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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EUCLID (c.330 – c.260 BCE)

Fourth century BCE – Alexandria, Egypt

Euclid

EUCLID

  1. A straight line can be drawn between any two points

  2. A straight line can be extended indefinitely in either direction

  3. A circle can be drawn with any given centre and radius

  4. All right angles are equal

  5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines will eventually meet (or, parallel lines never meet)

These five postulates form the basis of Euclidean geometry. Many mathematicians do not consider the fifth postulate (or parallel postulate) as a true postulate, but rather as a theorem that can be derived from the first four postulates. This ‘parallel’ axiom means that if a point lies outside a straight line, then only one straight line can be drawn through the point that never meets the other line in that plane.

The ideas of earlier Greek mathematicians, such as EUDOXUS, THEAETETUS and PYTHAGORAS are all evident, though much of the systematic proof of theories, as well as other original contributions, was Euclid’s.

The first six of his thirteen volumes were concerned with plane geometry; for example laying out the basic principles of triangles, squares, rectangles and circles; as well as outlining other mathematical cornerstones, including Eudoxus’ theory of proportion. The next four books looked at number theory, including the proof that there is an infinite number of prime numbers. The final three works focused on solid geometry.

Virtually nothing is known about Euclid’s life. He studied in Athens and then worked in Alexandria during the reign of Ptolemy I

Euclid’s approach to his writings was systematic, laying out a set of axioms (truths) at the beginning and constructing each proof of theorem that followed on the basis of proven truths that had gone before.

Elements begins with 23 definitions (such as point, line, circle and right angle), the five postulates and five ‘common notions’. From these foundations Euclid proved 465 theorems.

A postulate (or axiom) claims something is true or is the basis for an argument. A theorem is a proven position, which is a statement with logical constraints.

Euclid’s common notions are not about geometry; they are elegant assertions of logic:

  • Two things that are both equal to a third thing are also equal to each other

  • If equals are added to equals, the wholes are equal

  • If equals are subtracted from equals, the remainders are equal

  • Things that coincide with one and other are equal to one and other

  • The whole is greater than the part

One of the dilemmas that he presented was how to deal with a cone. It was known that the volume of a cone was one-third of the volume of a cylinder that had the same height and base diameter. He asked if you cut through a cone parallel to its base, would the circle formed on the top section be the same size as that on the bottom of the new, smaller cone?

If it were, then the cone would in fact be a cylinder and clearly that was not true. If they were not equal, then the surface of a cone must consist of a series of steps or indentations.

NON-EUCLIDEAN MATHEMATICS

Statue of Janus Bolyai

Janus Bolyai

The essential weakness in Euclidean mathematics lay in its treatment of two- and three- dimensional figures. This was examined in the nineteenth century by the Romanian mathematician Janus Bolyai. He attempted to prove Euclid’s parallel postulate, only to discover that it is in fact unprovable. The postulate means that only one line can be drawn parallel to another through a given point, but if space is curved and multidimensional, many other parallel lines can be drawn. Similarly the angles of a triangle drawn on the surface of a ball add up to more than 180 degrees.
CARL FRIEDRICH GAUSS was perhaps the first to ‘doubt the truth of geometry’ and began to develop a new geometry for curved and multidimensional space. The final and conclusive push came from BERNHARD RIEMANN, who developed Gauss’s ideas on the intrinsic curvature of surfaces.

Riemann argued that we should ignore Euclidean geometry and treat each surface by itself. This had a profound effect on mathematics, removing a priori reasoning and ensuring that any future investigation of the geometric nature of the universe would have to be at least in part, empirical. This provides a mechanism for examinations of multidimensional space using an adaptation of the calculus.

However, the discoveries of the last two hundred years that have shown time and space to be other than Euclidean under certain circumstances should not be seen to undermine Euclid’s achievements.

Moreover, Euclid’s method of establishing basic truths by logic, deductive reasoning, evidence and proof is so powerful that it is regarded as common sense.

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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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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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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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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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DANIEL BERNOULLI (1700- 82) JAMES CLERK MAXWELL (1831- 79)

1738 – Switzerland
1859 – England

‘Gases are composed of molecules which are in constant random motion and their properties depend upon this motion’

The volume of a gas is simply the space through which molecules are free to move. Collisions of the molecules with each other and the walls of a container are perfectly elastic, resulting in no decrease in kinetic energy. The average kinetic energy of a gas increases with an increase in temperature and decreases with a decrease in temperature. The theory has been extended to provide a model for two states of matter – liquids and solids.

Bernoulli had a great advantage over DEMOCRITUS. He knew that free atoms were more than simply tiny grains flying though space; they were tiny grains flying through space and obeying NEWTON’s Laws of Motion.
Bernoulli proposed a ‘bombardment theory’, which stated that a gas consisted of tiny particles in rapid, random motion like a swarm of angry bees. He realized that in the case of such a gas visualized as a host of tiny grains in perpetual frenzied motion, the atoms hammering relentlessly on the walls of any containing vessel would produce a force by bombarding the container. The effect of each individual impact would of course be vanishingly small. The effect of billions upon billions of atoms, hammering away incessantly, however, would be to push the walls back. A gas made of atoms would exert a jittery force that we would detect as a ‘pressure’.

Heating a gas would make its particles move faster.
The pressure of a gas such as steam was easy to measure using a piston in a hollow container. This was essentially a moveable wall. To deduce how the pressure of a gas would be affected by different conditions, Bernoulli first made some simplifying assumptions. He assumed the atoms were very small compared to the gulf between them. This allowed Bernoulli to ignore any force – whether of attraction or repulsion – that existed between them, as being unlikely to be ‘long range’. (This is an ‘ideal’ or ‘perfect’ gas. The behaviour of a real gas may differ from the ideal, for example at very high pressure). With the motion of each atom unaffected by its fellows, Newton’s laws dictated that it should fly at a constant speed in a straight line. The exception was when it slammed into a piston or the walls of the container. Bernoulli assumed that in such a collision a gas atom bounced off the walls of the surface without losing any speed, in the process imparting a miniscule force to the wall.

What would happen if the volume of the gas were reduced by applying an outside force to the piston? If the gas were reduced to half its original volume, the atoms would now have to fly only half as far between collisions, in any given time they would collide with the piston twice as many times and would exert twice the pressure. Similarly, if the gas were compressed to a third of its volume, its pressure would triple. This had been observed by ROBERT BOYLE in 1660 and named Boyle’s Law.

What would happen to the pressure of gas in a closed cylinder if the gas were heated while its volume remained unchanged? Exploiting the insight that the temperature of a gas was a measure of how fast on average its atoms were flying about, that when a gas was heated, its atoms speeded up, he deduced that as the atoms would be moving faster they would collide with the piston more often and create a greater force. Consequently the pressure of the gas would rise. This was observed by the French scientist JACQUES ALEXANDRE CESARE CHARLES in 1787, and christened Charles’ law.

After 120 years MAXWELL polished Bernoulli’s ideas into a rigorous mathematical theory. In Germany, LUDWIG  BOLTZMANN championed the atomic hypothesis, but was refuted by the Austrian ERNST MACH, who was convinced that science should not concern itself with any feature of the world that could not be observed directly with the senses.

BERNOULLI’S PRINCIPLE

‘As the velocity of a liquid or gas increases, its pressure decreases; and when the velocity decreases, its pressure increases’

At a narrow constriction in a pipe or tube, the speed of a gas or liquid is increased, but its pressure is decreased, according to Bernoulli’s principle. This effect is named the Venturi effect (and a pipe or tube with a narrow constriction the Venturi tube) after the Italian G.B. Venturi (1746-1822) who first observed it in constrictions in water channels. An atomiser works on the same principle.

 

The principle is expressed as a complex equation, but it can be summed up simply as the faster the flow the lower the pressure.

An aircraft wing’s curved upper surface is longer than the lower one, which ensures that air has to travel further and so faster over the top than it does below the wing. Hence the air pressure underneath is greater than on top of the wing, causing an upward force, called lift.

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LEONHARD EULER (1707- 83)

1755 – Switzerland

‘Analytical calculus – the study of infinite processes and their limits’

Swiss mathematician. His notation is even more far-reaching than that of LEIBNIZ and much of the mathematical notation that is in use to-day may be credited to Euler.

The number of theorems, equations and formulae named after him is enormous.
Euler made important discoveries in the analytic geometry of surfaces and the theory of differential equations.

Euler popularised the use of the symbols  Π (Pi);  e , for the base of the natural logarithm; and  i , for the imaginary unit.
Euler is credited with contributing the useful notations   f (x) , for the general function of  x ; and   Σ , to indicate a general sum of terms.

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JAMES WATT (1736-1819)

1765 – Glasgow, Lanarkshire, UK

‘Steam engine’

Watt’s steam engine was the driving force behind the industrial revolution and his development of the rotary engine in 1781 brought mechanisation to several industries such as weaving, spinning and transportation.

Portrait of JAMES WATT who developed the steam engine ©

JAMES WATT

Although THOMAS NEWCOMEN had developed the steam engine before Watt was even born, Newcomen’s machines had been confined to the world of mining.

In 1764, when Watt was asked to repair a scale model of Newcomen’s engine he noted its huge inefficiency. The heating and cooling of the cylinder with every stroke wasted huge amounts of fuel; and wasted time in bringing the cylinder back up to steam producing temperature, which limited the frequency of strokes. He realised that the key to improved efficiency lay in condensing the steam in a separate container – thereby allowing the cylinder and piston to remain always hot. Watt continued to improve his steam engine and developed a way to make it work with a circular, rotary motion. Another of his improvements was the production of steam under pressure, thus increasing the temperature gap between source and sink and raising the efficiency in a manner later described by SADI CARNOT and elucidated by JAMES JOULE.

Richard_Arkwright_by_Mather_Brown_1790

RICHARD ARKWRIGHT

RICHARD ARKWRIGHT was the first to realise the engine could be used to spin cotton, and later in weaving. Flour and paper mills were other early adopters, and in 1788 steam power was used to paddle marine transportation. In the same year, Watt developed the ‘centrifugal governor’ to regulate the speed of the engine and to keep it constant.

diagram of the Watt 10hp engine

Watt 10hp engine

Watt was the first to coin the term ‘horsepower’, which he used when comparing how many horses it would require to provide the same pull as one of his machines. In 1882 the British Association named the ‘watt’ unit of power in his honour.

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THOMAS GRAHAM (1805- 69)

1833 – UK

‘Under the same conditions, the rate of diffusion of a gas is inversely proportional to the square root of its density’

For example, hydrogen diffuses four times as fast as oxygen under the same conditions of temperature and pressure.

Gases have no fixed volume; they expand to fill the entire volume of their container. This spreading of gas particles is called diffusion. The lightest gases diffuse most rapidly.

Graham is referred to as the father of colloid chemistry. In 1854 he invented the process of dialysis, which is based on the principle that some material will diffuse across a semi-permeable membrane and some material will not.

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JULIUS ROBERT MAYER (1814- 78)

1842 – Germany

‘Heat is a form of energy and energy is conserved’

In equation form ΔE = H − W where ΔE is the change in the internal energy of a system, H is heat energy received by the system and W is work done by the system.

The first law of thermodynamics is simply a restatement of the law of the conservation of energy: energy is neither created nor destroyed, but may be changed from one form to another.

Mayer and HELMHOLTZ, independent of JOULE and each other, came to similar conclusions at around the same time.

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JAMES PRESCOTT JOULE (1818- 89)

1843 – England

‘A given amount of work produces a specific amount of heat’

4.18 joules of work is equivalent to one calorie of heat.

In 1798 COUNT RUMFORD suggested that mechanical work could be converted into heat. This idea was pursued by Joule who conducted thousands of experiments to determine how much heat could be obtained from a given amount of work.

Even in the nineteenth century, scientists did not fully understand the properties of heat. The common belief held that it was some form of transient fluid – retained and released by matter – called CALORIC. Gradually, the idea that it was another form of energy, expressed as the movement of molecules gained ground.
Heat is now regarded as a mode of transfer of energy – the transfer of energy by virtue of a temperature difference. Heat is the name of a process, not that of an entity.

Joule began his experiments by examining the relationship between electric current and resistance in the wire through which it passed, in terms of the amount of heat given off. This led to the formulation of Joule’s ideas in the 1840s, which mathematically determined the link.

Joule is remembered for his description of the conversion of electrical energy into heat; which states that the heat (Q) produced when an electric current (I) flows through a resistance (R) for a time (t) is given by Q=I2Rt

Its importance was that it undermined the concept of ‘caloric’ as it effectively determined that one form of energy was transforming itself into another – electrical energy to heat energy. Joule proved that heat could be produced from many different types of energy, including mechanical energy.

john collier portrait of james prescott joule (1200 x 1600)

JAMES JOULE

The apparatus pictured was used by James Joule to demonstrate equivalence of mechanical work and heat. He calculated the work done by the pull of gravity on the weight. That pull turned the paddle wheels, which mixed the water in the insulated container. The water was warmed by the mixing, showing that heat = work

Calorimeter used by Joule in his 1876 determination of the mechanical equivalent of heat.

Joule was the son of a brewer and all his experiments on the mechanical equivalent of heat depended upon his ability to measure extremely slight increases in temperature, using the sensitive thermometers available to him at the brewery. He formulated a value for the work required to produce a unit of heat. Performing an improved version of Count Rumford’s experiment, he used weights on a pulley to turn a paddle wheel immersed in water. The friction between the water and the paddle wheel caused the temperature of the water to rise slightly. The amount of work could be measured from the weights and the distance they fell, the heat produced could be measured by the rise in temperature.

Joule went on to study the role of heat and movement in gases and subsequently with WILLIAM THOMSON, who later became Lord Kelvin, described what became known as the ‘Joule-Thomson effect’ (1852-9). This demonstrated how most gases lose temperature on expansion due to work being done in pulling the molecules apart.

Thomson thought, as CARNOT had, that heat IN equals heat OUT during a steam engine’s cycle. Joule convinced him he was wrong.

The essential correctness of Carnot’s insight is that the work performed in a cycle divided by heat input depends only on the temperature of the source and that of the sink.

Synthesising Joule’s results with Carnot’s ideas, it became clear that a generic steam engine’s efficiency – work output divided by heat input – differed from one (100%) by an amount that could be expressed either as heat OUT at the sink divided by heat IN at the source, or alternatively as temperature of the sink divided by temperature of the source. Carnot’s insight that the efficiency of the engine depends on the temperature difference was correct. Temperature has to be measured using the right scale. The correct one had been hinted at by DALTON and GAY-LUSSAC’s experiments, in which true zero was -273degrees Celsius.

A perfect cyclical heat engine with a source at 100degrees Celsius and a sink at 7degrees has an efficiency of 1 – 280/373. The only way for the efficiency to equal 100% – for the machine to be a perfect transformer of heat into mechanical energy – is for the sink to be at absolute zero temperature.

Joule’s work helped in determining the first law of thermodynamics; the principle of the conservation of energy. This was a natural extension of his work on the ability of energy to transform from one type to another.

Joule contended that the natural world has a fixed amount of energy which is never added to nor destroyed, but which just changes form.

The SI unit of work and energy is named the joule (J)

link to James Joule - Manchester Museum of Science & Industry

Manchester Museum of Science & Industry

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LEON FOUCAULT (1819- 68)

1850 – France

‘A Foucault pendulum is a simple pendulum – a long wire with a heavy weight (bob) at the end – except that at the top it is attached to a joint which allows it to swing in any direction’

Foucault’s pendulum proved that the Earth is rotating

Once a Foucault pendulum is set in motion, it seems not to swing back and forth in the same direction but to rotate. In fact, it is the rotation of the Earth beneath the pendulum which gives rise to its apparent rotation.
The angle of rotation per hour, which is constant at any particular location, can be calculated from the formula 15 sin Φ, where Φ is the geographical latitude of the observer. At the North or South Pole, the pendulum would rotate through 360 degrees once a day. At the equator it would not rotate at all.

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OSBORNE REYNOLDS (1842-1912)

1883 – UK

‘The ratio of pressure forces to viscosity forces in a fluid flow’

The Reynolds number is a dimensionless quantity (that is, it has no units). The number has great importance in fluid dynamics.

The number depends upon the speed, density, viscosity and linear dimensions (such as the diameter of a pipe or height of a building) of the flow. Fluid flow is described as ‘Turbulent’ when the number is greater than 2000. It is considered ‘Laminar’ (steady) when the value is less than 2000.

Reynolds presented the concept of a number to determine the type of fluid flow in a paper –
‘An experimental investigation of the circumstances which determine whether motion of water shall be direct or sinuous and of the law of resistance in parallel channels’
– in the Philosophical Transactions of the Royal Society.

He observed that the tendency of water to eddy becomes much greater as the temperature rises –
he associated temperature rise with a decrease in viscosity (the resistance of a fluid to flow).

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[To] mechanical progress there is apparently no end: for as in the past so in the future, each step in any direction will remove limits and bring in past barriers which have till then blocked the way in other directions; and so what for the time may appear to be a visible or practical limit will turn out to be but a bend in the road.
— Osborne Reynolds
Opening address to the Mechanical Science Section, Meeting of the British Association, Manchester. In Nature (15 Sep 1887), 36, 475.

ERNST MACH (1838-1916)

1895 – Austria

‘The ratio of the velocity of an object in air to the velocity of sound in air is termed the Mach number’

picture of the BELL X 1 in flight

If the Mach number is 1, speed is called sonic. Below Mach 1 it’s subsonic; above Mach 1 it’s supersonic.

Captain Chuck Yeager was the first person to break the sound barrier, on 14 October 1947. His flight was in the Bell X-1 rocket under an US government research program.

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MAX PLANCK (1856-1947)

1900 – Germany

‘Energy is not a continuous quantity but it is quantised; it flows in discrete packets or quanta. When particles emit energy they do so only in quanta’

According to Quantum theory, the energy (E) of one quantum (photon) is given by E = hf where f is the frequency of radiation and h is Planck’s constant.
Its value is 6.63 x 10-34 joules per second

h is a tiny number, close to zero, but it is has a finite value. This implies energy is released in discrete chunks, a revolutionary notion.

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MAX PLANCK

By the late 1800s the science of thermodynamics was developing to the point that people were beginning to understand the nature of energy.
The traditional view was that energy was released in a continuous stream and that any amount of energy could be indefinitely divided into smaller and smaller ‘lumps’. Planck’s work on the laws of thermodynamics and black body radiation led him to abandon this classical notion of the dynamic principles of energy and formulate the quantum theory, which assumes that energy changes take place in distinct packages, or quanta, that cannot be subdivided. This successfully accounted for certain phenomena that Newtonian theory could not explain.

The basic laws of thermodynamics recognised that energy could not be created or destroyed, but was always conserved. The second law was drawn from an understanding that heat would not pass from a colder body to a hotter body.
The study of thermodynamics was based on the assumption that matter was ultimately composed of particles. LUDWIG BOLTZMAN had proposed an explanation of thermodynamics, saying the energy contained in a system is the collective result of the movements of many tiny particles rattling around. He believed the second law was only valid in a statistical sense; it only worked if you added up all the bits of energy in all the little particles.
Among his detractors was Max Karl Ernst Ludwig Planck.

Planck began his work on the second law of thermodynamics and the concept of entropy. He investigated how materials transform between solid, liquid and gaseous states. In doing so he found explanations for the laws governing the differing freezing and boiling points of various substances.
He also looked at the conduction of electricity through liquid solutions (electrolysis).

In the mid 1890s Planck turned his attention to the question of how heated substances radiate energy. Physicists were aware that all bodies radiate heat at all frequencies – although maximum radiation is emitted only at a certain frequency, which depends on the temperature of the body. The hotter the body, the higher the frequency for maximum radiation. (Frequency is the rate per second of a wave of any form of radiation).

Planck had been considering formulae for the radiation released by a body at high temperature. Using ideas developed by ROBERT KIRCHOFF, he knew it should be expressible as a combination of wavelength frequency and temperature. For a theoretical ‘black body’, physicists could not predict expressions that were in line with the behaviour of hot bodies at high frequencies and were in agreement with other equations showing their nature at low frequencies. Thus no law could be found which fitted all frequencies and obeyed the laws of classical physics simultaneously.
Plank resolved to find a theoretical formula that would work mathematically, even if it did not reflect known physical laws. His first attempts were partially successful, but did not take into account any notion of particles or quanta of energy, as he was certain of the continuous nature of energy. In an ‘act of despair’ he renounced classical physics and embraced quanta.

The final straw had been a concept developed by John Rayleigh and James Jeans that became known as the ‘ultraviolet catastrophe’ theory. They had developed a formula that predicted values for radiation distribution and worked at low frequencies, but not at high frequencies. It was at odds with Planck’s formula, which worked for high frequencies but broke down at low frequencies. In June 1900 Rayleigh had pointed out that classical mechanics, when applied to the oscillators of a black-body, leads to an energy distribution that increases in proportion to the square of the frequency. This conflicted with all known data.

Planck’s answer was to introduce what he called ‘energy elements’ or quanta and to express the energy emitted as a straightforward multiplication of frequency by a constant, which became known as ‘Planck’s constant’ (6.6256 x 10-34 Jsec-1). This only works with whole number multiples which means for the formula to have any practical use one must accept the radical theory that energy is only released in distinct, non-divisible chunks, known as ‘quanta’, or for a single chunk of energy, a ‘quantum’. This completely contradicts classical physics, which assumed that energy is emitted in a continuous stream. The individual quanta of energy were so small that when emitted at the everyday large levels observed, it appears that energy could seem to be flowing in a continuous stream.
Thus classical physics was cast into doubt and quantum theory was born.

Planck announced his theory on December 14 1900 in his paper ‘On the Theory of the Law of Energy Distribution in the Continuous Spectrum’. Planck said ‘energy is made up of a completely determinate number of finite equal parts, and for this purpose I use the constant of nature h = 6.55 x 10-27(erg sec)’

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When ALBERT EINSTEIN was able to explain the ‘photoelectric’ effect in 1905, suggesting that light is emitted in quanta called ‘photons’, by applying Planck’s theory – and likewise NIELS BOHR in his explanation of atomic theory in 1913 – the abstract idea was shown to explain physical phenomena.

Planck was awarded the Nobel Prize for Physics in 1918.

picture of the Nobel medal - link to nobelprize.org
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ROBERT GODDARD (1882-1945)

1915 – USA

‘Demonstrates that rocket engines can produce thrust in a vacuum’

‘Robert Goddard stands as the epitome of the early American desire to conquer space’

It was generally believed that it would be impossible for a rocket to move outside of the Earth’s atmosphere, as there was nothing for it to push against in order to gain propulsion. Goddard had already gone a long way to revoking this assumption by 1907 in completing calculations to show that a rocket could thrust in a vacuum, and had backed up this concept with physical experiment in 1915.

His booklet “A Method of Reaching Extreme Altitudes” described the multi-stage principle and presented advanced ideas on how to improve the performance of solid-fuel rockets.

‘I have read very attentively your remarkable book A Method for Reaching Extreme Altitudes edited in 1919 and I have found in it quite all the ideas which the German Professor H.Oberth published in 1924′ (in a letter from Soviet engineer & author Nikolai Alexsevitch Rynin)

In 1926 he launched the world’s first liquid-fuelled rocket using gasoline and liquid oxygen; the 2.5 second, 41 feet flight proved that liquid-fuel propellants could be used to power a rocket instead of exploding in a catastrophic detonation.
Over the next decade, Goddard filed patents for guidance, control and fuel pump mechanisms.

In spite of his success (by 1935 he had launched a rocket at Roswell, New Mexico which traveled faster than the speed of sound and another which achieved an altitude of 1.7 miles – a record at that time) the US Government largely ignored his efforts until the space race gathered momentum in the 1940s and 1950s.
The government was eventually forced to pay one million dollars to Goddard’s widow for patent infringement in acknowledgement of the use they had made of his designs as a basis from which to begin development.

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