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Fine-structure constant

In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by $α$ (the Greek letter alpha), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles.

It is a dimensionless quantity, independent of the system of units used, which is related to the strength of the coupling of an elementary charge e with the electromagnetic field, by the formula $α$. Its numerical value is approximately ≃ $1⁄undefined$, with a relative uncertainty of

The constant was named by Arnold Sommerfeld, who introduced it in 1916 when extending the Bohr model of the atom. $α−1$ quantified the gap in the fine structure of the spectral lines of the hydrogen atom, which had been measured precisely by Michelson and Morley in 1887.

Why the constant should have this value is not understood, but there are a number of ways to measure its value.

Definition
In terms of other fundamental physical constants, $α$ may be defined as: $$\alpha = \frac{e^2}{2 \varepsilon_0 h c} = \frac{e^2}{4 \pi \varepsilon_0 \hbar c} ,$$ where
 * $e$ is the elementary charge ;
 * $h$ is the Planck constant ;
 * $ħ$ is the reduced Planck constant, $4πε0ħcα = e2$
 * $c$ is the speed of light ;
 * $ε$$0$ is the electric constant.

Since the 2019 redefinition of the SI base units, the only quantity in this list that does not have an exact value in SI units is the electric constant (vacuum permittivity).

Alternative systems of units
The electrostatic CGS system implicitly sets $α$, as commonly found in older physics literature, where the expression of the fine-structure constant becomes $$ \alpha = \frac{e^2}{\hbar c} .$$

A nondimensionalised system commonly used in high energy physics sets $α$, where the expressions for the fine-structure constant becomes $$ \alpha = \frac{e^2}{4 \pi} .$$ As such, the fine-structure constant is just a quantity determining (or determined by) the elementary charge: $ħ = h/2π$ in terms of such a natural unit of charge.

In the system of atomic units, which sets $4πε0 = 1$, the expression for the fine-structure constant becomes $$\alpha = \frac{1}{c} .$$

Measurement
The CODATA recommended value of $ε0 = c = ħ = 1$ is This has a relative standard uncertainty of

This value for $e = √4πα ≈ 0.303$ gives $µ$$0$ = 4π × $1 H.m-1$, 0.8 times the standard uncertainty away from its old defined value, with the mean differing from the old value by only 0.13 parts per billion.

Historically the value of the reciprocal of the fine-structure constant is often given. The CODATA recommended value is

While the value of $α$ can be determined from estimates of the constants that appear in any of its definitions, the theory of quantum electrodynamics (QED) provides a way to measure $α$ directly using the quantum Hall effect or the anomalous magnetic moment of the electron. Other methods include the A.C. Josephson effect and photon recoil in atom interferometry. There is general agreement for the value of $α$, as measured by these different methods. The preferred methods in 2019 are measurements of electron anomalous magnetic moments and of photon recoil in atom interferometry. The theory of QED predicts a relationship between the dimensionless magnetic moment of the electron and the fine-structure constant $α$ (the magnetic moment of the electron is also referred to as the electron $g$-factor $e = me = ħ = 4πε0 = 1$). One of the most precise values of $α$ obtained experimentally (as of 2023) is based on a measurement of $α$ using a one-electron so-called "quantum cyclotron" apparatus, together with a calculation via the theory of QED that involved $12,672$ tenth-order Feynman diagrams:

This measurement of $137.036$ has a relative standard uncertainty of $α$. This value and uncertainty are about the same as the latest experimental results.

Further refinement of the experimental value was published by the end of 2020, giving the value

with a relative accuracy of $1.1$, which has a significant discrepancy from the previous experimental value.

Physical interpretations
The fine-structure constant, $137.036$, has several physical interpretations. $8.1$ is:

When perturbation theory is applied to quantum electrodynamics, the resulting perturbative expansions for physical results are expressed as sets of power series in $α$. Because $α$ is much less than one, higher powers of $d$ are soon unimportant, making the perturbation theory practical in this case. On the other hand, the large value of the corresponding factors in quantum chromodynamics makes calculations involving the strong nuclear force extremely difficult.

Variation with energy scale
In quantum electrodynamics, the more thorough quantum field theory underlying the electromagnetic coupling, the renormalization group dictates how the strength of the electromagnetic interaction grows logarithmically as the relevant energy scale increases. The value of the fine-structure constant $d$ is linked to the observed value of this coupling associated with the energy scale of the electron mass: the electron's mass gives a lower bound for this energy scale, because it (and the positron) is the lightest charged object whose quantum loops can contribute to the running. Therefore, $c$ is the asymptotic value of the fine-structure constant at zero energy. At higher energies, such as the scale of the Z boson, about 90 GeV, one instead measures an effective $α$ ≈ 1/127.

As the energy scale increases, the strength of the electromagnetic interaction in the Standard Model approaches that of the other two fundamental interactions, a feature important for grand unification theories. If quantum electrodynamics were an exact theory, the fine-structure constant would actually diverge at an energy known as the Landau pole – this fact undermines the consistency of quantum electrodynamics beyond perturbative expansions.

History
Based on the precise measurement of the hydrogen atom spectrum by Michelson and Morley in 1887, Arnold Sommerfeld extended the Bohr model to include elliptical orbits and relativistic dependence of mass on velocity. He introduced a term for the fine-structure constant in 1916. The first physical interpretation of the fine-structure constant $α$ was as the ratio of the velocity of the electron in the first circular orbit of the relativistic Bohr atom to the speed of light in the vacuum. Equivalently, it was the quotient between the minimum angular momentum allowed by relativity for a closed orbit, and the minimum angular momentum allowed for it by quantum mechanics. It appears naturally in Sommerfeld's analysis, and determines the size of the splitting or fine-structure of the hydrogenic spectral lines. This constant was not seen as significant until Paul Dirac's linear relativistic wave equation in 1928, which gave the exact fine structure formula.

With the development of quantum electrodynamics (QED) the significance of $α = e2⁄4πε0ħc$ has broadened from a spectroscopic phenomenon to a general coupling constant for the electromagnetic field, determining the strength of the interaction between electrons and photons. The term $α$ is engraved on the tombstone of one of the pioneers of QED, Julian Schwinger, referring to his calculation of the anomalous magnetic dipole moment.

History of measurements
The CODATA values in the above table are computed by averaging other measurements; they are not independent experiments.

Potential variation over time
Physicists have pondered whether the fine-structure constant is in fact constant, or whether its value differs by location and over time. A varying $α$ has been proposed as a way of solving problems in cosmology and astrophysics. String theory and other proposals for going beyond the Standard Model of particle physics have led to theoretical interest in whether the accepted physical constants (not just $α$) actually vary.

In the experiments below, $1⁄α$ represents the change in $α$ over time, which can be computed by $α$prev − $α$now. If the fine-structure constant really is a constant, then any experiment should show that $$\frac{\ \Delta \alpha\ }{\alpha} \overset{\underset{\mathsf{~def~}}{}}{=}  \frac{\ \alpha _\mathrm{prev}-\alpha _\mathrm{now}\ }{\alpha_\mathrm{now}} = 0 ~,$$ or as close to zero as experiment can measure. Any value far away from zero would indicate that $Z$ does change over time. So far, most experimental data is consistent with $v$ being constant.

Past rate of change
The first experimenters to test whether the fine-structure constant might actually vary examined the spectral lines of distant astronomical objects and the products of radioactive decay in the Oklo natural nuclear fission reactor. Their findings were consistent with no variation in the fine-structure constant between these two vastly separated locations and times.

Improved technology at the dawn of the 21st century made it possible to probe the value of $c$ at much larger distances and to a much greater accuracy. In 1999, a team led by John K. Webb of the University of New South Wales claimed the first detection of a variation in $Z$. Using the Keck telescopes and a data set of 128 quasars at redshifts $g_{e}$, Webb et al. found that their spectra were consistent with a slight increase in $α$ over the last 10–12 billion years. Specifically, they found that $$\frac{\ \Delta \alpha\ }{\alpha} \overset{\underset{\mathsf{~def~}}{}}{=}  \frac{\ \alpha _\mathrm{prev}-\alpha _\mathrm{now}\ }{\alpha_\mathrm{now}} =  \left(-5.7\pm 1.0 \right) \times 10^{-6} ~.$$

In other words, they measured the value to be somewhere between $α$ and $α$. This is a very small value, but the error bars do not actually include zero. This result either indicates that $α$ is not constant or that there is experimental error unaccounted for.

In 2004, a smaller study of 23 absorption systems by Chand et al., using the Very Large Telescope, found no measurable variation: $$ \frac{\Delta \alpha}{\alpha_\mathrm{em}}\ =\ \left(-0.6\pm 0.6\right) \times 10^{-6}~.$$

However, in 2007 simple flaws were identified in the analysis method of Chand et al., discrediting those results.

King et al. have used Markov chain Monte Carlo methods to investigate the algorithm used by the UNSW group to determine $1⁄137.03600$ from the quasar spectra, and have found that the algorithm appears to produce correct uncertainties and maximum likelihood estimates for $α$ for particular models. This suggests that the statistical uncertainties and best estimate for $2πe^{2}⁄ch$ stated by Webb et al. and Murphy et al. are robust.

Lamoreaux and Torgerson analyzed data from the Oklo natural nuclear fission reactor in 2004, and concluded that $2πe^{2}⁄ch$ has changed in the past 2 billion years by 45 parts per billion. They claimed that this finding was "probably accurate to within 20%". Accuracy is dependent on estimates of impurities and temperature in the natural reactor. These conclusions have to be verified.

In 2007, Khatri and Wandelt of the University of Illinois at Urbana-Champaign realized that the 21 cm hyperfine transition in neutral hydrogen of the early universe leaves a unique absorption line imprint in the cosmic microwave background radiation. They proposed using this effect to measure the value of $α$ during the epoch before the formation of the first stars. In principle, this technique provides enough information to measure a variation of 1 part in $α$ (4 orders of magnitude better than the current quasar constraints). However, the constraint which can be placed on $α$ is strongly dependent upon effective integration time, going as $α$. The European LOFAR radio telescope would only be able to constrain $α$ to about 0.3%. The collecting area required to constrain $α$ to the current level of quasar constraints is on the order of 100 square kilometers, which is economically impracticable at the present time.

Present rate of change
In 2008, Rosenband et al. used the frequency ratio of Al+ and Hg+ in single-ion optical atomic clocks to place a very stringent constraint on the present-time temporal variation of $α$, namely $α$ = $α$ per year. Note that any present day null constraint on the time variation of alpha does not necessarily rule out time variation in the past. Indeed, some theories that predict a variable fine-structure constant also predict that the value of the fine-structure constant should become practically fixed in its value once the universe enters its current dark energy-dominated epoch.

Spatial variation – Australian dipole
Researchers from Australia have said they had identified a variation of the fine-structure constant across the observable universe.

These results have not been replicated by other researchers. In September and October 2010, after released research by Webb et al., physicists C. Orzel and S.M. Carroll separately suggested various approaches of how Webb's observations may be wrong. Orzel argues that the study may contain wrong data due to subtle differences in the two telescopes a totally different approach; he looks at the fine-structure constant as a scalar field and claims that if the telescopes are correct and the fine-structure constant varies smoothly over the universe, then the scalar field must have a very small mass. However, previous research has shown that the mass is not likely to be extremely small. Both of these scientists' early criticisms point to the fact that different techniques are needed to confirm or contradict the results, a conclusion Webb, et al., previously stated in their study.

Other research finds no meaningful variation in the fine structure constant.

Anthropic explanation
The anthropic principle is an argument about the reason the fine-structure constant has the value it does: stable matter, and therefore life and intelligent beings, could not exist if its value were very different. One example is that, if modern grand unified theories are correct, then $α$ needs to be between around 1/180 and 1/85 to have proton decay to be slow enough for life to be possible.

Numerological explanations
As a dimensionless constant which does not seem to be directly related to any mathematical constant, the fine-structure constant has long fascinated physicists.

Arthur Eddington argued that the value could be "obtained by pure deduction" and he related it to the Eddington number, his estimate of the number of protons in the universe. This led him in 1929 to conjecture that the reciprocal of the fine-structure constant was not approximately but precisely the integer 137. By the 1940s experimental values for $α$ deviated sufficiently from 137 to refute Eddington's arguments.

Physicist Wolfgang Pauli commented on the appearance of certain numbers in physics, including the fine-structure constant, which he also noted approximates the prime number 137. This constant so intrigued him that he collaborated with psychoanalyst Carl Jung in a quest to understand its significance. Similarly, Max Born believed that if the value of $−0.0000047$ differed, the universe would degenerate, and thus that $−0.0000067$ = $α$ is a law of nature.

Richard Feynman, one of the originators and early developers of the theory of quantum electrodynamics (QED), referred to the fine-structure constant in these terms:

"There is a most profound and beautiful question associated with the observed coupling constant, $g_{e}$ – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.)

Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by humans. You might say the 'hand of God' wrote that number, and 'we don't know how He pushed His pencil.' We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out – without putting it in secretly!"

Conversely, statistician I. J. Good argued that a numerological explanation would only be acceptable if it could be based on a good theory that is not yet known but "exists" in the sense of a Platonic Ideal.

Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. However, no numerological explanation has ever been accepted by the physics community.

In the early 21st century, multiple physicists, including Stephen Hawking in his book A Brief History of Time, began exploring the idea of a multiverse, and the fine-structure constant was one of several universal constants that suggested the idea of a fine-tuned universe.

Quotes
"For historical reasons, $$1⁄α$⁄α$ is known as the fine structure constant. Unfortunately, this name conveys a false impression. We have seen that the charge of an electron is not strictly constant but varies with distance because of quantum effects; hence $$1⁄α$⁄α$ must be regarded as a variable, too. The value 1/137 is the asymptotic value of $$λ = 2πd$⁄α$ shown in Fig. 1.5a."

"The mystery about $α$ is actually a double mystery: The first mystery – the origin of its numerical value $α$ ≈ 1/137 – has been recognized and discussed for decades. The second mystery – the range of its domain – is generally unrecognized."

"When I die my first question to the Devil will be: What is the meaning of the fine structure constant?"

title: Fine-structure constant


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Haidinger's brush

Haidinger's brush, more commonly known as Haidinger's brushes is an image produced by the eye, an entoptic phenomenon, first described by Austrian physicist Wilhelm Karl von Haidinger in 1844. Haidinger saw it when he looked through various minerals that polarized light.

Many people are able to perceive polarization of light. Haidinger's brushes may be seen as a yellowish horizontal bar or bow-tie shape (with "fuzzy" ends, hence the name "brush") visible in the center of the visual field against the blue sky viewed while facing away from the sun, or on any bright background. It typically occupies roughly 3–5 degrees of vision, about twice or three times the width of one's thumb held at arm's length. The direction of light polarization is perpendicular to the yellow bar (i.e., vertical if the bar is horizontal). Fainter bluish or purplish areas may be visible between the yellow brushes (see illustration). Haidinger's brush may also be seen by looking at a white area on many LCD flat panel computer screens (due to the polarization effect of the display), in which case it is often diagonal.

Physiological causes
Haidinger's brush is usually attributed to the dichroism of the xanthophyll pigment found in the macula lutea. As described by the Fresnel laws, the behavior and distribution of oblique rays in the cylindrical geometry of the foveal blue cones produce an extrinsic dichroism. The size of the brush is consistent with the size of the macula.

It is thought that the macula's dichroism arises from some of its pigment molecules being arranged circularly; (the small proportion of circularly arranged molecules accounts for the faintness of the phenomenon.) Xanthophyll pigments tend to be parallel to visive nerves that (because the fovea is not flat), are almost orthogonal to the fovea in its central part but nearly parallel in its outer region. As a result, two different areas of the fovea can be sensitive to two different degrees of polarization.

Seeing Haidinger's brush

Many people find it difficult to see Haidinger's brush initially. It is very faint, much more so than generally indicated in illustrations, and, like other stabilized images, tends to appear and disappear.

It is most easily seen when it can be made to move. Because it is always positioned on the macula, there is no way to make it move laterally, but it can be made to rotate, by viewing a white surface through a rotating polarizer, or by slowly tilting one's head to one side.

To see Haidinger's brush, start by using a polarizer, such as a lens from a pair of polarizing sunglasses. Gaze at an evenly lit, textureless surface through the lens and rotate the polarizer.

An option is to use the polarizer built into a computer's LCD screen. Look at a white area on the screen, and slowly tilt the head (a CRT monitor has no polarizer, and will not work for this purpose unless a separate polarizer is used).

It appears with more distinctness against a blue background. With practice, it is possible to see it in the naturally polarized light of a blue sky. Minnaert recommended practicing first with a polarizer, then trying it without. The areas of the sky with the strongest polarization are those 90 degrees away from the sun. Minnaert said that after a minute of gazing at the sky, "a kind of marble effect will appear. This is followed shortly by Haidinger's brush." He commented that not all observers see it in the same way. Some see the yellow pattern as solid and the blue pattern as interrupted, as in the illustrations on this page. Some see the blue as solid and the yellow as interrupted, and some see it alternating between the two states.

Use
The fact that the sensation of Haidinger's brush corresponds with the visual field of the macula means that it can be utilised in training people to look at objects with their macula. People with certain types of strabismus may undergo an adaptation whereupon they look at the object of attention not with their fovea (at the centre of the macula) but with an eccentric region of the retina. This adaptation is known as eccentric fixation. To aid in training a person to look at an object with their fovea rather than their eccentric retinal zone, a training device can be used. One such apparatus utilises a rotating polarised plate backlit with a bright white light. Wearing blue spectacles (to enhance the Haidinger's brush image) and an occluder over the other eye, the user will hopefully notice the Haidinger's brush where their macula correlates with their visual field. The goal of the training is for the user to learn to look at the test object in such a way that the Haidinger's brush overlaps the test object (and the viewer is thus now looking at it with their fovea). The reason for such training is that the healthy fovea is far greater in its resolving power than any other part of the retina. Another diagnostic method that utilises birefringent properties of the retinal tissue is retinal birefringence scanning, that can be used in case of severe amblyopia or when the specialist lacks a cooperation from the patient.

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

title: Haidinger's brush


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Nellie Tayloe Ross

Nellie Davis Ross (née Tayloe; November 29, 1876 – December 19, 1977) was an American educator and politician who served as the 14th governor of Wyoming from 1925 to 1927, and as the 28th and first female director of the United States Mint from 1933 to 1953. She was the first woman to serve as governor of a U.S. state, and remains the only woman to have served as governor of Wyoming. She was a Democrat and supported Prohibition. She ran for re-election but refused to campaign herself.

Ross was born in St. Joseph, Missouri, to James Wynns Tayloe, a native of Tennessee, and Elizabeth Blair Green, who owned a plantation on the Missouri River. Her family moved to Miltonvale, Kansas in 1884, and she graduated from Miltonvale High School in 1892. She attended a teacher-training college for two years and taught kindergarten for four years.

On September 11, 1902, Ross married William B. Ross, whom she had met when visiting relatives in Tennessee in 1900. William B. Ross was governor of Wyoming from 1923 to his death on October 2, 1924. Ross succeeded her late husband's successor Frank Lucas as governor when she won the special election, becoming the first female American governor on January 5, 1925. She was a staunch supporter of Prohibition during the 1920s. She lost re-election in 1926, but remained an active member of the Democratic Party.

In 1933, Ross became the first female Director of the United States Mint. Despite initial mistrust, she forged a strong bond with Mary Margaret O'Reilly, the assistant director of the Mint and one of the United States' highest-ranking female civil servants of her time. Ross served five terms as Director, retiring in 1953. During her later years, she wrote for various women's magazines and traveled. Ross died in Washington, D. C., at the age of 101.

Early life and education
Born Nellie Davis Tayloe in St. Joseph, Missouri, Ross was the sixth child, and first daughter, of James Wynns Tayloe, a native of Stewart County, Tennessee, and his wife, Elizabeth Blair Green, who owned a plantation on the Missouri River. She spent much of her childhood in the Florence and Decatur in northern Alabama's Tennessee Valley. In 1884, when Ross was seven years of age, her family moved to Miltonvale in Cloud County in northern Kansas. This relocation happened after her father's old family home back in St. Joseph burned, and the sheriff was about to foreclose on the property.

After Ross graduated from Miltonville High School in 1892, her family moved to Omaha, Nebraska. During this time, she taught private piano lessons and attended a two-year training program for kindergarten teachers that was sponsored by the Omaha city school system. She then taught kindergarten for four years. Two of her brothers sent her on a trip to Europe in 1896.

While on a visit to her relatives in Dover, Tennessee, in 1900, Ross met William Bradford Ross, whom she married on September 11, 1902. They had three children (twins James Ambrose and George Taylor, and Alfred Duff). William Ross practiced law and planned to live in the American West. He moved to Cheyenne and established a law practice, bringing his wife to join him. Ross became a leader in Wyoming's Democratic Party served as Laramie County's prosecuting attorney from 1906 to 1907. In 1910 he was an unsuccessful candidate for Wyoming's at-large congressional seat, and in 1918 he was an unsuccessful candidate for the Democratic nomination for governor.

Governorship of Wyoming
In 1922, William Ross was elected governor of Wyoming by appealing to progressive voters in both parties. However, after little more than a year and a half in office, he died on October 2, 1924, from surgical complications following an appendectomy. The Democratic Party then nominated his widow, Nellie, to run for governor in a special election the following month.

Nellie Ross refused to campaign. She won the November 4, 1924, election with 43,323 votes (55.12%) against her opponent's 35,275 votes (44.88%). On January 5, 1925, she became the first female governor in the history of the United States. As governor she continued her late husband's policies, which called for tax cuts, government assistance for poor farmers, banking reform, and laws protecting children, women workers, and miners. She urged Wyoming to ratify a pending federal amendment prohibiting child labor. Like her husband, she advocated the strengthening of prohibition laws.

Ross ran for re-election in 1926, and relied on campaign surrogates including Cecilia Hennel Hendricks, the Democratic nominee for State Superintendent of Public Instruction, but was narrowly defeated by Frank Emerson. She attributed her loss in part to her refusal to campaign for herself and support for prohibition. She remained active in the Democratic Party and campaigned for Al Smith in the 1928 presidential election, even though the two disagreed on prohibition. At the 1928 Democratic National Convention, she received 33 votes from eleven states for vice president on the first ballot. She also gave a speech seconding Smith's nomination. After the convention, she served as vice chairman of the Democratic National Committee and as director of the DNC Women's Division.

Appointment by FDR
U.S. President Franklin D. Roosevelt appointed Ross as director of the U.S. Mint on May 3, 1933, making her the first woman to hold that position. Ross and the Mint's Assistant Director Mary Margaret O'Reilly, "the Sweetheart of the Treasury" who had worked at the Mint since 1904, had mutual suspicions to overcome. Ross, who had endured poor relations with Eleanor Roosevelt and others on FDR's campaign, did not trust the career staff. O'Reilly saw another political appointee with no experience at the Mint Bureau replacing Robert J. Grant, who had been Denver Mint superintendent before his directorship. After a brief period, the two women came to appreciate each other's merits.

Tenure
Ross and O'Reilly soon came to the usual division of labor between director and assistant: the director would handle public affairs and make policy decisions as needed, while the assistant dealt with the day-to-day business of the bureau. Ross undertook a heavy travel schedule, visiting Mint facilities, making speeches backing Roosevelt, and campaigning for Democratic candidates in Wyoming. This left O'Reilly running the Washington office as acting director. The two women carried on a businesslike but warm correspondence during these times, with O'Reilly writing to Ross (who had embarked on a tour of the mints) "I am so anxious to have your mind at ease about the office here [in Washington] that I have resorted to rather frequent telegrams. They are so much more direct and up to date than letters ... my love to you and every good wish for the success of your visits to our beloved mint institutions." Teva J. Scheer, biographer of Ross, suggests that O'Reilly would have found Ross's reports from the field valuable; they showed how the Mint recovered from the initial years of the Depression, when relatively few coins were produced, to the mid-1930s, when strong demand for coinage led the bureau to run the mints with two or even three shifts.

O'Reilly's retirement
In 1935, O'Reilly reached the mandatory federal retirement age of 70. Ross requested that President Roosevelt exempt O'Reilly from mandatory retirement because her knowledge of bureau affairs was so extensive and was badly needed. A special order of President Roosevelt gave O'Reilly an extra year in the Mint Service. During the extension, Ross hired Frank Leland Howard of the University of Virginia, who had a background in accounting, as O'Reilly's prospective replacement. Howard replaced O'Reilly when she retired on October 29, 1938, after two more extensions.

Legacy
Ross' tenure saw the Mint in 1944 investigate how several 1933 double eagles, never officially released, had come onto the market. She is known for establishing the Franklin half dollar and starting the making of proof coins for public sale. Ross served five full terms until her retirement in 1953 and was succeeded by William H. Brett, whom President Dwight D. Eisenhower nominated in 1954.

Later years and death
After her retirement, Ross contributed articles to various women's magazines and traveled extensively. She made her last trip to Wyoming in 1972 at the age of ninety-six. Five years later, she died in Washington, D.C., at the age of 101; at the time of her death, she was the oldest ex-governor in the United States. She is interred in the family plot in Lakeview Cemetery in Cheyenne.

title: Nellie Tayloe Ross


text:
Isabella of Angoulême

Isabella (Isabelle d'Angoulême, ; c. 1186/ 1188 – 4 June 1246) was Queen of England from 1200 to 1216 as the second wife of King John, Countess of Angoulême in her own right from 1202 until her death in 1246, and Countess of La Marche from 1220 to 1246 as the wife of Count Hugh.

Isabella had five children by King John, including his heir, later Henry III. In 1220, Isabella married Hugh X of Lusignan, Count of La Marche, by whom she had another nine children.

Some of Isabella's contemporaries, as well as later writers, claim that she formed a conspiracy against King Louis IX of France in 1241, after being publicly snubbed by his mother, Blanche of Castile, for whom she harbored a deep-seated hatred. In 1244, after the plot had failed, Isabella was accused of attempting to poison the king. To avoid arrest, she sought refuge in Fontevraud Abbey, where she died two years later, but none of this can be confirmed.

Queen consort of England
Isabella was the only daughter and heir of Aymer Taillefer, Count of Angoulême, by Alice of Courtenay, who was a sister of Peter II of Courtenay, Latin Emperor of Constantinople. Alice and Peter II were grandchildren of King Louis VI of France through their father Peter I of Courtenay.

Isabella became Countess of Angoulême in her own right on 16 June 1202, by which time she was already queen of England. Her marriage, at age 12 or 14, to King John took place on 24 August 1200, in Angoulême, a year after he annulled his first marriage to Isabel of Gloucester. She was crowned queen in an elaborate ceremony on 8 October at Westminster Abbey in London. Isabella was originally betrothed to Hugh IX le Brun, Count of Lusignan, grandson and heir of the Count of La Marche. As a result of John's temerity in taking her as his second wife, King Philip II of France confiscated all of their French lands and armed conflict ensued.

At the time of her marriage to John, the blonde-haired blue-eyed Isabella was already renowned by some for her beauty and has sometimes been called the Helen of the Middle Ages by historians. Isabella was much younger than her husband and possessed a volatile temper similar to his own. King John was infatuated with his young, beautiful wife; however, his acquisition of her had at least as much to do with spiting his enemies as romantic love. She was already engaged to Hugh IX le Brun when she was taken by John. It was said that he neglected his state affairs to spend time with Isabella, often remaining in bed with her until noon. However, these were rumors spread by John's enemies to discredit him as a weak and grossly irresponsible ruler, given that at the time John was engaging in a desperate war against King Philip II of France to hold on to the remaining Plantagenet duchies. The common people began to term her a "siren" or "Messalina" for her allure. Her mother-in-law, Eleanor of Aquitaine, readily accepted her as John's wife.

On 1 October 1207, at Winchester Castle, Isabella gave birth to a son and heir, the future King Henry III of England, who was named after his grandfather King Henry II. He was quickly followed by another son, Richard, and three daughters: Joan, Isabella and Eleanor. All five children survived into adulthood and made illustrious marriages; all but Joan produced offspring of their own.

Second marriage
When King John died in October 1216, Isabella's first act was to arrange the speedy coronation of her nine-year-old son at the city of Gloucester on 28 October. As the royal crown had recently been lost in the Wash, along with the rest of King John's treasure, she supplied her own golden circlet to be used in lieu of a crown. The following July, less than a year after his crowning as King Henry III of England, she left him in the care of his regent, William Marshal, 1st Earl of Pembroke, and returned to France to assume control of her inheritance of Angoulême.

In the spring of 1220, Isabella married Hugh X of Lusignan, "le Brun", Seigneur de Luisignan, Count of La Marche, the son of her former fiancé, Hugh IX, to whom she had been betrothed before her marriage to King John. It had been previously arranged that her eldest daughter Joan should marry Hugh, and the little girl was being brought up at the Lusignan court in preparation for her marriage. Hugh, however, upon seeing Isabella, whose beauty had not diminished, preferred the girl's mother. Joan was provided with another husband, King Alexander II of Scotland, whom she wed in 1221.

Isabella married Hugh without the consent of the king's council in England, as was required of a queen dowager. That council had the power not only to assign to her any subsequent husband, but to decide whether she should be allowed (or forced) to remarry at all. That Isabella flouted its authority moved the council to confiscate her dower lands and to stop the payment of her pension. Isabella and her husband retaliated by threatening to keep Joan, who had been promised in marriage to the King of Scotland, in France. The council first responded by sending furious letters to the Pope, signed in the name of young King Henry, urging him to excommunicate Isabella and her husband, but then decided to come to terms with Isabella, to avoid conflict with the Scottish king, who was eager to receive his bride. Isabella was granted the stannaries in Devon, and the revenue of Aylesbury for a period of four years, in compensation for her confiscated dower lands in Normandy, as well as the £3,000 arrears for her pension.

Isabella had nine more children by Hugh X. Their eldest son Hugh XI of Lusignan succeeded his father as Count of La Marche and Count of Angoulême in 1249.

Isabella's children from her royal marriage did not join her in Angoulême, remaining in England with their eldest brother Henry III.

Rebellion and death
Described by some contemporaries as "vain, capricious and troublesome," Isabella could not reconcile herself with her less prominent position in France. Though a former queen of England, Isabella was now mostly regarded as a mere countess and had to give precedence to other women. In 1241, when Isabella and Hugh were summoned to the French court to swear fealty to King Louis IX of France's brother, Alphonse, who had been invested as Count of Poitou, their mother, Queen Dowager Blanche openly snubbed her. This so infuriated Isabella, who had a deep-seated hatred of Blanche for having fervently supported the French invasion of England during the First Barons' War in May 1216, that she began to conspire actively against King Louis. Isabella and her husband, along with other disgruntled nobles, including her son-in-law Count Raymond VII of Toulouse, sought to create an English-backed confederacy which united the provinces of the south and west against the French king. She encouraged her son Henry in his invasion of Normandy in 1230, but then did not provide him the support she had promised.

In 1244, after the confederacy had failed and Hugh had made peace with King Louis, two royal cooks were arrested for attempting to poison the king; upon questioning they confessed to having been in Isabella's pay. Before Isabella could be taken into custody, she fled to Fontevraud Abbey, where she died on 4 June 1246.

By Isabella's own prior arrangement, she was first buried in the abbey's churchyard as an act of repentance for her many misdeeds. On a visit to Fontevraud, her son King Henry III of England was shocked to find her buried outside the abbey and ordered her immediately moved inside. She was finally placed beside Henry II and Eleanor of Aquitaine. Afterwards, most of her many Lusignan children, having few prospects in France, set sail for England and the court of Henry, their half-brother.

Issue

 * With King John of England, five children, all of whom survived into adulthood:
 * 1) King Henry III of England (1 October 1207 – 16 November 1272). Married Eleanor of Provence, by whom he had issue, including his heir, King Edward I of England.
 * 2) Richard, Earl of Cornwall and King of the Romans (5 January 1209 – 2 April 1272). Married firstly, Isabel Marshal, secondly, Sanchia of Provence, and thirdly, Beatrice of Falkenburg. Had issue.
 * 3) Joan (22 July 1210 – 1238), the wife of King Alexander II of Scotland. Her marriage was childless.
 * 4) Isabella (1214–1241), the wife of Emperor Frederick II, by whom she had issue.
 * 5) Eleanor (1215–1275), who would marry, firstly, William Marshal, 2nd Earl of Pembroke, and secondly, Simon de Montfort, 6th Earl of Leicester, by whom she had issue.

 * With Hugh X of Lusignan, Count of La Marche: nine children, all of whom survived into adulthood:
 * 1) Hugh XI of Lusignan (1221–1250), Count of La Marche and Count of Angoulême. Married Yolande de Dreux, Countess of Penthièvre and of Porhoet, by whom he had issue.
 * 2) Aymer of Lusignan (1222–1260), Bishop of Winchester
 * 3) Agnès de Lusignan (1223–1269). Married William II de Chauvigny (d. 1270), and had issue.
 * 4) Alice of Lusignan (1224 – 9 February 1256). Married John de Warenne, 6th Earl of Surrey, by whom she had issue.
 * 5) Guy of Lusignan (c. 1225 – 1264), killed at the Battle of Lewes. (Tufton Beamish maintains that he escaped to France after the Battle of Lewes and died there in 1269.)
 * 6) Geoffrey of Lusignan (c. 1226 – 1274). Married in 1259 Jeanne, Viscountess of Châtellerault, by whom he had issue.
 * 7) Isabella of Lusignan (c. 1226/1227 – 14 January 1299). Married, firstly, before 1244 Maurice IV, Seigneur de Craon (1224–1250), by whom she had issue; she married, secondly, Geoffrey de Rancon.
 * 8) William of Lusignan (c. 1228 – 1296). First earl of Pembroke. Married Joan de Munchensi, by whom he had issue.
 * 9) Marguerite de Lusignan (c. 1229 – 1288). Married, firstly, in 1243 Raymond VII of Toulouse; secondly, c. 1246 Aimery IX de Thouars, Viscount of Thouars and had issue.

In popular culture
She was played by actress Zena Walker in the TV series The Adventures of Robin Hood episode "Isabella" (1956), before her marriage to John, but not as a 12-year-old. She was portrayed by actress Victoria Abril in the 1976 film Robin and Marian. She was played by actress Lynsey Baxter in the 1979 TV mini-series "The Devil's Crown". She was played by actress Cory Pulman in the episode "The Pretender" (1986) of the TV series Robin of Sherwood. She was portrayed by actress Léa Seydoux in the 2010 film Robin Hood.

title: Isabella of Angoulême