title: Christiaan Huygens

text: The letters show Huygens's early interest in mathematics. In October 1646 there is the suspension bridge and the demonstration that a hanging chain is not a parabola, as Galileo thought. Huygens would later label that curve the "catenaria" (catenary) in 1690 while corresponding with Gottfried Leibniz.


title: Christiaan Huygens

text: In the next two years (1647-48), Huygens's letters to Mersenne covered various topics, including a mathematical proof of the law of free fall, the claim by Grégoire de Saint-Vincent of circle quadrature, which Huygens showed to be wrong, the rectification of the ellipse, projectiles, and the vibrating string. Some of Mersenne's concerns at the time, such as the cycloid (he sent Huygens Torricelli's treatise on the curve), the centre of oscillation, and the gravitational constant, were matters Huygens only took seriously towards the end of the 17th century. Mersenne had also written on musical theory. Huygens preferred meantone temperament; he innovated in 31 equal temperament (which was not itself a new idea but known to Francisco de Salinas), using logarithms to investigate it further and show its close relation to the meantone system.


title: Christiaan Huygens

text: In 1654, Huygens returned to his father's house in The Hague, and was able to devote himself entirely to research. The family had another house, not far away at Hofwijck, and he spent time there during the summer. Despite being very active, his scholarly life did not allow him to escape bouts of depression.


title: Christiaan Huygens

text: Subsequently, Huygens developed a broad range of correspondents, though picking up the threads after 1648 was hampered by the five-year "Fronde" in France. Visiting Paris in 1655, Huygens called on Ismael Boulliau to introduce himself, who took him to see Claude Mylon. The Parisian group of savants that had gathered around Mersenne held together into the 1650s, and Mylon, who had assumed the secretarial role, took some trouble to keep Huygens in touch. Through Pierre de Carcavi Huygens corresponded in 1656 with Pierre de Fermat, whom he admired greatly, though this side of idolatry. The experience was bittersweet and somewhat puzzling, since it became clear that Fermat had dropped out of the research mainstream, and his priority claims could probably not be made good in some cases. Besides, Huygens was looking by then to apply mathematics to physics, while Fermat's concerns ran to purer topics.


title: Christiaan Huygens

text: Like some of his contemporaries, Huygens was often slow to commit his results and discoveries to print, preferring to disseminate his work through letters instead. In his early days, his mentor Frans van Schooten provided technical feedback and was cautious for the sake of his reputation.


title: Christiaan Huygens

text: Between 1651 and 1657, Huygens published a number of works that showed his talent for mathematics and his mastery of both classical and analytical geometry, increasing his reach and reputation among mathematicians. Around the same time, Huygens began to question Descartes's laws of collision, which were largely wrong, deriving the correct laws algebraically and later by way of geometry. He showed that, for any system of bodies, the centre of gravity of the system remains the same in velocity and direction, which Huygens called the conservation of "quantity of movement". While others were studying impact around the same time, Huygens's theory of collisions was more general. These results were known through correspondence and in a short article in "Journal des Sçavans" but would remain largely unpublished until after his death, with the publication of "De Motu Corporum ex Percussione" ("Concerning the motion of colliding bodies").


title: Christiaan Huygens

text: In addition to his work on mechanics, he made important scientific discoveries, such as the identification of Saturn's moon Titan in 1655, and the invention of the pendulum clock in 1657, both of which brought him fame across Europe. On 3 May 1661, Huygens observed the planet Mercury transit over the Sun, using the telescope of instrument maker Richard Reeve in London, together with astronomer Thomas Streete and Reeve. Streete then debated the published record of the transit of Hevelius, a controversy mediated by Henry Oldenburg. Huygens passed to Hevelius a manuscript of Jeremiah Horrocks on the transit of Venus, 1639, which was printed for the first time in 1662.


title: Christiaan Huygens

text: Sir Robert Moray sent Huygens John Graunt's life table in 1662, and in time Huygens and his brother Lodewijk dabbled on life expectancy. Huygens eventually created the first graph of a continuous distribution function under the assumption of a uniform death rate, and used it to solve problems in joint annuities. In the same year, Huygens, who played the harpsichord, took an interest in Simon Stevin's theories on music; however, he showed very little concern to publish his theories on consonance, some of which were lost for centuries. For his contributions to science, the Royal Society of London elected Huygens a Fellow in 1665, making him its first foreign member when he was just 36 years old.


title: Christiaan Huygens

text: The Montmor Academy was the form the old Mersenne circle took after the mid-1650s. Huygens took part in its debates, and supported its "dissident" faction who favoured experimental demonstration to curtail fruitless discussion, and opposed amateurish attitudes. During 1663 he made what was his third visit to Paris; the Montmor Academy closed down, and Huygens took the chance to advocate a more Baconian program in science. Three years later, in 1666, he moved to Paris on an invitation to fill a position at King Louis XIV's new French Académie des sciences.


title: Christiaan Huygens

text: While in Paris, Huygens had an important patron and correspondent in Jean-Baptiste Colbert, First Minister to Louis XIV. However, his relationship with the French Academy was not always easy, and in 1670 Huygens, seriously ill, chose Francis Vernon to carry out a donation of his papers to the Royal Society in London, should he die. The aftermath of the Franco-Dutch War (1672–78), and particularly England's role in it, may have damaged his relationship with the Royal Society. Robert Hooke, as a Royal Society representative, lacked the finesse to handle the situation in 1673.


title: Christiaan Huygens

text: The physicist and inventor Denis Papin was assistant to Huygens from 1671. One of their projects, which did not bear fruit directly, was the gunpowder engine. Papin moved to England in 1678 to continue work in this area. Also in Paris, Huygens made further astronomical observations using the observatory recently completed in 1672. He introduced Nicolaas Hartsoeker to French scientists such as Nicolas Malebranche and Giovanni Cassini in 1678.


title: Christiaan Huygens

text: Huygens met Leibniz as a young diplomat, visiting Paris in 1672 on a vain mission to meet the French Foreign Minister Arnauld de Pomponne. At this time Leibniz was working on a calculating machine, and he moved on to London in early 1673 with diplomats from Mainz. From March 1673, Leibniz was tutored in mathematics by Huygens, who taught him analytical geometry. An extensive correspondence ensued, in which Huygens showed at first reluctance to accept the advantages of Leibniz's infinitesimal calculus.


title: Christiaan Huygens

text: Huygens moved back to The Hague in 1681 after suffering another bout of serious depressive illness. In 1684, he published "Astroscopia Compendiaria" on his new tubeless aerial telescope. He attempted to return to France in 1685 but the revocation of the Edict of Nantes precluded this move. His father died in 1687, and he inherited Hofwijck, which he made his home the following year.


title: Christiaan Huygens

text: On his third visit to England, Huygens met Isaac Newton in person on 12 June 1689. They spoke about Iceland spar, and subsequently corresponded about resisted motion.


title: Christiaan Huygens

text: Huygens returned to mathematical topics in his last years and observed the acoustical phenomenon now known as flanging in 1693. Two years later, on 8 July 1695, Huygens died in The Hague and was buried in an unmarked grave in the Grote Kerk there, as was his father before him.


title: Christiaan Huygens

text: Huygens first became internationally known for his work in mathematics, publishing a number of important results that drew the attention of many European geometers. Huygens's preferred method in his published works was that of Archimedes, though he used Descartes's analytic geometry and Fermat's infinitesimal techniques more extensively in his private notebooks.


title: Christiaan Huygens

text: Huygens's first publication was "Theoremata de Quadratura Hyperboles, Ellipsis et Circuli" ("Theorems on the quadrature of the hyperbola, ellipse, and circle"), published by the Elzeviers in Leiden in 1651. The first part of the work contained theorems for computing the areas of hyperbolas, ellipses, and circles that paralleled Archimedes's work on conic sections, particularly his "Quadrature of the Parabola". The second part included a refutation to Grégoire de Saint-Vincent's claims on circle quadrature, which he had discussed with Mersenne earlier.


title: Christiaan Huygens

text: Huygens demonstrated that the centre of gravity of a segment of any hyperbola, ellipse, or circle was directly related to the area of that segment. He was then able to show the relationships between triangles inscribed in conic sections and the centre of gravity for those sections. By generalizing these theorems to all conic sections, Huygens extended classical methods to generate new results.


title: Christiaan Huygens

text: Quadrature was a live issue in the 1650s and, through Mylon, Huygens intervened in the discussion of the mathematics of Thomas Hobbes. Persisting in trying to explain the errors Hobbes had fallen into, he made an international reputation.


title: Christiaan Huygens

text: Huygens's next publication was "De Circuli Magnitudine Inventa" ("New findings in the measurement of the circle"), published in 1654. In this work, Huygens was able to narrow the gap between the circumscribed and inscribed polygons found in Archimedes's "Measurement of the Circle", showing that the ratio of the circumference to its diameter or "π" must lie in the first third of that interval.


title: Christiaan Huygens

text: Using a technique equivalent to Richardson extrapolation, Huygens was able to shorten the inequalities used in Archimedes's method; in this case, by using the centre of the gravity of a segment of a parabola, he was able to approximate the centre of gravity of a segment of a circle, resulting in a faster and accurate approximation of the circle quadrature. From these theorems, Huygens obtained two set of values for "π": the first between 3.1415926 and 3.1415927, and the second between 3.1415926538 and 3.1415926533.


title: Christiaan Huygens

text: Huygens also showed that, in the case of the hyperbola, the same approximation with parabolic segments produces a quick and simple method to calculate logarithms. He appended a collection of solutions to classical problems at the end of the work under the title "Illustrium Quorundam Problematum Constructiones" ("Construction of some illustrious problems").


title: Christiaan Huygens

text: Huygens became interested in games of chance after he visited Paris in 1655 and encountered the work of Fermat, Blaise Pascal and Girard Desargues years earlier. He eventually published what was, at the time, the most coherent presentation of a mathematical approach to games of chance in "De Ratiociniis in Ludo Aleae" ("On reasoning in games of chance"). Frans van Schooten translated the original Dutch manuscript into Latin and published it in his "Exercitationum Mathematicarum" (1657).


title: Christiaan Huygens

text: The work contains early game-theoretic ideas and deals in particular with the problem of points. Huygens took from Pascal the concepts of a "fair game" and equitable contract (i.e., equal division when the chances are equal), and extended the argument to set up a non-standard theory of expected values. His success in applying algebra to the realm of chance, which hitherto seemed inaccessible to mathematicians, demonstrated the power of combining Euclidean synthetic proofs with the symbolic reasoning found in the works of Viète and Descartes.


title: Christiaan Huygens

text: Huygens included five challenging problems at the end of the book that became the standard test for anyone wishing to display their mathematical skill in games of chance for the next sixty years. People who worked on these problems included Abraham de Moivre, Jacob Bernoulli, Johannes Hudde, Baruch Spinoza, and Leibniz.


title: Christiaan Huygens

text: Huygens had earlier completed a manuscript in the manner of Archimedes's "On Floating Bodies" entitled "De Iis quae Liquido Supernatant" ("About parts floating above liquids"). It was written around 1650 and was made up of three books. Although he sent the completed work to Frans van Schooten for feedback, in the end Huygens chose not to publish it, and at one point suggested it be burned. Some of the results found here were not rediscovered until the eighteenth and nineteenth centuries.


title: Christiaan Huygens

text: Huygens first re-derives Archimedes's results for the stability of the sphere and the paraboloid by a clever application of Torricelli's principle (i.e., that bodies in a system move only if their centre of gravity descends). He then proves the general theorem that, for a floating body in equilibrium, the distance between its centre of gravity and its submerged portion its at a minimum. Huygens uses this theorem to arrive at original solutions for the stability of floating cones, parallelepipeds, and cylinders, in some cases through a full cycle of rotation. His approach was thus equivalent to the principle of virtual work. Huygens was also the first to recognize that, for homogeneous solids, their specific weight and their aspect ratio are the essentials parameters of hydrostatic stability.


title: Christiaan Huygens

text: Huygens was the leading European natural philosopher between Descartes and Newton. However, unlike many of his contemporaries, Huygens had no taste for grand theoretical or philosophical systems, and generally avoided dealing with metaphysical issues (if pressed, he adhered to the Cartesian and mechanical philosophy of his time). Instead, Huygens excelled in extending the work of his predecessors, such as Galileo, to derive solutions to unsolved physical problems that were amenable to mathematical analysis. In particular, he sought explanations that relied on contact between bodies and avoided action at a distance.


title: Christiaan Huygens

text: In common with Robert Boyle and Jacques Rohault, Huygens advocated an experimentally oriented, corpuscular-mechanical natural philosophy during his Paris years. This approach was sometimes labelled "Baconian," without being inductivist or identifying with the views of Francis Bacon in a simple-minded way.


title: Christiaan Huygens

text: After his first visit to England in 1661 and attending a meeting at Gresham College where he learned directly about Boyle's air pump experiments, Huygens spent time in late 1661 and early 1662 replicating the work. It proved a long process that brought to the surface both an experimental issue ("anomalous suspension") and a theoretical issue (""horror vacui""), and which ended in July 1663 as Huygens became a Fellow of the Royal Society. Huygens came to accept Boyle's view of the void against the Cartesian denial of it, while the replication of results of Boyle's experiments with the air pump trailed off messily.


title: Christiaan Huygens

text: Newton's influence on John Locke was mediated by Huygens, who assured Locke that Newton's mathematics was sound, leading to Locke's acceptance of a corpuscular-mechanical physics.


title: Christiaan Huygens

text: The general approach of the mechanical philosophers was to postulate theories of the kind now called "contact action." Huygens adopted this method, but not without seeing its difficulties and failures. Leibniz, his student in Paris, later abandoned the theory. Seeing the universe this way made the theory of collisions central to physics. Matter in motion made up the universe, and only explanations in those terms could be truly intelligible. While he was influenced by the Cartesian approach, he was less doctrinaire. He studied elastic collisions in the 1650s but delayed publication for over a decade.


title: Christiaan Huygens

text: Huygens concluded quite early that Descartes's laws for the elastic collision of two bodies must be wrong, and he formulated the correct laws, including the conservation of the product of mass times the square of the speed for hard bodies, and the conservation of quantity of motion in one direction for all bodies. An important step was his recognition of the Galilean invariance of the problems. Huygens had actually worked out the laws of collision from 1652 to 1656 in a manuscript entitled "De Motu Corporum ex Percussione", though his results took many years to be circulated. In 1661, he passed them on in person to William Brouncker and Christopher Wren in London. What Spinoza wrote to Henry Oldenburg about them in 1666, during the Second Anglo-Dutch War, was guarded. The war ended in 1667, and Huygens announced his results to the Royal Society in 1668. He later published them in the "Journal des Sçavans" in 1669.


title: Christiaan Huygens

text: In 1659 Huygens found the constant of gravitational acceleration and stated what is now known as the second of Newton's laws of motion in quadratic form. He derived geometrically the now standard formula for the centrifugal force, exerted on an object when viewed in a rotating frame of reference, for instance when driving around a curve. In modern notation:


title: Christiaan Huygens

text: with "m" the mass of the object, "w" the angular velocity, and "r" the radius. Huygens collected his results in a treatise under the title "De vi Centrifuga", unpublished until 1703, where the kinematics of free fall were used to produce the first generalized conception of force prior to Newton. The general formula for the centrifugal force, however, was published in 1673 and was a significant step in studying orbits in astronomy. It enabled the transition from Kepler's third law of planetary motion to the inverse square law of gravitation. Yet, the interpretation of Newton's work on gravitation by Huygens differed from that of Newtonians such as Roger Cotes: he did not insist on the "a priori" attitude of Descartes, but neither would he accept aspects of gravitational attractions that were not attributable in principle to contact between particles.


title: Christiaan Huygens

text: The approach used by Huygens also missed some central notions of mathematical physics, which were not lost on others. In his work on pendulums Huygens came very close to the theory of simple harmonic motion; the topic, however, was covered fully for the first time by Newton in Book II of the "Principia Mathematica" (1687). In 1678 Leibniz picked out of Huygens's work on collisions the idea of conservation law that Huygens had left implicit.


title: Christiaan Huygens

text: In 1657, inspired by earlier research into pendulums as regulating mechanisms, Huygens invented the pendulum clock, which was a breakthrough in timekeeping and became the most accurate timekeeper for almost 300 years until the 1930s. The pendulum clock was much more accurate than the existing verge and foliot clocks and was immediately popular, quickly spreading over Europe. He contracted the construction of his clock designs to Salomon Coster in The Hague, who built the clock. However, Huygens did not make much money from his invention. Pierre Séguier refused him any French rights, while Simon Douw in Rotterdam and Ahasuerus Fromanteel in London copied his design in 1658. The oldest known Huygens-style pendulum clock is dated 1657 and can be seen at the Museum Boerhaave in Leiden.


title: Christiaan Huygens

text: Part of the incentive for inventing the pendulum clock was to create an accurate marine chronometer that could be used to find longitude by celestial navigation during sea voyages. However, the clock proved unsuccessful as a marine timekeeper because the rocking motion of the ship disturbed the motion of the pendulum. In 1660, Lodewijk Huygens made a trial on a voyage to Spain, and reported that heavy weather made the clock useless. Alexander Bruce elbowed into the field in 1662, and Huygens called in Sir Robert Moray and the Royal Society to mediate and preserve some of his rights. Trials continued into the 1660s, the best news coming from a Royal Navy captain Robert Holmes operating against the Dutch possessions in 1664. Lisa Jardine doubts that Holmes reported the results of the trial accurately, as Samuel Pepys expressed his doubts at the time.


title: Christiaan Huygens

text: A trial for the French Academy on an expedition to Cayenne ended badly. Jean Richer suggested correction for the figure of the Earth. By the time of the Dutch East India Company expedition of 1686 to the Cape of Good Hope, Huygens was able to supply the correction retrospectively.


title: Christiaan Huygens

text: Sixteen years after the invention of the pendulum clock, in 1673, Huygens published his major work on horology entitled "Horologium Oscillatorium: Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae (The Pendulum Clock: or Geometrical demonstrations concerning the motion of pendula as applied to clocks"). It is the first modern work on mechanics where a physical problem is idealized by a set of parameters then analysed mathematically.


title: Christiaan Huygens

text: Huygens's motivation came from the observation, made by Mersenne and others, that pendulums are not quite isochronous: their period depends on their width of swing, with wide swings taking slightly longer than narrow swings. He tackled this problem by finding the curve down which a mass will slide under the influence of gravity in the same amount of time, regardless of its starting point; the so-called tautochrone problem. By geometrical methods which anticipated the calculus, Huygens showed it to be a cycloid, rather than the circular arc of a pendulum's bob, and therefore that pendulums needed to move on a cycloid path in order to be isochronous. The mathematics necessary to solve this problem led Huygens to develop his theory of evolutes, which he presented in Part III of his "Horologium Oscillatorium".


title: Christiaan Huygens

text: He also solved a problem posed by Mersenne earlier: how to calculate the period of a pendulum made of an arbitrarily-shaped swinging rigid body. This involved discovering the centre of oscillation and its reciprocal relationship with the pivot point. In the same work, he analysed the conical pendulum, consisting of a weight on a cord moving in a circle, using the concept of centrifugal force.


title: Christiaan Huygens

text: Huygens was the first to derive the formula for the period of an ideal mathematical pendulum (with mass-less rod or cord and length much longer than its swing), in modern notation:


title: Christiaan Huygens

text: with "T" the period, "l" the length of the pendulum and "g" the gravitational acceleration. By his study of the oscillation period of compound pendulums Huygens made pivotal contributions to the development of the concept of moment of inertia.


title: Christiaan Huygens

text: Huygens also observed coupled oscillations: two of his pendulum clocks mounted next to each other on the same support often became synchronized, swinging in opposite directions. He reported the results by letter to the Royal Society, and it is referred to as "an odd kind of sympathy" in the Society's minutes. This concept is now known as entrainment.


title: Christiaan Huygens

text: In 1675, while investigating the oscillating properties of the cycloid, Huygens was able to transform a cycloidal pendulum into a vibrating spring through a combination of geometry and higher mathematics. In the same year, Huygens designed a spiral balance spring and patented a pocket watch. These watches are notable for lacking a fusee for equalizing the mainspring torque. The implication is that Huygens thought his spiral spring would isochronize the balance in the same way that cycloid-shaped suspension curbs on his clocks would isochronize the pendulum.


title: Christiaan Huygens

text: He later used spiral springs in more conventional watches, made for him by Thuret in Paris. Such springs are essential in modern watches with a detached lever escapement because they can be adjusted for isochronism. Watches in Huygens's time, however, employed the very ineffective verge escapement, which interfered with the isochronal properties of any form of balance spring, spiral or otherwise.


title: Christiaan Huygens

text: Huygens's design came around the same time as, though independently of, Robert Hooke's. Controversy over the priority of the balance spring persisted for centuries. In February 2006, a long-lost copy of Hooke's handwritten notes from several decades of Royal Society meetings was discovered in a cupboard in Hampshire, England, presumably tipping the evidence in Hooke's favour.


title: Christiaan Huygens

text: Huygens had a long-term interest in the study of light refraction and lenses or dioptrics. From 1652 date the first drafts of a Latin treatise on the theory of dioptrics, known as the "Tractatus", which contained a comprehensive and rigorous theory of the telescope. Huygens was one of the few to raise theoretical questions regarding the properties and working of the telescope, and almost the only one to direct his mathematical proficiency towards the actual instruments used in astronomy.


title: Christiaan Huygens

text: Huygens repeatedly announced its publication to his colleagues but ultimately postponed it in favor of a much more comprehensive treatment, now under the name of the "Dioptrica". It consisted of three parts. The first part focused on the general principles of refraction, the second dealt with spherical and chromatic aberration, while the third covered all aspects of the construction of telescopes and microscopes. In contrast to Descartes' dioptrics which treated only ideal (elliptical and hyperbolical) lenses, Huygens dealt exclusively with spherical lenses, which were the only kind that could really be made and incorporated in devices such as microscopes and telescopes.


title: Christiaan Huygens

text: Huygens also worked out practical ways to minimize the effects of spherical and chromatic aberration, such as long focal distances for the objective of a telescope, internal stops to reduce the aperture, and a new kind of ocular in the form of a set of two planoconvex lenses, now known as the Huygens's eyepiece. The "Dioptrica" was never published in Huygens’s lifetime and only appeared in press in 1703, when most of its contents were already familiar to the scientific world.


title: Christiaan Huygens

text: Together with his brother Constantijn, Huygens began grinding his own lenses in 1655 in an effort to improve telescopes. He designed in 1662 what is now called the Huygenian eyepiece, with two lenses, as a telescope ocular. Lenses were also a common interest through which Huygens could meet socially in the 1660s with Spinoza, who ground them professionally. They had rather different outlooks on science, Spinoza being the more committed Cartesian, and some of their discussion survives in correspondence. He encountered the work of Antoni van Leeuwenhoek, another lens grinder, in the field of microscopy which interested his father.


title: Christiaan Huygens

text: Huygens also investigated the use of lenses in projectors. He is credited as the inventor of the magic lantern, described in correspondence of 1659. There are others to whom such a lantern device has been attributed, such as Giambattista della Porta and Cornelis Drebbel, though Huygens's design used lens for better projection (Athanasius Kircher has also been credited for that).


title: Christiaan Huygens

text: Huygens is especially remembered in optics for his wave theory of light, which he first communicated in 1678 to the Académie des sciences in Paris. Originally a preliminary chapter of his "Dioptrica", Huygens's theory was published in 1690 under the title "Traité de la Lumière" ("Treatise on light"), and contains the first fully mathematized, mechanistic explanation of an unobservable physical phenomenon (i.e., light propagation). Huygens refers to Ignace-Gaston Pardies, whose manuscript on optics helped him on his wave theory.


title: Christiaan Huygens

text: The challenge at the time was to explain geometrical optics, as most physical optics phenomena (such as diffraction) had not been observed or appreciated as issues. Huygens had experimented in 1672 with double refraction (birefringence) in the Iceland spar (a calcite), a phenomenon discovered in 1669 by Rasmus Bartholin. At first, he could not elucidate what he found but was later able to explain it using his wavefront theory and concept of evolutes. He also developed ideas on caustics. Huygens assumes that the speed of light is finite, based on a report by Ole Christensen Rømer in 1677 but which Huygens is presumed to have already believed. Huygens's theory posits light as radiating wavefronts, with the common notion of light rays depicting propagation normal to those wavefronts. Propagation of the wavefronts is then explained as the result of spherical waves being emitted at every point along the wave front (known today as the Huygens–Fresnel principle). It assumed an omnipresent ether, with transmission through perfectly elastic particles, a revision of the view of Descartes. The nature of light was therefore a longitudinal wave.


title: Christiaan Huygens

text: His theory of light was not widely accepted, while Newton's rival corpuscular theory of light, as found in his "Opticks" (1704), gained more support. One strong objection to Huygens's theory was that longitudinal waves have only a single polarization which cannot explain the observed birefringence. However, Thomas Young's interference experiments in 1801, and François Arago's detection of the Poisson spot in 1819, could not be explained through Newton's or any other particle theory, reviving Huygens's ideas and wave models. Fresnel became aware of Huygens's work and in 1821 was able to explain birefringence as a result of light being not a longitudinal (as had been assumed) but actually a transverse wave. The thus-named Huygens–Fresnel principle was the basis for the advancement of physical optics, explaining all aspects of light propagation until Maxwell's electromagnetic theory culminated in the development of quantum mechanics and the discovery of the photon.


title: Christiaan Huygens

text: In 1655, Huygens discovered the first of Saturn's moons, Titan, and observed and sketched the Orion Nebula using a refracting telescope with a 43x magnification of his own design. Huygens succeeded in subdividing the nebula into different stars (the brighter interior now bears the name of the "Huygenian region" in his honour), and discovered several interstellar nebulae and some double stars. He was also the first to propose that the appearance of Saturn, which have baffled astronomers, was due to "a thin, flat ring, nowhere touching, and inclined to the ecliptic”.


title: Christiaan Huygens

text: More than three years later, in 1659, Huygens published his theory and findings in "Systema Saturnium". It is considered the most important work on telescopic astronomy since Galileo's "Sidereus Nuncius" fifty years earlier. Much more than a report on Saturn, Huygens provided measurements for the relative distances of the planets from the Sun, introduced the concept of the micrometer, and showed a method to measure angular diameters of planets, which finally allowed the telescope to be used as an instrument to measure (rather than just sighting) astronomical objects. He was also the first to question the authority of Galileo in telescopic matters, a sentiment that was to be common in the years following its publication.


title: Christiaan Huygens

text: In the same year, Huygens was able to observe Syrtis Major, a volcanic plain on Mars. He used repeated observations of the movement of this feature over the course of a number of days to estimate the length of day on Mars, which he did quite accurately to 24 1/2 hours. This figure is only a few minutes off of the actual length of the Martian day of 24 hours, 37 minutes.


title: Christiaan Huygens

text: At the instigation of Jean-Baptiste Colbert, Huygens undertook the task of constructing a mechanical planetarium that could display all the planets and their moons then known circling around the Sun. Huygens completed his design in 1680 and had his clockmaker Johannes van Ceulen built it the following year. However, Colbert passed away in the interim and Huygens never got to deliver his planetarium to the French Academy of Sciences as the new minister, François-Michel le Tellier, decided not to renew Huygens's contract.


title: Christiaan Huygens

text: In his design, Huygens made an ingenious use of continued fractions to find the best rational approximations by which he could choose the gears with the correct number of teeth. The ratio between two gears determined the orbital periods of two planets. To move the planets around the Sun, Huygens used a clock-mechanism that could go forwards and backwards in time. Huygens claimed his planetarium was more accurate that a similar device constructed by Ole Rømer around the same time, but his planetarium design was not published until after his death in the "Opuscula Posthuma" (1703).


title: Christiaan Huygens

text: Shortly before his death in 1695, Huygens completed his most speculative work entitled "Cosmotheoros". At his direction, it was to be published only posthumously by his brother, which Constantijn Jr. did in 1698. In this work, Huygens speculated on the existence of extraterrestrial life, which he imagined similar to that on Earth. Such speculations were not uncommon at the time, justified by Copernicanism or the plenitude principle, but Huygens went into greater detail. However, it did so without the benefit of understanding Newton's laws of gravitation, or the fact that the atmospheres on other planets are composed of different gases. "Cosmotheoros," translated into English as "The celestial worlds discover’d", has been seen as part of speculative fiction in the tradition of Francis Godwin, John Wilkins, and Cyrano de Bergerac. Huygens's work was fundamentally utopian and owes some inspiration from the cosmography and planetary speculation of Peter Heylin.


title: Christiaan Huygens

text: Huygens wrote that availability of water in liquid form was essential for life and that the properties of water must vary from planet to planet to suit the temperature range. He took his observations of dark and bright spots on the surfaces of Mars and Jupiter to be evidence of water and ice on those planets. He argued that extraterrestrial life is neither confirmed nor denied by the Bible, and questioned why God would create the other planets if they were not to serve a greater purpose than that of being admired from Earth. Huygens postulated that the great distance between the planets signified that God had not intended for beings on one to know about the beings on the others, and had not foreseen how much humans would advance in scientific knowledge.


title: Christiaan Huygens

text: It was also in this book that Huygens published his estimates for the relative sizes of the solar system and his method for calculating stellar distances. He made a series of smaller holes in a screen facing the Sun, until he estimated the light was of the same intensity as that of the star Sirius. He then calculated that the angle of this hole was 1/27,664th the diameter of the Sun, and thus it was about 30,000 times as far away, on the (incorrect) assumption that Sirius is as luminous as the Sun. The subject of photometry remained in its infancy until the time of Pierre Bouguer and Johann Heinrich Lambert.


title: Christiaan Huygens

text: During his lifetime, Huygens's influence was considerable but began to fade shortly after his death. His skills as a geometer and his mechanical insights elicited the admiration of many of his contemporaries, including Newton, Leibniz, l'Hôpital, and the Bernoullis. For his work in physics, Huygens has been deemed one of the greatest scientists in history and a prominent figure in the Scientific Revolution, rivaled only by Newton in both depth of insight and the number of results obtained. Huygens was also instrumental in the development of institutional frameworks for scientific research on the European continent, making him a leading actor in the establishment of modern science.


title: Christiaan Huygens

text: In mathematics, Huygens mastered the methods of ancient Greek geometry, particularly the work of Archimedes, and was an adept user of the analytic geometry and infinitesimal techniques of Descartes, Fermat, and others. His mathematical style can be characterized as geometrical infinitesimal analysis of curves and of motion. Drawing inspiration and imagery from mechanics, it remained pure mathematics in form. Huygens brought this type of geometrical analysis to its greatest height but also to its conclusion, as more mathematicians turned away from classical geometry to the calculus for handling infinitesimals, limit processes, and motion.


title: Christiaan Huygens

text: Huygens was moreover one of the first to fully employ mathematics to answer questions of physics. Often this entailed introducing a simple model for describing a complicated situation, then analyzing it starting from simple arguments to their logical consequences, developing the necessary mathematics along the way. As he wrote at the end of a draft of "De vi Centrifuga":


title: Christiaan Huygens

text: Huygens favoured axiomatic presentations of his results, which require rigorous methods of geometric demonstration: although in the selection of primary axioms and hypotheses he allowed levels of uncertainty, the proofs of theorems derived from these could never be in doubt. Huygens's published works were seen as precise, unambiguous, and elegant, and exerted a big influence in Newton's presentation of his own major works.


title: Christiaan Huygens

text: Besides the application of mathematics to physics and physics to mathematics, Huygens relied on mathematics as methodology, particularly its power to generate new knowledge about the world. Unlike Galileo, who used mathematics primarily as rhetoric or synthesis, Huygens consistently employed mathematics as a method of discovery and analysis, and insisted that the reduction of the physical to the geometrical satisfy exacting standards of fit between the real and the ideal. In demanding such mathematical tractibility and precision, Huygens set an example for eighteenth-century scientists such as Johann Bernoulli, Jean le Rond d'Alembert, and Charles-Augustin de Coulomb.


title: Christiaan Huygens

text: Although never intended for publication, Huygens made use of algebraic expressions to represent physical entities in a handful of his manuscripts on collisions. This would make him one of the first to employ mathematical formulae to describe relationships in physics, as it is done today. Huygens also came close to the modern idea of limit while working on his "Dioptrica," though he never used the notion outside geometrical optics.


title: Christiaan Huygens

text: Huygens's standing as the greatest scientist in Europe was eclipsed by Newton's at the end of the seventeenth century, despite the fact that, as Hugh Aldersey-Williams notes, "Huygens's achievement exceeds that of Newton in some important respects". His very idiosyncratic style and reluctance to publish his work did much to diminish his influence in the aftermath of the Scientific Revolution, as adherents of Leibniz’ calculus and Newton's physics took centre stage.


title: Christiaan Huygens

text: His analysis of curves that satisfy certain physical properties, such as the cycloid, led to later studies of many other such curves like the caustic, the brachistochrone, the sail curve, and the catenary. His application of mathematics to physics, such as in his analysis of birefringence, would inspire new developments in mathematical physics and rational mechanics in the following centuries (albeit in the language of the calculus). Additionally, Huygens developed the oscillating timekeeping mechanisms, the pendulum and the balance spring, that have been used ever since in mechanical watches and clocks. These were the first reliable timekeepers fit for scientific use (e.g., it was possible for the first time to make accurate measurements of the inequality of the solar day, which astronomers in the past could not do). His work on this area anticipated the union of applied mathematics with mechanical engineering in the centuries that followed.


title: Christiaan Huygens

text: The European Space Agency spacecraft that landed on Titan, Saturn's largest moon, in 2005 was named after him.


title: Christiaan Huygens

text: A number of monuments to Christiaan Huygens can be found across important cities in the Netherlands, including Rotterdam, Delft, and Leiden.


title: Shaped charge

text: A shaped charge is an explosive charge shaped to form an explosively formed penetrator (EFP) to focus the effect of the explosive's energy. Different types of shaped charges are used for various purposes such as cutting and forming metal, initiating nuclear weapons, penetrating armor, or perforating wells in the oil and gas industry.


title: Shaped charge

text: A typical modern shaped charge, with a metal liner on the charge cavity, can penetrate armor steel to a depth of seven or more times the diameter of the charge (charge diameters, CD), though greater depths of 10 CD and above have been achieved. Contrary to a misconception (possibly resulting from the acronym for "high-explosive anti-tank", HEAT) the shaped charge EFP jet does not depend in any way on heating or melting for its effectiveness; that is, the EFP jet from a shaped charge does not melt its way through armor, as its effect is purely kinetic in nature – however the process does create significant heat and often has a significant secondary incendiary effect "after" penetration.


title: Shaped charge

text: The Munroe or Neumann effect is the focusing of blast energy by a hollow or void cut on a surface of an explosive. The earliest mention of hollow charges were mentioned in 1792. Franz Xaver von Baader (1765–1841) was a German mining engineer at that time; in a mining journal, he advocated a conical space at the forward end of a blasting charge to increase the explosive's effect and thereby save powder. The idea was adopted, for a time, in Norway and in the mines of the Harz mountains of Germany, although the only available explosive at the time was gunpowder, which is not a high explosive and hence incapable of producing the shock wave that the shaped-charge effect requires.


title: Shaped charge

text: The first true hollow charge effect was achieved in 1883, by Max von Foerster (1845–1905), chief of the nitrocellulose factory of Wolff & Co. in Walsrode, Germany.


title: Shaped charge

text: By 1886, Gustav Bloem of Düsseldorf, Germany, had filed for hemispherical cavity metal detonators to concentrate the effect of the explosion in an axial direction. The Munroe effect is named after Charles E. Munroe, who discovered it in 1888. As a civilian chemist working at the U.S. Naval Torpedo Station at Newport, Rhode Island, he noticed that when a block of explosive guncotton with the manufacturer's name stamped into it was detonated next to a metal plate, the lettering was cut into the plate. Conversely, if letters were raised in relief above the surface of the explosive, then the letters on the plate would also be raised above its surface. In 1894, Munroe constructed his first crude shaped charge:


title: Shaped charge

text: Among the experiments made ... was one upon a safe twenty-nine inches cube, with walls four inches and three quarters thick, made up of plates of iron and steel ... [W]hen a hollow charge of dynamite nine pounds and a half in weight and untamped was detonated on it, a hole three inches in diameter was blown clear through the wall ... The hollow cartridge was made by tying the sticks of dynamite around a tin can, the open mouth of the latter being placed downward.


title: Shaped charge

text: Although Munroe's experiment with the shaped charge was widely publicized in 1900 in "Popular Science Monthly", the importance of the tin can "liner" of the hollow charge remained unrecognized for another 44 years. Part of that 1900 article was reprinted in the February 1945 issue of "Popular Science", describing how shaped-charge warheads worked. It was this article that at last revealed to the general public how the United States Army "Bazooka" actually worked against armored vehicles during WWII.


title: Shaped charge

text: In 1910, Egon Neumann of Germany discovered that a block of TNT, which would normally dent a steel plate, punched a hole through it if the explosive had a conical indentation. The military usefulness of Munroe's and Neumann's work was unappreciated for a long time. Between the world wars, academics in several countries Myron Yakovlevich Sukharevskii (Мирон Яковлевич Сухаревский) in the Soviet Union, William H. Payment and Donald Whitley Woodhead in Britain, and Robert Williams Wood in the U.S. recognized that projectiles could form during explosions. However, it was not until 1932 that Franz Rudolf Thomanek, a student of physics at Vienna's "Technische Hochschule", conceived an anti-tank round that was based on the hollow charge effect. When the Austrian government showed no interest in pursuing the idea, Thomanek moved to Berlin's "Technische Hochschule", where he continued his studies under the ballistics expert Carl Julius Cranz. There in 1935, he and Hellmuth von Huttern developed a prototype anti-tank round. Although the weapon's performance proved disappointing, Thomanek continued his developmental work, collaborating with Hubert Schardin at the "Waffeninstitut der Luftwaffe" (Air Force Weapons Institute) in Braunschweig.


title: Shaped charge

text: By 1937, Schardin believed that hollow-charge effects were due to the interactions of shock waves. It was during the testing of this idea that, on February 4, 1938, Thomanek conceived the shaped-charge explosive (or "Hohlladungs-Auskleidungseffekt" (hollow-charge liner effect)). (It was Gustav Adolf Thomer who in 1938 first visualized, by flash radiography, the metallic jet produced by a shaped-charge explosion.) Meanwhile, Henry Hans Mohaupt, a chemical engineer in Switzerland, had independently developed a shaped-charge munition in 1935, which was demonstrated to the Swiss, French, British, and U.S. militaries.


title: Shaped charge

text: During World War II, shaped-charge munitions were developed by Germany (Panzerschreck, Panzerfaust, Panzerwurfmine, Mistel), Britain (PIAT, Beehive cratering charge), the Soviet Union (RPG-43, RPG-6), the U.S. (bazooka), and Italy ("Effetto Pronto Speciale" shells for various artillery pieces). The development of shaped charges revolutionized anti-tank warfare. Tanks faced a serious vulnerability from a weapon that could be carried by an infantryman or aircraft.


title: Shaped charge

text: One of the earliest uses of shaped charges was by German glider-borne troops against the Belgian Fort Eben-Emael in 1940. These demolition charges – developed by Dr. Wuelfken of the German Ordnance Office – were "unlined" explosive charges and didn't produce a metal jet like the modern HEAT warheads.


title: Shaped charge

text: Due to the lack of metal liner they shook the turrets but they did not destroy them, and other airborne troops were forced to climb on the turrets and smash the gun barrels.


title: Shaped charge

text: The common term in military terminology for shaped-charge warheads is high-explosive anti-tank (HEAT) warhead. HEAT warheads are frequently used in anti-tank guided missiles, unguided rockets, gun-fired projectiles (both spun (spin stabilized) and unspun), rifle grenades, land mines, bomblets, torpedoes, and various other weapons.


title: Shaped charge

text: During World War II, the precision of the charge's construction and its detonation mode were both inferior to modern warheads. This lower precision caused the jet to curve and to break up at an earlier time and hence at a shorter distance. The resulting dispersion decreased the penetration depth for a given cone diameter and also shortened the optimum standoff distance. Since the charges were less effective at larger standoffs, side and turret skirts (known as "Schürzen") fitted to some German tanks to protect against ordinary anti-tank rifles were fortuitously found to give the jet room to disperse and hence also reduce HEAT penetration.


title: Shaped charge

text: The use of add-on spaced armor skirts on armored vehicles may have the opposite effect and actually "increase" the penetration of some shaped-charge warheads. Due to constraints in the length of the projectile/missile, the built-in stand-off on many warheads is less than the optimum distance. In such cases, the skirting effectively increases the distance between the armor and the target, and the warhead detonates closer to its optimum standoff. Skirting should not be confused with cage armor which is primarily used to damage the fusing system of RPG-7 projectiles, but can also cause a HEAT projectile to pitch up or down on impact, lengthening the penetration path for the shaped charge's penetration stream. If the nose probe strikes one of the cage armor slats, the warhead will function as normal.


title: Shaped charge

text: In non-military applications shaped charges are used in explosive demolition of buildings and structures, in particular for cutting through metal piles, columns and beams and for boring holes. In steelmaking, small shaped charges are often used to pierce taps that have become plugged with slag. They are also used in quarrying, breaking up ice, breaking log jams, felling trees, and drilling post holes.


title: Shaped charge

text: Shaped charges are used most extensively in the petroleum and natural gas industries, in particular in the completion of oil and gas wells, in which they are detonated to perforate the metal casing of the well at intervals to admit the influx of oil and gas.


title: Shaped charge

text: A 4.5 kg (9.9 lb) shaped charge was used on the Hayabusa2 mission on asteroid 162173 Ryugu. The spacecraft dropped the explosive device onto the asteroid and detonated it with the spacecraft behind cover. The detonation dug a crater about 10 meters wide, to provide access to a pristine sample of the asteroid.


title: Shaped charge

text: A typical device consists of a solid cylinder of explosive with a metal-lined conical hollow in one end and a central detonator, array of detonators, or detonation wave guide at the other end. Explosive energy is released directly away from (normal to) the surface of an explosive, so shaping the explosive will concentrate the explosive energy in the void. If the hollow is properly shaped (usually conically), the enormous pressure generated by the detonation of the explosive drives the liner in the hollow cavity inward to collapse upon its central axis. The resulting collision forms and projects a high-velocity jet of metal particles forward along the axis. Most of the jet material originates from the innermost part of the liner, a layer of about 10% to 20% of the thickness. The rest of the liner forms a slower-moving slug of material, which, because of its appearance, is sometimes called a "carrot".


title: Shaped charge

text: Because of the variation along the liner in its collapse velocity, the jet's velocity also varies along its length, decreasing from the front. This variation in jet velocity stretches it and eventually leads to its break-up into particles. Over time, the particles tend to fall out of alignment, which reduces the depth of penetration at long standoffs.


title: Shaped charge

text: Also, at the apex of the cone, which forms the very front of the jet, the liner does not have time to be fully accelerated before it forms its part of the jet. This results in its small part of jet being projected at a lower velocity than jet formed later behind it. As a result, the initial parts of the jet coalesce to form a pronounced wider tip portion.


title: Shaped charge

text: Most of the jet travels at hypersonic speed. The tip moves at 7 to 14 km/s, the jet tail at a lower velocity (1 to 3 km/s), and the slug at a still lower velocity (less than 1 km/s). The exact velocities depend on the charge's configuration and confinement, explosive type, materials used, and the explosive-initiation mode. At typical velocities, the penetration process generates such enormous pressures that it may be considered hydrodynamic; to a good approximation, the jet and armor may be treated as inviscid, compressible fluids (see, for example,), with their material strengths ignored.


title: Shaped charge

text: A recent technique using magnetic diffusion analysis showed that the temperature of the outer 50% by volume of a copper jet tip while in flight was between 1100K and 1200K, much closer to the melting point of copper (1358 K) than previously assumed. This temperature is consistent with a hydrodynamic calculation that simulated the entire experiment. In comparison, two-color radiometry measurements from the late 1970s indicate lower temperatures for various shaped-charge liner material, cone construction and type of explosive filler. A Comp-B loaded shaped charge with a copper liner and pointed cone apex had a jet tip temperature ranging from 668 K to 863 K over a five shot sampling. Octol-loaded charges with a rounded cone apex generally had higher surface temperatures with an average of 810 K, and the temperature of a tin-lead liner with Comp-B fill averaged 842 K. While the tin-lead jet was determined to be liquid, the copper jets are well below the melting point of copper. However, these temperatures are not completely consistent with evidence that soft recovered copper jet particles show signs of melting at the core while the outer portion remains solid and cannot be equated with bulk temperature.


title: Shaped charge

text: The location of the charge relative to its target is critical for optimum penetration for two reasons. If the charge is detonated too close there is not enough time for the jet to fully develop. But the jet disintegrates and disperses after a relatively short distance, usually well under two meters. At such standoffs, it breaks into particles which tend to tumble and drift off the axis of penetration, so that the successive particles tend to widen rather than deepen the hole. At very long standoffs, velocity is lost to air drag, further degrading penetration.


title: Shaped charge

text: The key to the effectiveness of the hollow charge is its diameter. As the penetration continues through the target, the width of the hole decreases leading to a characteristic "fist to finger" action, where the size of the eventual "finger" is based on the size of the original "fist". In general, shaped charges can penetrate a steel plate as thick as 150% to 700% of their diameter, depending on the charge quality. The figure is for basic steel plate, not for the composite armor, reactive armor, or other types of modern armor.


title: Shaped charge

text: The most common shape of the liner is conical, with an internal apex angle of 40 to 90 degrees. Different apex angles yield different distributions of jet mass and velocity. Small apex angles can result in jet bifurcation, or even in the failure of the jet to form at all; this is attributed to the collapse velocity being above a certain threshold, normally slightly higher than the liner material's bulk sound speed. Other widely used shapes include hemispheres, tulips, trumpets, ellipses, and bi-conics; the various shapes yield jets with different velocity and mass distributions.


title: Shaped charge

text: Liners have been made from many materials, including various metals and glass. The deepest penetrations are achieved with a dense, ductile metal, and a very common choice has been copper. For some modern anti-armor weapons, molybdenum and pseudo-alloys of tungsten filler and copper binder (9:1, thus density is ≈18 Mg/m) have been adopted. Nearly every common metallic element has been tried, including aluminum, tungsten, tantalum, depleted uranium, lead, tin, cadmium, cobalt, magnesium, titanium, zinc, zirconium, molybdenum, beryllium, nickel, silver, and even gold and platinum. The selection of the material depends on the target to be penetrated; for example, aluminum has been found advantageous for concrete targets.


title: Shaped charge

text: In early antitank weapons, copper was used as a liner material. Later, in the 1970s, it was found tantalum is superior to copper, due to its much higher density and very high ductility at high strain rates. Other high-density metals and alloys tend to have drawbacks in terms of price, toxicity, radioactivity, or lack of ductility.


title: Shaped charge

text: For the deepest penetrations, pure metals yield the best results, because they display the greatest ductility, which delays the breakup of the jet into particles as it stretches. In charges for oil well completion, however, it is essential that a solid slug or "carrot" not be formed, since it would plug the hole just penetrated and interfere with the influx of oil. In the petroleum industry, therefore, liners are generally fabricated by powder metallurgy, often of pseudo-alloys which, if unsintered, yield jets that are composed mainly of dispersed fine metal particles.


title: Shaped charge

text: Unsintered cold pressed liners, however, are not waterproof and tend to be brittle, which makes them easy to damage during handling. Bimetallic liners, usually zinc-lined copper, can be used; during jet formation the zinc layer vaporizes and a slug is not formed; the disadvantage is an increased cost and dependency of jet formation on the quality of bonding the two layers. Low-melting-point (below 500 °C) solder- or braze-like alloys (e.g., SnPb, ZnPb, or pure metals like lead, zinc, or cadmium) can be used; these melt before reaching the well casing, and the molten metal does not obstruct the hole. Other alloys, binary eutectics (e.g. PbSb, SnPd, or AgCu), form a metal-matrix composite material with ductile matrix with brittle dendrites; such materials reduce slug formation but are difficult to shape.


title: Shaped charge

text: A metal-matrix composite with discrete inclusions of low-melting material is another option; the inclusions either melt before the jet reaches the well casing, weakening the material, or serve as crack nucleation sites, and the slug breaks up on impact. The dispersion of the second phase can be achieved also with castable alloys (e.g., copper) with a low-melting-point metal insoluble in copper, such as bismuth, 1–5% lithium, or up to 50% (usually 15–30%) lead; the size of inclusions can be adjusted by thermal treatment. Non-homogeneous distribution of the inclusions can also be achieved. Other additives can modify the alloy properties; tin (4–8%), nickel (up to 30% and often together with tin), up to 8% aluminium, phosphorus (forming brittle phosphides) or 1–5% silicon form brittle inclusions serving as crack initiation sites. Up to 30% zinc can be added to lower the material cost and to form additional brittle phases.


title: Shaped charge

text: Oxide glass liners produce jets of low density, therefore yielding less penetration depth. Double-layer liners, with one layer of a less dense but pyrophoric metal (e.g. aluminum or magnesium), can be used to enhance incendiary effects following the armor-piercing action; explosive welding can be used for making those, as then the metal-metal interface is homogeneous, does not contain significant amount of intermetallics, and does not have adverse effects to the formation of the jet.


title: Shaped charge

text: The penetration depth is proportional to the maximum length of the jet, which is a product of the jet tip velocity and time to particulation. The jet tip velocity depends on bulk sound velocity in the liner material, the time to particulation is dependent on the ductility of the material. The maximum achievable jet velocity is roughly 2.34 times the sound velocity in the material. The speed can reach 10 km/s, peaking some 40 microseconds after detonation; the cone tip is subjected to acceleration of about 25 million g. The jet tail reaches about 2–5 km/s. The pressure between the jet tip and the target can reach one terapascal. The immense pressure makes the metal flow like a liquid, though x-ray diffraction has shown the metal stays solid; one of the theories explaining this behavior proposes molten core and solid sheath of the jet. The best materials are face-centered cubic metals, as they are the most ductile, but even graphite and zero-ductility ceramic cones show significant penetration.


title: Shaped charge

text: For optimal penetration, a high explosive with a high detonation velocity and pressure is normally chosen. The most common explosive used in high performance anti-armor warheads is HMX (octogen), although never in its pure form, as it would be too sensitive. It is normally compounded with a few percent of some type of plastic binder, such as in the polymer-bonded explosive (PBX) LX-14, or with another less-sensitive explosive, such as TNT, with which it forms Octol. Other common high-performance explosives are RDX-based compositions, again either as PBXs or mixtures with TNT (to form Composition B and the Cyclotols) or wax (Cyclonites). Some explosives incorporate powdered aluminum to increase their blast and detonation temperature, but this addition generally results in decreased performance of the shaped charge. There has been research into using the very high-performance but sensitive explosive CL-20 in shaped-charge warheads, but, at present, due to its sensitivity, this has been in the form of the PBX composite LX-19 (CL-20 and Estane binder).


title: Shaped charge

text: A 'waveshaper' is a body (typically a disc or cylindrical block) of an inert material (typically solid or foamed plastic, but sometimes metal, perhaps hollow) inserted within the explosive for the purpose of changing the path of the detonation wave. The effect is to modify the collapse of the cone and resulting jet formation, with the intent of increasing penetration performance. Waveshapers are often used to save space; a shorter charge with a waveshaper can achieve the same performance as a longer charge without a waveshaper.


title: Shaped charge

text: Another useful design feature is "sub-calibration", the use of a liner having a smaller diameter (caliber) than the explosive charge. In an ordinary charge, the explosive near the base of the cone is so thin that it is unable to accelerate the adjacent liner to sufficient velocity to form an effective jet. In a sub-calibrated charge, this part of the device is effectively cut off, resulting in a shorter charge with the same performance.


title: Shaped charge

text: A linear shaped charge (LSC) has a lining with V-shaped profile and varying length. The lining is surrounded with explosive, the explosive then encased within a suitable material that serves to protect the explosive and to confine (tamp) it on detonation. "At detonation, the focusing of the explosive high pressure wave as it becomes incident to the side wall causes the metal liner of the LSC to collapse–creating the cutting force." The detonation projects into the lining, to form a continuous, knife-like (planar) jet. The jet cuts any material in its path, to a depth depending on the size and materials used in the charge. Generally, the jet penetrates around 1 to 1.2 times the charge width. For the cutting of complex geometries, there are also flexible versions of the linear shaped charge, these with a lead or high-density foam sheathing and a ductile/flexible lining material, which also is often lead. LSCs are commonly used in the cutting of rolled steel joists (RSJ) and other structural targets, such as in the controlled demolition of buildings. LSCs are also used to separate the stages of multistage rockets.


title: Shaped charge

text: The explosively formed penetrator (EFP) also known as the self-forging fragment (SFF), explosively formed projectile (EFP), self-forging projectile (SEFOP), are the products of a shaped charge. An EFP uses the action of the explosive's detonation wave (and to a lesser extent the propulsive effect of its detonation products) to project and deform a plate, dish or cone of ductile metal (such as copper, iron, or tantalum) into a compact high-velocity projectile, slug, rod or jet. This EFP is projected toward the target at about two kilometers per second.


title: Shaped charge

text: The EFP is relatively unaffected by first-generation reactive armor and can travel up to perhaps 1000 charge diameters (CD)s before its velocity becomes ineffective at penetrating armor due to aerodynamic drag, or successfully hitting the target becomes a problem. The impact of the EFP normally causes a large-diameter but relatively shallow hole, of, at most, a couple of CDs. If the EFP perforates the armor, spalling and extensive behind armor effects (BAE, also called behind armor damage, BAD) will occur. The BAE is mainly caused by the high-temperature and high-velocity armor and fragments being injected into the interior space and the blast overpressure caused by this debris. More modern EFP warhead versions, through the use of advanced initiation modes, can also produce long-rods (stretched slugs), multi-slugs and finned rod/slug projectiles. The long-rods are able to penetrate a much greater depth of armor, at some loss to BAE, multi-slugs are better at defeating light or area targets and the finned projectiles are much more accurate.


title: Shaped charge

text: The use of this warhead type is mainly restricted to lightly armored areas of main battle tanks (MBT) such as the top, belly and rear armored areas. It is well suited for the attack of other less heavily protected armored fighting vehicles (AFV) and in the breaching of material targets (buildings, bunkers, bridge supports, etc.). The newer rod projectiles may be effective against the more heavily armored areas of MBTs. Weapons using the EFP principle have already been used in combat; the "smart" submunitions in the CBU-97 cluster bomb used by the US Air Force and Navy in the 2003 Iraq war employed this principle, and the US Army is reportedly experimenting with precision-guided artillery shells under Project SADARM (Seek And Destroy ARMor). There are also various other projectile (BONUS, DM 642) and rocket submunitions (Motiv-3M, DM 642) and mines (MIFF, TMRP-6) that use EFP principle. Examples of EFP warheads are US patents 5038683 and US6606951.


title: Shaped charge

text: Some modern anti-tank rockets (RPG-27, RPG-29) and missiles (TOW 2B, Eryx, HOT, MILAN) use a tandem warhead shaped charge, consisting of two separate shaped charges, one in front of the other, typically with some distance between them. TOW-2A was the first to use tandem warheads in the mid-1980s, an aspect of the weapon which the US Army had to reveal under news media and Congressional pressure resulting from the concern that NATO antitank missiles were ineffective against Soviet tanks that were fitted with the new ERA boxes. The Army revealed that a 40 mm precursor shaped-charge warhead was fitted on the tip of the TOW-2B collapsible probe. Usually, the front charge is somewhat smaller than the rear one, as it is intended primarily to disrupt ERA boxes or tiles. Examples of tandem warheads are US patents 7363862 and US 5561261. The US Hellfire antiarmor missile is one of the few that have accomplished the complex engineering feat of having two shaped charges of the same diameter stacked in one warhead. Recently, a Russian arms firm revealed a 125mm tank cannon round with two same diameter shaped charges one behind the other, but with the back one offset so its penetration stream will not interfere with the front shaped charge's penetration stream. The reasoning behind both the Hellfire and the Russian 125 mm munitions having tandem same diameter warheads is not to increase penetration, but to increase the beyond-armour effect.


title: Shaped charge

text: In 1964 a Soviet scientist proposed that a shaped charge originally developed for piercing thick steel armor be adapted to the task of accelerating shock waves. The resulting device, looking a little like a wind tunnel, is called a Voitenko compressor. The Voitenko compressor initially separates a test gas from a shaped charge with a malleable steel plate. When the shaped charge detonates, most of its energy is focused on the steel plate, driving it forward and pushing the test gas ahead of it. Ames translated this idea into a self-destroying shock tube. A 66-pound shaped charge accelerated the gas in a 3-cm glass-walled tube 2 meters in length. The velocity of the resulting shock wave was 220,000 feet per second (67 km/s). The apparatus exposed to the detonation was completely destroyed, but not before useful data was extracted. In a typical Voitenko compressor, a shaped charge accelerates hydrogen gas which in turn accelerates a thin disk up to about 40 km/s. A slight modification to the Voitenko compressor concept is a super-compressed detonation, a device that uses a compressible liquid or solid fuel in the steel compression chamber instead of a traditional gas mixture. A further extension of this technology is the explosive diamond anvil cell, utilizing multiple opposed shaped-charge jets projected at a single steel encapsulated fuel, such as hydrogen. The fuels used in these devices, along with the secondary combustion reactions and long blast impulse, produce similar conditions to those encountered in fuel-air and thermobaric explosives.


title: Shaped charge

text: The proposed Project Orion nuclear propulsion system would have required the development of nuclear shaped charges for reaction acceleration of spacecraft. Shaped-charge effects driven by nuclear explosions have been discussed speculatively, but are not known to have been produced in fact. For example, the early nuclear weapons designer Ted Taylor was quoted as saying, in the context of shaped charges, ""A one-kiloton fission device, shaped properly, could make a hole ten feet (3 m) in diameter a thousand feet (305 m) into solid rock."" Also, a nuclear driven explosively formed penetrator was apparently proposed for terminal ballistic missile defense in the 1960s.


title: John Wetton

text: John Kenneth Wetton (12 June 1949 – 31 January 2017) was an English musician, singer, and songwriter. Known for his dexterous bass playing and booming baritone voice, Wetton first gained fame in the early 1970s. He performed with many progressive rock and hard rock bands, including Asia, King Crimson, U.K., Family, Roxy Music, Uriah Heep and Wishbone Ash.


title: John Wetton

text: Wetton was the singer and principal songwriter of the supergroup Asia, which proved to be his biggest commercial success. The debut Asia album sold ten million copies worldwide, and was "Billboard" magazine's number one album of 1982.


title: John Wetton

text: He later formed the duo Icon with his Asia band mate (and songwriting partner) Geoff Downes. From the 1990s he had a successful solo career. Wetton signed his name with his left hand but played bass right handed.


title: John Wetton

text: Wetton was born in Willington, Derbyshire, and grew up in Bournemouth, Dorset, where he attended Bournemouth School. His older brother Robert was a classical organist and choirmaster, and while practising organ would have John play the bass parts on a piano, since their home organ did not have a pedalboard. Wetton recalled that during these practices, "I got to like bass lines, because Bach bass lines are incredibly interesting. So I thought, this is good, I like bass lines, that's me." Though an enthusiast of classical music since childhood, he opted to go into rock and roll instead in order to avoid being compared to his brother. He played bass and sang in a number of early bands with Richard Palmer-James, including The Corvettes, The Palmer-James Group, Tetrad, and Ginger Man. A key early band was the jazzy Mogul Thrash; after live work with Renaissance, he joined Family and also did various recording sessions.


title: John Wetton

text: Wetton's big break came when his fellow Dorset native Robert Fripp invited him to join King Crimson in late 1972. This incarnation of the band also included violinist David Cross, former Yes drummer Bill Bruford, and percussionist Jamie Muir. His time in the band would allow Wetton to come into his own as a lead singer and writer. Wetton's old friend Richard Palmer-James also worked with the band as their primary lyricist. Wetton remained with the band until Fripp unexpectedly disbanded it in 1974. King Crimson maintained their interest in improvisation throughout this period, but moved away from the classical, jazz and English folk leanings of their earlier work. The 1972-1974 period featured a more aggressive fusion/avant-rock sound, led by Wetton's thunderous, melodic bass lines- whose "roaring and crunching" sound (enhanced with effects pedals and a rotating Leslie speaker cabinet (traditionally used with a Hammond Organ) often verged on heavy metal. Fripp once compared playing onstage with Wetton and drummer Bill Bruford to working with "a flying brick wall".


title: John Wetton

text: After the dissolution of King Crimson, Wetton continued to work on various projects, including a tour with Roxy Music and two albums with Uriah Heep. While still with King Crimson, Wetton had been asked by Roxy Music to "sit in" on their auditions for a replacement bass player and give his recommendations; dissatisfied with all the applicants, he offered to do the 1975 tour with the group himself so as to give them time to find a good bassist. In 1977, after failed attempts to reunite King Crimson and to create a new band with Rick Wakeman, Wetton formed U.K. with his King Crimson rhythm section partner Bill Bruford. Wetton recruited Roxy Music keyboardist/violinist Eddie Jobson, while Bruford brought in innovative guitarist Allan Holdsworth from his solo group. U.K. adopted a more composition-driven approach than King Crimson, per Wetton's preference.


title: John Wetton

text: After the break-up of U.K., Wetton released his first solo album, "Caught in the Crossfire" (1980). Later that year he had a brief stint in Wishbone Ash, appearing on their album "Number the Brave" (1981). In late 1981 he had a meeting with Geffen Records' boss John Kalodner who took him to task for playing bass in Bryan Ferry's backing band, feeling he should be fronting a group himself. At Kalodner's insistence, Wetton started writing with former Yes guitarist Steve Howe, with a view to forming their own band. Joined by keyboardist Geoff Downes, and drummer Carl Palmer (of Emerson, Lake & Palmer), this band would become Asia, and they produced one of the best selling albums of the 1980s. Their self-titled debut album "Asia" sold over 10 million copies worldwide, making the band a household name across the globe. John worked with Asia until 1983. In that year, Wetton was fired from Asia (at the insistence of Geffen Records) for then unknown reasons, but at least in part due to lower-than-expected sales of the "Alpha" (1983) album. He returned to Asia in 1985 (with Mandy Meyer replacing Steve Howe on guitar) to complete "Astra" (1985).


title: John Wetton

text: In the late 1980s, a collaboration between Wetton and Roxy Music guitarist Phil Manzanera was released as "Wetton/Manzanera" (1986). Around this time, Wetton began working with Geoff Downes and Carl Palmer to restart Asia. Some of the material they recorded was featured on 1990's "Then & Now" CD, including a radio hit in "Days Like These."


title: John Wetton

text: The 1990s saw Wetton mostly focusing on his solo career. In 1999, an aborted attempt to reform Asia resulted in Wetton and Carl Palmer forming a short-lived progressive group dubbed Qango with John Young and Dave Kilminster. Qango performed several shows in the UK, and recorded a live album, "Live in the Hood", before disbanding.


title: John Wetton

text: In the early 2000s, Wetton reunited with Geoff Downes for Icon. In 2006, a reunion of the original Asia line-up (Wetton, Downes, Howe, Palmer) finally occurred. A studio album titled "Phoenix" (2008), the original band's first since 1983's "Alpha", was released in April 2008 and peaked at No. 73 on the Billboard 200 albums chart in the United States. The original line-up released two more studio albums, "Omega" (2010) and "XXX" (2012) before Howe departed in January 2013 to focus on Yes. With new guitarist Sam Coulson, Asia released "Gravitas" in March of 2014.


title: John Wetton

text: In 2013, he guested on the album "Grandine il vento" with Renaissance, with whom he had played live 42 years before. That same year, he toured with "American Idol" finalist Leslie Hunt's Chicago-based band District 97 to commemorate the 40th anniversary of the King Crimson album "Larks' Tongues In Aspic".


title: John Wetton

text: Wetton also worked extensively as a session musician with such musicians as Brian Eno, Bryan Ferry and Ayreon.


title: John Wetton

text: Wetton died in his sleep from complications of colorectal cancer at the Macmillan Unit at Christchurch Hospital in Christchurch, Dorset, on 31 January 2017. He was survived by his wife Lisa, son Dylan, brother Robert and mother Margaret (Peggy).


title: John Wetton

text: Billy Sherwood, who was Wetton's producer, co-songwriter and co-performer on his 2011 solo album "Raised in Captivity", replaced him in Asia. On June 17, 2017, Asia performed a special concert in Wetton's memory, titled "An Extraordinary Life" (full title: "An Extraordinary Life - An Interactive Celebration of the Life & Music of John Wetton"), in reference to the eponymous song from the Asia album "Phoenix"; Fan-submitted performances were shown on a large video screen above the stage. Some King Crimson songs were also performed at the event.


title: John Wetton

text: Asteroid 72802 Wetton, discovered by Marc Buie at Kitt Peak National Observatory in 2001, was named in his memory. The official was published by the Minor Planet Center on 18 May 2019 ().


title: John Wetton

text: Artists who have cited Wetton as an influence, or have expressed their admiration for him, include Billy Sheehan, Juan Alderete of The Mars Volta and Racer X, Michael Sweet of Stryper, Ron Anderson, and Joseph D. Rowland of Pallbearer. Following Wetton's death, Eric Clapton published a short instrumental tribute entitled, "For John W."


title: Sharp Stick

text: Sharp Stick is a 2022 American comedy film written, directed, and produced by Lena Dunham. It stars Kristine Froseth, Jon Bernthal, Luka Sabbat, Scott Speedman, Dunham, Ebon Moss-Bachrach, Taylour Paige, and Jennifer Jason Leigh. The film premiered at the Sundance Film Festival on January 22, 2022, and was released theatrically in the United States on July 29, 2022, by Utopia. It received mixed reviews from critics. It was released on VOD on August 16, 2022.


title: Sharp Stick

text: 26-year-old babysitter Sarah Jo, who had a radical hysterectomy at age 15, loses her virginity to her employer, Josh, a married man.


title: Sharp Stick

text: In April 2020, Lena Dunham moved from London to Silver Lake, Los Angeles, in the midst of the COVID-19 pandemic. She passed the time watching a number of films from the 1970s, including "Belle de Jour", "A Woman Under the Influence", "Remember My Name", and "An Unmarried Woman". The films, as well as the impact of a hysterectomy, motivated Dunham to write, direct, and star in "Sharp Stick". "It was about processing my life. And then, obviously, it becomes about the characters — and not about you at all." After receiving the script, Jon Bernthal and Jennifer Jason Leigh were immediately on board to star. Taylour Paige, however, was initially hesitant with joining the cast: "If I'm being honest. I was like, 'Don't you think this character was written as a white person?" Dunham convinced Paige to star by telling her that she had written the part with her in mind.


title: Sharp Stick

text: With an all-female production crew, filming took place in secret in Atwater Village and Eagle Rock, Los Angeles, in early 2021. According to lead actress Kristine Froseth, "There was a good energy all around. We had an amazing intimacy coordinator. Everything was choreographed — no surprises." In March 2021, the film was presented to buyers at the 71st Berlin International Film Festival. In August 2021, Tommy Dorfman was confirmed to star. Dunham's husband Luis Felber composed the musical score.


title: Sharp Stick

text: The film premiered virtually at the 2022 Sundance Film Festival on January 22. In an interview, Dunham said "There are many greater tragedies than me not getting to see my movie premiere but I was so excited for my cast to get to see it together. We did it on such a small scale, and everyone really brought everything to it. It was such a harkening back to how I started. But we're planning a Zoom party. I guess people Zoomed into my wedding — and they'll Zoom into my premiere." In February 2022, Utopia acquired the film's distribution rights. It was released in theaters on July 29, 2022.


title: Project Jupyter

text: Project Jupyter () is a project with goals to develop open-source software, open standards, and services for interactive computing across multiple programming languages. It was spun off from IPython in 2014 by Fernando Pérez and Brian Granger. Project Jupyter's name is a reference to the three core programming languages supported by Jupyter, which are Julia, Python and R. Its name and logo are an homage to Galileo's discovery of the moons of Jupiter, as documented in notebooks attributed to Galileo. Project Jupyter has developed and supported the interactive computing products Jupyter Notebook, JupyterHub, and JupyterLab. Jupyter is financially sponsored by NumFOCUS.


title: Project Jupyter

text: The first version of Notebooks for IPython was released in 2011 by a team including Fernando Pérez, Brian Granger, and Min Ragan-Kelley. In 2014, Pérez announced a spin-off project from IPython called Project Jupyter. IPython continues to exist as a Python shell and a kernel for Jupyter, while the notebook and other language-agnostic parts of IPython moved under the Jupyter name. Jupyter supports execution environments (called "kernels") in several dozen languages, including Julia, R, Haskell, Ruby, and Python (via the IPython kernel).


title: Project Jupyter

text: In 2015, about 200,000 Jupyter notebooks were available on GitHub. By 2018, about 2.5 million were available. In January 2021, nearly 10 million were available, including notebooks about the first observation of gravitational waves and about the 2019 discovery of a supermassive black hole.


title: Project Jupyter

text: Major cloud computing providers have adopted the Jupyter Notebook or derivative tools as a frontend interface for cloud users. Examples include Amazon SageMaker Notebooks, Google's Colaboratory, and Microsoft's Azure Notebook.


title: Project Jupyter

text: Visual Studio Code supports local development of Jupyter notebooks. As of July 2022, the Jupyter extension for VS Code has been downloaded over 40 million times, making it the second-most popular extension in the VS Code Marketplace.


title: Project Jupyter

text: "The Atlantic" published an article entitled "The Scientific Paper Is Obsolete" in 2018, discussing the role of Jupyter Notebook and the Mathematica notebook in the future of scientific publishing. Economist Paul Romer, in response, published a blog post in which he reflected on his experiences using Mathematica and Jupyter for research, concluding in part that Jupyter "does a better job of delivering what Theodore Gray had in mind when he designed the Mathematica notebook."


title: Project Jupyter

text: Jupyter Notebook can colloquially refer to two different concepts, either the user facing application to edit code and text, or the underlying file format which is interoperable across many implementations.


title: Project Jupyter

text: Jupyter Notebook (formerly IPython Notebook) is a web-based interactive computational environment for creating notebook documents. Jupyter Notebook is built using several open-source libraries, including IPython, ZeroMQ, Tornado, jQuery, Bootstrap, and MathJax. A Jupyter Notebook application is a browser-based REPL containing an ordered list of input/output cells which can contain code, text (using Markdown), mathematics, plots and rich media.


title: Project Jupyter

text: Jupyter Notebook is similar to the notebook interface of other programs such as Maple, Mathematica, and SageMath, a computational interface style that originated with Mathematica in the 1980s. Jupyter interest overtook the popularity of the Mathematica notebook interface in early 2018.


title: Project Jupyter

text: JupyterLab is a newer user interface for Project Jupyter, offering a flexible user interface and more features than the classic notebook UI. The first stable release was announced on February 20, 2018. In 2015, a joint $6 million grant from The Leona M. and Harry B. Helmsley Charitable Trust, The Gordon and Betty Moore Foundation, and The Alfred P. Sloan Foundation funded work that led to expanded capabilities of the core Jupyter tools, as well as to the creation of JupyterLab.


title: Project Jupyter

text: GitHub announced in November 2022 that JupyterLab would be available in its online Coding platform called Codespace.


title: Project Jupyter

text: JupyterHub is a multi-user server for Jupyter Notebooks. It is designed to support many users by spawning, managing, and proxying many singular Jupyter Notebook servers.


title: Project Jupyter

text: A Jupyter Notebook document is a JSON file, following a versioned schema, usually ending with the ".ipynb" extension.


title: Project Jupyter

text: The main parts of the Jupyter Notebooks are: Metadata, Notebook format and list of cells. Metadata is a data Dictionary of definitions to set up and display the notebook. Notebook Format is a version number of the software. List of cells are different types of Cells for Markdown (display), Code (to execute), and output of the code type cells.


title: Project Jupyter

text: While ".ipynb" and JSON are the most common and default format it is possible to forgo some features (like storing images and metadata), and save notebook as markdown documents using extension like JupyText. Jupytext is often in conjunction with version control to make diffing and merging of notebook simpler.


title: Operation Midnight Climax

text: Operation Midnight Climax was an operation carried out by the CIA as a sub-project of Project MKUltra, the mind-control research program that began in the 1950s. It was initially established in 1954 by Sidney Gottlieb and placed under the direction of the Federal Bureau of Narcotics in Boston, Massachusetts with the "Federal Narcotics Agent and CIA consultant" George Hunter White under the pseudonym of Morgan Hall. Dr. Sidney Gottlieb was a chemist who was chief of the Chemical Division of the Technical Services Staff of the CIA. Under the Cold War and fears of the Soviet Union and China, Gottlieb felt inspired to investigate methods of mind control. Gottlieb based his plan for Project MKUltra and Operation Midnight Climax off of interrogation method research under Project Artichoke. Unlike Project Artichoke, Operation Midnight Climax gave Gottlieb permission to test drugs on unknowing citizens, which made way for the legacy of this operation. Hundreds of federal agents, field operatives, and scientists worked on these programs before they were shut down in the 1960s.


title: Operation Midnight Climax

text: Official results of these experiments were not released, but accounts from supervisors of the experiments give little insight to the findings. George Hunter White, an agent at the Federal Bureau of Narcotics, and Ira "Ike" Feldman, a former military intelligence officer, who oversaw San Francisco experiments, noticed that subjects spoke far more freely when under the influence of a combination of drugs and sex. "No one knows where they [human test subjects] are now, or what effects they may have suffered."


title: Operation Midnight Climax

text: Operation Midnight Climax started in 1954 and consisted of a web of CIA-run safehouses in San Francisco at 225c Chestnut Street, San Francisco, CA, and Mill Valley, California, as well as New York City. The safehouses were dramatically scaled back in 1963, following a report by CIA Inspector General John Earman which strongly recommended closing the facility. The San Francisco safehouses were closed in 1965, and the New York City safehouse soon followed in 1966. Operation Midnight Climax and Project MKUltra were considered to be so secretive that few people, even in the highest government positions, knew Gottlieb existed, let alone was conducting these experiments. However, some senior officers in the CIA knew enough about him to connect his work to LSD.


title: Operation Midnight Climax

text: Operation Midnight Climax was established in order to study the effects of LSD on non-consenting individuals. Prostitutes on the CIA payroll were instructed to lure clients back to the safehouses, where they were surreptitiously plied with a wide range of substances, including LSD, and monitored behind one-way glass. The prostitutes were instructed in the use of post-coital questioning to investigate whether the victims could be convinced to involuntarily reveal secrets. The victims were sometimes fed subliminal messages in attempts to induce them to involuntary actions, including criminal activity such as robbery, assault, and assassination. Many of the CIA operatives involved in the experiments voluntarily indulged in the drugs and prostitutes for recreational purposes. Additionally, information from Wilmington News Journal on October 15, 1978, reports from a FOIA request that, "the spy agency purchased two pounds of Yohimbine hydrochloride... by Dr. Robert V. Lashbrook, the chief aide to Dr. Sidney Gottlieb." The role of Dr. Lashbrook was to, "monitor and approve materials for Operation Midnight Climax."


title: Operation Midnight Climax

text: Senate investigators were told that the goals of these experiments were to study mind control and sexual behavior. More specifically, to learn about the secrets of brainwashing to gain control over enemy spies and protect U.S. agents. Other objectives included finding drugs that could incapacitate entire buildings via poisoned food, which would create "confusion-anxiety-fear," and other symptoms such as headaches and earaches. These drugs could also have amnesia effects, which were intended for use on foreign spies following interrogations and retiring CIA agents. Another aspect they tested was the effect of combining LSD and isolation, where the subjects would be dosed and isolated for months at a time with minimal food and water.


title: Operation Midnight Climax

text: In 1947, the CIA was prohibited on behalf of President Truman, due to fears of political abuse, from spying against American citizens, but these actions contradict the adherence to this prohibition. These acts were illegal and several significant operational techniques were developed in this theater, including extensive research into sexual blackmail, surveillance technology and the possible use of mind-altering drugs in field operations. Furthermore, the CIA operatives in charge of administering these experiments were told by superiors that the results of the experiments would be beneficial to the country. There is currently a debate over how ethical George Hunter White's actions were, with some arguing that if his motive was to legally make people suffer, he was unethical, while others argue that if he believed that the experiments would benefit national security, his actions could be justified. The subjects of Gottlieb's experiments also included mentally disabled children. Operation Midnight Climax program was soon expanded, and CIA operatives began dosing people in restaurants, bars, and beaches along with signing up to use the drugs themselves. The extent to which this widespread exposure of the public to mind-altering drugs contributed to the rise of the counter-culture movement in the late 1950s and 1960s is unknown, although Ken Kesey has attributed his role in the genesis of the influential San Francisco Bay Area psychedelic social scene that developed in the 1960s to his participation in Project MKUltra LSD experiments at the Menlo Park, California, VA Hospital.


title: Operation Midnight Climax

text: In 1974, the New York Times journalist Seymour Hersh published a story exposing the CIA's illegal spying on U.S. citizens and how the CIA had conducted non-consensual drug experiments. His report started the lengthy process of bringing long-suppressed details about MKUltra to light. Project MKUltra came to light in the spring of 1977 during a wide-ranging survey of the CIA's Technical Services Division. John K. Vance, a member of the CIA inspector general's staff, discovered that the agency was running a research project that included administering LSD and other drugs to unwilling human subjects. Additionally, several CIA FOIA requests revealed a collection of documents from several news sources in the late 1970s reporting information on Operation Midnight Climax.


title: Operation Midnight Climax

text: There were a handful of newspaper articles released in the 1970s by the San Francisco examiner, Wilmington News Journal, the Washington Post, and the Washington Star revolving around these revelations and elaborated on what the CIA was doing, but they fail to include much of the motive and explicit details as the CIA never released most of the findings and the information never went public.


title: Operation Midnight Climax

text: In 1975, President Ford set up the United States President' Commission on CIA Activities. The purpose of this commission, which is commonly referred to as the Rockefeller Commission, was to investigate possible illegal activities being performed by the CIA. Project MKUltra, Operation Midnight Climax, and other similar projects were a part of the investigation. According to the Rockefeller Commission Report, the CIA was charged with various illegal activities such as large-scale spying on American citizens, engaging in illegal wire-taps, and aiming their illegal activities at Americans who openly disagreed with the government. As a result of these findings, President Ford signed an Executive Order in 1976 that prohibited "experimentation with drugs on human subjects, except with the informed consent, in writing and witnessed by a disinterested party, of each such human subject." This attempted to prevent unethical projects from occurring in the future.


title: Operation Midnight Climax

text: In 1977, Senator Edward Kennedy conducted congressional hearings investigating MKUltra. Many ex-CIA employees were brought in for questioning; Congress interrogated them about "who oversaw these programs, how participants were identified, and if any of these programs had been continued." After the incident came to light, the United States government was compelled by their constituents to find out the reasoning for these unethical experiments on the United States citizens. As a result, four subpoenas were issued by Senator Edward M Kennedy, one by his subcommittee on Health and Scientific Research. A former CIA employee, whose name is known as Walter Pasternak, was noted for "hiding from investigators" stating that he would return after 24 hours. The documents that the senate investigation committee revealed showed receipts signed by the former CIA employee for "52,000 $100 bills that were distributed to persons involved in "Operation Midnight Climax."" Pasternak, the CIA employee, also provided the subcommittee with an account of how the activities were in relation to the CIA-funded research group that conducted human behavior experiments. Other CIA employees who were subpoenaed were Dr. Sidney Gottlieb and Robert Lashbrook and the consultant who was subpoenaed was a former Georgetown University professor, Dr. Charles Geschickter. Unfortunately, when the hearing date came around, "all four of them made the decision independently not to testify" The senate committee continued to investigate the issue and were able to get testimony from Pasternak, yet the information from him and others related to the project wasn't considered the most accurate, resulting in a lack of action taken by the U.S. government against the CIA.


title: Operation Midnight Climax

text: The CIA's LSD experiments continued until 1963 before being shut down. In 1963, John Vance, a member of the CIA Inspector General's staff, learned about the projects "surreptitious administration to unwitting nonvoluntary human subjects." Though the MKUltra directors argued for the continuation, the Inspector General insisted the agency follow ethical research guidelines, which brought the programs testing on non-consenting volunteers to an end.


title: Operation Midnight Climax

text: Unfortunately, the paper records of the operation were destroyed, and during the trials, many agents claimed they could not remember details about it and there were no records for congress to verify, thus, leading to no noted convictions or justice for the CIA and individuals involved.