilage replacement, and synthetic tissue models.


title: Gel

text: Many substances can form gels when a suitable thickener or gelling agent is added to their formula. This approach is common in manufacture of wide range of products, from foods to paints and adhesives.


title: Gel

text: In fiber optic communications, a soft gel resembling hair gel in viscosity is used to fill the plastic tubes containing the fibers. The main purpose of the gel is to prevent water intrusion if the buffer tube is breached, but the gel also buffers the fibers against mechanical damage when the tube is bent around corners during installation, or flexed. Additionally, the gel acts as a processing aid when the cable is being constructed, keeping the fibers central whilst the tube material is extruded around it.


title: We Can Remember It for You Wholesale

text: "We Can Remember It for You Wholesale" is a science fiction novelette by American writer Philip K. Dick, first published in "The Magazine of Fantasy & Science Fiction" in April 1966. It features a melding of reality, false memory, and real memory. The story was adapted into the 1990 film "Total Recall" with Arnold Schwarzenegger as the story's protagonist; that film was remade in 2012 with Colin Farrell as the protagonist.


title: We Can Remember It for You Wholesale

text: Douglas Quail works a menial office job in the "not too distant future." His biggest dream has always been to visit Mars but he is constantly dissuaded by his wife. Quail eventually discovers Rekal Incorporated, where he goes to receive memory implants of having traveled to Mars. To the shock of the Rekal technicians, under sedation, Quail somehow regains erased memories of who he really is. Quail's memories reveal that he really is a secret agent who has been to Mars.


title: We Can Remember It for You Wholesale

text: The Rekal representative, McClane, refunds half of Quail's money and sends him home. Quail thinks that the operation was a failure because his memories are blurry, and he remembers his trip to the office to get the procedure done. He returns home still believing the memories are fake but discovers a box of fauna smuggled from Mars in his desk. He confronts his wife about whether or not he has actually been to Mars, and she angrily leaves him. Two armed men suddenly enter and reveal that Quail has a telepathic transmitter in his head that allows them to read his thoughts. Through this interaction, Quail suddenly remembers why he had his memories erased: Quail wasn't just a secret agent, he was an assassin who killed a political opponent for Earth's government.


title: We Can Remember It for You Wholesale

text: With his memories returned, the armed men appeal to Quail to surrender, but Quail, with his abilities awakened as well, fights them off and escapes. Wondering what to do, Quail's former commanders suddenly speak to him through the telepathic transmitter. Quail suggests going through another mind-wipe, but this time replacing his current awareness of being an assassin with the pleasant memory of an exciting life. His commanders agree, feeling that it is their obligation to help their former agent.


title: We Can Remember It for You Wholesale

text: Quail turns himself in and is placed with a psychiatrist to figure out what his own personal desires are. When he was young, Quail used to fantasize that as a child he came across minuscule [rodent-like] aliens that were going to launch a full invasion of Earth with their superior technology. However, young Quail was so kind and accepting of the aliens that they decided to hold off on their invasion as long as he was alive. While finding the fantasy narcissistic, his commanders agree to plant the memories at Rekal. To everyone's shock, those memories turn out to be real as well.


title: We Can Remember It for You Wholesale

text: "We Can Remember It for You Wholesale" was first published in the April 1966 issue of "The Magazine of Fantasy & Science Fiction". It has been republished in the following collections:


title: We Can Remember It for You Wholesale

text: The plot was loosely adapted into the 1990 film "Total Recall", directed by Paul Verhoeven and starring Arnold Schwarzenegger. A remake was directed by Len Wiseman and released on August 3, 2012. While the owners of Carolco had licensed the story from Dick for the 1990 version, the 2012 film was largely based on the original and does not credit Dick as a writer. Both films include the main concepts of Dick's story but contain many alterations.


title: U.S. Cellular

text: United States Cellular Corporation (doing business as UScellular) is an American mobile network operator. It is a subsidiary of Telephone and Data Systems Inc. (which owns an 84% stake). The company was formed in 1983 and is headquartered in Chicago, Illinois. UScellular is the fourth-largest wireless carrier in the United States, with 4,755,000 customers in 426 markets in 23 states as of the third quarter of 2022. It was previously known as United States Cellular and U.S. Cellular.


title: U.S. Cellular

text: United States Cellular was founded as a subsidiary of Telephone and Data Systems Inc. (TDS) and incorporated on December 23, 1983. In 1985, the company began operations in Knoxville, Tennessee (June), and Tulsa, Oklahoma (August). Don Nelson was named the first president in 1987 and TDS took the company public in 1988 where United States Cellular adopted USM as its ticker symbol on the American Stock Exchange. In 1999, United States Cellular relaunched under the “U.S. Cellular” brand name and image across all markets nationwide.


title: U.S. Cellular

text: Don Nelson retired and Jack Rooney took over as CEO. In 2001, U.S. Cellular received the Wireless Titan Award as the top wireless carrier in terms of customer service from Wireless Review magazine. The company purchased PrimeCo Wireless Communications in 2002 and launched in Chicagoland on November 22. It built on this growth by signing famed Chicagoan Joan Cusack as national spokesperson. In January 2003, U.S. Cellular acquired naming rights to the baseball stadium used by the Chicago White Sox. Formerly known as Comiskey Park, the stadium was officially renamed U.S Cellular Field (it was renamed Guaranteed Rate Field in 2016). That same year, U.S. Cellular and Cingular (now owned by AT&T Mobility) exchanged wireless assets and U.S. Cellular received new spectrum in markets of 13 states that were adjacent to or overlapped existing operations in exchange for its Georgia and northern Florida licenses. U.S. Cellular also launched Easyedge, its suite of wireless data services. In 2005, U.S. Cellular entered the St. Louis market, making it the second largest market U.S. Cellular served, after Chicago. In October of 2008, U.S. Cellular launched Mobile Broadband, a service enabling customers to access data on its cell phones 10 times faster than before. It brought DSL-like service and capabilities to customers through EVDO (Evolution-Data Optimized) technology, commonly referred to as 3G. As of Q2 2008, U.S. Cellular was preparing to roll out 3G/EVDO revision A to select markets.


title: U.S. Cellular

text: In 2010 CEO Jack Rooney retired and Mary N. Dillon assumed the position of CEO. In May of 2011, U.S. Cellular announced that it will offer 4G LTE. In a surprising move, U.S. Cellular announced the sale of several markets to Sprint Corporation including Chicago. Mary Dillon departed as CEO in 2013 and Kenneth R. Meyers took over. June of 2016, Google announced that it partnered with U.S. Cellular as part of its Google Fi service. U.S. Cellular contributed its network and LTE service to the "network of networks" along with T-Mobile US and Sprint Corporation.


title: U.S. Cellular

text: In March of 2020, U.S. Cellular debuted launch of 5G in Wisconsin and Iowa and Laurent Therivel was selected to succeed retiring Kenneth R. Meyers as CEO in June. At the end of the third quarter, U.S. Cellular rebranded as UScellular and upgraded its logo.


title: U.S. Cellular

text: Originally, U.S. Cellular used analog, then Digital AMPS "TDMA" cell phones in most markets, but the company started shifting to 1xRTT CDMA technology in 2003. After the switch, U.S. Cellular discontinued all analog and TDMA services. Starting in 2009, U.S. Cellular converted its network to EVDO, which offered 3G speeds.


title: U.S. Cellular

text: U.S. Cellular began offering 4G LTE coverage to customers in the first quarter of 2012. The rollout started in cities in Iowa, Wisconsin, Maine, North Carolina, Texas and Oklahoma. In 2012, U.S. Cellular added 4G LTE in additional markets throughout the country.


title: U.S. Cellular

text: Its LTE network was primarily built upon two low-frequency LTE bands; 12 and 5. Through an agreement with King Street Wireless, U.S. Cellular has access to the lower 700 MHz A, B, and C blocks across most of its markets. Spectrum bandwidth includes, 5*5, or 10*10 MHz on band 12 700 MHz 5*5 MHz on band 5 850 MHz 5*5, or 10*10 MHz on band 4 AWS 1. U.S. Cellular also has 5Mhz or 10Mhz of spectrum on Band 66 (AWS-3) in some markets.


title: U.S. Cellular

text: The company began VoLTE trials during 2016, launched its first market with VoLTE during the first quarter of 2017.


title: U.S. Cellular

text: In December 2019, the FCC found U.S. Cellular shared misinformation about its 4G LTE coverage by as much as 38%, only managing to reach the federally mandated minimum speeds 45% of the time.


title: U.S. Cellular

text: In June 2019, U.S. Cellular successfully bid for high frequency spectrum in the Federal Communications Commission’s (FCC) Millimeter Wave Spectrum Auctions and purchased licenses covering 98 percent of its subscribers for $256.0 million or 1.7 cents per MHz pop. This laid the foundation for October 2019, when U.S. Cellular officially announced plans to launch its 5G service. The company launched its first phone with support, the Samsung Galaxy S20, as well as coverage maps for its first commercial 5G network in both urban and rural parts of Iowa and Wisconsin in February 2020.


title: U.S. Cellular

text: UScellular has roaming agreements with AT&T Mobility, T-Mobile U.S. and Verizon. This allows customers to roam on these networks with LTE or 5G speeds with no extra charges.


title: U.S. Cellular

text: The following is a list of known CDMA, LTE, and 5G NR frequency bands which UScellular employs in the United States:


title: U.S. Cellular

text: Since 2009, UScellular has donated nearly $22.6 million along with countless experiences and technology items to nonprofit organizations across the country in three areas: STEM Learning, Bridging the Digital Divide and Celebrating Associate Passions/Local Communities.


title: U.S. Cellular

text: In March of 2021, UScellular donated $150,000 to to open five new Girls Who Code clubs in Kansas, Oklahoma, Virginia and Maine to help increase access to future opportunities, especially among young women.


title: U.S. Cellular

text: The company made a $100,000 DonorsChoose donation in 2021 for to provide STEM learning support for 500 teachers and 50,000 students.


title: U.S. Cellular

text: In 2021, USCellular launched the After School Access Project with a pledge to provide up to $13 million in hotspots and service in 2022 to help up to 50,000 youth get connected.


title: U.S. Cellular

text: In August 2022, the company is donated $4.7 million in wireless hotspots and service to 17 YWCA locations and 16,000 YWCA members across the country to help youth access the connectivity they need outside of the classroom.


title: U.S. Cellular

text: UScellular associates participated in 3,800 volunteer experiences and the company matched $296,000 in personal donations for 2021.


title: U.S. Cellular

text: In 2021, UScellular donated $40,000 to Red Cross disaster support, recycled and repurposed 187,000 devices and avoided 238 million gallons of water pollution.


title: U.S. Cellular

text: UScellular had served as the presenting sponsor of the 80/35 Music Festival in Des Moines, Iowa. It also served as the title sponsor of a NASCAR Xfinity Series race until 2019, the U.S. Cellular 250, at Iowa Speedway in Newton, Iowa.


title: U.S. Cellular

text: The sonic logo, tag, audio mnemonic was produced by Musikvergnuegen and written by Walter Werzowa from the Austrian 1980s sampling band Edelweiss.


title: Quartic function

text: A "quartic equation", or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form


title: Quartic function

text: Sometimes the term biquadratic is used instead of "quartic", but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form


title: Quartic function

text: Since a quartic function is defined by a polynomial of even degree, it has the same infinite limit when the argument goes to positive or negative infinity. If "a" is positive, then the function increases to positive infinity at both ends; and thus the function has a global minimum. Likewise, if "a" is negative, it decreases to negative infinity and has a global maximum. In both cases it may or may not have another local maximum and another local minimum.


title: Quartic function

text: The degree four ("quartic" case) is the highest degree such that every polynomial equation can be solved by radicals, according to the Abel–Ruffini theorem.


title: Quartic function

text: Lodovico Ferrari is credited with the discovery of the solution to the quartic in 1540, but since this solution, like all algebraic solutions of the quartic, requires the solution of a cubic to be found, it could not be published immediately. The solution of the quartic was published together with that of the cubic by Ferrari's mentor Gerolamo Cardano in the book "Ars Magna".


title: Quartic function

text: The Soviet historian I. Y. Depman claimed that even earlier, in 1486, Spanish mathematician Valmes was burned at the stake for claiming to have solved the quartic equation. Inquisitor General Tomás de Torquemada allegedly told Valmes that it was the will of God that such a solution be inaccessible to human understanding. However, Petr Beckmann, who popularized this story of Depman in the West, said that it was unreliable and hinted that it may have been invented as Soviet antireligious propaganda. Beckmann's version of this story has been widely copied in several books and internet sites, usually without his reservations and sometimes with fanciful embellishments. Several attempts to find corroborating evidence for this story, or even for the existence of Valmes, have failed.


title: Quartic function

text: The proof that four is the highest degree of a general polynomial for which such solutions can be found was first given in the Abel–Ruffini theorem in 1824, proving that all attempts at solving the higher order polynomials would be futile. The notes left by Évariste Galois prior to dying in a duel in 1832 later led to an elegant complete theory of the roots of polynomials, of which this theorem was one result.


title: Quartic function

text: Each coordinate of the intersection points of two conic sections is a solution of a quartic equation. The same is true for the intersection of a line and a torus. It follows that quartic equations often arise in computational geometry and all related fields such as computer graphics, computer-aided design, computer-aided manufacturing and optics. Here are examples of other geometric problems whose solution involves solving a quartic equation.


title: Quartic function

text: In computer-aided manufacturing, the torus is a shape that is commonly associated with the endmill cutter. To calculate its location relative to a triangulated surface, the position of a horizontal torus on the -axis must be found where it is tangent to a fixed line, and this requires the solution of a general quartic equation to be calculated.


title: Quartic function

text: A quartic equation arises also in the process of solving the crossed ladders problem, in which the lengths of two crossed ladders, each based against one wall and leaning against another, are given along with the height at which they cross, and the distance between the walls is to be found.


title: Quartic function

text: In optics, Alhazen's problem is ""Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer."" This leads to a quartic equation.


title: Quartic function

text: The eigenvalues of a 4×4 matrix are the roots of a quartic polynomial which is the characteristic polynomial of the matrix.


title: Quartic function

text: The characteristic equation of a fourth-order linear difference equation or differential equation is a quartic equation. An example arises in the Timoshenko-Rayleigh theory of beam bending.


title: Quartic function

text: Letting and be the distinct inflection points of the graph of a quartic function, and letting be the intersection of the inflection secant line and the quartic, nearer to than to , then divides into the golden section:


title: Quartic function

text: Moreover, the area of the region between the secant line and the quartic below the secant line equals the area of the region between the secant line and the quartic above the secant line. One of those regions is disjointed into sub-regions of equal area.


title: Quartic function

text: with real coefficients and the nature of its roots is mainly determined by the sign of its discriminant


title: Quartic function

text: There are some cases that do not seem to be covered, and in fact they cannot occur. For example, , = 0 and ≤ 0 is not one of the cases. In fact, if and = 0 then > 0, since formula_11 so this combination is not possible.


title: Quartic function

text: with ≠ 0 are given in the following formula, which is deduced from the one in the section on Ferrari's method by back changing the variables (see ) and using the formulas for the quadratic and cubic equations.


title: Quartic function

text: where and are the coefficients of the second and of the first degree respectively in the associated depressed quartic


title: Quartic function

text: It is reducible if , where and are non-constant polynomials with rational coefficients (or more generally with coefficients in the same field as the coefficients of ). Such a factorization will take one of two forms:


title: Quartic function

text: In either case, the roots of are the roots of the factors, which may be computed using the formulas for the roots of a quadratic function or cubic function.


title: Quartic function

text: Detecting the existence of such factorizations can be done using the resolvent cubic of. It turns out that:


title: Quartic function

text: In fact, several methods of solving quartic equations (Ferrari's method, Descartes' method, and, to a lesser extent, Euler's method) are based upon finding such factorizations.


title: Quartic function

text: is almost palindromic, as (it is palindromic if ). The change of variables in produces the quadratic equation . Since , the quartic equation may be solved by applying the quadratic formula twice.


title: Quartic function

text: For solving purposes, it is generally better to convert the quartic into a depressed quartic by the following simple change of variable. All formulas are simpler and some methods work only in this case. The roots of the original quartic are easily recovered from that of the depressed quartic by the reverse change of variable.


title: Quartic function

text: However, this induces a division by zero if . This implies , and thus that the depressed equation is bi-quadratic, and may be solved by an easier method (see above). This was not a problem at the time of Ferrari, when one solved only explicitly given equations with numeric coefficients. For a general formula that is always true, one thus needs to choose a root of the cubic equation such that . This is always possible except for the depressed equation .


title: Quartic function

text: This equation is of the form , which can be rearranged as or . Therefore, equation (") may be rewritten as


title: Quartic function

text: This equation is easily solved by applying to each factor the quadratic formula. Solving them we may write the four roots as


title: Quartic function

text: where and denote either or . As the two occurrences of must denote the same sign, this leaves four possibilities, one for each root.


title: Quartic function

text: Descartes introduced in 1637 the method of finding the roots of a quartic polynomial by factoring it into two quadratic ones. Let


title: Quartic function

text: This can be simplified by starting again with the depressed quartic , which can be obtained by substituting for . Since the coefficient of is , we get , and:


title: Quartic function

text: which is done elsewhere. This resolvent cubic is equivalent to the resolvent cubic given above (equation (1a)), as can be seen by substituting U = 2m.


title: Quartic function

text: If is a square root of a non-zero root of this resolvent (such a non-zero root exists except for the quartic , which is trivially factored),


title: Quartic function

text: The symmetries in this solution are as follows. There are three roots of the cubic, corresponding to the three ways that a quartic can be factored into two quadratics, and choosing positive or negative values of for the square root of merely exchanges the two quadratics with one another.


title: Quartic function

text: The above solution shows that a quartic polynomial with rational coefficients and a zero coefficient on the cubic term is factorable into quadratics with rational coefficients if and only if either the resolvent cubic ("") has a non-zero root which is the square of a rational, or is the square of rational and ; this can readily be checked using the rational root test.


title: Quartic function

text: A variant of the previous method is due to Euler. Unlike the previous methods, both of which use "some" root of the resolvent cubic, Euler's method uses all of them. Consider a depressed quartic . Observe that, if


title: Quartic function

text: Therefore, . In other words, is one of the roots of the resolvent cubic (") and this suggests that the roots of that cubic are equal to , , and . This is indeed true and it follows from Vieta's formulas. It also follows from Vieta's formulas, together with the fact that we are working with a depressed quartic, that . (Of course, this also follows from the fact that .) Therefore, if , , and are the roots of the resolvent cubic, then the numbers , , , and are such that


title: Quartic function

text: It is a consequence of the first two equations that is a square root of and that is the other square root of . For the same reason,


title: Quartic function

text: Since, in general, there are two choices for each square root, it might look as if this provides choices for the set }, but, in fact, it provides no more than  such choices, because the consequence of replacing one of the square roots by the symmetric one is that the set } becomes the set }.


title: Quartic function

text: In order to determine the right sign of the square roots, one simply chooses some square root for each of the numbers , , and and uses them to compute the numbers , , , and from the previous equalities. Then, one computes the number . Since , , and are the roots of ("), it is a consequence of Vieta's formulas that their product is equal to and therefore that . But a straightforward computation shows that


title: Quartic function

text: If this number is , then the choice of the square roots was a good one (again, by Vieta's formulas); otherwise, the roots of the polynomial will be , , , and , which are the numbers obtained if one of the square roots is replaced by the symmetric one (or, what amounts to the same thing, if each of the three square roots is replaced by the symmetric one).


title: Quartic function

text: Of course, this will make no sense if or is equal to , but is a root of (") only when , that is, only when we are dealing with a biquadratic equation, in which case there is a much simpler approach.


title: Quartic function

text: The symmetric group on four elements has the Klein four-group as a normal subgroup. This suggests using a whose roots may be variously described as a discrete Fourier transform or a Hadamard matrix transform of the roots; see Lagrange resolvents for the general method. Denote by , for from  to , the four roots of . If we set


title: Quartic function

text: then since the transformation is an involution we may express the roots in terms of the four in exactly the same way. Since we know the value , we only need the values for , and . These are the roots of the polynomial


title: Quartic function

text: Substituting the by their values in term of the , this polynomial may be expanded in a polynomial in whose coefficients are symmetric polynomials in the . By the fundamental theorem of symmetric polynomials, these coefficients may be expressed as polynomials in the coefficients of the monic quartic. If, for simplification, we suppose that the quartic is depressed, that is , this results in the polynomial


title: Quartic function

text: This polynomial is of degree six, but only of degree three in , and so the corresponding equation is solvable by the method described in the article about cubic function. By substituting the roots in the expression of the in terms of the , we obtain expression for the roots. In fact we obtain, apparently, several expressions, depending on the numbering of the roots of the cubic polynomial and of the signs given to their square roots. All these different expressions may be deduced from one of them by simply changing the numbering of the .


title: Quartic function

text: These expressions are unnecessarily complicated, involving the cubic roots of unity, which can be avoided as follows. If is any non-zero root of ("), and if we set


title: Quartic function

text: We therefore can solve the quartic by solving for and then solving for the roots of the two factors using the quadratic formula.


title: Quartic function

text: There is an alternative solution using algebraic geometry In brief, one interprets the roots as the intersection of two quadratic curves, then finds the three reducible quadratic curves (pairs of lines) that pass through these points (this corresponds to the resolvent cubic, the pairs of lines being the Lagrange resolvents), and then use these linear equations to solve the quadratic.


title: Quartic function

text: The four roots of the depressed quartic may also be expressed as the coordinates of the intersections of the two quadratic equations and i.e., using the substitution that two quadratics intersect in four points is an instance of Bézout's theorem. Explicitly, the four points are for the four roots of the quartic.


title: Quartic function

text: These four points are not collinear because they lie on the irreducible quadratic and thus there is a 1-parameter family of quadratics (a pencil of curves) passing through these points. Writing the projectivization of the two quadratics as quadratic forms in three variables:


title: Quartic function

text: the pencil is given by the forms for any point in the projective line — in other words, where and are not both zero, and multiplying a quadratic form by a constant does not change its quadratic curve of zeros.


title: Quartic function

text: This pencil contains three reducible quadratics, each corresponding to a pair of lines, each passing through two of the four points, which can be done formula_72 =  different ways. Denote these , , and . Given any two of these, their intersection has exactly the four points.


title: Quartic function

text: The reducible quadratics, in turn, may be determined by expressing the quadratic form as a  matrix: reducible quadratics correspond to this matrix being singular, which is equivalent to its determinant being zero, and the determinant is a homogeneous degree three polynomial in and and corresponds to the resolvent cubic.


title: Charles James Fox

text: Charles James Fox (24 January 1749 – 13 September 1806), styled "The Honourable" from 1762, was a prominent British Whig statesman whose parliamentary career spanned 38 years of the late 18th and early 19th centuries. He was the arch-rival of the Tory politician William Pitt the Younger; his father Henry Fox, 1st Baron Holland, a leading Whig of his day, had similarly been the great rival of Pitt's famous father, William Pitt, 1st Earl of Chatham ("Pitt the Elder").


title: Charles James Fox

text: Fox rose to prominence in the House of Commons as a forceful and eloquent speaker with a notorious and colourful private life, though at that time with rather conservative and conventional opinions. However, with the coming of the American War of Independence and the influence of the Whig Edmund Burke, Fox's opinions evolved into some of the most radical to be aired in the British Parliament of his era.


title: Charles James Fox

text: Fox became a prominent and staunch opponent of King George III, whom he regarded as an aspiring tyrant. He supported the American Patriots and even dressed in the colours of George Washington's army. Briefly serving as Britain's first Foreign Secretary during the ministry of the Marquess of Rockingham in 1782, he returned to the post in a coalition government with his old enemy, Lord North, in 1783. However, the King forced Fox and North out of government before the end of the year and replaced them with the 24-year-old Pitt the Younger. Fox spent the following 22 years facing Pitt and the government from the opposition benches of the House of Commons.


title: Charles James Fox

text: Though Fox had little interest in the actual exercise of power and spent almost the entirety of his political career in opposition, he became noted as an anti-slavery campaigner, a supporter of the French Revolution and a leading parliamentary advocate of religious tolerance and individual liberty. His friendship with his mentor, Burke, and his parliamentary credibility were both casualties of Fox's support for France during the French Revolutionary Wars, but Fox went on to attack Pitt's wartime legislation and to defend the liberty of religious minorities and political radicals. After Pitt's death in January 1806, Fox served briefly as Foreign Secretary in the 'Ministry of All the Talents' of William Grenville before he died on 13 September 1806, aged 57.


title: Charles James Fox

text: Fox was born at 9 Conduit Street, London, the second surviving son of Henry Fox, 1st Baron Holland, and Lady Caroline Lennox, a daughter of Charles Lennox, 2nd Duke of Richmond. Henry Fox (1705–1774) was an ally of Robert Walpole and rival of Pitt the Elder, and had amassed a considerable fortune by exploiting his position as Paymaster General of the forces. Charles James Fox's elder brother Stephen (1745–1774) became the 2nd Baron Holland, and his younger brother Henry (1755–1811) had a distinguished military career.


title: Charles James Fox

text: Fox was the darling of his father, who found Charles "infinitely engaging & clever & pretty" and, from the time that his son was three years old, apparently preferred his company at meals to that of anyone else. The stories of Charles's over-indulgence by his doting father are legendary. It was said that Charles once expressed a great desire to break his father's watch and was not restrained or punished when he duly smashed it on the floor. On another occasion, when Henry had promised his son that he could watch the demolition of a wall on his estate and found that it had already been destroyed, he ordered the workmen to rebuild the wall and demolish it again, with Charles watching.


title: Charles James Fox

text: Given "carte blanche" to choose his own education, Fox in 1758 attended a fashionable Wandsworth school run by a Monsieur Pampellonne, followed by Eton College, where he began to develop his lifelong love of classical literature. In later life he was said to have always carried a copy of Horace in his coat pocket. He was taken out of school by his father in 1761 to attend the coronation of George III, who would become one of his most bitter enemies, and once more in 1763 to travel to the Continent (where he visited Paris and Spa). On this trip Charles was given a substantial amount of money with which to learn to gamble by his father, who also arranged for him to lose his virginity, aged fourteen, to a Madame de Quallens. Fox returned to Eton later that year, "attired in red-heeled shoes and Paris cut-velvet, adorned with a pigeon-wing hair style tinted with blue powder, and a newly acquired French accent", and was duly flogged by Dr. Barnard, the headmaster. Charles Fox was once known as a macaroni, despite him being a tad too overweight to look decent in his tight clothing. These three pursuits – gambling, womanising and the love of things and fashions foreign – would become, once inculcated in his adolescence, notorious habits of Fox's later life.


title: Charles James Fox

text: Fox entered Hertford College, Oxford, in October 1764, but left without graduating, being rather contemptuous of its "nonsenses". He went on several further expeditions to Europe, becoming well known in the great Parisian salons, meeting influential figures such as Voltaire, Edward Gibbon, the duc d'Orléans and the Marquis de Lafayette, and becoming the co-owner of a number of racehorses with the duc de Lauzun.


title: Charles James Fox

text: For the 1768 general election, Henry Fox bought his son a seat in Parliament for the West Sussex constituency of Midhurst, though Charles was still nineteen and technically ineligible for Parliament. Fox was to address the House of Commons some 254 times between 1768 and 1774 and rapidly gathered a reputation as a superb orator, but he had not yet developed the radical opinions for which he would become famous. Thus, he spent much of his early years unwittingly manufacturing ammunition for his later critics and their accusations of hypocrisy. A supporter of the Grafton and North ministries, Fox was prominent in the campaign to punish the radical John Wilkes for challenging the Commons. "He thus opened his career by speaking in behalf of the Commons against the people and their elected representative." Consequently, both Fox and his brother Stephen were insulted and pelted with mud in the street by the pro-Wilkes London crowds.


title: Charles James Fox

text: Between 1770 and 1774, Fox's seemingly promising career in the political establishment was spoiled. He was appointed to the Board of Admiralty by Lord North in February 1770, but on the 15th of the same month, he resigned due to his enthusiastic opposition to the government's Royal Marriages Act, the provisions of which – incidentally – cast doubt on the legitimacy of his parents' marriage. On 28 December 1772, North appointed him to the board of the Treasury; in February 1774, Fox again surrendered his post, this time over the Government's allegedly feeble response to the contemptuous printing and public distribution of copies of parliamentary debates. Behind these incidents lay his family's resentment towards Lord North for refusing to elevate the Holland barony to an earldom. But the fact that such a young man could seemingly treat ministerial office so lightly was noted at court. George III, also observing Fox's licentious private behaviour, took it to be presumption and judged that Fox could not be trusted to take anything seriously.


title: Charles James Fox

text: After 1774, Fox began to reconsider his political position under the influence of Edmund Burke – who had sought out the promising young Whig and would become his mentor – and the unfolding events in America. He drifted from his rather unideological family-oriented politics into the orbit of the Rockingham Whig party.


title: Charles James Fox

text: During this period, Fox became possibly the most prominent and vituperative parliamentary critic of Lord North and the conduct of the American War. In 1775, he denounced North in the Commons as


title: Charles James Fox

text: Fox, who occasionally corresponded with Thomas Jefferson and had met Benjamin Franklin in Paris, correctly predicted that Britain had little practical hope of subduing the colonies and interpreted the American cause approvingly as a struggle for liberty against the oppressive policies of a despotic and unaccountable executive. It was at this time that Fox and his supporters took up the habit of dressing in buff and blue, the colours of the uniforms in Washington's army. Fox's friend, the Earl of Carlisle, observed that any setback for the British Government in America was "a great cause of amusement to Charles." Even after the American defeat at Long Island in 1776, Fox stated that


title: Charles James Fox

text: On 31 October the same year, Fox responded to the King's address to Parliament with "one of his finest and most animated orations, and with severity to the answered person", so much so that, when he sat down, no member of the Government would attempt to reply.


title: Charles James Fox

text: Crucial to any understanding of Fox's political career from this point was his mutual antipathy with George III – probably the most enthusiastic prosecutor of the American War. Fox became convinced that the King was determined to challenge the authority of Parliament and the balance of the constitution established in 1688, and to achieve Continental-style tyranny. George in return thought that Fox had "cast off every principle of common honour and honesty ... [a man who is] as contemptible as he is odious ... [and has an] aversion to all restraints." It is difficult to find two political figures in British history more greatly contrasted in temperament than Fox and George: the former a notorious gambler and rake; the latter famous for his virtues of frugality and family. On 6 April 1780, John Dunning's motion that "The influence of the Crown has increased, is increasing, and ought to be diminished" passed the Commons by a vote of 233 to 215. Fox thought it "glorious", saying on 24 April that


title: Charles James Fox

text: Fox, however, had not been present in the House for the beginning of the Dunning debate, as he had been occupied in the adjoining eleventh-century Westminster Hall, serving as chairman of a mass public meeting before a large banner that read "Annual Parliaments and Equal Representation". This was the period when Fox, hardening against the influence of the Crown, was embraced by the radical movement of the late eighteenth century. When the shocking Gordon riots exploded in London in June 1780, Fox, though deploring the violence of the crowd, declared that he would "much rather be governed by a mob than a standing army." Later, in July, Fox was returned for the populous and prestigious constituency of Westminster, with around 12,000 electors, and acquired the title "Man of the People".


title: Charles James Fox

text: When North finally resigned under the strains of office and the disastrous American War in March 1782, after Earl Cornwallis surrendered at the Battle of Yorktown, and was gingerly replaced with the new ministry of the Marquess of Rockingham, Fox was appointed Foreign Secretary. But Rockingham, after finally acknowledging the independence of the former Thirteen Colonies, died unexpectedly on 1 July. Fox refused to serve in the successor administration of the Earl of Shelburne, splitting the Whig party; Fox's father had been convinced that Shelburne – a supporter of the elder Pitt – had thwarted his ministerial ambitions at the time of the Treaty of Paris in 1763. Fox now found himself in common opposition to Shelburne with his old and bitter enemy, Lord North. Based on this single conjunction of interests and the fading memory of the happy co-operation of the early 1770s, the two men who had vilified one another throughout the American war together formed a coalition and forced their Government, with an overwhelming majority composed of North's Tories and Fox's opposition Whigs, on to the King.


title: Charles James Fox

text: The Fox-North Coalition came to power on 2 April 1783, in spite of the King's resistance. It was the first time that George had been allowed no role in determining who should hold government office. On one occasion, Fox, who returned enthusiastically to the post of Foreign Secretary, ended an epistle to the King: "Whenever Your Majesty will be graciously pleased to condescend even to hint your inclinations upon any subject, that it will be the study of Your Majesty's Ministers to show how truly sensible they are of Your Majesty's goodness." The King replied: "No answer." George III seriously thought of abdicating at this time, after the comprehensive defeat of his American policy and the imposition of Fox and North, but refrained from doing so, mainly because of the thought of his succession by his son George, Prince of Wales, the notoriously extravagant womaniser, gambler and associate of Fox. Indeed, in many ways the King considered Fox his son's tutor in debauchery. "George III let it be widely broadcast that he held Fox principally responsible for the Prince's many failings, not least a tendency to vomit in public."


title: Charles James Fox

text: Happily for George, the unpopular coalition would not outlast the year. The Treaty of Paris was signed on 3 September 1783, formally ending the American Revolutionary War. Fox proposed an East India Bill to place the government of the ailing and oppressive British East India Company, at that time in control of a considerable expanse of India, on a sounder footing with a board of governors responsible to Parliament and more resistant to Crown patronage. It passed the Commons by 153 to 80, but, when the King made it clear that any peer who voted in favour of the bill would be considered a personal enemy of the Crown, the Lords divided against Fox by 95 to 76. George now felt justified in dismissing Fox and North from government and in nominating William Pitt in their place; at twenty-four years of age, the youngest British prime minister in history was appointed to office, apparently on the authority of the votes of 19 peers. Fox used his parliamentary majority to oppose Pitt's nomination, and every subsequent measure that he put before the House, until March 1784, when the King dissolved Parliament and, in the following general election, Pitt was returned with a substantial majority.


title: Charles James Fox

text: In Fox's own constituency of Westminster, the contest was particularly fierce. An energetic campaign in his favour was run by Georgiana, Duchess of Devonshire, allegedly a lover of Fox's who was said to have won at least one vote for him by kissing a shoemaker with a rather romantic idea of what constituted a bribe. In the end, Fox was re-elected by a very slender margin, but legal challenges (encouraged, to an extent, by Pitt and the King) prevented a final declaration of the result for over a year. In the meantime, Fox sat for the Scottish pocket borough of Tain or Northern Burghs, for which he was qualified by being made an unlikely burgess of Kirkwall in Orkney (which was one of the Burghs in the district). The experience of these years was crucial in Fox's political formation. His suspicions had been confirmed; it seemed to him that George III had personally scuppered both the Rockingham-Shelburne and Fox-North governments, interfered in the legislative process and now dissolved Parliament when its composition inconvenienced him. Pitt – a man of little property and no party – seemed to Fox a blatant tool of the Crown. However, the King and Pitt had great popular support, and many in the press and general population saw Fox as the trouble-maker challenging the composition of the constitution and the King's remaining powers. He was often caricatured as Oliver Cromwell and Guy Fawkes during this period, as well as Satan, "Carlo Khan" (see James Sayers) and Machiavelli.


title: Charles James Fox

text: One of Pitt's first major actions as prime minister was, in 1785, to put a scheme of parliamentary reform before the Commons, proposing to rationalise somewhat the existing, decidedly unrepresentative, electoral system by eliminating thirty-six rotten boroughs and redistributing seats to represent London and the larger counties. Fox supported Pitt's reforms, despite apparent political expediency, but they were defeated by 248 to 174. Reform would not be considered seriously by Parliament for another decade.


title: Charles James Fox

text: In 1787, the most dramatic political event of the decade came to pass in the form of the Impeachment of Warren Hastings, the Governor of Bengal until 1785, on charges of corruption and extortion. Fifteen of the eighteen Managers appointed to the trial were Foxites, one of them being Fox himself. Although the matter was really Burke's area of expertise, Fox was, at first, enthusiastic. If the trial could demonstrate the misrule of British India by Hastings and the East India Company more widely, then Fox's India Bill of 1784 – the point on which the Fox-North Coalition had been dismissed by the King – would be vindicated. The trial was also expedient for Fox in that it placed Pitt in an uncomfortable political position. The premier was forced to equivocate over the Hastings trial, because to oppose Hastings would have been to endanger the support of the King and the East India Company, while to support him openly would have alienated country gentlemen and principled supporters like Wilberforce. As the trial's intricacies dragged on (it would be 1795 before Hastings was finally acquitted), Fox's interest waned and the burden of managing the trial devolved increasingly on Burke.


title: Charles James Fox

text: In late October 1788, George III descended into a bout of mental illness. He had declared that Pitt was "a rascal" and Fox "his Friend". The King was placed under restraint, and a rumour went round that Fox had poisoned him. Thus the opportunity revealed itself for the establishment of a regency under Fox's friend and ally, the Prince of Wales, which would take the reins of government out of the hands of the incapacitated George III and allow the replacement of his "minion" Pitt with a Foxite ministry.


title: Charles James Fox

text: Fox, however, was incommunicado in Italy as the crisis broke; he had resolved not to read any newspapers while he was abroad, except the racing reports. Three weeks passed before he returned to Britain on 25 November 1788, and then he was taken seriously ill (partly due to the stress of his rapid journey across Europe). He would not recover entirely until December 1789. He again absented himself to Bath from 27 January to 21 February 1789.


title: Charles James Fox

text: When Fox did make it into Parliament, he seemed to make a serious political error. In the Commons on 10 December, he declared that it was the right of the Prince of Wales to install himself as regent immediately. It is said that Pitt, upon hearing this, slapped his thigh in an uncharacteristic display of emotion and declared that he would "unwhig" Fox for the rest of his life. Fox's argument did indeed seem to contradict his lifelong championing of Parliament's rights over the Crown. Pitt pointed out that the Prince of Wales had no more right to the throne than any other Briton, though he might well have a better claim to it as the King's firstborn son. It was Parliament's constitutional right to decide who the monarch could be.


title: Charles James Fox

text: There was more than naked thirst for power in Fox's seemingly hypocritical Tory assertion. Fox believed that the King's illness was permanent, and therefore that George III was, constitutionally speaking, dead. To challenge the Prince of Wales's right to succeed him would be to challenge fundamental contemporary assumptions about property rights and primogeniture. Pitt, on the other hand, considered the King's madness temporary (or, at least, hoped that it would be), and thus saw the throne as temporarily unoccupied rather than vacant.


title: Charles James Fox

text: While Fox drew up lists for his proposed Cabinet under the new Prince Regent, Pitt spun out the legalistic debates over the constitutionality of and precedents for instituting a regency, as well as the actual process of drawing up a Regency Bill and navigating it through Parliament. He negotiated a number of restrictions on the powers of the Prince of Wales as regent (which would later provide the basis of the Regency Act of 1811), but the bill finally passed the Commons on 12 February. As the Lords too prepared to pass it, they learned that the King's health was improving and decided to postpone further action. The King soon regained lucidity in time to prevent the establishment of his son's regency and the elevation of Fox to the premiership, and, on 23 April, a service of thanksgiving was conducted at St Paul's in honour of George III's return to health. Fox's opportunity had passed.


title: Charles James Fox

text: Fox welcomed the French Revolution of 1789, interpreting it as a late Continental imitation of Britain's Glorious Revolution of 1688. In response to the Storming of the Bastille on 14 July, he famously declared, "How much the greatest event it is that ever happened in the world! and how much the best!" In April 1791, Fox told the Commons that he "admired the new constitution of France, considered altogether, as the most stupendous and glorious edifice of liberty, which had been erected on the foundation of human integrity in any time or country." He was thus somewhat bemused by the reaction of his old Whig friend, Edmund Burke, to the dramatic events across the Channel. In his "Reflections on the Revolution in France", Burke warned that the revolution was a violent rebellion against tradition and proper authority, motivated by Utopian, abstract ideas disconnected from reality, which would lead to anarchy and eventual dictatorship. Fox read the book and found it "in very bad taste" and "favouring Tory principles", but avoided pressing the matter for a while to preserve his relationship with Burke. The more radical Whigs, like Sheridan, broke with Burke more readily at this point.


title: Charles James Fox

text: Fox instead turned his attention – despite the politically volatile situation – to repealing the Test and Corporation Acts, which restricted the liberties of Dissenters and Catholics. On 2 March 1790, Fox gave a long and eloquent speech to a packed House of Commons.


title: Charles James Fox

text: Burke, with fear of the radical upheaval in France foremost in his mind, took Pitt's side in the debate, dismissing Nonconformists as "men of factious and dangerous principles", to which Fox replied that Burke's "strange dereliction from his former principles ... filled him with grief and shame". Fox's motion was defeated in the Commons by 294 votes to 105.


title: Charles James Fox

text: Later, Fox successfully supported the Roman Catholic Relief Act 1791, extending the rights of British Catholics. He explained his stance to his Roman Catholic friend, Charles Butler, declaring:


title: Charles James Fox

text: On the world stage of 1791, war with Great Britain was threatened more with Spain and Russia than revolutionary France. Fox opposed the bellicose stances of Pitt's ministry in the Nootka Sound crisis and over the Russian occupation of the Turkish port of Ochakiv on the Black Sea. Fox contributed to the peaceful resolution of these entanglements and gained a new admirer in Catherine the Great, who bought a bust of Fox and placed it between Cicero and Demosthenes in her collection. On 18 April, Fox spoke in the Commons – together with William Wilberforce, Pitt and Burke – in favour of a measure to abolish the slave trade, but – despite their combined rhetorical talents – the vote went against them by a majority of 75.


title: Charles James Fox

text: On 6 May 1791, a tearful confrontation on the floor of the Commons finally shattered the quarter-century friendship of Fox and Burke, as the latter dramatically crossed the floor of the House to sit down next to Pitt, taking the support of a good deal of the more conservative Whigs with him. Officially, and rather irrelevantly, this happened during a debate on the particulars of a bill for the government of Canada. Later, on his deathbed in 1797, Burke would have his wife turn Fox away rather than allow a final reconciliation.


title: Charles James Fox

text: Fox continued to defend the French Revolution, even as its fruits began to collapse into war, repression and the Reign of Terror. Though there were few developments in France after 1792 that Fox could positively favour, Fox maintained that the old monarchical system still proved a greater threat to liberty than the new, degenerating experiment in France. Fox thought of revolutionary France as the lesser of two evils and emphasised the role of traditional despots in perverting the course of the revolution: he argued that Louis XVI and the French aristocracy had brought their fates upon themselves by abusing the constitution of 1791 and that the coalition of European autocrats, which was currently dispatching its armies against France's borders, had driven the revolutionary government to desperate and bloody measures by exciting a profound national crisis. Fox was not surprised when Pitt and the King brought Britain into the war as well and would afterwards blame the pair and their prodigal European subsidies for the long-drawn-out continuation of the French Revolutionary Wars. In 1795, he wrote to his nephew, Lord Holland:


title: Charles James Fox

text: Rather ironically, while Fox was being denounced by many in Britain as a Jacobin traitor, across the Channel he featured on a 1798 list of the Britons to be transported after a successful French invasion of Britain. According to the document, Fox was a "false patriot; having often insulted the French nation in his speeches, and particularly in 1786." According to one of his biographers, Fox's "loyalties were not national but were offered to people like himself at home or abroad". In 1805 Francis Horner wrote, "I could name to you gentlemen, with good coats on, and good sense in their own affairs, who believe that Fox...is actually in the pay of France".


title: Charles James Fox

text: But Fox's radical position soon became too extreme for many of his followers, particularly old Whig friends like the Duke of Portland, Earl Fitzwilliam and the Earl of Carlisle. Around July 1794 their fear of France outgrew their resentment towards Pitt for his actions in 1784, and they crossed the floor to the Government benches. Fox could not believe that they "would disgrace" themselves in such a way. After these defections, the Foxites could no longer constitute a credible parliamentary opposition, reduced, as they were, to some fifty MPs.


title: Charles James Fox

text: Fox, however, still insisted on challenging the repressive wartime legislation introduced by Pitt in the 1790s that would become known as "Pitt's Terror". In 1792, Fox had seen through the only piece of substantial legislation in his career, the Libel Act 1792, which restored to juries the right to decide what was and was not libellous, in addition to whether a defendant was guilty. E. P. Thompson thought it "Fox's greatest service to the common people, passed at the eleventh hour before the tide turned toward repression." Indeed, the act was passed by Parliament on 21 May, the same day as a royal proclamation against seditious writings was issued, and more libel cases would be brought by the government in the following two years than had been in all the preceding years of the eighteenth century.


title: Charles James Fox

text: Fox spoke in opposition to the King's Speech on 13 December 1793, but was defeated in the subsequent division by 290 to 50. He argued against war measures like the stationing of Hessian troops in Britain, the employment of royalist French émigrés in the British army and, most of all, Pitt's suspension of habeas corpus in 1794. He told the Commons that:


title: Charles James Fox

text: In 1795, the King's carriage was assaulted in the street, providing an excuse for Pitt to introduce the infamous Two Acts: the Seditious Meetings Act 1795, which prohibited unlicensed gatherings of over fifty people, and the Treasonable Practices Act, which greatly widened the legal definition of treason, making any assault on the constitution punishable by seven years' transportation. Fox spoke ten times in the debate on the acts. He argued that, according to the principles of the proposed legislation, Pitt should have been transported a decade before in 1785, when he had been advocating parliamentary reform. Fox warned the Commons that


title: Charles James Fox

text: He argued that "the best security for the due maintenance of the constitution was in the strict and incessant vigilance of the people over parliament itself. Meetings of the people, therefore, for the discussion of public objects were not merely legal, but laudable."


title: Charles James Fox

text: Parliament passed the acts. But Fox enjoyed a swell of extra-parliamentary support during the course of the controversy. A substantial petitioning movement arose in support of him, and on 16 November 1795, he addressed a public meeting of between two- and thirty-thousand people on the subject. However, this came to nothing in the long run. The Foxites were becoming disenchanted with the Commons, overwhelmingly dominated by Pitt, and began to denounce it to one another as unrepresentative.


title: Charles James Fox

text: By May 1797, an overwhelming majority – both in and outside of Parliament – had formed in support of Pitt's war against France.


title: Charles James Fox

text: Fox's following in Parliament had shrivelled to about 25, compared with around 55 in 1794 and at least 90 during the 1780s. Many of the Foxites purposefully seceded from Parliament in 1797; Fox himself retired for lengthy periods to his wife's house in Surrey. The distance from the stress and noise of Westminster was an enormous psychological and spiritual relief to Fox, but still he defended his earlier principles: "It is a great comfort to me to reflect how steadily I have opposed this war, for the miseries it seems likely to produce are without end."


title: Charles James Fox

text: On 1 May 1798, Fox proposed a toast to "Our Sovereign, the Majesty of the People". The Duke of Norfolk had made the same toast in January at Fox's birthday dinner and had been dismissed as Lord Lieutenant of the West Riding of Yorkshire as a result. Pitt thought of sending Fox to the Tower of London for the duration of the parliamentary session but instead removed him from the Privy Council. Fox believed that it was "impossible to support the Revolution [of 1688] and the Brunswick Succession upon any other principle" than the sovereignty of the people.


title: Charles James Fox

text: After Pitt's resignation in February 1801, Fox had undertaken a partial return to politics. Having opposed the Addington ministry (though he approved of its negotiation of the Treaty of Amiens) as a Pitt-style tool of the King, Fox gravitated towards the Grenvillite faction, which shared his support for Catholic emancipation and composed the only parliamentary alternative to a coalition with the Pittites.


title: Charles James Fox

text: During the French Revolutionary Wars, Fox supported the French Republic against the monarchies that comprised the Second Coalition. Fox thought the "coup d'état" of 1799 that brought Napoleon to power "a very bad beginning ... the manner of the thing [was] quite odious", but he was convinced that the French leader sincerely desired peace in order to consolidate his rule and rebuild his shattered country.


title: Charles James Fox

text: By July 1800, Fox had "forgiven" the means by which he had come into power and claimed Napoleon had "surpassed...Alexander & Caesar, not to mention the great advantage he has over them in the Cause he fights in". In October 1801, a preliminary peace agreement between Britain and France was published and Fox was delighted. In a speech to his constituents on 10 October Fox said, "We have not, I acknowledge, obtained the objects for which the War was undertakenso much the betterI rejoice that we have not. I like the Peace the more on this very account". Many of his friends were shocked at such open language, but as Fox said in his reply to a remonstrance from Grey: "...the truth is, I am gone something further in hate to the English Government than perhaps you and the rest of my friends are, and certainly further than can with prudence be avowed. The triumph of the French Government over the English does in fact afford me a degree of pleasure which it is very difficult to disguise".


title: Charles James Fox

text: After the subsequent Treaty of Amiens was signed in March 1802, Fox joined the thousands of English tourists flocking across the Channel to see the sights of the revolution. Fox and his retinue were kept under surveillance by officials from the British embassy during their trip of 20 July to 17 November. In Paris, he presented his wife for the first time in seven years of marriage, creating yet another stir back at court in London, and had three interviews with Napoleon, who – though he tried to flatter his most prominent British sympathiser – had to spend most of the time arguing about the freedom of the press and the perniciousness of a standing army.


title: Charles James Fox

text: Fox's stay in France enabled him, through his connections with Talleyrand and Lafayette, to search the French archives for his planned history of the reign of James II, the Glorious Revolution and the reign of William III. Fox left the work unfinished at his death, however, and only covered the first year of James' reign (1685). It was posthumously published in 1808 as "A History of the Early Part of the Reign of James II".


title: Charles James Fox

text: Fox confessed in December 1802 that he was "obstinate" in his belief that Napoleon's "wish is Peace, nay that he is afraid of war to the last degree". In March 1803 he believed that Napoleon's belligerence towards Piedmont, Malta and Switzerland was regrettable but did not constitute a "casus belli", writing to the Duchess of Devonshire "if I am to shew a feeling for the wounded honour of the country you or somebody must shew me the wound, for the life of me I cannot find as single instance since the definitive treaty where the Govt. of France has behaved ill to "us"".


title: Charles James Fox

text: When war broke out again in May 1803, Fox blamed the Prime Minister Henry Addington for not standing up to the King. The British government had not left Napoleon "any alternative but War or the most abject humiliation" and that the war "is entirely the fault of our Ministers and not of Bonaparte". Upon hearing of the spectacular French victories at Ulm and Austerlitz later in 1805, Fox commented: "These are wonders indeed but they are not "much" more than I expected". When Pitt (who had taken over from Addington as premier in 1804) tried to persuade Prussia into an anti-French alliance, Prussia refused, to Fox's delight.


title: Charles James Fox

text: He was a close friend and colleague of Samuel Whitbread and supported by Fox, Whitbread in 1805, led the campaign to have Viscount Melville removed from office; Melville resigned. However, The House of Lords found Melville not guilty and he was acquitted of all charges.


title: Charles James Fox

text: When Pitt died on 23 January 1806, Fox was the last remaining great political figure of the era and could no longer be denied a place in government. When Grenville formed a "Ministry of All the Talents" out of his supporters, the followers of Addington and the Foxites, Fox was once again offered the post of Foreign Secretary, which he accepted in February. Fox was convinced (as he had been since Napoleon's accession) that France desired a lasting peace and that he was "sure that two civil sentences from the Ministers would ensure Peace". Therefore, peace talks were speedily entered into by Fox and his old friend Talleyrand, now French foreign minister. The mood had completely changed by July, however, and Fox was forced to acknowledge that his assessment of Napoleon's pacific intentions was wrong. Negotiations over Hanover, Naples, Sicily, and Malta faltered and Talleyrand vetoed Russian participation in the negotiations. King George believed this was a ploy to divide Britain and Russia as French interests would suffer if she had to deal with an Anglo-Russian alliance. Fox was forced to agree that the King's belief was "but too well founded".


title: Charles James Fox

text: In June, Lord Yarmouth was sent on a peace mission to Paris. Fox wrote to him: "I feel my own Glory highly interested in such an event, but to make peace by acceding to worse terms than those first suggested...wd. be as repugnant to my own feelings as it wd. be to the Duty I owe to K. & Country". Yarmouth confirmed that Russia was negotiating separately with France. Fox was appalled at what he called this "extraordinary step". When Yarmouth reported successive new French demands, Fox replied that the British government "continues ardently to wish for the Conclusion of Peace". In August, Lord Lauderdale was sent to join Yarmouth (with full negotiating powers), and he reported back to Fox of "the complete system of Terror which prevails here". Fox's French friends were too frightened to call on him.


title: Charles James Fox

text: Though the administration failed to achieve either Catholic emancipation or peace with France, Fox's last great achievement would be the abolition of the slave trade in 1807. Though Fox was to die before abolition was enacted, he oversaw a Foreign Slave Trade Bill in spring 1806 that prohibited British subjects from contributing to the trading of slaves with the colonies of Britain's wartime enemies, thus eliminating two-thirds of the slave trade passing through British ports.


title: Charles James Fox

text: On 10 June 1806, Fox offered a resolution for total abolition to Parliament: "this House, conceiving the African slave trade to be contrary to the principles of justice, humanity, and sound policy, will, with all practicable expedition, proceed to take effectual measures for abolishing the said trade..." The House of Commons voted 114 to 15 in favour and the Lords approved the motion on 24 June. Fox said that:


title: Charles James Fox

text: Fox died – still in office – at Chiswick House, west of London, on 13 September 1806, not eight months after the younger Pitt. An autopsy revealed a hardened liver, thirty-five gallstones and around seven pints of transparent fluid in his abdomen. Fox left £10,000-worth of debts, though this was only a quarter of the £40,000 that the charitable public had to raise to pay off Pitt's arrears. Although Fox had wanted to be buried near his home in Chertsey, his funeral took place in Westminster Abbey on 10 October 1806, the anniversary of his initial election for Westminster in 1780. Unlike Pitt's, Fox's funeral was a private affair, but the multitude that turned out to pay their respects were at least as large as those at his rival's service.


title: Charles James Fox

text: Fox's private life (as far as it was private) was notorious, even in an age noted for the licentiousness of its upper classes. Fox was famed for his rakishness and his drinking; vices which were both indulged frequently and immoderately. Fox was also an inveterate gambler, once claiming that winning was the greatest pleasure in the world, and losing the second greatest. Between 1772 and 1774, Fox's fathershortly before dyinghad to pay off £120,000 of Charles' debts; the equivalent of around £ million in . Fox was twice bankrupted between 1781 and 1784, and at one point his creditors confiscated his furniture. Fox's finances were often "more the subject of conversation than any other topic." By the end of his life, Fox had lost about £200,000 gambling.


title: Charles James Fox

text: In appearance, Fox was dark, corpulent and hairy, to the extent that when he was born his father compared him to a monkey. His round face was dominated by his luxuriant eyebrows, with the result that he was known among fellow Whigs as 'the Eyebrow.' Though he became increasingly dishevelled and fat in middle age, the young Fox had been very fashionable; he had been the leader of the 'Maccaroni' set of extravagant young followers of Continental fashions. Fox liked riding horses and watching and playing cricket, but his impulsive nature and considerable bulk led to his often being run out between wickets.


title: Charles James Fox

text: Fox was frequently ridiculed – most famously by Gillray, for whom he served as a stock Jacobin villain. The King disliked Fox greatly, regarding him as beyond morality and the corrupter of his own eldest son, and the late eighteenth-century movements of Christian evangelism and middle-class 'respectability' also frowned on his excesses. Fox was apparently not greatly bothered by these criticisms and kept a collection of his caricatures, which he found amusing. His friend, Frederick Howard, 5th Earl of Carlisle, said of him, since "the respect of the world was not easily retrievable, he became so callous to what was said of him, as never to repress a single thought, or even temper a single expression when he was before the public." Particularly after 1794, Fox rarely consulted the opinions of anyone outside of his own circle of friends and supporters.


title: Charles James Fox

text: Fox was also regarded as a notorious womaniser. In 1784 or 1785, Fox met and fell in love with Elizabeth Armistead, a former courtesan and mistress of the Prince of Wales who had little interest in politics or Parliament. He married her in a private ceremony at Wyton in Huntingdonshire on 28 September 1795, but did not make the fact public until October 1802, and Elizabeth was never really accepted at court. Fox would increasingly spend time away from Parliament at Armistead's rural villa, St. Ann's Hill, near Chertsey in Surrey, where Armistead's influence gradually moderated Fox's wilder behaviour and together they would read, garden, explore the countryside and entertain friends. In his last days, the sceptical Fox allowed scriptural readings at his bedside in order to please his religious wife. She survived him by thirty-six years.


title: Charles James Fox

text: Despite his celebrated flaws, history records Fox as an amiable figure. The Tory wit George Selwyn wrote that, "I have passed two evenings with him, and never was anybody so agreeable, and the more so from his having no pretensions to it". Selwyn also said that "Charles, I am persuaded, would have no consideration on earth but for what was useful to his own ends. You have heard me say, that I thought he had no malice or rancour; I think so still and am sure of it. But I think that he has no feeling neither, for anyone but himself; and if I could trace in any one action of his life anything that had not for its object his own gratification, I should with pleasure receive the intelligence because then I had much rather (if it were possible) think well of him than not". Sir Philip Francis said of Fox: "The essential defect in his character and the cause of all his failures, strange as it may seem, was that he had no heart". Edward Gibbon remarked that "Perhaps no human being was ever more perfectly exempt from the taint of malevolence, vanity, or falsehood." Central to understanding Fox's life was his view that "friendship was the only real happiness in the world." For Fox, politics was the extension of his activities at Newmarket and Brooks's to Westminster. "Fox had little or no interest in the exercise of power." The details of policy – particularly of economics – bored him, in contrast with the intensity of Burke's legal pursuit of Warren Hastings, and of Pitt's prosecution of the war against France. Moreover, the Foxites were "the witty and wicked" satellites of their leader, as much friends as political allies.


title: Charles James Fox

text: In a letter published in "The Daily Telegraph" in 2020, Lord Lexden compared him to Prime Minister Boris Johnson, saying that "Johnson is an 18th Century figure in many ways" and that the two leaders may be commended in similar ways.


title: Charles James Fox

text: In the 19th century, liberals portrayed Fox as their hero, praising his courage, perseverance and eloquence. They celebrated his opposition to war in alliance with European despots against the people of France eager for their freedom, and they praised his fight for liberties at home. The liberals saluted his fights for parliamentary reform, Catholic Emancipation, intellectual freedom, and justice for the Dissenters. They were especially pleased with his fight for the abolition of the slave trade. More recent historians put Fox in the context of the 18th century, and emphasize the brilliance of his battles with Pitt. A statue of Fox stands, alongside other notable Parliamentarians, in St Stephen's Hall in the Palace of Westminster.


title: Charles James Fox

text: While not wholly forgotten today Fox is no longer the famous hero he had been, and is less well remembered than Pitt. After 1794, the word 'Whig' gave way to the word "Foxite" as the self-description of the members of the opposition to Pitt. In many ways, the Pittite-Foxite division of Parliament after the French Revolution established the basis for the ideological Conservative-Liberal divide of the nineteenth century. Fox and Pitt went down in parliamentary history as legendary political and oratorical opponents who would not be equalled until the days of Gladstone and Disraeli more than half a century later. Even Fox's great rival was willing to acknowledge the old Whig's talents. When, in 1790, the comte de Mirabeau disparaged Fox in Pitt's presence, Pitt stopped him, saying, "You have never seen the wizard within the magic circle."


title: Charles James Fox

text: The Fox Club was established in London in 1790 and held the first of its Fox dinners – annual events celebrating Fox's birthday – in 1808; the last recorded dinner took place at Brooks's in 1907. As Charles Grey, 2nd Earl Grey asked a Newcastle-upon-Tyne Fox dinner in 1819: "What subject is there, whether of foreign or domestic interest, or that in the smallest degree affects our Constitution which does not immediately associate itself with the memory of Mr Fox?" Fox's name was invoked numerous times in debates by supporters of Catholic Emancipation and the Great Reform Act in the early nineteenth century. John Russell, 6th Duke of Bedford kept a bust of Fox in his pantheon of Whig grandees at Woburn Abbey and erected a statue of him in Bloomsbury Square. Sarah Siddons kept a portrait of Fox in her dressing room. In 1811, the Prince of Wales took the oaths of office as regent with a bust of Fox at his side. Whig households would collect locks of Fox's hair, books of his conflated speeches and busts in his likeness.


title: Charles James Fox

text: The town of Foxborough, Massachusetts, was named in honour of the staunch supporter of American independence. Fox is remembered in his home town of Chertsey by a bust on a high plinth ("pictured left"), erected in 2006 in a new development by the railway station. Fox is also commemorated in a termly dinner held in his honour at his "alma mater", Hertford College, Oxford, by students of English, history and the romance languages.


title: Charles James Fox

text: Fox was the subject of the epigraph in John F. Kennedy's Pulitzer-prize winning book "Profiles in Courage": "He well knows what snares are spread about his path, from personal animosity…and possibly from popular delusion. But he has put to hazard his ease, his security, his interest, his power, even his…popularity. …He is traduced and abused for his supposed motives. He will remember that obloquy is a necessary ingredient in the composition of all true glory: he will remember…that calumny and abuse are essential parts of triumph. …He may live long, he may do much. But here is the summit. He never can exceed what he does this day." — Edmund Burke’s eulogy of Charles James Fox for his attack upon the tyranny of the East India Company. House of Commons, 1 December 1783


title: Charles James Fox

text: Fox featured as a character in the 1994 movie "The Madness of King George", portrayed by Jim Carter; in the 2006 movie "Amazing Grace", played by Michael Gambon; and in the 2008 movie "The Duchess," played by Simon McBurney. Fox is also portrayed in the 1999 BBC mini series "Aristocrats".


title: SlutWalk

text: SlutWalk is a transnational movement calling for an end to rape culture, including victim blaming and slut shaming of sexual assault victims. Participants protest against explaining or excusing rape by referring to any aspect of a woman's appearance. The rallies began on April 3, 2011, in Toronto, Ontario, Canada, after a Toronto Police officer suggested that "women should avoid dressing like sluts" as a precaution against sexual assault. Subsequent rallies have occurred globally.


title: SlutWalk

text: The protest takes the form of a march, mainly by young women, where some dress in clothes considered to be "slutty" such as short skirts, stockings and scanty tops. In the various Slutwalks around the world, there are usually speaker meetings and workshops, live music, sign-making sessions, leafleting, open microphones, chanting, dances, martial arts, and receptions or after-parties with refreshments. In many of the rallies and online, women speak publicly for the first time about their identity as rape survivors. The movement's ideology has been questioned and its methodology criticized by some.


title: SlutWalk

text: On January 24, 2011, Toronto Police Constable Michael Sanguinetti and another officer from 31 Division spoke on crime prevention, addressing the issue of campus rape at a York University safety forum at Osgoode Hall Law School. During the talk, Sanguinetti interrupted the more senior officer and said: "I've been told I'm not supposed to say this – however, women should avoid dressing like sluts in order not to be victimized."


title: SlutWalk

text: After an article that reported on the situation received international attention, Sanguinetti apologized for the remark saying:


title: SlutWalk

text: I made a comment which was poorly thought out and did not reflect the commitment of the Toronto Police Service to the victims of sexual assaults. Violent crimes such as sexual assaults can have a traumatizing effect on their victims... My comment was hurtful in this respect. I am embarrassed by the comment I made and it shall not be repeated.


title: SlutWalk

text: The apology was attached to an email distributed to the Osgoode community by law school dean Lorne Sossin who said they've been told the officer "is being disciplined and will be provided with further professional training." Co-founders Sonya Barnett and Heather Jarvis decided to redefine the word "slut" as someone who is in control of their own sexuality, to reclaim the word "slut" as a site of power for women. They observe that historically, "slut" has had negative connotations, and that their goal is to reclaim the term. Their website states:


title: SlutWalk

text: We are tired of being oppressed by slut-shaming; of being judged by our sexuality and feeling unsafe as a result. Being in charge of our sexual lives should not mean that we are opening ourselves to an expectation of violence, regardless if we participate in sex for pleasure or work. No one should equate enjoying sex with attracting sexual assault.


title: SlutWalk

text: Barnett considered the apology was not enough, since the officer's stereotypical idea still exists in society.


title: SlutWalk

text: The comment that was made by Officer Sanguinetti comes from a place where sexual profiling and victim blaming is inherent and a large trait and we'd like that changed," Barnett said, "It isn't about just one idea or one police officer who practices victim blaming, it's about changing the system and doing something constructive with anger and frustration.


title: SlutWalk

text: Toronto Police spokeswoman Meaghan Gray said cautioning women on their state of dress is not part of any police training. "In fact, this is completely contradictory to what officers are taught," she said. "They are taught that nothing a woman does contributes to a sexual assault." Toronto Police Chief Bill Blair also spoke on the matter: "If that type of, frankly, archaic thinking still exists among any of my officers, it highlights for me the need to continue to train my officers and sensitize them to the reality of victimization." Sanguinetti's statement, according to Blair, is meant to "place the blame upon victims, and that's not where the blame should ever be placed."


title: SlutWalk

text: Rosemary Gartner, a University of Toronto criminologist, said linking style of dress to sexual assault is "ridiculous." "If that were the case, there would be no rapes of women who wear veils and we know there are rapes in those countries," she said. Darshika Selvasivam, vice-president of the York Federation of Students, said she found the use of the word "extremely alarming." Linking provocative clothing to sexual assault "is a huge myth" and all it does is "blame the survivor of a sexual assault while taking the onus away from the perpetrator," she said. A university spokesperson also said the school was "surprised and shocked" by the comment, although it does have a good and collaborative relationship with police.


title: SlutWalk

text: Slutwalk organizer Sonya Barnett named the case of Justice Robert Dewar as one of the main reasons to create the movement, and it became also the main cause of Slutwalk Winnipeg.


title: SlutWalk

text: On February 18, 2011 Justice Robert Dewar convicted Thompson resident Kenneth Rhodes, who worked for the city council, of sexual assault and sentenced him to two years house arrest. Dewar described Rhodes as a "clumsy Don Juan" who had the mistaken belief "sex was in the air" and a "heightened expectation" sex would occur. Dewar said the victim and a friend were dressed in tube tops and high heels when they met Rhodes and another man outside a bar "and made it publicly known that they wanted to party." The court in Winnipeg, Manitoba, heard that the victim had willingly gone off with Rhodes and kissed him. But after she rebuffed his further advances three times, he raped her by the side of the road once they were alone. Rhodes admitted telling the woman 'it would only hurt for a little while' during the assault.


title: SlutWalk

text: He pleaded not guilty at his trial saying he thought the woman had consented to sex. Dewar rejected his defence but said aspects of it could be considered in sentencing. Prosecutors had asked for a three-year sentence, but Dewar gave Rhodes a conditional or suspended sentence, and ordered him to write a letter of apology to his victim. Politicians of all stripes joined student and feminist groups and those who work with sexual assault victims in decrying the comments.


title: SlutWalk

text: University of Winnipeg politics professor Shannon Sampert said this is the collateral damage that occurs when you have poorly trained judges in the system. "The victim in this case gets to relive her experiences once again in a new trial, hoping that this judge won't require gender sensitivity training," said Sampert. She said surveys repeatedly show one of the primary reasons women do not report being raped is because of a fear of being victimized again by the justice system.


title: SlutWalk

text: On February 25, nearly 100 people gathered to call for Justice Robert Dewar's resignation. "These statements by Dewar are reinforcing the myth of implied consent and the myth that a victim of sexual assault is ultimately responsible for their own victimisation," said Alanna Makinson of the Canadian Federation of Students, during the protest. Although this was not a part of Slutwalk, the launch of Slutwalk Toronto on April 3 gave the case national diffusion within Canada. On October 16, Slutwalk Winnipeg took place to reiterate the protest against the judge.


title: SlutWalk

text: On November 9, Justice Dewar formally apologized. According to the judicial council, Dewar said he wished to "express my unequivocal apology to the (victim) for the hurt she must have experienced from my comments. Some of the letters of complaint, from persons who have worked directly with past victims, have pointed out that some of my comments were also traumatic for them. I very much regret that as well."


title: SlutWalk

text: Alberta Chief Justice Neil Wittmann, who reviewed the complaints against Dewar, said Dewar's comments "showed a clear lack of sensitivity towards victims of sexual assault" but do not merit his removal from the bench. According to the judicial council, Dewar has met with a "gender equality" expert and is "pursuing further professional development in this area as part of his commitment to become a better judge."


title: SlutWalk

text: The Manitoba Court of Appeal later overturned Rhodes' conviction and ordered a new trial be set. The appeal court ruled Dewar did not properly assess the credibility of the accused and the alleged victim in reaching his verdict. Rhodes was sentenced to three years in prison in 2013.


title: SlutWalk

text: The first Slutwalk was organized in Toronto, Ontario, on April 3, 2011. Although the organizers expected around 200 people to show up, over 3,000 gathered at Queen's Park. "We want Police Services to truly get behind the idea that victim-blaming, slut-shaming, and sexual profiling are never acceptable.[...] The idea that a slut is a lesser person and deserving of sexual assault isn't exclusive to the police. Media also has to get behind this idea." Sonya Barnett explained.


title: SlutWalk

text: The day began with speeches before moving to the Toronto Police Headquarters. The invitation in Slutwalk Toronto website also warned: "Whether a fellow slut or simply an ally, you don't have to wear your sexual proclivities on your sleeve: we just ask that you come. Singles, couples, parents, sisters, brothers, children, friends." Some women attended the protest wearing jeans and T-shirts, while others turned out in fishnets and stilettos.


title: SlutWalk

text: On May 25, 2012, a new Slutwalk was organized in Toronto. There were fewer participants than the previous occurrence, although the presence of men was more noticeable. Outfits ranged from sneakers and tank tops to bikinis to costumes. Some attendees went topless. A delegation from the Abbey of the Divine Wood, a Toronto mission of the Sisters of Perpetual Indulgence, manifested in their nuns habits and carried signs including one which read: "Sisters Are Sluts 2".


title: SlutWalk

text: At Queen's Park, several speakers took the stage—a multi purpose truck—and delivered speeches, some of them spontaneous testimonies. A few paid tribute to the memory of Toronto sex workers' rights activist Wendy Babcock, who took part in the first Slutwalk and died on August 9, 2011, at the age of 32. There were also multiple shows of support for Cece McDonald, a Minneapolis transgender woman facing a 41-month prison sentence for stabbing and killing a man after being harassed and slashed across the face.


title: SlutWalk

text: On April 4, 2011, a Slutwalk in Sackville, New Brunswick was organized through the Sociology Student Association of Mount Allison University, and was coordinated to follow exactly a day after Toronto's SlutWalk. According to Rebecca Cheff, one of the organizer of the SlutWalk, "the goal is to walk towards the police station and speak to [the police officers] about victim blaming and to raise awareness as they're the frontline worker in sexual assault scenarios." "There is a big misconception that people that dress a certain way ask for sexual assault, and that needs to stop now," said SlutWalk student organizer, Lauren Hutchison. The phrase "still not asking for it" has become a rally cry behind many of these protests and has also been posterized on the bodies of men and women at these walks worldwide.