Platonic Solid: In Euclidean Geometry, A Platonic Solid Is A Regular, Convex Polyhedron With Congruent

5 NASA Software Codes You Can Download – For Free!

One of the biggest steps of any mission starts right here on Earth at a computer desk – NASA runs on software, period. Rovers can’t move, spacecraft can’t fly, even rockets can’t blast off without the software codes that run them all.

We’ve compiled hundreds of these powerful codes into one location at software.nasa.gov. And guess what? You can start downloading them right now for free! Here are just a few you can use:  

1. TetrUSS (Tetrahedral Unstructured Software System)

TetrUSS has been used extensively for space launch vehicle analysis and design, like on the Space Launch System, which is planned to take humans to Mars.

You really could say it’s helping us to “blast off.” Outside of NASA, this software has been used to analyze Mars planetary entry vehicles, ballistics and even high-altitude sky diver aerodynamics. Basically if anything has moved through any planetary atmosphere, this software has played a role.

2. KNIFE (part of the FUN3D software and released as a package)

The name may be a bit intimidating, but with good reason – KNIFE packs a powerful punch. 

It was created to help us learn more about the sonic booms that resonate when planes break the sound barrier, but it has also helped develop green energy sources such as wind turbines and techniques to minimize drag for long-haul trucking. Maybe we should re-name this versatile and handy code, “Swiss Army KNIFE?”

3. Cart3D (Automated Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation)

If software codes went to high school, Cart3D would be Prom Queen. This software is so popular, it is being used in almost every mission area here at NASA. 

Engineers and scientists are currently using it to model everything from advanced drones to quieter supersonic aircraft.

4. FACET (Future Air Traffic Management Concepts Evaluation Tool)

Frequent flyers: this may be your favorite code without even knowing it. FACET was developed to evaluate futuristic concepts in air traffic management, and it has served as a testbed for assessing today’s regular operations. 

To sum it up, this software code helps airports keep planes organized in the air and on the ground.

5. GIPSY-OASIS

GIPSY-OASIS is part of the GPS system to end all GPS systems. It’s so accurate, John Deere used it to help create self-driving tractors.

 How? John Deere already had a navigation system in the works, but it could only be used in certain parts of the world. 

Our ground stations are all across the globe, and our software ensures accuracy down to a few inches. And so, a new breed of tractor was born!  Did we mention this software is free?

These are just a few examples of the software NASA has available for free public and consumer use. To browse the catalog online, check out software.nasa.gov.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

The math trick that college will never teach you! : Parametric Integration

Parametric integration is one such technique that once you are made aware of it, you will never for the love of god forget it. It goes by many names : ‘Differentiation under the Integral sign’, ‘Feynman’s famous trick’ , ‘Parametric Integration’ and so on.

Let me demonstrate :

Now this integral might seem familiar to you if you have taken a calculus course before and to evaluate it is rather simple as well.

Knowing this you can do lots of crazy stuff. Lets differentiate this expression wrt to the parameter in the integral – s (Hence the name parametric integration ). i.e 

Look at that, by simple differentiation we have obtained the expression for another integral. How cool is that! It gets even better.

Lets differentiate it once more: 

.

.

.

If you keep on differentiating the expression n times, one gets this : 

Now substituting the value of s to be 1, we obtain the following integral expression for the factorial. This is known as the gamma function.

There are lots of ways to derive the above expression for the gamma function, but parametric integration is in my opinion the most subtle way to arrive at it. :D

This is a really powerful technique and I strong suggest that if you have taken calculus, then please do read this article.

Have a great day!

EDIT:  It had to be gamma(n+1) not gamma(n) .Thank you @mattchelldavis

List of medieval European scientists

Anthemius of Tralles (ca. 474 – ca. 534): a professor of geometry and architecture, authored many influential works on mathematics and was one of the architects of the famed Hagia Sophia, the largest building in the world at its time. His works were among the most important source texts in the Arab world and Western Europe for centuries after.

John Philoponus (ca. 490–ca. 570): also known as John the Grammarian, a Christian Byzantine philosopher, launched a revolution in the understanding of physics by critiquing and correcting the earlier works of Aristotle. In the process he proposed important concepts such as a rudimentary notion of inertia and the invariant acceleration of falling objects. Although his works were repressed at various times in the Byzantine Empire, because of religious controversy, they would nevertheless become important to the understanding of physics throughout Europe and the Arab world.

Paul of Aegina (ca. 625–ca. 690): considered by some to be the greatest Christian Byzantine surgeon, developed many novel surgical techniques and authored the medical encyclopedia Medical Compendium in Seven Books. The book on surgery in particular was the definitive treatise in Europe and the Islamic world for hundreds of years.

The Venerable Bede (ca. 672–735): a Christian monk of the monasteries of Wearmouth and Jarrow who wrote a work On the Nature of Things, several books on the mathematical / astronomical subject of computus, the most influential entitled On the Reckoning of Time. He made original discoveries concerning the nature of the tides and his works on computus became required elements of the training of clergy, and thus greatly influenced early medieval knowledge of the natural world.

Rabanus Maurus (c. 780 – 856): a Christian monk and teacher, later archbishop of Mainz, who wrote a treatise on Computus and the encyclopedic work De universo. His teaching earned him the accolade of "Praeceptor Germaniae," or "the teacher of Germany."

Abbas Ibn Firnas (810 – 887): a polymath and inventor in Muslim Spain, made contributions in a variety of fields and is most known for his contributions to glass-making and aviation. He developed novel ways of manufacturing and using glass. He broke his back at an unsuccessful attempt at flying a primitive hang glider in 875.

Pope Sylvester II (c. 946–1003): a Christian scholar, teacher, mathematician, and later pope, reintroduced the abacus and armillary sphere to Western Europe after they had been lost for centuries following the Greco-Roman era. He was also responsible in part for the spread of the Hindu-Arabic numeral system in Western Europe.

Maslamah al-Majriti (died 1008): a mathematician, astronomer, and chemist in Muslim Spain, made contributions in many areas, from new techniques for surveying to updating and improving the astronomical tables of al-Khwarizmi and inventing a process for producing mercury oxide.[citation needed] He is most famous, though, for having helped transmit knowledge of mathematics and astronomy to Muslim Spain and Christian Western Europe.

Abulcasis (936-1013): a physician and scientist in Muslim Spain, is considered to be the father of modern surgery. He wrote numerous medical texts, developed many innovative surgical instruments, and developed a variety of new surgical techniques and practices. His texts were considered the definitive works on surgery in Europe until the Renaissance.

Constantine the African (c. 1020&–1087): a Christian native of Carthage, is best known for his translating of ancient Greek and Roman medical texts from Arabic into Latin while working at the Schola Medica Salernitana in Salerno, Italy. Among the works he translated were those of Hippocrates and Galen.

Arzachel (1028–1087): the foremost astronomer of the early second millennium, lived in Muslim Spain and greatly expanded the understanding and accuracy of planetary models and terrestrial measurements used for navigation. He developed key technologies including the equatorium and universal latitude-independent astrolabe.

Avempace (died 1138): a famous physicist from Muslim Spain who had an important influence on later physicists such as Galileo. He was the first to theorize the concept of a reaction force for every force exerted.

Adelard of Bath (c. 1080 – c. 1152): was a 12th-century English scholar, known for his work in astronomy, astrology, philosophy and mathematics.

Avenzoar (1091–1161): from Muslim Spain, introduced an experimental method in surgery, employing animal testing in order to experiment with surgical procedures before applying them to human patients.[4] He also performed the earliest dissections and postmortem autopsies on both humans as well as animals.

Robert Grosseteste (1168–1253): Bishop of Lincoln, was the central character of the English intellectual movement in the first half of the 13th century and is considered the founder of scientific thought in Oxford. He had a great interest in the natural world and wrote texts on the mathematical sciences of optics, astronomy and geometry. In his commentaries on Aristotle's scientific works, he affirmed that experiments should be used in order to verify a theory, testing its consequences. Roger Bacon was influenced by his work on optics and astronomy.

Albert the Great (1193–1280): Doctor Universalis, was one of the most prominent representatives of the philosophical tradition emerging from the Dominican Order. He is one of the thirty-three Saints of the Roman Catholic Church honored with the title of Doctor of the Church. He became famous for his vast knowledge and for his defence of the pacific coexistence between science and religion. Albert was an essential figure in introducing Greek and Islamic science into the medieval universities, although not without hesitation with regard to particular Aristotelian theses. In one of his most famous sayings he asserted: "Science does not consist in ratifying what others say, but of searching for the causes of phenomena." Thomas Aquinas was his most famous pupil.

John of Sacrobosco (c. 1195 – c. 1256): was a scholar, monk, and astronomer (probably English, but possibly Irish or Scottish) who taught at the University of Paris and wrote an authoritative and influential mediaeval astronomy text, the Tractatus de Sphaera; the Algorismus, which introduced calculations with Hindu-Arabic numerals into the European university curriculum; the Compotus ecclesiasticis on Easter reckoning; and the Tractatus de quadrante on the construction and use of the astronomical quadrant.

Jordanus de Nemore (late 12th, early 13th century): was one of the major pure mathematicians of the Middle Ages. He wrote treatises on mechanics ("the science of weights"), on basic and advanced arithmetic, on algebra, on geometry, and on the mathematics of stereographic projection.

Villard de Honnecourt (fl. 13th century): a French engineer and architect who made sketches of mechanical devices such as automatons and perhaps drew a picture of an early escapement mechanism for clockworks.

Roger Bacon (1214–94): Doctor Admirabilis, joined the Franciscan Order around 1240 where, influenced by Grosseteste, Alhacen and others, he dedicated himself to studies where he implemented the observation of nature and experimentation as the foundation of natural knowledge. Bacon wrote in such areas as mechanics, astronomy, geography and, most of all, optics. The optical research of Grosseteste and Bacon established optics as an area of study at the medieval university and formed the basis for a continuous tradition of research into optics that went all the way up to the beginning of the 17th century and the foundation of modern optics by Kepler.[8]

Ibn al-Baitar (died 1248): a botanist and pharmacist in Muslim Spain, researched over 1400 types of plants, foods, and drugs and compiled pharmaceutical and medical encyclopedias documenting his research. These were used in the Islamic world and Europe until the 19th century.

Theodoric Borgognoni (1205-1296): was an Italian Dominican friar and Bishop of Cervia who promoted the uses of both antiseptics and anaesthetics in surgery. His written work had a deep impact on Henri de Mondeville, who studied under him while living in Italy and later became the court physician for King Philip IV of France.

William of Saliceto (1210-1277): was an Italian surgeon of Lombardy who advanced medical knowledge and even challenged the work of the renowned Greco-Roman surgeon Galen (129-216 AD) by arguing that allowing pus to form in wounds was detrimental to the health of he patient.

Thomas Aquinas (1227–74): Doctor Angelicus, was an Italian theologian and friar in the Dominican Order. As his mentor Albert the Great, he is a Catholic Saint and Doctor of the Church. In addition to his extensive commentaries on Aristotle's scientific treatises, he was also said to have written an important alchemical treatise titled Aurora Consurgens. However, his most lasting contribution to the scientific development of the period was his role in the incorporation of Aristotelianism into the Scholastic tradition.

Arnaldus de Villa Nova (1235-1313): was an alchemist, astrologer, and physician from the Crown of Aragon who translated various Arabic medical texts, including those of Avicenna, and performed optical experiments with camera obscura.

John Duns Scotus (1266–1308): Doctor Subtilis, was a member of the Franciscan Order, philosopher and theologian. Emerging from the academic environment of the University of Oxford. where the presence of Grosseteste and Bacon was still palpable, he had a different view on the relationship between reason and faith as that of Thomas Aquinas. For Duns Scotus, the truths of faith could not be comprehended through the use of reason. Philosophy, hence, should not be a servant to theology, but act independently. He was the mentor of one of the greatest names of philosophy in the Middle Ages: William of Ockham.

Mondino de Liuzzi (c. 1270-1326): was an Italian physician, surgeon, and anatomist from Bologna who was one of the first in Medieval Europe to advocate for the public dissection of cadavers for advancing the field of anatomy. This followed a long-held Christian ban on dissections performed by the Alexandrian school in the late Roman Empire.

William of Ockham (1285–1350): Doctor Invincibilis, was an English Franciscan friar, philosopher, logician and theologian. Ockham defended the principle of parsimony, which could already be seen in the works of his mentor Duns Scotus. His principle later became known as Occam's Razor and states that if there are various equally valid explanations for a fact, then the simplest one should be chosen. This became a foundation of what would come to be known as the scientific method and one of the pillars of reductionism in science. Ockham probably died of the Black Plague. Jean Buridan and Nicole Oresme were his followers.

Jacopo Dondi dell'Orologio (1290-1359): was an Italian doctor, clockmaker, and astronomer from Padua who wrote on a number of scientific subjects such as pharmacology, surgery, astrology, and natural sciences. He also designed an astronomical clock.

Richard of Wallingford (1292-1336): an English abbot, mathematician, astronomer, and horologist who designed an astronomical clock as well as an equatorium to calculate the lunar, solar and planetary longitudes, as well as predict eclipses.

Jean Buridan (1300–58): was a French philosopher and priest. Although he was one of the most famous and influent philosophers of the late Middle Ages, his work today is not renowned by people other than philosophers and historians. One of his most significant contributions to science was the development of the theory of impetus, that explained the movement of projectiles and objects in free-fall. This theory gave way to the dynamics of Galileo Galilei and for Isaac Newton's famous principle of Inertia.

Guy de Chauliac (1300-1368): was a French physician and surgeon who wrote the Chirurgia magna, a widely read publication throughout medieval Europe that became one of the standard textbooks for medical knowledge for the next three centuries. During the Black Death he clearly distinguished Bubonic Plague and Pneumonic Plague as separate diseases, that they were contagious from person to person, and offered advice such as quarantine to avoid their spread in the population. He also served as the personal physician for three successive popes of the Avignon Papacy.

John Arderne (1307-1392): was an English physician and surgeon who invented his own anesthetic that combined hemlock, henbane, and opium. In his writings, he also described how to properly excise and remove the abscess caused by anal fistula.

Nicole Oresme (c. 1323–82): was one of the most original thinkers of the 14th century. A theologian and bishop of Lisieux, he wrote influential treatises in both Latin and French on mathematics, physics, astronomy, and economics. In addition to these contributions, Oresme strongly opposed astrology and speculated about the possibility of a plurality of worlds.

Giovanni Dondi dell'Orologio (c. 1330-1388): was a clockmaker from Padua, Italy who designed the astarium, an astronomical clock and planetarium that utilized the escapement mechanism that had been recently invented in Europe. He also attempted to describe the mechanics of the solar system with mathematical precision.

Southeast Asia’s Ramayana Epic Versions.

The Ramayana epic is well known in many parts of Asia as the Homer’s Iliad is to the West. It is a story with many versions of the tale, told throughout South and Southeast Asia and shows the history and influence of Hinduism throughout the Southeast Asian region. Here is a list of the well known versions from different countries in SEA. Some differ and have been adapted to the local culture but all tell the same tale.

1.) Indonesia ~ Kakawin Ramayana

Kakawin Ramayana is an Old Javanese rendering of the Sanskrit Ramayana in kakawin meter. It is believed to have been written in Central Java (modern Indonesia) in approximately 870 AD during the era of Medang Kingdom. Kakawin Rāmâyaṇa is a so-called kakawin, the Javanese form of kāvya, a poem modeled on traditional Sanskrit meters. Among the Javanese, Kakawin Ramayana has always been considered the pinnacle of artistic expression. The large number of preserved manuscripts attest to it popularity and adaptation. It is the lengthiest of all the Old Javanese kakawins of the Hindu-Buddhist period of Java.

2.) Myanmar ~ Yama Zatdaw

Yama Zatdaw is the Burmese version of the Ramayana. There are nine known pieces of the Yama Zatdaw in Myanmar. The Burmese name for the story itself is Yamayana, while zatdaw refers to the acted play or being part of jataka tales of Theravada Buddhism. The Yama Zatdaw was introduced by oral tradition during King Anawratha’s reign although it was not known clearly whether the story was Valmiki’s Sanskrit epic Ramayana or not. In the Nathlaung Temple, the Visnu temple, within the walls of old city Bagan, there are some stone sculptures, one of which is Ramachandra. Based on Burmese literature, at least, Hanuman has been known in Burma definitely before 1527 AD.

3) Thailand ~ Ramakien

The Ramakien (รามเกียรติ์, “Glory of Rama”, sometimes also spelled Ramakien) is Thailand’s national epic, derived from the Hindu epic Ramayana. The word is derived from Sanskrit word Ramakhyan (Ram + Akhyan) where Akhyan means a long story or epic. A number of versions of the epic were lost in the destruction of Ayutthaya in 1767. Three versions currently exist, one of which was prepared in 1797 under the supervision of (and partly written by) King Rama I. His son, Rama II, rewrote some parts of his father’s version for khon drama. The work has had an important influence on Thai literature, art and drama (both the khon and nang dramas being derived from it). While the main story is identical to that of the Ramayana, many other aspects were transposed into a Thai context, such as the clothes, weapons, topography, and elements of nature, which are described as being Thai in style. Although Thailand is considered a Theravada Buddhist society, the Hindu mythology latent in the Ramakien serves to provide Thai legends with a creation myth, as well as representations of various spirits which complement beliefs derived from Thai animism. A painted representation of the Ramakian is displayed at Bangkok’s Wat Phra Kaew, and many of the statues there depict characters from it.

4.) Philippines ~ Darangen

The Philippines is one of the last places in Southeast Asia where most people wouldn’t expect influences of Hinduism & Buddhism in the culture and country. Yet despite heavy colonization and Westernization, many parts of the Philippines were Indianized and practiced a form of Hinduism & Buddhism as the rest of Southeast Asia. Traces of that history can still be found in artifacts recovered and in epics. One such epic is the Darangen of the Maranao. Darangen comes from two root words, meaning “to narrate in song.” The Darangen was first told in the fourteenth century A.D. The Darangen Epic of the Maranaos, including the Maharadia Rawana, is an indigenized version of the Ramayana. Most people believe that the popular traditional Singkil dance  is indigenous to the Maguindanao ethnic group or to the Maranao ethnic group in Mindanao or both. But in fact, the Singkil is a Maguindanao and Maranao interpretation of the Ramayana epic, as retold in the Darangen Epic, where the original polytheistic accounts were restated and transformed to conform to monotheistic Islam to which the Maranaos and Maguindanaos adhere. Note,however, that the Singkil is not religious and it is not Muslim. It is a secular dance of the Maranaos and the Maguindanaos, the majority of whom are Muslims.

5.) Laos ~ Phra Lak Phra Lam

Phra Lak Phra Ram is the national epic of the Lao people, and is adapted from Valmiki’s Hindu epic, the Ramayana. Similar to some Malay versions of the Hikayat Seri Rama, the epic has lost the association with Hinduism and is instead considered a Jataka Story, a previous lifetime of the Buddha. It is also very popular in Northeastern Thailand, or Isan, a region of Thailand mostly populated by ethnic Lao and formerly part of Lanxang.

6.) Malaysia ~ Hikayat Seri Rama

Hikayat Seri Rama is the Malay literary adaptation of the Hindu Ramayana epic. The main story remains the same as the original Sanskrit version but some aspects of it were slightly modified to a local context such as the spelling and pronunciation of names. Numerous branch stories had also been developed as accretions to or extensions of this epic with the upgrading of minor characters to major ones, or the invention of totally new characters. For example, Malay writers and storytellers have produced variations in which Laksmana (Lakshman) plays a larger role, sometimes becoming more important than Rama the elder prince much like the Lao Phra Lak Phra Lam. Rama, although righteous and virtuous, was perceived to be weak and his character is often moved to the background while the younger Laksmana is admired for his courage and willingness to react decisively.

7.) Cambodia ~ Reamker

Reamker is a Cambodian epic poem, based on the Sanskrit’s Ramayana epic. The name means “Glory of Rama”. It adapts the Hindu ideas to Buddhist themes and shows the balance of good and evil in the world. More than just a reordering of the epic tale, the Reamker is a mainstay of the royal ballet’s repertoire. Like the Ramayana, it is a philosophical allegory, exploring the ideals of justice and fidelity as embodied by the protagonists, Prince Rama and Queen Sita. The epic is well known among the Khmer people for its portrayal in Khmer dance theatre, called the Lkhaon, in various festivals across Cambodia. Scenes from the Reamker are painted on the walls of the Royal Palace in Khmer style, and its predecessor is carved into the walls of the Angkor Wat and Banteay Srei temples. It is considered an integral part of Cambodian culture. The Reamker differs from the original Ramayana in some ways, featuring additional scenes and emphasis on Hanuman and Sovanna Maccha. In the Reamker, issues of trust, loyalty, love, and revenge play out in dramatic encounters among princes and giants, monkeys and mermaids, and a forlorn princess. Though it is understood that Preah Ream is an incarnation of the Hindu god Vishnu, his characteristics and those of the others in the story are interpreted in Cambodia as those of mere mortals, not of the gods as is the case in India. The complex interplay of strengths and weaknesses, though couched in episodes lined with magic, nonetheless represents a decidedly human social behavior.

Photo Sources: [x], [x], [x], [x], [x], [x], [x]

Happy almost birthday, Shakespeare! Or should I say Bard-thday? Recently, in honour of the 400th anniversary of William Shakespeare’s death (conveniently for celebratory purposes, he was born on April 23 1564 and died on the same day in 1616), I was given the incredible opportunity to have a private audience to go through the University of Glasgow’s copy of the First Folio, page by page. I’ve written a short article for the University Library’s blog, which you can find here, but I wanted to share some other images on my own blog that I didn’t have room for on the official post!

The University of Glasgow’s First Folio (more properly known as Mr. William Shakespeare’s Comedies, Histories, & Tragedies) is able to tell so many more stories than those of the plays contained in its pages- of the history of the antiquarian book trade, of the printing practices of the Renaissance, of book ownership and value. Rest assured, you’ll probably be seeing posts from me in the future about all of these things, as well as the typographical ornaments used in the book, which I found fascinating. The University’s Folio is particularly interesting due to the notations by past owners, including one who had apparently seen at least one of the original Chamberlain’s Men “By eyewittnesse”. But my favourite bit of the later additions is the morbid little poem on the reverse of one of the flyleaves: “Pitty it is the fam’d Shakespeare/ Shall ever want his chin or haire.”

Smuggling salt is Slovenian culture!

Be proud of smuggling salt, people! We certainly are!

NASA’s new searchable media library is a treasure trove of space pics and video

Do you like space? Do you like looking at it, wishing you were there instead of here, perhaps? Well NASA just did something that will make your day. The U.S...

The U.S. space agency launched a new web-based search engine for much of its catalog of images, video and audio files, which you can browse by keyword and metadata, so that you never have to remember the dismal reality that you’re earthbound ever again.

Drosophila melanogaster (fruit fly) seminal vesicle

Dr. Barbara Laurinyecz

Szeged, Hungary

Technique: Confocal, Fluorescence (600x)

Sasando

pic: wikipedia

The sasando is a harp-like musical instrument from East Nusa Tenggara, Indonesia, specifically in the island of Rote. The name is derived from the Rote dialect word “sasandu” meaning “vibrating or sounded instrument.” It can have 28 or 56 strings.

There’s a folktale that explained the origins of the sasando. Once, there was a boy called Sangguana who lived in Rote. One day, he was tired and fell asleep under a palmyra tree, and dreamt that he played beautiful music with a unique instrument that made an enchanting sound. When he woke up, Sangguana was able to vividly remember the melody he played in the dream. He wanted to hear it once more, so he slept again, and dreamt of the same song and the same instrument. Sangguana had to wake up, eventually, but, not wanting to lose the instrument from his dream, he made an instrument out of palmyra leaves based on the one he saw in his dream, which became the basis for the sasando.

if you want to see how it sounds: (start 0:30)

What the heck is ‘Johnston’s Fluid Beef’? According to this Victorian age flyer in the Canada Medical and Surgical Journal of April 1883, it is “the most perfect food for invalids ever introduced, concentrated preparation for nutritious beef tea or soup, specially recommended by the Medical Faculty.” But the directions for use on page 4 may be a recipe for botulism: “Add a small teaspoon to a cup of boiling water and season to taste; or as a sandwich paste it may be used on toast, with or without butter. The can may remain open for weeks without detriment to the contents.”

The story of ‘Johnston’s Fluid Beef’ began in 1870 in the Franco-Prussian War, when Napoleon III ordered a million cans of beef to feed troops. John Lawson Johnston, a Scot living in Montreal, had the task of providing it. Transportation and storage were problematic, so Johnston created a product known as Johnston’s Fluid Beef, later called Bovril, to meet the need. By 1888, Johnston’s Fluid Beef became a British staple sold in 3,000 U.K. public houses, grocers and dispensing chemists, and remains so today. A major downturn in sales occurred in 2004 when the company changed its formula to make Bovril vegetarian. The Guardian reported in 2007: “Rather than any new-found vegetarian gusto, the move [by Bovril] to yeast extract in 2004 was largely triggered by concerns about beef consumption and BSE [bovine spongiform encephalopathy], which affected Bovril’s export market.” But by 2006, the beef was back in Bovril and the company survives. Modern directions for use are recommended.