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Odo of Bayeux

Odo of Bayeux (died 1097) was Bishop of Bayeux in Normandy, and was also made Earl of Kent in England following the Norman Conquest. He was the maternal half-brother of duke, and later king, William the Conqueror, and was, for a time, William's primary administrator in the Kingdom of England, although he was eventually tried for defrauding the William's government. It is likely Odo commissioned the Bayeux Tapestry, a large tableau of the Norman Conquest, perhaps to present to his brother William. He later fell out with his brother over Odo's support for military adventures in Italy. William, on his deathbed, freed Odo. Odo died in Palermo Sicily on the way to crusade.

Early life
Odo was the son of William the Conqueror's mother Herleva and Herluin de Conteville. Count Robert of Mortain was his younger brother. There is uncertainty about his birth date. Some historians have suggested he was born around 1035. Duke William made him bishop of Bayeux in 1049. It has been suggested that his birth was as early as 1030, making him about nineteen rather than fourteen at the time.

Norman Conquest and after
Although Odo was an ordained Christian cleric, he is best known as a warrior and statesman, participating in the Council of Lillebonne. He funded ships for the Norman invasion of England and is one of the very few proven companions of William the Conqueror known to have fought at the Battle of Hastings in 1066. The Bayeux Tapestry, probably commissioned by him to adorn his own cathedral, appears to labour the point that he did not actually fight, that is to say shed blood, at Hastings, but rather encouraged the troops from the rear. The Latin annotation embroidered onto the Tapestry above his image reads: HIC ODO EPS BACULU TENENS CONFORTAT PUEROS ("EPS" abbreviating episcopus "bishop" and "BACULU" omitting a final m – baculum "cudgel"), in English "Here Odo the bishop holding a club strengthens the boys". It has been suggested that his clerical status forbade him from using a sword, though this is doubtful: the club was a common weapon and used often by leadership including by Duke William himself, as also depicted in the same part of the Tapestry. Odo was accompanied by William the carrier of his crozier and a retinue of servants and members of his household.

In 1067, Odo became Earl of Kent, and for some years he was a trusted royal minister. On some occasions when William was absent (back in Normandy), he served as regent of England, and at times he led the royal forces against rebellions (e.g. the Revolt of the Earls): the precise sphere of his powers is not certain. There are also other occasions when he accompanied William back to Normandy.

During this time Odo acquired vast estates in England, larger in extent than anyone except the king: he had land in twenty-three counties, primarily in the south east and in East Anglia.

Trial, imprisonment and rebellion
In 1076, at the Trial of Penenden Heath, Odo was tried in front of a large and senior assembly over the course of three days at Penenden Heath in Kent for defrauding the Crown and the Diocese of Canterbury. At the conclusion of the trial he was forced to return a number of properties and his assets were re-apportioned.

In 1082, Odo was suddenly disgraced and imprisoned for having planned a military expedition to Italy. His motives are not certain. Chroniclers writing a generation later said Odo desired to make himself pope during the Investiture Controversy while Pope Gregory VII was in severe difficulty in his conflict with Henry IV, Holy Roman Emperor, and the position of pope was in contention; but the contemporary evidence is ambiguous. Whatever the reason, Odo spent the next five years in prison and his English estates were taken back by the king, as was his office as Earl of Kent. Odo was not deposed as Bishop of Bayeux.

On his deathbed in 1087, King William I was reluctantly persuaded by his half-brother, Robert, Count of Mortain, to release Odo. After the king's death, Odo returned to England. William's eldest son, Robert Curthose, had been made duke of Normandy, while Robert's brother William Rufus had received the throne of England. The bishop supported Robert Curthose's claim to England. The Rebellion of 1088 failed and William Rufus permitted Odo to leave the kingdom. Afterwards, Odo remained in the service of Robert in Normandy.

Odo joined the First Crusade as part of his nephew Robert's army that was bound for Jerusalem, but died on the way whilst visiting Palermo in January or February 1097. He was buried in Palermo Cathedral.

Commentary on Odo
William Stearns Davis writes in Life on a Medieval Barony (1923):

Bishop Odo of Bayeux fought at Hastings (1066) before any such authorized champions of the church existed. ... That bishops shall restrain from warfare is really a pious wish not easily in this sinful world to be granted.

Portrayals on screen
On screen, Odo has been portrayed by John Nettleton in the two-part BBC TV play Conquest (1966), part of the series Theatre 625, and by Denis Lill in the TV drama Blood Royal: William the Conqueror (1990).

title: Odo of Bayeux


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Surface tension

Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to float on a water surface without becoming even partly submerged.

At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion).

There are two primary mechanisms in play. One is an inward force on the surface molecules causing the liquid to contract. Second is a tangential force parallel to the surface of the liquid. This tangential force is generally referred to as the surface tension. The net effect is the liquid behaves as if its surface were covered with a stretched elastic membrane. But this analogy must not be taken too far as the tension in an elastic membrane is dependent on the amount of deformation of the membrane while surface tension is an inherent property of the liquid–air or liquid–vapour interface.

Because of the relatively high attraction of water molecules to each other through a web of hydrogen bonds, water has a higher surface tension (72.8 millinewtons (mN) per meter at 20 °C) than most other liquids. Surface tension is an important factor in the phenomenon of capillarity.

Surface tension has the dimension of force per unit length, or of energy per unit area. The two are equivalent, but when referring to energy per unit of area, it is common to use the term surface energy, which is a more general term in the sense that it applies also to solids.

In materials science, surface tension is used for either surface stress or surface energy.

Causes
Due to the cohesive forces, a molecule located away from the surface is pulled equally in every direction by neighboring liquid molecules, resulting in a net force of zero. The molecules at the surface do not have the same molecules on all sides of them and therefore are pulled inward. This creates some internal pressure and forces liquid surfaces to contract to the minimum area.

There is also a tension parallel to the surface at the liquid-air interface which will resist an external force, due to the cohesive nature of water molecules.

The forces of attraction acting between molecules of the same type are called cohesive forces, while those acting between molecules of different types are called adhesive forces. The balance between the cohesion of the liquid and its adhesion to the material of the container determines the degree of wetting, the contact angle, and the shape of meniscus. When cohesion dominates (specifically, adhesion energy is less than half of cohesion energy) the wetting is low and the meniscus is convex at a vertical wall (as for mercury in a glass container). On the other hand, when adhesion dominates (when adhesion energy is more than half of cohesion energy) the wetting is high and the similar meniscus is concave (as in water in a glass).

Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled into a spherical shape by the imbalance in cohesive forces of the surface layer. In the absence of other forces, drops of virtually all liquids would be approximately spherical. The spherical shape minimizes the necessary "wall tension" of the surface layer according to Laplace's law.

Another way to view surface tension is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone. The interior molecules have as many neighbors as they can possibly have, but the boundary molecules are missing neighbors (compared to interior molecules) and therefore have higher energy. For the liquid to minimize its energy state, the number of higher energy boundary molecules must be minimized. The minimized number of boundary molecules results in a minimal surface area. As a result of surface area minimization, a surface will assume a smooth shape.

Physical units
Surface tension, represented by the symbol γ (alternatively σ or T), is measured in force per unit length. Its SI unit is newton per meter but the cgs unit of dyne per centimeter is also used. For example, $$ \gamma = 1 ~\mathrm{\frac{dyn}{cm}} = 1 ~\mathrm{\frac{erg}{cm^2}} = 1~\mathrm{\frac{10^{-7}\,m\cdot N}{10^{-4}\, m^2}} = 0.001~\mathrm{\frac{N}{m}} = 0.001~\mathrm{\frac{J}{m^2}}.$$

Definition
Surface tension can be defined in terms of force or energy.

In terms of force
Surface tension $γ$ of a liquid is the force per unit length. In the illustration on the right, the rectangular frame, composed of three unmovable sides (black) that form a "U" shape, and a fourth movable side (blue) that can slide to the right. Surface tension will pull the blue bar to the left; the force $F$ required to hold the movable side is proportional to the length $L$ of the immobile side. Thus the ratio $F⁄L$ depends only on the intrinsic properties of the liquid (composition, temperature, etc.), not on its geometry. For example, if the frame had a more complicated shape, the ratio $F⁄L$, with $L$ the length of the movable side and $F$ the force required to stop it from sliding, is found to be the same for all shapes. We therefore define the surface tension as

$$\gamma=\frac{F}{2L}.$$ The reason for the $1⁄2$ is that the film has two sides (two surfaces), each of which contributes equally to the force; so the force contributed by a single side is $γL = F⁄2$.

In terms of energy
Surface tension $γ$ of a liquid is the ratio of the change in the energy of the liquid to the change in the surface area of the liquid (that led to the change in energy). This can be easily related to the previous definition in terms of force: if $F$ is the force required to stop the side from starting to slide, then this is also the force that would keep the side in the state of sliding at a constant speed (by Newton's Second Law). But if the side is moving to the right (in the direction the force is applied), then the surface area of the stretched liquid is increasing while the applied force is doing work on the liquid. This means that increasing the surface area increases the energy of the film. The work done by the force $F$ in moving the side by distance $Δx$ is $W = FΔx$; at the same time the total area of the film increases by $ΔA = 2LΔx$ (the factor of 2 is here because the liquid has two sides, two surfaces). Thus, multiplying both the numerator and the denominator of $γ = 1⁄2F⁄L$ by $Δx$, we get $$\gamma=\frac{F}{2L}=\frac{F \Delta x}{2 L \Delta x}=\frac{W}{\Delta A} .$$ This work $W$ is, by the usual arguments, interpreted as being stored as potential energy. Consequently, surface tension can be also measured in SI system as joules per square meter and in the cgs system as ergs per cm2. Since mechanical systems try to find a state of minimum potential energy, a free droplet of liquid naturally assumes a spherical shape, which has the minimum surface area for a given volume. The equivalence of measurement of energy per unit area to force per unit length can be proven by dimensional analysis.

Water
Several effects of surface tension can be seen with ordinary water: 1. Beading of rain water on a waxy surface, such as a leaf. Water adheres weakly to wax and strongly to itself, so water clusters into drops. Surface tension gives them their near-spherical shape, because a sphere has the smallest possible surface area to volume ratio.

2. Formation of drops occurs when a mass of liquid is stretched. The animation (below) shows water adhering to the faucet gaining mass until it is stretched to a point where the surface tension can no longer keep the drop linked to the faucet. It then separates and surface tension forms the drop into a sphere. If a stream of water were running from the faucet, the stream would break up into drops during its fall. Gravity stretches the stream, then surface tension pinches it into spheres.

3. Flotation of objects denser than water occurs when the object is nonwettable and its weight is small enough to be borne by the forces arising from surface tension. For example, water striders use surface tension to walk on the surface of a pond in the following way. The nonwettability of the water strider's leg means there is no attraction between molecules of the leg and molecules of the water, so when the leg pushes down on the water, the surface tension of the water only tries to recover its flatness from its deformation due to the leg. This behavior of the water pushes the water strider upward so it can stand on the surface of the water as long as its mass is small enough that the water can support it. The surface of the water behaves like an elastic film: the insect's feet cause indentations in the water's surface, increasing its surface area and tendency of minimization of surface curvature (so area) of the water pushes the insect's feet upward.

4. Separation of oil and water (in this case, water and liquid wax) is caused by a tension in the surface between dissimilar liquids. This type of surface tension is called "interface tension", but its chemistry is the same.

5. Tears of wine is the formation of drops and rivulets on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between the differing surface tensions of water and ethanol; it is induced by a combination of surface tension modification of water by ethanol together with ethanol evaporating faster than water.

Surfactants
Surface tension is visible in other common phenomena, especially when surfactants are used to decrease it:

 * Soap bubbles have very large surface areas with very little mass. Bubbles in pure water are unstable. The addition of surfactants, however, can have a stabilizing effect on the bubbles (see Marangoni effect). Surfactants actually reduce the surface tension of water by a factor of three or more.
 * Emulsions are a type of colloidal dispersion in which surface tension plays a role. Tiny droplets of oil dispersed in pure water will spontaneously coalesce and phase separate. The addition of surfactants reduces the interfacial tension and allow for the formation of oil droplets in the water medium (or vice versa). The stability of such formed oil droplets depends on many different chemical and environmental factors.

Surface curvature and pressure

If no force acts normal to a tensioned surface, the surface must remain flat. But if the pressure on one side of the surface differs from pressure on the other side, the pressure difference times surface area results in a normal force. In order for the surface tension forces to cancel the force due to pressure, the surface must be curved. The diagram shows how surface curvature of a tiny patch of surface leads to a net component of surface tension forces acting normal to the center of the patch. When all the forces are balanced, the resulting equation is known as the Young–Laplace equation: $$\Delta p = \gamma \left( \frac{1}{R_x} + \frac{1}{R_y} \right)$$ where: The quantity in parentheses on the right hand side is in fact (twice) the mean curvature of the surface (depending on normalisation). Solutions to this equation determine the shape of water drops, puddles, menisci, soap bubbles, and all other shapes determined by surface tension (such as the shape of the impressions that a water strider's feet make on the surface of a pond). The table below shows how the internal pressure of a water droplet increases with decreasing radius. For not very small drops the effect is subtle, but the pressure difference becomes enormous when the drop sizes approach the molecular size. (In the limit of a single molecule the concept becomes meaningless.)
 * $Δp$ is the pressure difference, known as the Laplace pressure.
 * $δθ_{x}$ is surface tension.
 * $δθ_{y}$ and $γ$ are radii of curvature in each of the axes that are parallel to the surface.

Floating objects

When an object is placed on a liquid, its weight $Δp$ depresses the surface, and if surface tension and downward force become equal then it is balanced by the surface tension forces on either side $Δp$, which are each parallel to the water's surface at the points where it contacts the object. Notice that small movement in the body may cause the object to sink. As the angle of contact decreases, surface tension decreases. The horizontal components of the two $F_{w}$ arrows point in opposite directions, so they cancel each other, but the vertical components point in the same direction and therefore add up to balance $F_{s}$. The object's surface must not be wettable for this to happen, and its weight must be low enough for the surface tension to support it. If $F_{w}$ denotes the mass of the needle and $F_{s}$ acceleration due to gravity, we have

$$ F_\mathrm{w} = 2 F_\mathrm{s} \sin \theta \quad\Leftrightarrow\quad m g = 2 \gamma L \sin \theta $$

Liquid surface
To find the shape of the minimal surface bounded by some arbitrary shaped frame using strictly mathematical means can be a daunting task. Yet by fashioning the frame out of wire and dipping it in soap-solution, a locally minimal surface will appear in the resulting soap-film within seconds.

The reason for this is that the pressure difference across a fluid interface is proportional to the mean curvature, as seen in the Young–Laplace equation. For an open soap film, the pressure difference is zero, hence the mean curvature is zero, and minimal surfaces have the property of zero mean curvature.

Contact angles
The surface of any liquid is an interface between that liquid and some other medium. The top surface of a pond, for example, is an interface between the pond water and the air. Surface tension, then, is not a property of the liquid alone, but a property of the liquid's interface with another medium. If a liquid is in a container, then besides the liquid/air interface at its top surface, there is also an interface between the liquid and the walls of the container. The surface tension between the liquid and air is usually different (greater) than its surface tension with the walls of a container. And where the two surfaces meet, their geometry must be such that all forces balance.

Where the two surfaces meet, they form a contact angle, $R_{x}$, which is the angle the tangent to the surface makes with the solid surface. Note that the angle is measured through the liquid, as shown in the diagrams above. The diagram to the right shows two examples. Tension forces are shown for the liquid–air interface, the liquid–solid interface, and the solid–air interface. The example on the left is where the difference between the liquid–solid and solid–air surface tension, $F_{s}$, is less than the liquid–air surface tension, $F_{w}$, but is nevertheless positive, that is

$$\gamma_\mathrm{la} > \gamma_\mathrm{ls} - \gamma_\mathrm{sa} > 0$$

In the diagram, both the vertical and horizontal forces must cancel exactly at the contact point, known as equilibrium. The horizontal component of $m$ is canceled by the adhesive force, $g$.

$$f_\mathrm{A} = f_\mathrm{la} \sin \theta$$

The more telling balance of forces, though, is in the vertical direction. The vertical component of $γ_{ls} − γ_{sa}$ must exactly cancel the difference of the forces along the solid surface, $γ_{la}$.

$$f_\mathrm{ls} - f_\mathrm{sa} = -f_\mathrm{la} \cos \theta$$

Since the forces are in direct proportion to their respective surface tensions, we also have:

$$\gamma_\mathrm{ls} - \gamma_\mathrm{sa} = -\gamma_\mathrm{la} \cos \theta$$

where
 * $f_{la}$ is the liquid–solid surface tension,
 * $f_{A}$ is the liquid–air surface tension,
 * $f_{la}$ is the solid–air surface tension,
 * $R_{y}$ is the contact angle, where a concave meniscus has contact angle less than 90° and a convex meniscus has contact angle of greater than 90°.

This means that although the difference between the liquid–solid and solid–air surface tension, $f_{ls} − f_{sa}$, is difficult to measure directly, it can be inferred from the liquid–air surface tension, $γ_{ls}$, and the equilibrium contact angle, $θ$, which is a function of the easily measurable advancing and receding contact angles (see main article contact angle).

This same relationship exists in the diagram on the right. But in this case we see that because the contact angle is less than 90°, the liquid–solid/solid–air surface tension difference must be negative:

$$\gamma_\mathrm{la} > 0 > \gamma_\mathrm{ls} - \gamma_\mathrm{sa}$$

Special contact angles
Observe that in the special case of a water–silver interface where the contact angle is equal to 90°, the liquid–solid/solid–air surface tension difference is exactly zero.

Another special case is where the contact angle is exactly 180°. Water with specially prepared Teflon approaches this. Contact angle of 180° occurs when the liquid–solid surface tension is exactly equal to the liquid–air surface tension.

$$\gamma_\mathrm{la} = \gamma_\mathrm{ls} - \gamma_\mathrm{sa} > 0\qquad \theta = 180^\circ$$

Liquid in a vertical tube

An old style mercury barometer consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with a vacuum (called Torricelli's vacuum) in the unfilled volume (see diagram to the right). Notice that the mercury level at the center of the tube is higher than at the edges, making the upper surface of the mercury dome-shaped. The center of mass of the entire column of mercury would be slightly lower if the top surface of the mercury were flat over the entire cross-section of the tube. But the dome-shaped top gives slightly less surface area to the entire mass of mercury. Again the two effects combine to minimize the total potential energy. Such a surface shape is known as a convex meniscus.

We consider the surface area of the entire mass of mercury, including the part of the surface that is in contact with the glass, because mercury does not adhere to glass at all. So the surface tension of the mercury acts over its entire surface area, including where it is in contact with the glass. If instead of glass, the tube was made out of copper, the situation would be very different. Mercury aggressively adheres to copper. So in a copper tube, the level of mercury at the center of the tube will be lower than at the edges (that is, it would be a concave meniscus). In a situation where the liquid adheres to the walls of its container, we consider the part of the fluid's surface area that is in contact with the container to have negative surface tension. The fluid then works to maximize the contact surface area. So in this case increasing the area in contact with the container decreases rather than increases the potential energy. That decrease is enough to compensate for the increased potential energy associated with lifting the fluid near the walls of the container.

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon known as capillary action. The height to which the column is lifted is given by Jurin's law:

$$h = \frac {2\gamma_\mathrm{la} \cos\theta}{\rho g r}$$

where

 * $θ$ is the height the liquid is lifted,
 * $γ_{la}$ is the liquid–air surface tension,
 * $θ$ is the density of the liquid,
 * $h$ is the radius of the capillary,
 * $ρ$ is the acceleration due to gravity,
 * $r$ is the angle of contact described above. If $g$ is greater than 90°, as with mercury in a glass container, the liquid will be depressed rather than lifted.

Puddles on a surface

Pouring mercury onto a horizontal flat sheet of glass results in a puddle that has a perceptible thickness. The puddle will spread out only to the point where it is a little under half a centimetre thick, and no thinner. Again this is due to the action of mercury's strong surface tension. The liquid mass flattens out because that brings as much of the mercury to as low a level as possible, but the surface tension, at the same time, is acting to reduce the total surface area. The result of the compromise is a puddle of a nearly fixed thickness.

The same surface tension demonstration can be done with water, lime water or even saline, but only on a surface made of a substance to which water does not adhere. Wax is such a substance. Water poured onto a smooth, flat, horizontal wax surface, say a waxed sheet of glass, will behave similarly to the mercury poured onto glass.

The thickness of a puddle of liquid on a surface whose contact angle is 180° is given by:

$$h = 2 \sqrt{\frac{\gamma} {g\rho}}$$

where

 * $θ$ is the depth of the puddle in centimeters or meters.
 * $θ$ is the surface tension of the liquid in dynes per centimeter or newtons per meter.
 * $h$ is the acceleration due to gravity and is equal to 980 cm/s2 or 9.8 m/s2
 * $γ$ is the density of the liquid in grams per cubic centimeter or kilograms per cubic meter

In reality, the thicknesses of the puddles will be slightly less than what is predicted by the above formula because very few surfaces have a contact angle of 180° with any liquid. When the contact angle is less than 180°, the thickness is given by:

$$h = \sqrt{\frac{2\gamma_\mathrm{la}\left( 1 - \cos \theta \right)} {g\rho}}.$$

For mercury on glass, $γ_{sa}$ = 487 dyn/cm, $γ_{ls} − γ_{sa}$ = 13.5 g/cm3 and $g$ = 140°, which gives $γ_{la}$ = 0.36 cm. For water on paraffin at 25 °C, $ρ$ = 72 dyn/cm, $θ$ = 1.0 g/cm3, and $γ$ = 107° which gives $γ_{la}$ = 0.44 cm.

The formula also predicts that when the contact angle is 0°, the liquid will spread out into a micro-thin layer over the surface. Such a surface is said to be fully wettable by the liquid.

The breakup of streams into drops

In day-to-day life all of us observe that a stream of water emerging from a faucet will break up into droplets, no matter how smoothly the stream is emitted from the faucet. This is due to a phenomenon called the Plateau–Rayleigh instability, which is entirely a consequence of the effects of surface tension.

The explanation of this instability begins with the existence of tiny perturbations in the stream. These are always present, no matter how smooth the stream is. If the perturbations are resolved into sinusoidal components, we find that some components grow with time while others decay with time. Among those that grow with time, some grow at faster rates than others. Whether a component decays or grows, and how fast it grows is entirely a function of its wave number (a measure of how many peaks and troughs per centimeter) and the radii of the original cylindrical stream.

Thermodynamic theories of surface tension
J.W. Gibbs developed the thermodynamic theory of capillarity based on the idea of surfaces of discontinuity. Gibbs considered the case of a sharp mathematical surface being placed somewhere within the microscopically fuzzy physical interface that exists between two homogeneous substances. Realizing that the exact choice of the surface's location was somewhat arbitrary, he left it flexible. Since the interface exists in thermal and chemical equilibrium with the substances around it (having temperature $ρ$ and chemical potentials $γ_{Hg}$), Gibbs considered the case where the surface may have excess energy, excess entropy, and excess particles, finding the natural free energy function in this case to be $$U - TS - \mu_1 N_1 - \mu_2 N_2 \cdots $$, a quantity later named as the grand potential and given the symbol $$\Omega$$.

Considering a given subvolume $$V$$ containing a surface of discontinuity, the volume is divided by the mathematical surface into two parts A and B, with volumes $$V_\text{A}$$ and $$V_\text{B}$$, with $$V = V_\text{A} + V_\text{B}$$ exactly. Now, if the two parts A and B were homogeneous fluids (with pressures $$p_\text{A}$$, $$p_\text{B}$$) and remained perfectly homogeneous right up to the mathematical boundary, without any surface effects, the total grand potential of this volume would be simply $$-p_\text{A} V_\text{A} - p_\text{B} V_\text{B}$$. The surface effects of interest are a modification to this, and they can be all collected into a surface free energy term $$\Omega_\text{S}$$ so the total grand potential of the volume becomes: $$\Omega = -p_\text{A} V_\text{A} - p_\text{B} V_\text{B} + \Omega_\text{S}.$$

For sufficiently macroscopic and gently curved surfaces, the surface free energy must simply be proportional to the surface area: $$\Omega_\text{S} = \gamma A,$$ for surface tension $$\gamma$$ and surface area $$A$$.

As stated above, this implies the mechanical work needed to increase a surface area A is $ρ_{Hg}$, assuming the volumes on each side do not change. Thermodynamics requires that for systems held at constant chemical potential and temperature, all spontaneous changes of state are accompanied by a decrease in this free energy $$\Omega$$, that is, an increase in total entropy taking into account the possible movement of energy and particles from the surface into the surrounding fluids. From this it is easy to understand why decreasing the surface area of a mass of liquid is always spontaneous, provided it is not coupled to any other energy changes. It follows that in order to increase surface area, a certain amount of energy must be added.

Gibbs and other scientists have wrestled with the arbitrariness in the exact microscopic placement of the surface. For microscopic surfaces with very tight curvatures, it is not correct to assume the surface tension is independent of size, and topics like the Tolman length come into play. For a macroscopic-sized surface (and planar surfaces), the surface placement does not have a significant effect on $θ$; however, it does have a very strong effect on the values of the surface entropy, surface excess mass densities, and surface internal energy, which are the partial derivatives of the surface tension function $$\gamma(T, \mu_1, \mu_2, \cdots)$$.

Gibbs emphasized that for solids, the surface free energy may be completely different from surface stress (what he called surface tension): the surface free energy is the work required to form the surface, while surface stress is the work required to stretch the surface. In the case of a two-fluid interface, there is no distinction between forming and stretching because the fluids and the surface completely replenish their nature when the surface is stretched. For a solid, stretching the surface, even elastically, results in a fundamentally changed surface. Further, the surface stress on a solid is a directional quantity (a stress tensor) while surface energy is scalar.

Fifteen years after Gibbs, J.D. van der Waals developed the theory of capillarity effects based on the hypothesis of a continuous variation of density. He added to the energy density the term $$c (\nabla \rho)^2,$$ where c is the capillarity coefficient and ρ is the density. For the multiphase equilibria, the results of the van der Waals approach practically coincide with the Gibbs formulae, but for modelling of the dynamics of phase transitions the van der Waals approach is much more convenient. The van der Waals capillarity energy is now widely used in the phase field models of multiphase flows. Such terms are also discovered in the dynamics of non-equilibrium gases.

Thermodynamics of bubbles
The pressure inside an ideal spherical bubble can be derived from thermodynamic free energy considerations. The above free energy can be written as: $$\Omega = -\Delta P V_\text{A} - p_\text{B} V + \gamma A$$ where $$\Delta P = p_\text{A} - p_\text{B}$$ is the pressure difference between the inside (A) and outside (B) of the bubble, and $$V_\text{A}$$ is the bubble volume. In equilibrium, $h_{Hg}$, and so, $$\Delta P\,dV_\text{A} = \gamma\, dA.$$

For a spherical bubble, the volume and surface area are given simply by $$V_\text{A} = \tfrac43\pi R^3 \quad\rightarrow\quad dV_\text{A} = 4\pi R^2 \,dR,$$ and $$A = 4\pi R^2 \quad\rightarrow\quad dA = 8\pi R\, dR.$$

Substituting these relations into the previous expression, we find $$\Delta P = \frac{2}{R}\gamma,$$ which is equivalent to the Young–Laplace equation when $h_{H_{2}O}$.

Influence of temperature

Surface tension is dependent on temperature. For that reason, when a value is given for the surface tension of an interface, temperature must be explicitly stated. The general trend is that surface tension decreases with the increase of temperature, reaching a value of 0 at the critical temperature. For further details see Eötvös rule. There are only empirical equations to relate surface tension and temperature:
 * Eötvös:  $$\gamma V^{2/3} = k(T_\mathrm{C}-T) .$$ Here $T$ is the molar volume of a substance, $μ_{i}$ is the critical temperature and $γ$ is a constant valid for almost all substances. A typical value is $V$ = $k$. For water one can further use $k$ = 18 ml/mol and $dW = γ dA$ = 647 K (374 °C). A variant on Eötvös is described by Ramay and Shields: $$\gamma V^{2/3} = k \left(T_\mathrm{C} - T - 6\,\mathrm{K}\right)$$ where the temperature offset of 6 K provides the formula with a better fit to reality at lower temperatures.
 * Guggenheim–Katayama: $$\gamma = \gamma^\circ \left( 1-\frac{T}{T_\mathrm C} \right)^n $$ $dΩ = 0$ is a constant for each liquid and $2.1 J K^{−1} mol^{−2⁄3}$ is an empirical factor, whose value is $V$ for organic liquids. This equation was also proposed by van der Waals, who further proposed that $R_{x} = R_{y}$ could be given by the expression $$K_2 T^{1/3}_\mathrm{C} P^{2/3}_\mathrm{C},$$ where $T_{C}$ is a universal constant for all liquids, and $T_{C}$ is the critical pressure of the liquid (although later experiments found $γ°$ to vary to some degree from one liquid to another).

Both Guggenheim–Katayama and Eötvös take into account the fact that surface tension reaches 0 at the critical temperature, whereas Ramay and Shields fails to match reality at this endpoint.

Influence of solute concentration
Solutes can have different effects on surface tension depending on the nature of the surface and the solute:
 * Little or no effect, for example sugar at water|air, most organic compounds at oil/air
 * Increase surface tension, most inorganic salts at water|air
 * Non-monotonic change, most inorganic acids at water|air
 * Decrease surface tension progressively, as with most amphiphiles, e.g., alcohols at water|air
 * Decrease surface tension until certain critical concentration, and no effect afterwards: surfactants that form micelles

What complicates the effect is that a solute can exist in a different concentration at the surface of a solvent than in its bulk. This difference varies from one solute–solvent combination to another.

Gibbs isotherm states that: $$\Gamma = - \frac{1}{RT} \left( \frac{\partial \gamma}{\partial \ln C} \right)_{T,P} $$

 * $n$ is known as surface concentration, it represents excess of solute per unit area of the surface over what would be present if the bulk concentration prevailed all the way to the surface. It has units of mol/m2
 * $11⁄9$ is the concentration of the substance in the bulk solution.
 * $Γ$ is the gas constant and $C$ the temperature

Certain assumptions are taken in its deduction, therefore Gibbs isotherm can only be applied to ideal (very dilute) solutions with two components.

Influence of particle size on vapor pressure
The Clausius–Clapeyron relation leads to another equation also attributed to Kelvin, as the Kelvin equation. It explains why, because of surface tension, the vapor pressure for small droplets of liquid in suspension is greater than standard vapor pressure of that same liquid when the interface is flat. That is to say that when a liquid is forming small droplets, the equilibrium concentration of its vapor in its surroundings is greater. This arises because the pressure inside the droplet is greater than outside.

$$P_\mathrm{v}^\mathrm{fog}=P_\mathrm{v}^\circ e^{V 2\gamma/(RT r_\mathrm{k})}$$

 * $γ°$ is the standard vapor pressure for that liquid at that temperature and pressure.
 * $R$ is the molar volume.
 * $T$ is the gas constant
 * $K_{2}$ is the Kelvin radius, the radius of the droplets.

The effect explains supersaturation of vapors. In the absence of nucleation sites, tiny droplets must form before they can evolve into larger droplets. This requires a vapor pressure many times the vapor pressure at the phase transition point.

This equation is also used in catalyst chemistry to assess mesoporosity for solids.

The effect can be viewed in terms of the average number of molecular neighbors of surface molecules (see diagram).

The table shows some calculated values of this effect for water at different drop sizes:

The effect becomes clear for very small drop sizes, as a drop of 1 nm radius has about 100 molecules inside, which is a quantity small enough to require a quantum mechanics analysis.

Methods of measurement
Because surface tension manifests itself in various effects, it offers a number of paths to its measurement. Which method is optimal depends upon the nature of the liquid being measured, the conditions under which its tension is to be measured, and the stability of its surface when it is deformed. An instrument that measures surface tension is called tensiometer.

 * Du Noüy ring method: The traditional method used to measure surface or interfacial tension. Wetting properties of the surface or interface have little influence on this measuring technique. Maximum pull exerted on the ring by the surface is measured.
 * Wilhelmy plate method: A universal method especially suited to check surface tension over long time intervals. A vertical plate of known perimeter is attached to a balance, and the force due to wetting is measured.
 * Spinning drop method: This technique is ideal for measuring low interfacial tensions. The diameter of a drop within a heavy phase is measured while both are rotated.
 * Pendant drop method: Surface and interfacial tension can be measured by this technique, even at elevated temperatures and pressures. Geometry of a drop is analyzed optically. For pendant drops the maximum diameter and the ratio between this parameter and the diameter at the distance of the maximum diameter from the drop apex has been used to evaluate the size and shape parameters in order to determine surface tension.
 * Bubble pressure method (Jaeger's method): A measurement technique for determining surface tension at short surface ages. Maximum pressure of each bubble is measured.
 * Drop volume method: A method for determining interfacial tension as a function of interface age. Liquid of one density is pumped into a second liquid of a different density and time between drops produced is measured.
 * Capillary rise method: The end of a capillary is immersed into the solution. The height at which the solution reaches inside the capillary is related to the surface tension by the equation discussed above.
 * Stalagmometric method: A method of weighting and reading a drop of liquid.
 * Sessile drop method: A method for determining surface tension and density by placing a drop on a substrate and measuring the contact angle (see Sessile drop technique).
 * Du Noüy–Padday method: A minimized version of Du Noüy method uses a small diameter metal needle instead of a ring, in combination with a high sensitivity microbalance to record maximum pull. The advantage of this method is that very small sample volumes (down to few tens of microliters) can be measured with very high precision, without the need to correct for buoyancy (for a needle or rather, rod, with proper geometry). Further, the measurement can be performed very quickly, minimally in about 20 seconds.
 * Vibrational frequency of levitated drops: The natural frequency of vibrational oscillations of magnetically levitated drops has been used to measure the surface tension of superfluid 4He. This value is estimated to be 0.375 dyn/cm at $V$ = 0 K.
 * Resonant oscillations of spherical and hemispherical liquid drop: The technique is based on measuring the resonant frequency of spherical and hemispherical pendant droplets driven in oscillations by a modulated electric field. The surface tension and viscosity can be evaluated from the obtained resonant curves.
 * Drop-bounce method: This method is based on aerodynamic levitation with a split-able nozzle design. After dropping a stably levitated droplet onto a platform, the sample deforms and bounces back, oscillating in mid-air as it tries to minimize its surface area. Through this oscillation behavior, the liquid's surface tension and viscosity can be measured.

Surface tension of water
The surface tension of pure liquid water in contact with its vapor has been given by IAPWS as

$$\gamma_\text{w} = 235.8\left(1 - \frac{T}{T_\text{C}}\right)^{1.256} \left[1 - 0.625\left(1 - \frac{T}{T_\text{C}}\right)\right]~\text{mN/m},$$

where both $R$ and the critical temperature $P_{C}$ = 647.096 K are expressed in kelvins. The region of validity the entire vapor–liquid saturation curve, from the triple point (0.01 °C) to the critical point. It also provides reasonable results when extrapolated to metastable (supercooled) conditions, down to at least −25 °C. This formulation was originally adopted by IAPWS in 1976 and was adjusted in 1994 to conform to the International Temperature Scale of 1990.

The uncertainty of this formulation is given over the full range of temperature by IAPWS. For temperatures below 100 °C, the uncertainty is ±0.5%.

Surface tension of seawater
Nayar et al. published reference data for the surface tension of seawater over the salinity range of 20 ≤ $T$ ≤ 131 g/kg and a temperature range of 1 ≤ $γ$ ≤ 92 °C at atmospheric pressure. The range of temperature and salinity encompasses both the oceanographic range and the range of conditions encountered in thermal desalination technologies. The uncertainty of the measurements varied from 0.18 to 0.37 mN/m with the average uncertainty being 0.22 mN/m.

Nayar et al. correlated the data with the following equation $$ \gamma_\mathrm{sw} = \gamma_\mathrm{w} \left( 1+ 3.766\times 10^{-4} S +2.347\times 10^{-6} S t\right)$$ where $K_{2}$ is the surface tension of seawater in mN/m, $P_{v}°$ is the surface tension of water in mN/m, $T$ is the reference salinity in g/kg, and $S$ is temperature in degrees Celsius. The average absolute percentage deviation between measurements and the correlation was 0.19% while the maximum deviation is 0.60%.

The International Association for the Properties of Water and Steam (IAPWS) has adopted this correlation as an international standard guideline.

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

title: Surface tension


text:
Embleton, Northumberland

Embleton is a village and civil parish in the English county of Northumberland. Besides the village of Embleton itself, the civil parish includes the settlement of Christon Bank, situated about a mile to the west.

Embleton village has a main street with one shop. There is a small green with the village pump on it, out of use now but at one time the source of the water supply. The village is about 0.5 mi from Embleton Bay. The sandy beach is backed by dunes where a variety of flowers bloom: bluebells, cowslips, burnet roses and bloody cranesbill, amongst others. Also near the beach is Embleton's 18-hole Dunstanburgh Castle Golf Course which opened in 1900 and was updated in 1922.

Christon Bank lies on the East Coast Main Line railway, and until 1965 was the site of a station.

Beyond the bounds of the parish, Dunstanburgh Castle stands at the southern end of Embleton Bay. Close by, to the south, is the fishing village of Craster.

Landmarks
Close by the church is Embleton Tower, a pele tower which was the vicarage until 1974.

The Creighton Memorial Hall is said to be the largest village hall in the county and is named after Mandell Creighton, who was vicar 1875–1884 and later became Bishop of London.

One road is named after the Embleton-born W. T. Stead, a journalist and social campaigner who died in the sinking of the Titanic.

Religious sites
The Church of the Holy Trinity is large with several interesting features and is historically connected with Merton College, Oxford. Creighton, the vicar, had a poor opinion of the villagers: "'In many ways the moral standard of the village was very low, and it was a difficult place to improve. There was no resident squire, the chief employers of labour were on much the same level of cultivation as those they employed, and in some cases owned the public-houses and paid the wages there.'"

Notable people

 * Robert de Emeldon (died 1355), Lord Treasurer of Ireland, and a personal friend of King Edward III, was born in Embleton in the thirteenth century.
 * Richard de Emeldon, who was Robert's cousin, and was later five times mayor of Newcastle upon Tyne and one of its leading citizens, was also born here.
 * W. T. Stead, journalist and social campaigner.

title: Embleton, Northumberland


text:
Wikipedia:Lists of common misspellings

The lists of common spelling mistakes linked below are used to correct typographical errors throughout Wikipedia. Each entry lists a typo, followed by the correct spelling in parentheses; clicking on the typo will search for it throughout Wikipedia. See Typo for information on and coordination of spellchecking work.

Note that not all occurrences of these spellings will be misspellings: if they are in song titles, for instance, they must be left as the song writer intended (but it is worth checking back to sources); if they are in transliterations such as "Tao Te Ching" or in pieces of text in languages other than English then they may also be correct. The guiding rule should be to include words if they are more likely to be incorrect spellings than correct spellings even if it means that occasionally there will be false positives.

Keep in mind some words could be corrected to multiple different possibilities and some are names of brands, songs, or products. These are just the most common. Please don't delete a misspelling from this page just because it causes false positives. A better way of getting rid of false positives is to comment them out. This can be done by changing the initial asterisk (*) on a line into a colon. Doing this will make it easy to put potential spelling errors back if you want to re-run a check for them at some future time.

A misspelling should occur in Wikipedia at least once a year to be considered "common" and therefore have a place in this list. If you know a certain misspelling has not occurred in the past year, you should delete it from the list to reduce clutter and make the lists easier to use.

When adding a misspelling, it is a good idea to also add all grammatical variants of the word at the same time. Alphabetize according to the misspelling.

Note that spellings sometimes vary between varieties of English, notably between American English and Commonwealth English. Since Wikipedia accepts all variant spellings, please refer to American and British English spelling differences.

Many users have found that using Google to search for misspelled words is more efficient than Wikipedia, such as this Google search.

Alternatively you can search a recent database dump for typos in a few minutes using User:Bluemoose/DataBaseSearchTool. This works best when the database is not very old.

title: Wikipedia:Lists of common misspellings


text:
Sanitization

Sanitization is the cleaning and disinfection of an area or an item. Sanitizing involves the use of heat or chemicals to reduce the number of microorganisms to safe levels. It can also refer to:

 * Data sanitization, preventing recovery of erased information
 * Sanitization (classified information), in government/military contexts
 * Censorship, preventing publication of information
 * HTML sanitization, removing potentially unsafe constructs from web pages
 * Sanitation harvest, or sanitation cutting, removing plants to counter insects or diseases

title: Sanitization


text:
Lulu (opera)

Lulu (composed from 1929 to 1935, premièred incomplete in 1937 and complete in 1979) is an opera in three acts by Alban Berg. Berg adapted the libretto from Frank Wedekind's two Lulu plays, Erdgeist (Earth Spirit, 1895) and Die Büchse der Pandora (Pandora's Box, 1904).

The opera tells the story of a mysterious young woman known as Lulu, who follows a downward spiral from a well-kept mistress in Vienna to a street prostitute in London, while being both a victim and a purveyor of destruction. It explores the idea of the femme fatale and the duality between her feminine and masculine qualities.

Berg died before completing the third and final act, and in the following decades the opera was typically performed incomplete. Since the 1979 publication of the version including Friedrich Cerha's orchestration of the act 3 sketches, it has become standard. Lulu is especially notable for using serialism at a time that was particularly inhospitable to it. Theodor W. Adorno wrote, "The opera Lulu is one of those works that reveals the extent of its quality the longer and more deeply one immerses oneself in it."

Composition
Berg did not begin work on Lulu until after he had completed his other opera, Wozzeck, in 1929. Thanks to Wozzeck's success Berg had economic security that enabled him to embark on a second opera. But life in the musical world was becoming increasingly difficult in the 1930s in both Vienna and Germany due to rising antisemitism and the Nazi cultural ideology that denounced the music of Berg, Webern, and others. Even to have an association with someone Jewish could lead to denunciation, and Berg had studied with the Jewish composer Arnold Schoenberg. Wozzeck's success was short-lived, as theatre after theatre succumbed to political pressure and refused to produce it, Erich Kleiber's 30 November 1932 production being the last, while sets and scenery were systematically destroyed. Wozzeck was also banned in the Soviet Union as "bourgeois". Berg found that opportunities for his work to be performed in Germany were growing scarce, and in September 1935 his music was proscribed as Entartete Musik (degenerate music) under the label Kulturbolschewismus (Cultural Bolshevism).

Despite these conditions, Berg worked on Lulu in seclusion at his lodge, the Waldhaus, in Carinthia. In the spring of 1934 he learned from Wilhelm Furtwängler that production of Lulu in Berlin would be impossible with the current cultural and political situation. It was at this point that he set the work on the opera aside to prepare a concert suite, in the event that the opera could never be performed, and also considered expanding it into a Lulu Symphony. This was his Symphonische Stücke aus der Oper "Lulu" (Lulu Suite) for soprano and orchestra. Kleiber performed the piece at the Berlin State Opera on 30 November, and despite an enthusiastic reception by some sections of the audience, condemnation by the authorities prompted Kleiber's resignation four days later and departure from Germany. The reaction of periodicals such as Die Musik and Zeitschrift für Musik was particularly hostile. On December 7, Goebbels made a speech equating atonality with "the Jewish intellectual infection," while the January 1935 issue of Die Musik suggested that any reviewer who had written anything favourable about the suite should be dismissed.

In January 1935, the Russian-born American violinist Louis Krasner, who had championed Berg's work in the United States, approached Berg to commission a violin concerto. Berg was reluctant to set aside Lulu for this, but the money ($1,500) was welcomed, as Berg was in financial difficulties, financially and artistically ruined by the Reichskulturkammer (Nazi cultural committee). At first there was only a tentative agreement, but at the end of March he told Krasner he would compose it and had started some preliminary work. But it was the tragic death of 18-year-old Manon Gropius (the daughter of Walter Gropius and Alma Mahler, whom the Bergs treated as their own daughter) on April 22 that prompted Berg to set aside Lulu for the concerto, which he dedicated to her. The concerto was completed swiftly, between April and August of that year, but the time he spent on it prevented him from completing the opera before his sudden death on December 24.

The following portions of the third and final act were fully scored: the first 268 bars; the instrumental interlude between scenes 1 and 2; and the finale of the opera, beginning with the monologue of Countess Geschwitz. (The last two of these passages comprise the fourth and fifth movements of the Lulu Suite that Berg compiled for concert performance.) The rest of the work remained in short score with indications of instrumentation for much of it. Berg heard the Symphonic Pieces in a BBC radio broadcast from the Queen's Hall, London, on 20 March 1935, conducted by Sir Adrian Boult and produced by Edward Clark. It was the first time he had ever heard any of the music of Lulu. He did not hear these excerpts performed live until a concert in Vienna on December 11, a fortnight before his death.

Roles
Berg specified that a number of cast members should take more than one role. Thus, the singers of Lulu's three husbands return as her clients while a prostitute: one performer each appears as the Doctor and the Professor, as the Painter and the Negro, and as Dr. Schön and Jack the Ripper. Other specified combinations are one mezzo-soprano as the Dresser, the Schoolboy, and the Groom; one tenor as the Prince, the Manservant, and the Marquis; one bass as the Animal Tamer and the Athlete, and another bass as the Theatre Manager and the Banker. Another aspect of the cast list that differs from Wedekind's original is that all characters in the two plays receive a proper name. Berg removed these names except for the five leading roles of Lulu, Schön, Alwa, Geschwitz and Schigolch. Some of Wedekind's other names have sometimes been applied to Berg's characters; for example, the Athlete is often called "Rodrigo Quast", but this name is not in the score.

Synopsis
It is the late 19th century in an unnamed metropolis (usually taken to be Vienna). Lulu is married to Dr Goll, a physician. Lulu, who goes by the name Nelly, is having her portrait painted by Walter Schwarz, an artist who is in love with her. Dr Ludwig Schön, a newspaper editor and widower, and his son Alwa, a composer, are briefly present. As the artist pursues Lulu, they are surprised by her husband, who suffers a fatal stroke. Lulu marries Schwarz, and they appear to prosper with Schön's help. But Lulu is troubled when she discovers Schön has become engaged. The latter visits her and reveals how he has taken her from the street and raised her, but they have been in a relationship. He says that Schigolch, an elderly beggar, is her father. When Schön tells Schwarz about Lulu's past, he is horrified and he kills himself. Schön then puts Lulu on the stage, where she creates a scene over his fiancée and compels him to write a letter breaking off the engagement. Lulu marries Schön, who is jealous of her admirers, of which there are many, including the Countess Geschwitz and Alwa, on whom he eavesdrops, learning that Lulu poisoned his first wife. He gives her a gun and tells her to shoot herself. Instead she kills him, for which she is tried and imprisoned, but she contrives to escape after changing places with Countess Geschwitz. Alwa and Lulu flee to Paris, from where they once again flee, destitute, to London, where Lulu is obliged to work the streets, but brings home Jack the Ripper, who murders her.

(Stage directions and musical notes in italics)

Prologue
The animal tamer appears from behind the curtain, whip in hand

A circus animal tamer welcomes the audience, Hereinspaziert in die Menagerie (Come on in to the menagerie) and describes the various animals in his menagerie, such as tigers, bears and monkeys. He lifts the curtain, and calls for the snake to be brought on. A stage hand carries out Lulu (Lulu motif) dressed as Pierrot, while the animal tamer describes her in biblical terms as the source of evil, fated to murder, Sie ward geschaffen, Unheil anzustiften ... Zu morden – ohne dass es einer spürt. (She was created, evil to instigate ... to murder – without leaving any clues), and orders her off, while inviting the audience to see what will unfold. He then retires behind the curtain, which rises on scene 1.

Act 1
''Scene 1: A spacious but shabby artist's studio. A podium, folding screen, easel with unfinished portrait of Lulu, divan with tiger skin, step ladder and sculpture. Lulu is standing on the podium, posing as Pierrot, holding a shepherd's crook''

The Painter is painting Lulu's portrait. Dr. Schön is watching, and is joined by his son, Alwa. He excuses himself because he has to go to a rehearsal, and he and Schön leave. Alone with Lulu, the Painter makes passes at her. She rejects him initially, as he pursues her round the studio (canon, beginning with Lulu motif: Gnädige Frau ... Frau Medizinalrat – Wer hätte das gedacht!; Dearest Lady ... Frau Medizinalrat – Who would have imagined it!), during which the ladder falls and the statue breaks. At one stage, he calls her Eva. She explains that she is expecting her husband. Eventually she succumbs to his advances. The artist has locked the studio door, and when Dr. Goll arrives, there is consternation. Goll breaks the door down, and on finding Lulu and the artist together, dies of a stroke. At first they do not realise her husband is dead and call a doctor. Lulu is alone with her husband's corpse (canzonetta: Auf einmal springt er auf; In a moment he will spring to life). When she accepts that he is dead, she reflects that she is now rich, to the artist's horror, Jetzt bin ich reich – Es ist grauenerregend (Now I am rich – How revolting). They sing a duet in which he questions her beliefs, and the answer is always the same, ''Eine Frage: Kannst Du die Wahrheit sagen? – Ich weiss es nicht'' (A question: Can you tell the truth? – I don't know). While Lulu is changing into her street clothes, the artist addresses her husband's corpse (arioso: Ich möchte tauschen mit Dir, Du Toter! Ich geb' sie Dir zurück; I would trade places with you, dead man. I would give her back to you).

Interlude

''Scene 2: An elegant drawing room in Lulu's apartment, the studio beyond, her finished portrait on the wall. Lulu, on a chaise-longue is gazing into her hand mirror''

The artist enters with the mail, again addressing her as Eve. In the mail he learns he has sold another painting of her, and mentions he has sold a number of paintings since they were married. She places one, a letter from Countess Corticelli, in her bosom. Another brings notice of Schön's engagement, which seems to trouble her. They sing a love duettino, Ich finde, Du siehst heute reizend aus – Ich komme aus dem Bad (I find you so beautiful today – I have just come from my bath). She is visited by Schigolch, who remarks of the artist (chamber music, Den hab'ich mir auch ganz anders vorgestellt; I thought he would be different than he is). Schigolch is an asthmatic beggar who seems to have been featured in her past in an unspecified way, he asks for money which she gives him, and when he calls her "Lulu", she says she has not been called that in a long time. As she is showing him out, Schön arrives (sonata movement) and recognises him, referring to him as Lulu's father, which she does not deny. Schön asks Lulu to stay out of his life from now on, since he is engaged and it would be scandalous for them to see each other socially, but she says she belongs only to him (coda: love theme. Wenn ich einem Menschen auf dieser Welt angehöre, gehöre ich Ihnen; If I belong to any man in this world, I belong to you). Their discussion reveals that all the good fortune Lulu has experienced comes from Schön's interventions, and that they have been meeting regularly. The exchange becomes increasingly agitated, until the return of the artist, who asks what has transpired. Lulu leaves in a huff, while Schön implies that he has had a longstanding affair with Lulu, since she was 12, and rescued her from the streets as a flower seller. The artist becomes increasingly distressed as he learns how little he knows about Lulu, not even her name, which appears to be different for every lover. Schön informs him about Schigolch being her father, and that after the death of his wife, Lulu appeared to be trying to take her place, so that he arranged to marry her off to Goll. Increasingly Schön urges the artist to confront Lulu, which he agrees to, leaving the room, but a terrible groan is heard offstage and Schön discovers the artist has locked the door. Lulu returns and they discuss what to do next, but are interrupted by the arrival of Alwa, who announces that revolution has broken out on the streets of Paris, which is causing consternation at the newspaper office. Lulu brings a hatchet, and they force open the door to find the artist dead. From a partly audible telephone conversation Schön has, which he implies is with the police, it is revealed that the artist cut his throat. Lulu, once again, is unmoved by the tragedy, while Schön and Alwa hope that the political news will sweep aside the scandal. When Schön calls her Ungeheuer! (Monster!), Lulu hints that she and Schön will be married after all (Lulu motif: Sie heiraten mich ja doch!; You will marry me after all). The curtain falls as the doorbell rings, which they believe is the police.

Interlude (Love theme)

Scene 3: In Lulu's dressing room in the theatre, a folding screen upstage, a poster of Lulu's portrait is seen

Lulu is changing behind the screen, Alwa is pouring champagne. The two discuss whether Schön will come that night, and a Prince who wants to take her to Africa. Alwa recalls his mother's death, and how he had hoped that Lulu would replace her, while Lulu observes that his father put her on the stage in the hope that someone rich would marry her and take her off his hands. Lulu emerges in a ballet dress, Alwa appears smitten and they drink. At the sound of a bell, Lulu leaves to take the stage. Alwa watches her leave and then contemplates writing an opera based on her life, but as he draws out the scenes he concludes that they are too gruesome. Applause can be heard, and the Prince enters and reveals his wish to marry Lulu. It is apparent her sudden fame is due to favourable reviews published by Schön. Suddenly the bell starts ringing incessantly and an uproar is heard offstage. Alwa appears startled and Lulu enters suddenly, flinging herself in a chair, followed by the dresser and theatre manager, who explain that she fainted. She implies it was because she saw Schön with his fiancée, Mit seiner Braut! (With his bride!) whereupon Schön himself enters and Lulu refuses to continue because his fiancée is in the audience. All try to persuade Lulu to return to the stage, in a sextet Das hättest Du Dir besser erspart! (This you could have spared yourself!), then Schön dismisses the company leaving Lulu and himself alone. He admonishes her, Wie kannst Du die Szene gegen mich ausspielen? (how can you play this scene to get me?), they argue and she taunts him with the Prince and his inability to break off their relationship. It is apparent that he is torn between the two women, and she begins to exploit his weakness, compelling him to write a letter that she dictates, breaking off the engagement (Letter duet: Sehr geehrtes Fräulein …; Most respected Fräulein ...). Schön expresses feelings of impending doom, Jetzt – kommt – die Hinrichtung... (Now – comes – the execution) and Lulu, having achieved her purpose, prepares to return to the stage

Act 2
''Scene 1: In Lulu's house, a magnificent German Renaissance style room with a gallery and staircase. A folding Chinese screen in front of the fireplace. Again, Lulu's portrait can be seen, this time on an easel. Lulu is in an armchair in a morning gown, Countess Geschwitz on an ottoman, in masculine clothes, her face veiled. Dr. Schön is standing.''

Countess Geschwitz, an admirer of Lulu, who is now married to Schön, is visiting her to invite her to a ball. She has brought flowers and, complimenting her on her portrait, wishes to paint her herself. Schön is clearly uncomfortable and Lulu shows Geschwitz out. Schön, left alone, appears disturbed and jealous and speaks of madness, producing a revolver, Der Irrsinn hat sich meiner Vernunft schon bemächtigt (Madness has conquered my reason already). On her return Lulu tries to convince Schön to take the afternoon off and go for a drive with her (cavatina: Könntest Du Dich für heute Nachmittag nicht freimachen?; Can't you make this afternoon free?), but he points out that he is due at the stock exchange. Lulu starts to lavish affection on Schön, and they go into the bedroom, whereupon Geschwitz reenters the house and hides behind the screen. Schigolch and two other admirers, the athlete, who is carrying the struggling schoolboy (played by a woman, i.e. a travesti role), all enter. Schigolch says that he also lives in the house and that they have paid him to leave them with Lulu, who then reappears. She is dressed for the ball, décolleté with orchids between her breasts. She leans in to the schoolboy, urging him to smell the flowers. As she leaves they begin to discuss the Prince, who has gone abroad (canon: Er hat sie nämlich ursprünglich heiraten wollen; She was the one he originally wanted to marry) and Schigolch says that he too wishes to marry Lulu, Wer hat sie nicht ursprünglich heiraten wollen! (Who has not always wanted to marry her!), a sentiment with which they all agree, as he explains that Lulu is not his daughter.

When Lulu returns, she also agrees that she never had a father. They discuss Schön, who has left for the exchange, and what Lulu calls his Verfolgungswahn (paranoia), but a servant announces his return and the athlete and schoolboy also hide while Schigolch starts to leave. However, it is Alwa who enters, not his father, and she orders refreshments as they sit and start to talk and flirt. Schön enters unnoticed, sees his son, and he too hides. Their conversation becomes more intense and Alwa declares his love for Lulu, Liebst Du mich Mignon? (Do you love me, Mignon?), burying his head in her lap. At this point, Lulu confesses to Alwa that she poisoned his mother. Meanwhile, unnoticed by the couple, Schön sees the athlete and draws his revolver, but the athlete indicates it is Alwa he should kill, and hides again. Lulu notices them and announces his presence.

Schön reveals himself, once again announcing revolution in Paris, newspaper in hand, and drags Alwa away. The athlete briefly reappears, pursued by Schön, revolver in hand. Schön, believing the athlete escaped, begins to harangue Lulu (aria in five strophes: Du Kreatur, die mich durch den Strassenkot zum Martertode schleift!; You wretch, that drags me through the faeces in the streets to martyrdom!), handing the revolver to Lulu, who appears unperturbed, and implying she should kill herself before he kills Alwa. She points the revolver at him, but instead she fires at the ceiling. Increasingly agitated, Schön seizes the revolver and begins to search the house for Lulu's lovers, but finds only Geschwitz, whom he locks in another room. Again he gives Lulu the gun, implying her suicide will save his reputation from being considered a cuckold, meine Stirn zu verzieren (my head to decorate) – i.e. with horns. Lulu sings the Lied der Lulu (Wenn sich die Menschen um meinetwillen umgebracht haben; When men have killed for my sake) in which she asks for a divorce, saying she can only be als was ich bin (what I am). Schön only replies that he will murder her and make it look like suicide, forcing her to her knees and pointing the gun at her while holding it in her hand (5th strophe: Nieder, Mörderin! In die Knie!; Get down, murderess, on your knees!). While Schön is momentarily distracted by the schoolboy's sudden appearance, Lulu empties the remaining five rounds into him. But he is still alive, and realises he has yet another 'rival', Und – da – ist – noch – einer! (And – there – is – another!). He calls for his son, who reappears, while Lulu appears remorseful, and then he dies. Lulu goes to leave but Alwa bars her way. She begs him not to give her up (arietta: Du kannst mich nicht dem Gericht ausliefern!; You cannot deliver me up to the Law!), which he refuses to do despite her offers to be his for the rest of her life, Ich will Dir treu sein mein Leben lang (I will be faithful to you my whole life long). Once again, a doorbell announces the arrival of the police.

''Interlude in the form of a silent film. Both film and the musical accompaniment are in the form of a palindrome. The film depicts four main events, pivoting on Lulu's one year in prison, and four following her imprisonment, forming the palindrome. The first sequence shows the arrest, detention, trial and the prison door closing. The second sequence shows the reverse with the prison door opening, the medical assessment, the isolation ward in hospital, and her escape. In each mirror event the number of people involved is the same, for example three people arrest her and three liberate her. As the palindrome progresses, Lulu loses hope in detention, is tried and transferred to prison, where she becomes resigned to her fate. There hope returns as she contracts cholera and after a further "trial" by doctors is transferred to hospital where hope grows as Geschwitz visits her, they change clothes, and Lulu escapes disguised as the other woman. During the palindrome many details and symbols, before and after prison, match each other, including Lulu's portrait, a recurring visual motif throughout the opera.''

''Scene 2: The same place as scene 1, one year later, an air of neglect, daylight has been shut out. The portrait is now leaning against the fireplace, facing away from the audience,''

Geschwitz, Alwa and the athlete are anxiously awaiting Schigolch and discussing the escape plan. The athlete is dressed as Alwa's footman and is planning to marry Lulu and take her to Paris as an acrobat. Geschwitz appears frail and will take Lulu's place in hospital. She is funding the escape, but refuses Alwa's offer of financial help. She is going to sacrifice her own freedom by taking Lulu's place so that nobody will discover she has escaped until it is too late. When Schigolch arrives, he and Geschwitz depart for the hospital, while the other two men discuss their plans. Alwa has sold the newspaper and written a melodrama for Lulu to star in. They begin to argue over money but are interrupted by the schoolboy (chamber music II, Mit wem habe ich; With whom have I), who has just broken out of prison and devised a scheme to free Lulu. Alwa and the athlete lie to him that Lulu is dead, showing him a newspaper article about her illness, then throw him out. Schigolch arrives with Lulu (melodrama: Hü, kleine Lulu: – wir müssen heut' noch über die Grenze; Well, little Lulu: we must cross the border today), looking very pale and weak from her illness. The athlete is disgusted at seeing her in this state, abandons his plan and goes off saying that he will summon the police instead. Schigolch goes to buy train tickets. As soon as he has gone, Lulu, who has been acting the part of the invalid, makes an instant recovery. Now alone with Alwa, she explains the plot in detail. Geschwitz went to Hamburg to nurse cholera patients and deliberately infected both herself and Lulu with contaminated clothing so that they were both placed in an isolation ward together. After Geschwitz was discharged, she returned to visit Lulu and they changed places (melodrama: Jetzt liegt sie dort drüben als die Mörderin des Doktor Schön; Now she lies there as the murderer of Dr. Schön), while Lulu feigned illness to get rid of the athlete. Now alone with Alwa, the portrait is returned to the easel and Lulu seduces the willing Alwa once again. They declare their love for each other in a second love duet, uns sehen, so oft wir wollen (to see each other as often as we want) reaching its climax with Alwa's hymn to Lulu (hymne: Durch dieses Kleid empfinde ich Deinen Wuchs wie Musik; Through this dress I feel your body like music), and make plans to go away together. At the end of the duet and scene she asks him, Ist das noch der Diwan, – auf dem sich – dein Vater – verblutet hat? (Isn't this the sofa on which your father bled to death?).

Act 3
''Scene 1: A spacious drawing room in Lulu's luxurious house in Paris. Lulu's portrait hangs on the wall. The guests are assembled''

Lulu is living in Paris under the alias of a French countess. A grand birthday party is taking place at her house and the athlete who is planning to get married proposes a toast to her. The Marquis shows an unusual interest in the 15-year-old girl. The guests move to the gaming room to play baccarat. The conversation moves to discussing shares in the Jungfrau Railway, which most of the guests at the party have invested in to varying extents, and which appear to be performing magnificently.

The Marquis has discovered Lulu's true identity, and is blackmailing her (duet:Sag es nur gleich heraus, wieviel du haben willst; Tell me without delay, how much money you want), threatening to hand her over to the authorities. She offers herself to him, having had a previous affair, but his interests lie more in trafficking women and girls for commercial sexual exploitation, Lied des Mächenhändlers: Ich sagte dir doch, daß ich auch Mächenhändler bin (song of the human tafficker: I told you I am a white slave trader). Again, Lulu sings about who she is and what she has become, as in her act II Lied; ''Ich tauge nicht für diesen Beruf. Als ich fünfzehn Jahre alt war, hätte mir das gefallen können'' (I'm no good for this sort of work, when I was fifteen it was different, I might have enjoyed it). The Marquis indicates he could summon the policeman stationed out in the street and claim the reward for her capture, but he would get a far higher price by selling her to a Cairo brothel to which he has sent a picture of her portrait as Eve. She offers to pay him, but he is aware that Alwa's fortune is all in the railway shares, and he wants cash, giving her a deadline later that day. She reads a note the athlete handed her just before the Marquis confronted her and learns that he too wants to blackmail her. Geschwitz accuses her of not returning the favours and affection she showed Lulu when they were in hospital. The athlete returns and makes apparent that he is still interested in Lulu's affections and also gives her a deadline, duet: ''Einen Moment! Hast du meinen Brief gelesen?'' (One Moment! Have you read my note?). A telegram arrives for the Banker informing him the railway shares are now worthless. When Schigolch arrives, asking for money for his girlfriend (duet: Ich brauche nämlich notwendig Geld...Ich miete meiner Geliebten eine Wohnung; I need some money now, I am renting an apartment for my lover), Lulu collapses in despair but confides in him.

Schigolch too has designs upon Lulu, but she persuades him that if he can arrange for the athlete's death she will give him the money, which he says he will do if she can persuade the athlete to come to his home, which she promises. The Marquis suspects the athlete, but he denies it. Lulu then convinces the athlete that if he spends the night with Geschwitz, she will pay Lulu, who can then pay him the blackmail money. She then persuades the countess that she will give herself to her if she spends the night with the athlete. Although puzzled, Geschwitz agrees to the bargain. Having achieved this, Lulu turns to her valet and orders him to change clothes with her. The news of the railway collapse spreads through the company to general despair. Lulu, dressed as her valet, informs Alwa they have been discovered and the police are on their way, and they escape. Again the scene ends with the arrival of the police, who confront the valet before realising their mistake.

''Scene 2: A windowless garret in London, with a leaking skylight. A bucket collects water dripping from the skylight. On the floor a torn mattress. A door leads to Lulu's bedroom''

Alwa and Schigolch are discussing their predicament. They and Lulu are now living in poverty and on the run. It is Lulu's first day of work as a Freudenmädchen (sex worker), from which they intend to make a living, although Alwa is ambivalent. When they hear Lulu approaching with her first client, a professor, they hide. The professor remains silent throughout, is very gentle and pays her generously. Lulu is thrilled. Geschwitz, now shabbily dressed, then arrives with the portrait of Lulu, which she has removed from the frame and brought from Paris. Lulu is disturbed at seeing it, but Alwa is inspired and hangs it on the wall, believing it will please the clients, and they discuss the fate of the artist, quartet: Ihr Körper stand auf dem Höhepunkt (Her body, then, was at it highest peak). Lulu goes out to prove her attractiveness, leaving with Geschwitz. Alwa reveals that Lulu had contracted venereal disease from the Marquis and in turn passed it on to him.

Lulu returns with her second client, the Negro, ''Komm nur herein, mein Schatz! Komm!'' (Come in, my love! Come in!), who becomes angry at being asked to pay in advance and attacks her. Alwa rushes to her defence but is killed by the Negro, who then leaves, followed by Lulu in despair while Schigolch removes the body. Geschwitz returns, saying Lulu sent her away, while Schigolch leaves. She produces a gun and considers killing herself, bitterly believing that Lulu would shed mir keine Träne nach (not one tear for me), then changes her mind and goes to hang herself, pausing first in reverence before Lulu's portrait. She is interrupted by the entrance of Lulu and her third client, Jack the Ripper. When asked, she says Geschwitz is her crazy sister. Jack makes to leave, saying he has little money and she is asking too much. She pleads with him and they haggle over the price, while she reveals it is her first day on the job, as he suspected. He also guesses the true nature of Geschwitz's feelings for Lulu. Lulu says she is drawn to Jack and eventually offers to give herself to him without payment. They go into the bedroom. Geschwitz, left to herself, resolves to return to Germany to become a lawyer and work for women's rights. On hearing Lulu's screams, she rushes to the bedroom door but Jack emerges with a blood-stained knife that he plunges into her body, and she collapses. Jack calmly washes his hands in the basin, not believing his luck at having killed two women at once, Ich bin doch ein verdammter Glückspilz! (I am just the luckiest of men!), complains about the lack of a towel and leaves. In her dying breath Geschwitz declares her eternal love for Lulu, ''Lulu! Mein Engel! Laß dich noch einmal sehn! Ich bin dir nah! Bleibe dir nah! In Ewigkeit!'' (Lulu! My Angel! Let me see you one more time! I am close! Stay close! For eternity!).

Dramatic
The character of Lulu has been described as embodying both elements of female sexuality's dualism, earth-mother and whore. In the words of Karl Kraus, she is the woman "who became the destroyer of all because everyone destroyed her". Berg's involvement with the lower depths of society in his two dramatic works, Wozzeck and Lulu, surprised even Schoenberg. Like Wozzeck, Lulu is social criticism, a tragedy in which the protagonists are portrayed as victims, gradually becoming enslaved to social forces they are too weak to deal with. Significantly, Lulu is canonically startlingly young, only about 15 years of age when the drama begins, and Schigolch, who may or may not be her father, is implied to have been her first sexual experience. Palindromes in the piece take many forms, such as the rise and fall of Lulu and the recycling of the actors: the three men whose deaths she contributes to become Lulu's three clients, and the man she murdered murders her. Alwa, thought to be the antithesis of Lulu, was changed from Wedekind's dramatist to Berg's composer and is assumed to be a stand-in for Berg himself. In all cases, the music underscores and confirms Berg's dramatic allusions.

Pit orchestra

 * Woodwinds:
 * 3 flutes (all doubling piccolos)
 * 3 oboes (3rd doubling English horn)
 * 3 clarinets in B♭ (1st and 2nd doubling E♭ clarinets)
 * bass clarinet in B♭
 * alto saxophone in E♭
 * 3 bassoons (3rd doubling contrabassoon)

 * Brass:
 * 4 horns in F
 * 3 trumpets in C
 * 3 trombones
 * tuba

 * Percussion
 * timpani
 * triangle
 * tambourine
 * snare drum
 * jazz drum
 * bass drum
 * cymbals
 * switch
 * 2 tam-tams (high and low)
 * xylophone
 * vibraphone

 * Keyboard:
 * piano

 * Strings:
 * harp
 * violins I
 * violins II
 * violas
 * cellos
 * double basses

Special groups
The onstage jazz band in act 1, scene 3 (instrumentalists can be drawn from the pit players) consists of:

 * 2 clarinets in B♭
 * alto saxophone in E♭
 * tenor saxophone in B♭
 * 2 Jazz trumpets in C
 * 2 Jazz trombones
 * sousaphone

 * Jazz drum set (3 players)
 * banjo
 * piano
 * 3 violins with jazz horns
 * contrabass

In act 3, scene 2, Cerha's edition uses a small onstage ensemble that requires:

 * piccolo
 * flute
 * 3 clarinets in B♭
 * bass clarinet in B♭
 * contrabassoon

Lulu is arguably the first seminal work of western art music that used the vibraphone, an instrument that had previously been associated with jazz. However, it has been used in smaller works by major composers prior to Lulu, such as Maurice Ravel's orchestrations of Don Quichotte à Dulcinée and Ronsard à son âme [fr] (1933 and 1935 respectively), as well as Darius Milhaud's incidental music to L'annonce faite à Marie (1932).

Structure
Berg was obsessed with symmetry in his works and Lulu is no exception, the whole being perceived as a palindrome or mirror. Lulu's popularity in the first act is mirrored by the squalor she lives in during act 3, and this is emphasised by Lulu's husbands in act 1 being played by the same singers as her clients in act 3. The motifs associated with each are repeated.

This mirrorlike structure is further emphasised by the film interlude at act 2 at the very centre of the work. The events shown in the film are a miniature version of the mirror structure of the opera as a whole (Lulu enters prison and then leaves again) and the music accompanying the film is an exact palindrome – it reads the same forwards as backwards. The centre of this palindrome is indicated by an arpeggio played on the piano, first rising, then falling (shown here on the top staff).

Berg assigns specific vocal styles to each character with descriptive orchestral representation, recapitulative episodes to emphasise psychological significance and pitch-sets. Recapitulation includes having single singers performing multiple roles. The use of pitch includes the use of twelve-tone rows.

Serialism
Cell z (also one of the basic cells in Béla Bartók's String Quartet No. 4) is the basic cell of Lulu and generates trope I:

Although some of Lulu is freely composed, Berg also makes use of Schoenberg's twelve-tone technique. Rather than using one tone row for the entire work, however, he gives each character his or her own tone row, meaning that the tone rows act rather like the leitmotifs in Richard Wagner's operas.

From this one tone row, Berg derives tone rows for many of the characters. For example, the tone row associated with Lulu herself is: F, G, A♭, B♭, C, D, F♯, D♯, E, A, B, C♯. This row is constructed by extracting one note (F) from the basic row's first trichord, then taking the next note (G) from the basic row's second trichord, then taking the third note (A♭) from the basic row's third trichord, and so on, cycling through the basic row three times.

The tone row associated with Alwa is arrived at by repeating the basic tone row over and over and taking every seventh note; this results in the following tone row: B♭, F♯, E♭, G♯, F, B, E, D, A, C, C♯, G

Similarly, the tone row associated with Dr. Schön is arrived at by repeating the basic tone row (as in the previous example) and taking the first note, missing one note, taking the next, missing two, taking the next, missing three, taking the next, missing three, taking the next, missing two, taking the next, missing one, taking the next, missing one, taking the next, missing two, taking the next, and so on; this results in the following tone row: B♭, E♭, G, G♯, D, F, E, A, B, C, F♯, C♯

Posthumous history
The opera was first performed by the Zürich Opera in an incomplete form on June 2, 1937. Erwin Stein made a vocal score of the whole of act 3 following Berg's death, and Helene Berg, Alban's widow, approached Schoenberg to complete the orchestration. Schoenberg at first accepted, but upon being sent copies of Berg's sketches he changed his mind, saying that it would be a more time-consuming task than he had thought. Helene subsequently forbade anybody else to complete the opera, and for over 40 years only the first two acts could be given complete, usually with the act 3 portions of the Lulu Suite played in place of act 3. The last recording made of the original two-act version—Christoph von Dohnányi conducting the Vienna Philharmonic, with Anja Silja in the title role (Decca/London, recorded 1976 and released 1978)—presented it in this form.

Director Heinz Ruckert shot the silent film featured at the midpoint according to Berg's exacting specifications. The film wordlessly depicts Lulu's arrest, trial, incarceration, and ultimate liberation thanks to the cunning of the Countess Geschwitz. Like the music for this sequence (and the opera as a whole), the film has a palindromic structure. The original film is lost save for four stills which remain in the Zürich Stadtarchiv. Each successive production requires a new film to be shot with the stage actors, though many recent productions have omitted the film altogether.

Performance history
After the Zürich premiere, the opera was seen at La Fenice on 4 September 1949 during the Venice Biennale, conducted by Sanzogno. The German premiere was at the Grillo-Theater in Essen on 7 March 1953 with Carla Spletter in the title role, and the Netherlands premiere on July 7 of that year at the Stadsschouwburg in Amsterdam as part of the Holland Festival, both with Die Bühnen der Stadt Essen conducted by Gustav König and broadcast to the UK on the BBC on 10 August. This was followed by a production at Hamburg in 1957 with Helga Pilarczyk in a Günther Rennert production, conducted by Leopold Ludwig which was also seen at the Paris Opera in 1960 and La Scala in 1963, and Sadler's Wells 1962.

In its two-act form plus sketches of the third act, Lulu made its American debut at the Santa Fe Opera in New Mexico during the 1963 season, with the American soprano Joan Carroll in the title role, together with Donald Gramm (Schön), Elaine Bonazzi (Geschwitz), and George Shirley (Alwa), with Robert Craft conducting. The Opera's general director, John Crosby, attempted to negotiate for Santa Fe to stage the American premiere of the full three-act opera, but was not successful. A notable Lulu, Silja, made her debut in a Wieland Wagner production at the Staatsoper Stuttgart in 1966 (which was later filmed, with Carlos Alexander as Schön). In 1967 the Metropolitan Opera presented the Hamburg State Opera production with Ludwig conducting, Toni Blankenheim (Schön), Anneliese Rothenberger (Lulu), Kerstin Meyer (Geschwitz), Gerhard Unger (Alwa), Kim Borg (Schigolch) and Maria von Ilosvay (Theatre dresser). This production was recorded by Electrola the following year. Celebrated Lulus have included Evelyn Lear, Teresa Stratas, Nancy Shade, Karan Armstrong, Julia Migenes, Barbara Hannigan, Christine Schäfer, and Marlis Petersen.

Helene Berg's death in 1976 paved the way for a new completed version of the opera to be made by Friedrich Cerha. There was insufficient time to have the score of this three-act version ready for the first production of the work at the Metropolitan Opera in April 1977 (in a production by John Dexter, with Carole Farley in the title role), so the incomplete version was used. Published in 1979, the Cerha completion premiered on 24 February the same year at the Opera Garnier and was conducted by Pierre Boulez, with Stratas singing the lead role; the production (by Patrice Chéreau) was a sensation and the recording won the Gramophone Award for 1979.

The U.S. premiere of the complete opera was on 28 July 1979 at Santa Fe, with Nancy Shade (Lulu), William Dooley (Schön), Katherine Ciesinski (Geschwitz) and Barry Busse (Alwa). The Metropolitan Opera first presented it in December 1980, a performance later released on DVD. Its 2015 production, with Marlis Petersen in the title role, was broadcast in high definition on 21 November. That production featured projections and animated drawings by William Kentridge. The same production, with a different cast, also played at De Nationale Opera, Amsterdam (2015), the English National Opera, London in 2016, and the Teatro dell'Opera di Roma (2017).

Books

 * , see also The Complete Opera Book
 * , see also The Complete Opera Book
 * , see also The Complete Opera Book
 * , see also The Complete Opera Book
 * , see also The Complete Opera Book
 * , see also The Complete Opera Book
 * , see also The Complete Opera Book

Chapters, articles and theses

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Discography and recordings

 * Synopsis pp. 18–23; Libretto pp. 116–203
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title: Lulu (opera)