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

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.

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.
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.

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.

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

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.

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.

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.

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.

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.

NEXT

 

GRAVITY

 

LIGHT

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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.

TIMELINE

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.

DANIEL BERNOULLI

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.

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.

BERNOULLI’S PRINCIPLE

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

 

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.

 
 
 

TIMELINE

 

MECHANICS

HENRY CAVENDISH (1731-1810)

1766 – England

Three Papers Containing Experiments On Factitious Airs

(gases made from reactions between liquids and solids)

1798 – Density of the earth
Using a torsion balance and the application of NEWTON’s theory of gravity, Cavendish concluded that the earth’s density was 5.5 times that of water.

Born of the English aristocracy and inheritor of a huge sum of money half way through his life, Cavendish is remembered for his work in chemistry.
He demonstrated that hydrogen (inflammable air) and carbon dioxide (fixed air) were gases distinct from ‘atmospheric air’.
His claim to the discovery that water was not a distinct element – a view held since the time of ARISTOTLE – but a compound made from two parts hydrogen to one part oxygen, became confused with similar observations made by ANTOINE LAVOISIER.

CAVENDISH

1871 – England

Almost all his discoveries remained unpublished until the late nineteenth century when his notes were found and JAMES CLERK MAXWELL dedicated himself to publishing Cavendish’s work, a task he completed in 1879.
By then many potential breakthroughs, significant at the time, had been surpassed by history.

In 1871 the endowment of the Cavendish Laboratory was made to Cambridge University by Cavendish’s legatees.

TIMELINE

JOSEPH PRIESTLEY (1733-1804)

1774 – England

JOSEPH PRIESTLY

Priestly stumbled upon oxygen in 1774 while heating mercury oxide and discovered that it greatly enhanced the burning of a candle’s flame

Priestly did not realise the true impact of his findings and it was left to ANTOINE LAVOISIER whom he told of his findings in 1775 to establish the central place oxygen has in the fields of chemistry and biology.

Priestly named the gas ‘dephlogisticated air’, in keeping with the accepted theory that all flammable substances contained the elusive substance ‘phlogiston’ which was central to the combustion process and was released (and lost) during it.

TIMELINE

 

CHEMISTRY

BENJAMIN THOMPSON (1753-1814) known as Count Rumford

1798 – England

Mechanical work can be converted into heat. Heat is the energy of motion of particles

Heat is a form of energy associated with the random motion of atoms or molecules. Temperature is a measure of the hotness of an object.

COUNT RUMFORD

In the eighteenth century, scientists imagined heat as a flow of a fluid substance called CALORIC.
Each object contained a certain amount of caloric. If caloric flowed out, the object’s temperature decreased; if more caloric flowed into the object, its temperature increased.

Like PHLOGISTON, caloric was a weightless fluid, a quality that could be transmitted from one substance to another, so that the first warmed the second up.
What is being transmitted is heat energy.

Working for the Elector of Bavaria, Rumford investigated the heat generated during the reaming out of the metal core when the bore of a cannon is formed. According to the caloric theory, the heat was released from the shards of metal during boring; Rumford noticed that if the tools were blunt and removed little or no metal, more heat was generated, rather than less.
Rumford postulated that the heat source had to be the work done in drilling the hole. Heat was not an indestructible caloric fluid, as LAVOISIER had argued, but something that could come and go. Mechanical energy could produce heat and heat could lead to mechanical energy.

One analogy he drew was to a bell; heat was like sound, with cold being similar to low notes and hot, to high ones. Temperature was therefore just the frequency of the bell. A hot object would emit ‘calorific rays’, whilst a cold one would emit ‘frigorific rays’ – an idea raised in Plutarch’s De Primo Frigido. Cold was an entity in itself, not simply the absence of heat.

Rumford thought there was no separate caloric fluid and that the heat content of an object was associated with motion or internal vibrations – motion which in the case of the cannon was bolstered by the friction of the tools.
He had recognized the relationship between heat energy and the physicists’ concept of ‘work’ – the transfer of energy from a system into the surroundings, caused by the work done, results in a difference in temperature. This transfer of energy measured as a temperature difference is called ‘heat’.

Half a century was to pass before in 1849, JAMES JOULE established the ‘mechanical equivalent of heat’ and JAMES CLERK MAXWELL launched the kinetic theory. According to Maxwell, the heat content of a body is equivalent to the sum of the individual energies of motion (kinetic energies) of its constituent atoms and molecules.

US born Rumford founded the Royal Institution in London and invented the calorimeter, a device for measuring heat.

TIMELINE

 

HEAT

EDWARD JENNER (1749-1823)

EDWARD JENNER

1798 – England

Vaccination

TIMELINE

 

MICROBES

THOMAS MALTHUS (1766-1834)

1798 – England

If unchecked, the human population would grow geometrically while the food supply could only grow arithmetically. In two centuries the population would be to the food supply 256:9

(In an arithmetic series of numbers there is a common difference between any number and its successor, while in a geometric series each number is a constant multiple of the preceding number)

When Malthus, an obscure country curate, published his Essay on the Principle of Population it excited much attention and placed its author in the centre of a controversial political debate on population. The essay was denounced as unholy, atheistic and subversive of the social order. FRIEDRICH ENGELS, the cofounder of communism, criticised Malthus’ essay for underestimating science;

‘But science increases as fast as population – in the most normal conditions it also grows in geometrical progression – and what is impossible for science? ‘

THOMAS MALTHUS

Malthusian ideas form the foundations of some theories on the relationship between economics, population and the environment.
DARWIN wrote in his book ‘The Origin of Species’ that his theory ‘is the doctrine of Malthus applied with manifold force to the whole animal and vegetable kingdoms’.

TIMELINE

JOHN DALTON (1766-1844)

1801 – England

The total pressure of a mixture of gases is the sum of the partial pressures exerted by each of the gases in the mixture

Partial pressures of gases:
Dalton stated that the pressure of a mixture of gases is equal to the sum of the pressures of the gases in the mixture. On heating gases they expand and he realised that each gas acts independently of the other.

Each gas in a mixture of gases exerts a pressure, which is equal to the pressure it would exert if it were present alone in the container; this pressure is called partial pressure.

Dalton’s law of partial pressures contributed to the development of the kinetic theory of gases.

His meteorological observations confirmed the cause of rain to be a fall in temperature, not pressure and he discovered the ‘dew point’ and that the behaviour of water vapour is consistent with that of other gases.

He showed that a gas could dissolve in water or diffuse through solid objects.

The varying solubility of gases

Further to this, his experiments on determining the solubility of gases in water, which, unexpectedly for Dalton, showed that each gas differed in its solubility, led him to speculate that perhaps the gases were composed of different ‘atoms’, or indivisible particles, which each had different masses.
On further examination of his thesis, he realised that not only would it explain the different solubility of gases in water, but would also account for the ‘conservation of mass’ observed during chemical reactions – as well as the combinations into which elements apparently entered when forming compounds – because the atoms were simply ‘rearranging’ themselves and not being created or destroyed.

In his experiments, he observed that pure oxygen will not absorb as much water vapour as pure nitrogen – his conclusion was that oxygen atoms were bigger and heavier than nitrogen atoms.

‘ Why does not water admit its bulk of every kind of gas alike? …. I am nearly persuaded that the circumstance depends on the weight and number of the ultimate particles of the several gases ’

In a paper read to the Manchester Society on 21 October 1803, Dalton went further,

‘ An inquiry into the relative weight of the ultimate particles of bodies is a subject as far as I know, entirely new; I have lately been prosecuting this enquiry with remarkable success ’

Dalton described how he had arrived at different weights for the basic units of each elemental gas – in other words the weight of their atoms, or atomic weight.

 

Dalton had noticed that when elements combine to make a compound, they always did so in fixed proportions and went on to argue that the atoms of each element combined to make compounds in very simple ratios, and so the weight of each atom could be worked out by the weight of each element involved in a compound – the idea of the Law of Multiple Proportions.

When oxygen and hydrogen combined to make water, 8 grammes of oxygen was used for every 1 gramme of hydrogen. If oxygen consisted of large numbers of identical oxygen atoms and hydrogen large numbers of hydrogen atoms, all identical, and the formation of water from oxygen and hydrogen involved the two kinds of atoms colliding and sticking to make large numbers of particles of water (molecules) – then as water has an identity as distinctive as either hydrogen or oxygen, it followed that water molecules are all identical, made of a fixed number of oxygen atoms and a fixed number of hydrogen atoms.

Dalton realised that hydrogen was the lightest gas, and so he assigned it an atomic weight of 1. Because of the weight of oxygen that combined with hydrogen in water, he first assigned oxygen an atomic weight of 8.

There was a basic flaw in Dalton’s method, because he did not realise that atoms of the same element can combine. He assumed that a compound of atoms, a molecule, had only one atom of each element. It was not until Italian scientist AMADEO AVOGADRO’s idea of using molecular proportions was introduced that he would be able to calculate atomic weights correctly.

In his book of 1808, ‘A New System of Chemical Philosophy’ he summarised his beliefs based on key principles: atoms of the same element are identical; distinct elements have distinct atoms; atoms are neither created nor destroyed; everything is made up of atoms; a chemical change is simply the reshuffling of atoms; and compounds are made up of atoms from the relevant elements. He published a table of known atoms and their weights, (although some of these were slightly wrong), based on hydrogen having a mass of one.

Nevertheless, the basic idea of Dalton’s atomic theory – that each element has its own unique sized atoms – has proved to be resoundingly correct.

If oxygen atoms all had a certain weight which is unique to oxygen and hydrogen atoms all had a certain weight that was unique to hydrogen, then a fixed number of oxygen atoms and a fixed number of hydrogen atoms combined to form a fixed weight of water molecules. Each water molecule must therefore contain the same weight of oxygen atoms relative to hydrogen atoms.

Here then is the reason for the ‘law of fixed proportions’. It is irrelevant how much water is involved – the same factors always hold – the oxygen atoms in a single water molecule weigh 8 times as much as the hydrogen atoms.

Dalton wrongly assumed that elements would combine in one-to-one ratios as a base principle, only converting into ‘multiple proportions’ (for example from carbon monoxide, CO, to carbon dioxide, CO₂) under certain conditions. Each water molecule (H₂O) actually contains two atoms of hydrogen and one atom of oxygen. An oxygen atom is actually 16 times as heavy as a hydrogen atom. This does not affect Dalton’s reasoning.

The law of fixed proportions holds because a compound consists of a large number of identical molecules, each made of a fixed number of atoms of each component element.

Although the debate over the validity of Dalton’s thesis continued for decades, the foundation for the study of modern atomic theory had been laid and with ongoing refinement was gradually accepted.

A_New_System_of_Chemical_Philosophy

TIMELINE

 

THE ATOM

 

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THOMAS YOUNG (1773-1829)

1801 – England

Interference between waves can be constructive or destructive

Huygens‘ wave theory was neglected for more than a hundred years until it was revived by Young in the opening years of the nineteenth century. Young rejected Newton’s view that if light consisted of waves it would not travel in a straight line and therefore sharp shadows would not be possible. He said that if the wavelength of light was extremely small, light would not spread around corners and shadows would appear sharp. His principle of interference provided strong evidence in support of the wave theory.

Young’s principle advanced the wave theory of light of CHRISTIAAN HUYGENS. Further advances came from EINSTEIN and PLANCK.

In Young’s double slit experiment a beam of sunlight is allowed to enter a darkened room through a pinhole. The beam is then passed through two closely spaced small slits in a cardboard screen. You would expect to see two bright lights on a screen placed behind the slits. Instead a series of alternate light and dark stripes are observed, known as interference fringes, produced when one wave of light interferes with another wave of light.

Two identical waves traveling together either reinforce each other (constructive interference) or cancel each other out (destructive interference). This effect is similar to the pattern produced when two stones are thrown into a pool of water.

THOMAS YOUNG

The mathematical explanation of this effect was provided by AUGUSTIN FRESNEL (1788-1827). The wave theory was further expanded by EINSTEIN in 1905 when he showed that light is transmitted as photons.

Light, an electromagnetic radiation, is transported in photons that are guided along their path by waves. This is known as ‘wave-particle duality’.

The current view of the nature of light is based on quantum theory.

TIMELINE

 

WAVES

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