GALILEO GALILEI (1564-1642)

1632 – Italy

‘Discounting air resistance, all bodies fall with the same motion; started together, they fall together. The motion is one with constant acceleration; the body gains speed at a steady rate’

From this idea we get the equations of accelerated motion:
v = at and s = 1/2at2
where v is the velocity, a is the acceleration and s is the distance traveled in time t

The Greek philosopher ARISTOTLE (384-322 BCE) was the first to speculate on the motion of bodies. He said that the heavier the body, the faster it fell.
It was not until 18 centuries later that this notion was challenged by Galileo.

The philosophers of ancient Greece had known about statics but were ignorant of the science of dynamics.
They could see that a cart moves because a horse pulls it, they could see that an arrow flies because of the power of the bow, but they had no explanation for why an arrow goes on flying through the air when there is nothing to pull it like the horse pulls the cart. Aristotle made the assumption that there must be a force to keep things moving. Galileo contradicted. He believed that something will keep moving at the same speed unless a force slows it down.

He contended that an arrow or a thrown stone had two forces acting upon it at the same time – ‘momentum’ pushes it horizontally and it only falls to the ground because the resistance of the air (a force) slows it down enough for it to be pulled to the ground by another force pushing downwards upon it; that which we now know as ‘gravity’.
This is the principle of inertia and led him to correctly predict that the path of a projectile is a parabola.

His insights were similar to the first two of the three laws of motion that Newton described 46 years later in ‘Principia’. Although he did not formulate laws with the clarity and mathematical certainty of Newton, he did lay the foundations of the modern understanding of how things move.

Galileo resisted the notion of gravity because he felt the idea of what seemed to be a mystical force seemed unconvincing, but he appreciated the concept of inertia and realized that there is no real difference between something that is moving at a steady speed and something that is not moving at all – both are unaffected by forces. To make an object go faster or slower, or begin to move, a force is needed.

Galileo would take a problem, break it down into a series of simple parts, experiment on those parts and then analyse the results until he could describe them in a series of mathematical expressions. His meticulous experiments (‘cimento‘) on inclined planes provided a study of the motion of falling bodies.

He correctly assumed that gravity would act on a ball rolling down a sloping wooden board that had a polished, parchment lined groove cut into it to act as a guide, in proportion to the angle of the slope. He discovered that whatever the angle of the slope, the time for the ball to travel along the first quarter of the track was the same as that required to complete the remaining three-quarters. The ball was constantly accelerating. He repeated his experiments hundreds of times, getting the same results. From these experiments he formulated his laws of falling bodies.
Mathematics provided the clue to the pattern – double the distance traveled and the ball will be traveling four times faster, treble it and the ball will be moving nine times faster. The speed increases as a square of the distance.
He found that the size of the ball made no difference to the timing and surmised that, neglecting friction, if the surface was horizontal – once a ball was pushed it would neither speed up nor slow down.

His findings were published in his book, ‘Dialogue Concerning the Two Chief World Systems’, which summarised his work on motion, acceleration and gravity.

His theory of uniform acceleration for falling bodies contended that in a vacuum all objects would accelerate at exactly the same rate towards the earth.

Legend has it that Galileo gave a demonstration, dropping a light object and a heavy one from the top of the leaning Tower of Pisa. Dropping two cannonballs of different sizes and weights he showed that they landed at the same time. The demonstration probably never happened, but in 1991 Apollo 15 astronauts re-performed Galileo’s experiment on the moon. Astronaut David Scott dropped a feather and a hammer from the same height. Both reached the surface at the same time, proving that Galileo was right.

Another myth has it that whilst sitting in Pisa cathedral he was distracted by a lantern that was swinging gently on the end of a chain. It seemed to swing with remarkable regularity and experimenting with pendulums, he discovered that a pendulum takes the same amount of time to swing from side to side – whether it is given a small push and it swings with a small amplitude, or it is given a large push. If something moves faster, he realised, then the rate at which it accelerates depends on the strength of the force that is moving it faster, and how heavy the object is. A large force accelerates a light object rapidly, while a small force accelerates a heavy object slowly. The way to vary the rate of swing is to either change the weight on the end of the arm or to alter the length of the supporting rope.
The practical outcome of these observations was the creation of a timing device that he called a ‘pulsilogium’.

Drawing by GALILEO of the surface of the moon

Galileo confirmed and advanced COPERNICUS’ sun centered system by observing the skies through his refracting telescope, which he constructed in 1609. Galileo is mistakenly credited with the invention of the telescope. He did, however, produce an instrument from a description of the Dutch spectacle maker Hans Lippershey’s earlier invention (patent 1608).

He discovered that Venus goes through phases, much like the phases of the Moon. From this he concluded that Venus must be orbiting the Sun. His findings, published in the ‘Sidereal Messenger‘ (1610) provided evidence to back his interpretation of the universe. He discovered that Jupiter has four moons, which rotate around it, directly contradicting the view that all celestial bodies orbited earth, ‘the centre of the universe’.

‘The Earth and the planets not only spin on their axes; they also revolve about the Sun in circular orbits. Dark ‘spots’ on the surface of the Sun appear to move; therefore, the Sun must also rotate’

1610 – Galileo appointed chief mathematician to Cosmo II, the Grand Duke of Tuscany, a move that took him out of Papal jurisdiction.

1613 – writes to Father Castelli, suggesting that biblical interpretation be reconciled with the new findings of science.

1615 – a copy of the letter is handed to the inquisition in Rome.

1616 – Galileo warned by the Pope to stop his heretical teachings or face imprisonment.

1632 – when Galileo published his masterpiece, ‘Dialogue Concerning the Two Chief World Systems’ – (Ptolemaic and Copernican) – which eloquently defended and extended the Copernican system, he was struggling against a society dominated by religious dogma, bent on suppressing his radical ideas – his theories were thought to contravene the teachings of the Catholic Church. He again attracted the attention of the Catholic Inquisition.
His book took the form of a discussion between three characters; the clever Sagredo (who argues for Copernicus), the dullard Simplicio (who argues hopelessly for Aristotle) and Salviati (who takes the apparently neutral line but is clearly for Sagredo).

In 1633 he was tried for heresy.

‘That thou heldest as true the false doctrine taught by many that the Sun was the centre of the universe and immoveable, and that the Earth moved, and had also a diurnal motion. That on this same matter thou didst hold a correspondence with certain German mathematicians.’
‘…a proposition absurd and false in philosophy and considered in theology ad minus erroneous in faith…’.

Threatened with torture, Galileo was forced to renounce his theories and deny that the Earth moves around the Sun. He was put under house arrest for the rest of his life.

After Galileo’s death in 1642 scientific thought gradually accepted the idea of the Sun-centered solar system. In 1992, after more than three and a half centuries, the Vatican officially reversed the verdict of Galileo’s trial.

Galileo’s thermoscope operated on the principle that liquids expand when their temperature increases. A thermoscope with a scale on it is basically a thermometer and in its construction Galileo was probably following directions given by Heron of Alexandria 1500 years earlier in ‘Pneumatics’. As with the telescope, Galileo is often incorrectly given credit for the invention of the thermometer.

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ARCHIMEDES (c.287 – c.212 BCE)

Third Century BCE – Syracuse (a Greek city in Sicily)

‘Archimedes’ Screw – a device used to pump water out of ships and to irrigate fields’

Archimedes investigated the principles of static mechanics and pycnometry (the measurement of the volume or density of an object). He was responsible for the science of hydrostatics, the study of the displacement of bodies in water.

Archimedes’ Principle

Buoyancy – ‘A body fully or partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body’
The upthrust (upward force) on a floating object such as a ship is the same as the weight of water it displaces. The volume of the displaced liquid is the same as the volume of the immersed object. This is why an object will float. When an object is immersed in water, its weight pulls it down, but the water, as Archimedes realised, pushes back up with a force that is equal to the weight of water the object pushes out-of-the-way. The object sinks until its weight is equal to the upthrust of the water, at which point it floats.
Objects that weigh less than the water displaced will float and objects that weigh more will sink. Archimedes showed this to be a precise and easily calculated mathematical principle.

 
 

Syracuse’s King Hiero, suspecting that the goldsmith had not made his crown of pure gold as instructed, asked Archimedes to find out the truth without damaging the crown.

Archimedes first immersed in water a piece of gold that weighed the same as the crown and pointed out the subsequent rise in water level. He then immersed the crown and showed that the water level was higher than before. This meant that the crown must have a greater volume than the gold, even though it was the same weight. Therefore it could not be pure gold and Archimedes thus concluded that the goldsmith had substituted some gold with a metal of lesser density such as silver. The fraudulent goldsmith was executed.

Archimedes came to understand and explain the principles behind the compound pulley, windlass, wedge and screw, as well as finding ways to determine the centre of gravity of objects.
He showed that the ratio of weights to one another on each end of a balance goes down in exact mathematical proportion to the distance from the pivot of the balance.

Perhaps the most important inventions to his peers were the devices created during the Roman siege of Syracuse in the second Punic war.

He was killed by a Roman soldier during the sack of the city.

 
 
 
 

(image source)

Π The Greek symbol pi (enclosed in a picture of an apple) - Pi is a name given to the ratio of the circumference of a circle to the diameterPi

‘All circles are similar and the ratio of the circumference to the diameter of a circle is always the same number, known as the constant, Pi’

Pi-unrolled-720.gif

 
 

The Greek tradition disdained the practical.  Following PLATO the Greeks believed pure mathematics was the key to the perfect truth that lay behind the imperfect real world, so that anything that could not be completely worked out with a ruler and compass and elegant calculations was not true.

In the eighteenth century CE the Swiss mathematician LEONHARD EULER was the first person to use the letter  Π , the initial letter of the Greek word for perimeter, to represent this ratio.

The earliest reference to the ratio of the circumference of a circle to the diameter is an Egyptian papyrus written in 1650 BCE, but Archimedes first calculated the most accurate value.

He calculated Pi to be 22/7, a figure which was widely used for the next 1500 years. His value lies between 3 1/2 and 3 10/71, or between 3.142 and 3.141 accurate to two decimal places.

 

‘The Method of Exhaustion – an integral-like limiting process used to compute the area and volume of two-dimensional lamina and three-dimensional solids’

Archimedes realised how much could be achieved through practical approximations, or, as the Greeks called them, mechanics. He was able to calculate the approximate area of a circle by first working out the area of the biggest hexagon that would fit inside it and then the area of the smallest that would fit around it, with the idea in mind that the area of the circle must lie approximately halfway between.

By going from hexagons to polygons with 96 sides, he could narrow the margin for error considerably. In the same way he worked out the approximate area contained by all kinds of different curves from the area of rectangles fitted into the curve. The smaller and more numerous the rectangles, the closer to the right figure the approximation became.

This is the basis of what thousands of years later came to be called integral calculus.
Archimedes’ reckonings were later used by Kepler, Fermat, Leibniz and Newton.

In his treatise ‘On the Sphere and the Cylinder’, Archimedes was the first to deduce that the volume of a sphere is 4/3 Pi r3  where r  is the radius.
He also deduced that a sphere’s surface area can be worked out by multiplying that of its greatest circle by four; or, similarly, a sphere’s volume is two-thirds that of its circumscribing cylinder.

Like the square and cube roots of 2, Pi is an irrational number; it takes a never-ending string of digits to express Pi as a number. It is impossible to find the exact value of Pi – however, the value can be calculated to any required degree of accuracy.
In 2002 Yasumasa Kanada (b.1949) of Tokyo University used a supercomputer with a memory of 1024GB to compute the value to 124,100,000,000 decimal places. It took 602 hours to perform the calculation.

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EPICURUS (341 – 270 BCE)

Third Century BCE

“Epicurus’s philosophy combines a physics based on an atomistic materialism with a rational hedonistic ethics that emphasizes moderation of desires and cultivation of friendships.”

Summarized by the Roman author Lucretius, who wrote ‘On the Nature of the Universe’ in 55 BCE – “The light and heat of the Sun; these are composed of minute atoms which, when they are shoved off, lose no time in shooting right across the interspace of air in the direction imparted by the shove”. This may be considered as accurate for the time, when most people thought that sight was associated with something reaching out from the eye (EMPEDOCLES) .

Plato wrote of a marriage between the inner light and the outer light.

Euclid worried about the speed with which sight worked. He pointed out that if you close your eyes, then open them again, even the distant stars reappear immediately in your sight, although the influence of sight has had to travel all the way from your eyes to the stars and back again before you could see them.

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AL-BIRUNI (973-1050)

The Persian scholar al-Biruni lived around the same time as ibn-Sina. He pioneered the idea that light travels faster than sound, promoted the idea that the Earth rotates on its axis and measured the density of 18 precious stones and metals.

portrait of al-biruni

He classified gems according to the properties: colour; powder colour; dispersion (whether white light splits up into the colours of the rainbow when it goes through the gem); hardness; crystal shape; density.
He used crystal shape to help him decide whether a gemstone was quartz or diamond.

He noted that flowers have 3,4,5 or 8 petals, but never 7 or 9.

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IBN SINA (AVICENNA) (980-1037)

‘al Qann fi al-Tibb’ (The Canon of Medicine), also ‘ The Book of the Remedy

Avicenna lived under the Sammarid caliphs in Bukhara. He identified different forms of energy – heat, light and mechanical – and the idea of a force.

drawing of Ibn Sina ©

AVICENNA

Before GALEN, scientists describing nature followed the old Greek traditions of giving the definitions and following them up with the body of logical development. The investigator was then obliged merely to define the various types of ‘nature’ to be found. With Galen this procedure was changed.

Instead of hunting for these natures and defining more and more of them, reproducing ARISTOTLE’s ideas, AVICENNA, a Persian physician, planned inductive and deductive experimental approaches to determine the conditions producing observable results.

His tome surveyed the entire field of medical knowledge from ancient times up to the most up to date Muslim techniques. Avicenna was the first to note that tuberculosis is contagious; that diseases can spread through soil and water and that a person’s emotions can affect their state of physical health. He was the first to describe meningitis and realize that nerves transmit pain. The book also contained a description of 760 drugs. Its comprehensive and systematic approach meant that once it was translated into Latin in the twelfth century it became the standard medical textbook in Europe for the next 600 years.

Arabic Canon of Medicine by Avicenna 1632. Many physicians in the Islamic world were outstanding medical teachers and practitioners. Avicenna (980-1037 CE) was born near Bokhara in Central Asia. Known as the 'Prince of Physicians', his Canon of Medicine (medical encyclopedia) remained the standard text in both the East and West until the 16th century and still forms the basis of Unani theory and practice today. Divided into five books, this opening shows the start of the third book depicting diseases of the brain.

Arabic Canon of Medicine by Avicenna 1632

Avicenna thought of light as being made up of a stream of particles, produced in the Sun and in flames on Earth, which travel in straight lines and bounce off objects that they strike.

A pinhole in a curtain in a darkened room causes an inverted image to be projected, upside-down, onto a wall opposite the curtained window. The key point is that light travels in straight lines. A straight line from the top of a tree some distance away, in a garden that the window of the camera obscura faces onto – passing through the hole in the curtain – will carry on down to a point near the ground on the wall opposite. A straight line from the base of the tree will go upwards through the hole to strike the wall opposite near the ceiling. Straight lines from every other point on the tree will go through the hole to strike the wall in correspondingly determined spots, the result is an upside-down image of the tree (and of everything else in the garden).

He realized that refraction is a result of light traveling at different speeds in water and in air.

He used several logical arguments to support his contention that sight is not a result of some inner light reaching outward from the eye to probe the world around it, but is solely a result of light entering the eye from the world outside – realizing that ‘after-images’ caused by a bright light will persist when the eyes are closed and reasoning that this can only be the result of something from outside affecting the eyes. By effectively reversing the extro-missive theory of Euclid, he formulated the idea of a cone emanating from outside the eye entering and thus forming an image inside the eye – he thus introduced the modern idea of the ray of light.

The idea which was to have the most profound effect on the scientific development of an understanding of the behaviour of light was the thought of the way images are formed on a sunny day by the ‘camera obscura’.

AL HAZEN (c.965-1039)

Born in Basra and working in Egypt under al-Hakim, Abu Ali al-Hassan ibn al-Haytham was one of the three greatest scientists of Islam (along with al-Biruni and ibn-Sina). He explained how vision works in terms of geometric optics and had a huge influence on Western science. He is regarded as one of the earliest advocates of the scientific method.

The mathematical technique of ‘casting out of nines’, used to verify squares and cubes, is attributed to al-Hazen.

Al-Hazen dissented with the J’bir Ayam hypothesis of transmutation, thus providing two different strands for Alchemy in Europe from the Islāmic world.

diagram explaining the working of the eye

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ALCHEMY

photo of an ancient document showing some of the symbols commonly used by alchemists

Alchemical symbols

Understanding of the alchemists is hampered by their predilection for making their writings incomprehensible ( instant knowledge was not to be available to the uninitiated ) and the popular view that their quest was simply to isolate the Philosophers’ Stone and to use it to transform base metals into gold. There was in fact a genuine search for mental and spiritual advance

Using a world-view totally unlike that recognised today, the alchemists’ ideas of ‘spirit’ and ‘matter’ were intermingled – the ability to use ‘spirit’ in their experiments was the difficult part.

alchemical symbol for gold

To transform copper to gold: – copper could be heated with sulphur to reduce it to its ‘basic form’ (a black mass which is in fact copper sulphide) – its ‘metallic form’ being ousted by the treatment. The idea of introducing the ‘form of gold’ to this mass by manipulating and mixing suitable quantities of spirit stymied alchemists for over fifteen centuries.

Whilst this transmutation of metals was the mainstream concern of alchemy, there emerged in the sixteenth century a school that brought the techniques and philosophies of alchemy to bear on the preparation of medicines, the main figures involved being PARACELSUS and JOHANN VAN HELMONT.

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cartoon of ALCHEMISTS AT WORK

ALCHEMISTS AT WORK

THE EIGHTEENTH CENTURY

COMBUSTION and PHLOGISTON

Noticing that burning a candle in an upturned container, the open end of which is submerged in water, causes the water to rise into the container, Philon of Byzantium inferred correctly that some of the air in the container had been used up in the combustion. However, he proposed that this is because this portion of the air had been converted into ‘fire particles’, which were smaller than ‘air particles’.

In 1700 the German physician Georg Ernst Stahl (1660-1734) invoked ‘phlogiston’ to explain what happens when things burn. He suggested that a burning substance was losing an undetectable elementary principle analogous to the ‘sulfur’ of J’BIR IHBIN AYAM, which he re-named ‘phlogiston’. This could explain why a log (rich in phlogiston) could seem to be heavier than its ashes (deficient in phlogiston). The air that is required for burning served to transport the phlogiston away.

The English chemist JOSEPH PRIESTLY (1733-1804), although a supporter of the phlogiston theory, ironically contributed to its downfall. He heated mercury in air to form red mercuric oxide and then applied concentrated heat to the oxide and noticed that it decomposed again to form mercury whilst giving off a strange gas in which things burnt brightly and vigorously. He concluded that this gas must be ‘phlogiston poor’.

Priestly combined this result with the work of the Scottish physician Daniel Rutherford (1749-1819), who had found that keeping a mouse in an enclosed airtight space resulted in its death (by suffocation) and that nothing could be burnt in the enclosed atmosphere; he formed the idea that the trapped air was so rich in phlogiston that it could accept no more. Rutherford called this ‘phlogisticated air’ and so Priestly called his own gas ‘dephlogisticated air’.

In 1774 Priestley visited the French chemist ANTOINE LAVOISIER (1743-1794).
Lavoisier repeated Priestly’s experiments with careful measurements.
Reasoning that air is made up of a combination of two gases – one that will support combustion and life, another that will not; what was important about Lavoisier’s experiments was not the observation – others had reached a similar conclusion – but the interpretation.

Lavoisier called Priestley’s ‘dephlogisticated air’, ‘oxygene’, meaning ‘acidifying principle’, believing at the time that the active principle was present in all acids (it is not). He called the remaining, ‘phlogisticated’, portion of normal air, ‘azote’, meaning ‘without life’

Oxygen is the mirror image of phlogiston. In burning and rusting (the two processes being essentially the same) a substance picks up one of the gases from the air. Oxygen is consumed, there is no expulsion of ‘phlogiston’.

Lavoisier had been left with almost pure nitrogen, which makes up about four fifths of the air we breath. We now know azote as nitrogen. Rutherford’s ‘mephitic air’ was carbon dioxide.

CALORIC

Like phlogiston, caloric was a weightless fluid, rather like elemental fire, a quality that could be transmitted from one substance to another, so that the first warmed the second up.

It was believed that all substances contained caloric and that when a kettle was being heated over a fire, the fuel gave up its caloric to the flame, which passed it into the metal, which passed it on to the water. Similarly, two pieces of wood rubbed together would give heat because abrasion was releasing caloric trapped within.

What is being transmitted is heat energy. It was the crucial distinction between the physical and the chemical nature of substances that confused the Ancients and led to their minimal elemental schemes.

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CHRISTIAN THEOLOGY & WESTERN SCIENCE

bust said to depict a likeness of Socrates

The speculative Greek philosophers, considering the great overarching principles that controlled the Cosmos, were handicapped by a reluctance to test their speculations by experimentation.
At the other end of the spectrum were the craftsmen who fired and glazed pottery, who forged weapons out of bronze and iron. They in turn were hindered by their reluctance to speculate about the principles that governed their craft.

WESTERN SCIENCE is often credited with discoveries and inventions that have been observed in other cultures in earlier centuries.
This can be due to a lack of reliable records, difficulty in discerning fact from legend, problems in pinning down a finding to an individual or group or simple ignorance.

The Romans were technologists and made little contribution to pure science and then from the fall of Rome to the Renaissance science regressed. Through this time, science and technology evolved independently and to a large extent one could have science without technology and technology without science.

Later, there developed a movement to ‘Christianise Platonism’ (Thierry of Chartres).

Platonism at its simplest is the study and debate of the various arguments put forward by the Greek philosopher PLATO (428/7-348/7 BCE).
The philosopher Plotinus is attributed with having founded neo-Platonism, linking Christian and Gnostic beliefs to debate various arguments within their doctrines. One strand of thought linked together three intellectual states of being: the Good (or the One), the Intelligence and the Soul. The neo-Platonic Academy in Greece was closed by the Emperor Justinian (CE 483-565) in CE 529.
During the early years of the Renaissance, texts on neo-platonism began to be reconsidered, translated and discoursed.

Aristotle’s four causes from the ‘Timaeus’ were attributed to the Christian God, who works through secondary causes (such as angels).

Efficient Cause – Creator – God the Father

Formal Cause – Secondary agent – God the Son

Material Cause – The four elements: earth, air, fire & water.
Because these four are only fundamental forms of the single type of matter, they cannot be related to any idea of ‘elements’ as understood by modern science – they could be transmuted into each other. Different substances, although composed of matter would have different properties due to the differing amounts of the qualities of form and spirit. Thus a lump of lead is made of the same type of matter (fundamental form) as a lump of gold, but has a different aggregation of constituents. Neither lead nor gold would contain much spirit – not as much as air, say, and certainly not as much as God, who is purely spiritual. ( ALCHEMY )

Final Cause – Holy Spirit

All other is ‘natural’ – underwritten by God in maintaining the laws of nature without recourse to the supernatural.
Science was the method for investigating the world. It involved carrying out careful experiments, with nature as the ultimate arbiter of which theories were right and which were wrong.

Robert Grosseteste (1168-1253) Bishop of Lincoln (Robert ‘Bighead’) – neo-platonic reading of Genesis – emanation of God’s goodness, like light, begins creation. Light is thus a vehicle of creation and likewise knowledge (hence ‘illumination’), a dimensionless point of matter with a dimensionless point of light superimposed upon it (dimensions are created by God). Spherical radiation of light carries matter with it until it is dissipated. Led to studies of optical phenomena (rainbow, refraction, reflection).

stained glass window depicting Robert Grosseteste (created 1896)

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ROGER BACON (1214- 94)

(Doctor Mirabilis) ‘The Marvelous Doctor’

(Franciscan friar) Oxford – 1257

‘Mathematics (The first of the sciences, the alphabet of philosophy, door & key to the sciences), not Logic, should be the basis of all study’

Converted from Aristotelian to a neo-Platonist.

Etching of ROGER BACON Franciscan friar (1214- 94)

ROGER BACON

The Multiplication of Species; the means of causation (change) radiate from one object to another like the propagation of light.

‘An agent directs its effect to making the recipient similar to itself because the recipient is always potentially what the agent is in actuality.’

Thus heat radiating from a fire causes water placed near the fire,
but not in it, to become like the fire (hot). The quality of fire is multiplied in the water (multiplication of species).

All change may be analysed mathematically. Every multiplication is according to line, angles or figures. This thinking comes from the ninth century al-Kinde and his thoughts on rays and leads to a mathematical investigation into light.

Fear of the Mongols, Muslims and the Anti-Christ motivated the Franciscans. Franciscan neo-Platonism was based on Augustinian thought with a mathematical, Pythagorean, approach to nature. Bacon subscribed to this apocalyptical view, suffered trial and was imprisoned.
The Dominicans chose Aristotle – with a qualitative, non-mathematical approach to the world.

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LEONARDO DA VINCI (1452-1519)

1502 – Florence, Italy

‘In the Renaissance science was reinvented’

Image of the VITRUVIAN MAN

VITRUVIAN MAN

Leonardo is celebrated as the Renaissance artist who created the masterpieces ‘The Last Supper’ (1495-97) and ‘The Mona Lisa’ (1503-06). Much of his time was spent in scientific enquiry, although most of his work remained unpublished and largely forgotten centuries after his death. The genius of his designs so far outstripped contemporary technology that they were rendered literally inconceivable.

The range of his studies included astronomy, geography, palaeontology, geology, botany, zoölogy, hydrodynamics, optics, aerodynamics and anatomy. In the latter field he undertook a number of human dissections, largely on stolen corpses, to make detailed sketches of the body. He also dissected bears, cows, frogs, monkeys and birds to compare their anatomy with that of humans.

It is perhaps in his study of muscles where Leonardo’s blend of artistry and scientific analysis is best seen. In order to display the layers of the body, he developed the drawing technique of cross-sections and illustrated three-dimensional arrays of muscles and organs from different perspectives.

Leonardo’s superlative skill in illustration and his obsession with accuracy made his anatomical drawings the finest the world had ever seen. One of Leonardo’s special interests was the eye and he was fascinated by how the eye and brain worked together. He was probably the first anatomist to see how the optic nerve leaves the back of the eye and connects to the brain. He was probably the first, too, to realise how nerves link the brain to muscles. There had been no such idea in GALEN’s anatomy.

Possibly the most important contribution Leonardo made to science was the method of his enquiry, introducing a rational, systematic approach to the study of nature after a thousand years of superstition. He would begin by setting himself straightforward scientific queries such as ‘how does a bird fly?’ He would observe his subject in its natural environment, make notes on its behaviour, then repeat the observation over and over to ensure accuracy, before making sketches and ultimately drawing conclusions. In many instances he would directly apply the results of his enquiries into nature to designs for inventions for human use.

Self portrait of LEONARDO DA VINCI

LEONARDO DA VINCI

He wrote ‘Things of the mind left untested by the senses are useless’. This methodical approach to science marks a significant stepping-stone from the DARK AGES to the modern era.

1469 Leonardo apprenticed to the studio of Andrea Verrocchio in Florence

1482 -1499 Leonardo’s work for Ludovico Siorza, the Duke of Milan, included designs for weaponry such as catapults and missiles.
Pictor et iggeniarius ducalis ( painter and engineer of the Duke )’.
Work on architecture, military and hydraulic engineering, flying machines and anatomy.

1502 Returns to Florence to work for Pope Alexander VI’s son, Cesare Borgia, as his military engineer and architect.

1503 Begins to paint the ‘Mona Lisa’.

1505-07 Wrote about the flight of birds and filled his notebooks with ideas for flying machines, including a helicopter and a parachute. In drawing machines he was keen to show how individual components worked.

1508 Studies anatomy in Milan.

1509 Draws maps and geological surveys of Lombardy and Lake Isea.

1516 Journeys to France on invitation of Francis I.

1519 April 23 – Dies in Clos-Luce, near Amboise, France.

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WILLIAM GILBERT (1540-1603)

1600 – England

‘Gilbert’s principal area of study related to magnetism, however, his method of enquiry is equally significant’

portrait of WILLIAM GILBERT ©

WILLIAM GILBERT

Gilbert rejected the scholastics’ approach to science, preferring the experimental method, which he applied to the Earth’s magnetic properties.
He carried out some of the first systematic studies of the lodestone in Europe and showed that the Earth acts as a bar magnet with magnetic poles.

His celebrated text, ‘De magnete, magnetisque corporibus, et de magno magnete tellure‘ (On the Magnetic, Magnetic Bodies and the Great Magnet Earth – 1600) is considered to be one of the first truly scientific texts.
Gilbert received his medical training in Cambridge and practiced as a physician in London. He became president of the College of Physicians and was physician to Queen Elizabeth I.

In the time of Elizabeth I and Shakespeare, England was still largely a place of superstition and religious fervor. Gilbert concurred with Copernicus, a potentially dangerous sentiment in an era when elsewhere in Europe others such as Giordano Bruno and later GALILEO were being persecuted (and in the case of Bruno, executed) for sharing the same opinion.


Magnetism was to cast its influence in the eighteenth century, displayed through the electric fluid of GALVANI and VOLTA
.

He distinguished the properties of magnetism from the attractive effect produced by friction with amber. In so doing he introduced the term that was to become electricity.
He introduced a number of expressions to the English language including: magnetic pole, electric force and electric attraction.
A term of magneto motive force, the gilbert, is named after him.

Gilbert and others postulated that magnetism is the force holding the planets in their orbits.

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WILLEBRORD SNELLIUS (1580-1626)

1621 – Holland

woodblock print portrait of WILLEBRORD SNELL ©

WILLEBRORD SNELL

‘During refraction of light, the ratio of the sines of the angles of incidence ( i ) and refraction ( r ) is a constant equal to the refractive index of the medium’

In equation form: n1sini = n2 sinr 
where n1 and n2 are the respective refractive indices of the two media.

The refractive index of a substance is a measure of its ability to bend light. The higher the number the better light is refracted. The refractive index of diamond, 2.42, is the highest of all gems.

Refraction is the change in direction of a ray of light when it crosses the boundary between two media. It happens because light has different speeds in different media. A ray of light entering a medium where the speed of light is less (from air to water, for example) bends towards the perpendicular to the boundary of the two media. It bends away from the perpendicular when it crosses from water to air. Refraction was known to ancient Greeks, but Snell, a Dutch mathematician, was the first to study it.

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GALILEO GALILEI (1564-1642)

1632 – Italy

‘Discounting air resistance, all bodies fall with the same motion; started together, they fall together. The motion is one with constant acceleration; the body gains speed at a steady rate’

Portrait of GALILEO GALILEI ©

GALILEO GALILEI

From this idea we get the equations of accelerated motion:
v = at and s = 1/2at2
where v is the velocity, a is the acceleration and s is the distance traveled in time t

The Greek philosopher ARISTOTLE (384-322 BCE) was the first to speculate on the motion of bodies. He said that the heavier the body, the faster it fell.
It was not until 18 centuries later that this notion was challenged by Galileo.

The philosophers of ancient Greece had known about statics but were ignorant of the science of dynamics.
They could see that a cart moves because a horse pulls it, they could see that an arrow flies because of the power of the bow, but they had no explanation for why an arrow goes on flying through the air when there is nothing to pull it like the horse pulls the cart. Aristotle made the assumption that there must be a force to keep things moving. Galileo contradicted. He believed that something will keep moving at the same speed unless a force slows it down.

He contended that an arrow or a thrown stone had two forces acting upon it at the same time – ‘momentum’ pushes it horizontally and it only falls to the ground because the resistance of the air (a force) slows it down enough for it to be pulled to the ground by another force pushing downwards upon it; that which we now know as ‘gravity’.
This is the principle of inertia and led him to correctly predict that the path of a projectile is a parabola.

His insights were similar to the first two of the three laws of motion that Newton described 46 years later in ‘Principia’. Although he did not formulate laws with the clarity and mathematical certainty of Newton, he did lay the foundations of the modern understanding of how things move.

Galileo resisted the notion of gravity because he felt the idea of what seemed to be a mystical force seemed unconvincing, but he appreciated the concept of inertia and realized that there is no real difference between something that is moving at a steady speed and something that is not moving at all – both are unaffected by forces. To make an object go faster or slower, or begin to move, a force is needed.

Galileo would take a problem, break it down into a series of simple parts, experiment on those parts and then analyse the results until he could describe them in a series of mathematical expressions. His meticulous experiments (‘cimento‘) on inclined planes provided a study of the motion of falling bodies.

He correctly assumed that gravity would act on a ball rolling down a sloping wooden board that had a polished, parchment lined groove cut into it to act as a guide, in proportion to the angle of the slope. He discovered that whatever the angle of the slope, the time for the ball to travel along the first quarter of the track was the same as that required to complete the remaining three-quarters. The ball was constantly accelerating. He repeated his experiments hundreds of times, getting the same results. From these experiments he formulated his laws of falling bodies.
Mathematics provided the clue to the pattern – double the distance traveled and the ball will be traveling four times faster, treble it and the ball will be moving nine times faster. The speed increases as a square of the distance.
He found that the size of the ball made no difference to the timing and surmised that, neglecting friction, if the surface was horizontal – once a ball was pushed it would neither speed up nor slow down.

His findings were published in his book, ‘Dialogue Concerning the Two Chief World Systems’, which summarised his work on motion, acceleration and gravity.

His theory of uniform acceleration for falling bodies contended that in a vacuum all objects would accelerate at exactly the same rate towards the Earth.

Legend has it that Galileo gave a demonstration, dropping a light object and a heavy one from the top of the leaning Tower of Pisa. Dropping two cannonballs of different sizes and weights he showed that they landed at the same time. The demonstration probably never happened, but in 1991 Apollo 15 astronauts re-performed Galileo’s experiment on the Moon. Astronaut David Scott dropped a feather and a hammer from the same height. Both reached the surface at the same time, proving that Galileo was right.

Another myth has it that whilst sitting in Pisa cathedral he was distracted by a lantern that was swinging gently on the end of a chain. It seemed to swing with remarkable regularity and experimenting with pendulums, he discovered that a pendulum takes the same amount of time to swing from side to side – whether it is given a small push and it swings with a small amplitude, or it is given a large push. If something moves faster, he realised, then the rate at which it accelerates depends on the strength of the force that is moving it faster, and how heavy the object is. A large force accelerates a light object rapidly, while a small force accelerates a heavy object slowly. The way to vary the rate of swing is to either change the weight on the end of the arm or to alter the length of the supporting rope.
The practical outcome of these observations was the creation of a timing device that he called a ‘pulsilogium’.

Drawing by GALILEO of the surface of the moon

Galileo confirmed and advanced COPERNICUS‘ Sun-centered system by observing the skies through his refracting telescope, which he constructed in 1609. Galileo is mistakenly credited with the invention of the telescope. He did, however, produce an instrument from a description of the Dutch spectacle maker Hans Lippershey’s earlier invention (patent 1608).

He discovered that Venus goes through phases, much like the phases of the Moon. From this he concluded that Venus must be orbiting the Sun. His findings, published in the ‘Sidereal Messenger‘ (1610) provided evidence to back his interpretation of the universe. He discovered that Jupiter has four moons, which rotate around it, directly contradicting the view that all celestial bodies orbited Earth, ‘the centre of the universe’.

‘The Earth and the planets not only spin on their axes; they also revolve about the Sun in circular orbits. Dark ‘spots’ on the surface of the Sun appear to move; therefore, the Sun must also rotate’

1610 – Galileo appointed chief mathematician to Cosmo II, the Grand Duke of Tuscany, a move that took him out of Papal jurisdiction.

1613 – writes to Father Castelli, suggesting that biblical interpretation be reconciled with the new findings of science.

1615 – a copy of the letter is handed to the inquisition in Rome.

1616 – Galileo warned by the Pope to stop his heretical teachings or face imprisonment.

1632 – when Galileo published his masterpiece, ‘Dialogue Concerning the Two Chief World Systems’ – (Ptolemaic and Copernican) – which eloquently defended and extended the Copernican system, he was struggling against a society dominated by religious dogma, bent on suppressing his radical ideas – his theories were thought to contravene the teachings of the Catholic Church. He again attracted the attention of the Catholic Inquisition.
His book took the form of a discussion between three characters; the clever Sagredo (who argues for Copernicus), the dullard Simplicio (who argues hopelessly for Aristotle) and Salviati (who takes the apparently neutral line but is clearly for Sagredo).

In 1633 he was tried for heresy.

‘That thou heldest as true the false doctrine taught by many that the Sun was the centre of the universe and immoveable, and that the Earth moved, and had also a diurnal motion. That on this same matter thou didst hold a correspondence with certain German mathematicians.’
‘…a proposition absurd and false in philosophy and considered in theology ad minus erroneous in faith…’.

Threatened with torture, Galileo was forced to renounce his theories and deny that the Earth moves around the Sun. He was put under house arrest for the rest of his life.

After Galileo’s death in 1642 scientific thought gradually accepted the idea of the Sun-centered solar system. In 1992, after more than three and a half centuries, the Vatican officially reversed the verdict of Galileo’s trial.

Galileo’s thermoscope operated on the principle that liquids expand when their temperature increases. A thermoscope with a scale on it is basically a thermometer and in its construction Galileo was probably following directions given by Hiero of Alexandria 1500 years earlier in ‘Pneumatics’. As with the telescope, Galileo is often incorrectly given credit for the invention of the thermometer.

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EVANGELISTA TORICELLI (1608- 47)

1640 – Italy

‘Together with VINCENZO VIVIANI (1622-1703) realised that the weight of air pushing on a reservoir of mercury can force the liquid to rise into a tube that contains no air; that is, a vacuüm’

In 1650 OTTO VON GUERICKE (1602-1686) invented an air pump and showed that if you remove the air from the centre of two hemispheres that are resting together, the pressure of the outside air is sufficient to prevent a team of horses from pulling them apart.

1657 – Formed the Accademia del Cimento with eight other Florentines to build their own apparatus and conduct experiments to advance the pursuit of knowledge. Disbanded after ten years as a condition of its patron Leopoldo de Medici’s appointment as cardinal, its dissolution followed Galileo’s trial by the Catholic Church and marked the decline of free scientific research in Italy.

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BLAISE PASCAL (1623- 62)

1647 – France

Portrait of BLAISE PASCAL

BLAISE PASCAL

‘When pressure is applied anywhere to an enclosed fluid, it is transmitted uniformly in all directions’

EVANGELISTA TORICELLI (1608-47) had argued that air pressure falls at higher altitudes.

Using a mercury barometer, Pascal proved this on the summit of the 1200m high Puy de Dome in 1647. His studies in this area led to the development of PASCAL’S PRINCIPLE, the law that has practical applications in devices such as the car jack and hydraulic brakes. This is because the small force created by moving a lever such as the jacking handle in a sizable sweep equates to a large amount of pressure sufficient to move the jack head a few centimetres.
The unit of pressure is now termed the pascal.

‘The study of the likelihood of an event’

Together with PIERRE DE FERMAT, Pascal developed the theory of probabilities (1654) using the now famous PASCAL’S TRIANGLE.

Chance is something that happens in an unpredictable way. Probability is the mathematical concept that deals with the chances of an event happening.

Probability theory can help you understand everything from your chances of winning a lottery to your chances of being struck by lightning. You can find the probability of an event by simply dividing the number of ways the event can happen by the total number of possible outcomes.
The probability of drawing an ace from a full pack of cards is 4/52 or 0.077.

Probability ranges from 1 (100%) – Absolutely certain, through Very Likely 0.9 (90%) and Quite Likely 0.7 (70%), Evens (Equally Likely) 0.5 (50%), Not Likely 0.3 (30%) and Not Very Likely 0.2 (20%), to Never – Probability 0 (0%).

Picture of the 'Pascaline'. The French mathematician Blaise Pascal invented the a mechanical calculation machine. He called it the Pascaline. The Pascaline was made out of clock gears and levers and could solve basic mathematical problems like addition and subtraction.

 
 

The computer language Pascal is named in recognition of his invention in 1644 of a mechanical calculating machine that could add and subtract.

 
 
 

Like many of his contemporaries, Pascal did not separate philosophy from science; in his book ‘Pensees’ he applies his mathematical probability theory to the problem of the existence of God. In the absence of evidence for or against God’s existence, says Pascal, the wise man will choose to believe, since if he is correct he will gain his reward, and if he is incorrect he stands to lose nothing.

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ROBERT BOYLE (1627- 91)

1662 – England

‘The volume of a given mass of a gas at constant temperature is inversely proportional to its pressure’

If you double the pressure of a gas, you halve its volume. In equation form: pV = constant; or p1V1 = p2V2 where the subscripts 1 & 2 refer to the values of pressure and volume at any two readings during the experiment.

Born at Lismore Castle, Ireland, Boyle was a son of the first Earl of Cork. After four years at Eton College, Boyle took up studies in Geneva in 1638. In 1654 he moved to Oxford where in 1656, with the philosopher John Locke and the architect Christopher Wren, he formed the experimental Philosophy Club and met ROBERT HOOKE, who became his assistant and with whom he began making the discoveries for which he became famous.

Robert Boyle. New Experiments Physico-Mechanical. Oxford: Thomas Robinson, 1662

New Experiments Physico-Mechanical 1662

In 1659, with Hooke, Boyle made an efficient vacuum pump, which he used to experiment on respiration and combustion, and showed that air is necessary for life as well as for burning. They placed a burning candle in a jar and then pumped the air out. The candle died. Glowing coal ceased to give off light, but would start glowing again if air was let in while the coal was still hot. In addition they placed a bell in the jar and again removed the air. Now they could not hear it ringing and so they found that sound cannot travel through a vacuum.

Boyle proved Galileo’s proposal that all matter falls at equal speed in a vacuum.

He established a direct relationship between air pressure and volumes of gas. By using mercury to trap some air in the short end of a ‘J’ shaped test tube, Boyle was able to observe the effect of increased pressure on its volume by adding more mercury. He found that by doubling the mass of mercury (in effect doubling the pressure), the volume of the air in the end halved; if he tripled it, the volume of air reduced to a third. His law concluded that as long as the mass and temperature of the gas is constant, then the pressure and volume are inversely proportional.

Boyle appealed for chemistry to free itself from its subservience to either medicine or alchemy and is responsible for the establishment of chemistry as a distinct scientific subject. His work promoted an area of thought which influenced the later breakthroughs of ANTOINE LAVOISIER (1743-93) and JOSEPH PRIESTLY (1733-1804) in the development of theories related to chemical elements.

Boyle extended the existing natural philosophy to include chemistry – until this time chemistry had no recognised theories.

The idea that events are component parts of regular and predictable processes precludes the action of magic.
Boyle sought to refute ARISTOTLE and to confirm his atomistic or ‘corpuscular’ theories by experimentation.

In 1661 he published his most famous work, ‘The Skeptical Chymist’, in which he rejected Aristotle’s four elements – earth, water, fire and air – and proposed that an element is a material substance consisting at root of ‘primitive and simple, or perfectly unmingled bodies’, that it can be identified only by experiment and can combine with other elements to form an infinite number of compounds.

The book takes the form of a dialogue between four characters. Boyle represents himself in the form of Carneades, a person who does not fit into any of the existing camps, as he disagrees with alchemists and sees chemists as lazy hobbyists. Another character, Themistius, argues for Aristotle’s four elements; while Philoponus takes the place of the alchemist, Eleutherius stands in as an interested bystander.

In the conclusion he attacks chemists.

page from one of Boyle's publications“I think I may presume that what I have hitherto Discursed will induce you to think, that Chymists have been much more happy finding Experiments than the Causes of them; or in assigning the Principles by which they may be best explain’d”
He pushes the point further: “me thinks the Chymists, in the searches after truth, are not unlike the Navigators of Solomon’s Tarshish Fleet, who brought home Gold and Silver and Ivory, but Apeas and Peacocks too; For so the Writings of several (for I say not, all) of your Hermetick Philosophers present us, together with divers Substantial and noble Experiments, Theories, which either like Peacock’s feathers made a great show, but are neither solid nor useful, or else like Apes, if they have some appearance of being rational, are blemished with some absurdity or other, that when they are Attentively consider’d, makes them appear Ridiculous”

The critical message from the book was that matter consisted of atoms and clusters of atoms. These atoms moved about, and every phenomenon was the result of the collisions of the particles.

He was a founder member of The Royal Society in 1663. Unlike the Accademia del Cimento the Royal Society thrived.

Like FRANCIS BACON he experimented relentlessly, accepting nothing to be true unless he had firm empirical grounds from which to draw his conclusions. He created flame tests in the detection of metals and tests for identifying acidity and alkalinity.

It was his insistence on publishing chemical theories supported by accurate experimental evidence – including details of apparatus and methods used, as well as failed experiments – which had the most impact upon modern chemistry.

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ROBERT HOOKE (1635-1703)

1670 – England

‘Within the limits of elasticity, the extension ( Strain ) of an elastic material is proportional to the applied stretching force ( Stress )’

Hooke’s law applies to all kinds of materials, from rubber balls to steel springs. The law helps define the limits of elasticity of a material.

In equation form; the law is expressed as F = kx, where F is force, x change in length and k is a constant. The constant is known as Young’s Modulus, after THOMAS YOUNG who in 1802 gave physical meaning to k.

Boyle and Hooke formed the nucleus of scientists at Gresham College in Oxford who were to create the Royal Society in 1662 and Hooke served as its secretary until his death. Newton disliked Hooke’s combative style (Hooke accused Newton of plagiarism, sparking a lifelong feud between the two) and refused to attend Royal Society meetings while Hooke was a secretary.

Hooke mistrusted his contemporaries so much that when he discovered his law he published it as a Latin anagram, ceiiinosssttvu, in his book on elasticity.

Two years later, when he was sure that the law could be proved by experiments on springs, he revealed that the anagram meant Ut tensio sic vis. That is, the power of any spring is in the same proportion with the tension thereof.

At the same time, in 1665 Hooke published his work Micrographia presenting fifty-seven illustrations drawn by him of the wonders seen with the microscope.

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ANTON VAN LEEUWENHOEK (1632-1723)

1674 – Netherlands

Portrait of Leeuwenhoek

Leeuwenhoek was probably inspired to take up microscopy after seeing a copy of HOOKE’s Micrographia, though as a draper he was likely to have already been using lenses to examine cloth.
Unlike Hooke, Leeuwenhoek did not use a two lens compound microscope, but a single high quality lens, which could be described simply as a magnifying glass rather than a microscope. Leeuwenhoek is known to have made over 500 of these single–lens microscopes. They are simple devices just a few inches long, with the lens mounted in a tiny hole in a brass plate. The specimen is mounted on a point that sticks up in front of the lens. Two screws move the specimen for focusing. All else that is needed is careful lighting and a very steady, sharp eye.

After an introduction to Henry Oldenburg of the Royal Society in London from Dutch physician and anatomist Regnier de Graaf (discoverer of the egg-making follicles in the human ovary which now bear his name), Leeuwenhoek was encouraged to write to the Society’s journal ‘Philosophical Transactions’.

Leeuwenhoek’s letters were translated into Latin and English from the Dutch and he reported seeing tiny creatures in lake-water.

‘ I found floating therein divers earthly particles, and some green streaks, spirally wound serpentwise, and orderly arranged after the manner of copper or tin worms which distillers use to cool their liquors as they distil over. The whole circumference of each of these streaks was about the thickness of a hair of one’s head ’

Leeuwenhoek’s descriptions of ‘animalcules’ in water from different sources – rainwater, pond water, well water, sea water and so on – were verified by independent witnesses, including the vicar of Delft. Hooke too confirmed his findings with his own observations performed in front of expert witnesses, including Sir Christopher Wren.
Leeuwenhoek came close to understanding that bacteria were germs that cause disease but it took another century before LOUIS PASTEUR made that step.

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ISAAC NEWTON (1642-1727)

1687 – England

‘Any two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them’

portrait of NEWTON ©

NEWTON

The force is known as gravitation
Expressed as an equation:

F = GmM/r2

where F is Force, m and M the masses of two bodies, r the distance between them and G the gravitational constant
This follows from KEPLER’s laws, Newton’s laws of motion and the laws of conic sections. Gravitation is the same thing as gravity. The word gravity is particularly used for the attraction of the Earth for other objects.

Gravitation
Newton stated that the law of gravitation is universal; it applies to all bodies in the universe. All historical speculation of different mechanical principles for the earth from the rest of the cosmos were cast aside in favour of a single system. He demonstrated that the planets were attracted toward the Sun by a force varying as the inverse square of the distance and generalized that all heavenly bodies mutually attract one another. Simple mathematical laws could explain a huge range of seemingly disconnected physical facts, providing science with the straightforward explanations it had been seeking since the time of the ancients. That the constant of gravitation is in fact constant was proved by careful experiment, that the focus of a body’s centre of gravity appears to be a point at the centre of the object was proved by his calculus.

Calculus
The angle of curve, by definition, is constantly changing, so it is difficult to calculate at any particular point. Similarly, it is difficult to calculate the area under a curve. Using ARCHIMEDES’ method of employing polygons and rectangles to work out the areas of circles and curves, and to show how the tangent or slope of any point of a curve can be analyzed, Newton developed his work on the revolutionary mathematical and scientific ideas of RENE DESCARTES, which were just beginning to filter into England, to create the mathematics of calculus. Calculus studies how fast things change.
The idea of fluxions has become known as differentiation, a means of determining the slope of a line, and integration, of finding the area beneath a curve.

Newton’s ideas on universal gravitation did not emerge until he began a controversial correspondence with ROBERT HOOKE in around 1680. Hooke claimed that he had solved the problem of planetary motion with an inverse square law that governed the way that planets moved. Hooke was right about the inverse square law, but he had no idea how it worked or how to prove it, he lacked the genius that permitted Newton to combine Kepler’s laws of planetary motion with the assumption that an object falling towards Earth was the same kind of motion as the Earth’s falling toward the Sun.
It was not until EDMUND HALLEY challenged Newton in 1684 to show how planets could have the elliptical orbits described by Johannes Kepler, supposing the force of attraction by the Sun to be the reciprocal of their distance from it – and Newton replied that he already knew – that he fully articulated his laws of gravitation.

It amounts to deriving Kepler’s first law by starting with the inverse square hypothesis of gravitation. Here the Sun attracts each of the planets with a force that is inversely proportional to the square of the distance of the planet from the Sun. From Kepler’s second law, the force acting on the planets is centripetal. Newton says this is the same as gravitation.

In the previous half century, Kepler had shown that planets have elliptical orbits and GALILEO had shown that things accelerate at an even pace as they fall towards the ground. Newton realized that his ideas about gravity and the laws of motion, which he had only applied to the Earth, might apply to all physical objects, and work for the heavens too. Any object that has mass will be pulled towards any other object. The larger the mass, the greater the pull. Things were not simply falling but being pulled by an invisible force. Just as this force (of gravity) pulls things towards the Earth, it also keeps the Moon in its orbit round the Earth and the planets moving around the Sun. With mathematical proofs he showed that this force is the same everywhere and that the pull between two things depends on their mass and the square of the distance between them.

Title page of Philosophiae Naturalis Principia Mathematica

Title page of Philosophiae Naturalis Principia Mathematica

Newton published his law of gravitation in his magnum opus Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) in 1687. In it Newton analyzed the motion of orbiting bodies, projectiles, pendulums and free fall near the Earth.

The first book of Principia states the laws of motion and deals with the general principles of mechanics. The second book is concerned mainly with the motion of fluids. The third book is considered the most spectacular and explains gravitation.

Why do two objects attract each other?
‘I frame no hypotheses’, said Newton

It was Newton’s acceptance of the possibility that there are mysterious forces in the world, his passions for alchemy and the study of the influence of the Divine that led him to the idea of an invisible gravitational force – something that the more rationally minded Galileo had not been able to accept.
Newton’s use of mathematical expression of physical occurrences underlined the standard for modern physics and his laws underpin our basic understanding of how things work on an everyday scale. The universality of the law of gravitation was challenged in 1915 when EINSTEIN published the theory of general relativity.

1670-71 Newton composes ‘Methodis Fluxionum‘, his main work on calculus, which is not published until 1736. His secrecy meant that in the intervening period, the German mathematician LEIBNIZ could publish his own independently discovered version – he gave it the name calculus, which stuck.

LAWS OF MOTION

1687 – England

  • First Law: An object at rest will remain at rest and an object in motion will remain in motion at that velocity until an external force acts on the object

  • Second Law: The sum of all forces (F) that act on an object is equal to the mass (m) of the object multiplied by the acceleration (a), or F = ma

  • Third Law: To every action, there is an equal and opposite reaction

The first law

introduces the concept of inertia, the tendency of a body to resist change in its velocity. The law is completely general, applying to all objects and any force. The inertia of an object is related to its mass. Things keep moving in a straight line until they are acted on by a force. The Moon tries to move in a straight line, but gravity pulls it into an orbit.
Weight is not the same as mass.

The second law

explains the relationship between mass and acceleration, stating that a force can change the motion of an object according to the product of its mass and its acceleration. That is, the rate and direction of any change depends entirely on the strength of the force that causes it and how heavy the object is. If the Moon were closer to the Earth, the pull of gravity between them would be so strong that the Moon would be dragged down to crash into the Earth. If it were further away, gravity would be weaker and the Moon would fly off into space.

The third law

shows that forces always exist in pairs. Every action and reaction is equal and opposite, so that when two things crash together they bounce off one another with equal force.

LIGHT

1672 – New Theory about Light and Colours is his first published work and contains his proof that white light is made up of all colours of the spectrum. By using a prism to split daylight into the colours of the rainbow and then using another to recombine them into white light, he showed that white light is made up of all the colours of the spectrum, each of which is bent to a slightly different extent when it passes through a lens – each type of ray producing a different spectral colour.

Newton also had a practical side. In the 1660s his reflecting telescope bypassed the focusing problems caused by chromatic aberration in the refracting telescope of the type used by Galileo. Newton solved the problem by swapping the lenses for curved mirrors so that the light rays did not have to pass through glass but reflected off it.

At around the same time, the Dutch scientist CHRISTIAAN HUYGENS came up with the convincing but wholly contradictory theory that light travels in waves like ripples on a pond. Newton vigorously challenged anyone who tried to contradict his opinion on the theory of light, as Robert Hooke and Leibniz, who shared similar views to Huygens found out. Given Newton’s standing, science abandoned the wave theory for the best part of two hundred years.

1704 – ‘Optiks’ published. In it he articulates his influential (if partly inaccurate) particle or corpuscle theory of light. Newton suggested that a beam of light is a stream of tiny particles or corpuscles, traveling at huge speed. If so, this would explain why light could travel through a vacuüm, where there is nothing to carry it. It also explained, he argued, why light travels in straight lines and casts sharp shadows – and is reflected from mirrors. His particle theory leads to an inverse square law that says that the intensity of light varies as the square of its distance from the source, just as gravity does. Newton was not dogmatic in Optiks, and shows an awareness of problems with the corpuscular theory.

In the mid-eighteenth century an English optician John Dolland realized that the problem of coloured images could largely be overcome by making two element glass lenses, in which a converging lens made from one kind of glass was sandwiched together with a diverging lens made of another type of glass. In such an ‘achromatic’ lens the spreading of white light into component colours by one element was cancelled out by the other.

During Newton’s time as master of the mint, twenty-seven counterfeiters were executed.

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CHRISTIAAN HUYGENS (1629- 95)

1690 – Holland

portrait of CHRISTIAAN HUYGENS ©

HUYGENS

‘Every point on a wavefront can act as a new source of waves’

A line perpendicular to the wave fronts is called a ray and this ray shows the direction of the wave.

The Huygens construction, published in ‘Traite de la Lumiere‘ (’Treatise on Light’, 1690) gives an explanation for the way light is reflected and refracted.

Huygens said that light consists of a disturbance spreading from its source as spherical pressure waves having wave fronts perpendicular to the direction of their motion and correctly anticipated that in a denser medium light would travel more slowly. This hypothesis was largely ignored at the time as it conflicted with NEWTON‘s theory. Huygens’ view, when re-discovered and championed by THOMAS YOUNG (1773-1829) would eventually become the more commonly accepted version.

He invented a pendulum clock (1656) and also discovered Titan, the first observed moon of Saturn (1665).

Saturn's moon Titan. Notable Features - Relatively smooth surface with almost no craters; Color variation across the planet (previously thought to be seas of methane, but that has been disproved. True origin has not been discovered.) At least one lake of liquid ethane is on the surface at the present time

Huygens discovered that a simple pendulum does not keep perfect time but completes smaller swings faster than big swings. This is because the weight or ‘bob’ of the pendulum follows a circular path. Huygens’ realisation that a pendulum mimicking a circle’s curve does not maintain a perfectly equal swing and that in order to do this it actually needs to follow a ‘cycloidal’ arc, set him on the path to designing the first successful pendulum clock.

Published ‘Horologium‘ (1658), ‘Horologium Oscillatorium‘ (1673) in which he showed that if the bob’s path were a cycloid (the curved path traced out by a point on the rim of a wheel as it rolls along) instead of a circle, it would be isynchronous (keeping equal time) no matter what the length of the swing. He made the pendulum’s swing cycloidal by suspending a rigid pendulum rod on two chords whose swing either way was limited by two plates called cycloidal checks.

GALILEO had considered the timekeeping possibilities of a swinging pendulum and Huygens successfully tied it with an escapement mechanism.
He explored the mathematics associated with pendulums – which led him, together with HOOKE, to an early prediction of the link between the elliptical orbits of the planets and the inverse square law of gravity. His work was a milestone, playing a key part in the understanding of centrifugal force. It helped to confirm Newton’s laws of motion by showing how an object will travel in a straight line unless pulled into a curved path by some other force.

Huygens was one of the founders of the French Académie des sciences in Paris.

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THOMAS NEWCOMEN (1663-1729)

1712 – England

‘Uses the property of condensing steam to create a partial vacuüm in a cylinder and therefore pull a piston. The system was highly inefficient but was used to pump water from mines’

Today, the credit for the steam engine is usually given to James Watt, while the name Thomas Newcomen remains shrouded in obscurity.

The design of his low-pressure steam engine involved heating water underneath a large piston that was encased in a cylinder.

Steam that was released as a result of the heating forced the piston upwards. A jet of water was then released from a tank above the piston. The sudden cooling of the steam made it condense, creating a partial vacuüm which atmospheric pressure then pushed down on, forcing the piston downwards again. The piston was attached to a two-headed lever, the other side of which was attached to a pump in the mineshaft. As it moved up and down, the lever moved likewise and a pumping motion was created in the shaft, which could be used to eject floodwater.

The first engine could remove about 120 gallons per minute, completing about twelve strokes in that time, and had the equivalent of about 5.5 horsepower. Even though the engine was still not particularly powerful, was hugely inefficient to run, and burnt huge amounts of coal, it would work reliably 24-hours a day.

The steam engine originally developed by Newcomen for work in the mines was quickly developed by engineers like JAMES WATT and RICHARD TREVITHICK (1771-1833) into the steam locomotive.

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DANIEL FAHRENHEIT (1686-1736)

1715 – Netherlands

‘The kelvin scale is more suitable for scientific purposes and the celsius scale is neater, based on decimals. The advantage of using the fahrenheit scale is that it is designed with everyday use in mind, rarely needing negative degrees’

Even as late as the start of the eighteenth century, scientists had no reliable means of accurately measuring temperature and a uniform scale by which to describe the limited measurements they could make.

Fahrenheit thermometer

FAHRENHEIT THERMOMETER

GALILEO had used the knowledge that air expands when heated and contracts when cooled to build a primitive instrument. Using a cylindrical tube placed in water, he noted that when the air in the device was hotter, it pushed the level of the water downwards, just as it rose when the air-cooled. He realised that readings from the device were unreliable because the volume and therefore the behaviour of the air also fluctuated according to atmospheric pressure. Gradually scientists began using more stable substances to improve the accuracy of the reading, with alcohol being introduced as a possible substitute late in the seventeenth century.

Fahrenheit knew that the boiling points of different liquids varied according to fluctuations in atmospheric pressure; the lower the pressure, the lower the boiling point. A producer of meteorological instruments, he first achieved progress in 1709 with an improved alcohol thermometer. Building on the work of GUILLAUME AMONTONS (1663-1705) who investigated the properties of mercury, Fahrenheit took the measurement of temperature into another domain. He produced his first mercury thermometer, particularly useful in its application over a wide range of temperatures, in 1714.

In 1715 he complemented his breakthroughs in instrument making with the development of the fahrenheit temperature scale. Taking 0degrees to be the lowest temperature he could produce (from a blend of ice and salt), he used the freezing point of water and the temperature of the human body as his other key markers in its formulation.

In his initial calculations, he placed water’s freezing point at 30degrees F and the body’s temperature at 90degrees F. Later revisions changed this to 32degrees for the freezing point of water and 96degrees for the body temperature of humans. The boiling point of water worked out to be 212degrees F, giving a hundred and eighty incremental steps between freezing and boiling.

picture of the head and face of DANIEL FAHRENHEIT ©

DANIEL FAHRENHEIT

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