- THE FIRST MILLENIUM
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’
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.
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 Newton’s genius that allowed him to derive Kepler’s laws of planetary motion from 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.
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.
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.
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
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.
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.
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.
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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1682 – England
Despite his many achievements, it is arguable that the most important factor influencing the legacy of Edmund Halley is his friendship with Newton.
He encouraged Newton to undertake the ‘Principia’ in the first place; he went on to edit and proof read the text, write the preface and to finance its publication in 1687.
Had Edmund Halley not been born, his comet would still exist, albeit under a different name. Newton’s Principia, at least in the form the world knows it today, almost certainly would not.
Halley was a prolific mapmaker, showing prevailing winds, tides and magnetic variations in his cartography.
Halley’s Comet will return to the skies in 2062.
1684 – Germany
‘A new method for maxima and minima, as well as tangents … and a curious type of calculation’
Newton invented calculus (fluxions) as early as 1665, but did not publish his major work until 1687. The controversy continued for years, but it is now thought that each developed calculus independently.
Terminology and notation of calculus as we know it today is due to Leibniz. He also introduced many other mathematical symbols: the decimal point, the equals sign, the colon (:) for division and ratio, and the dot for multiplication.
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.
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.
He 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 insistence on experimental analysis as the arbiter of elemental status 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 the 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.
“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.
1674 – Netherlands
Leeuwenhoek was probably inspired to take up microscopy after seeing a copy of HOOKE’s Micrographia, though as a draper he was likely to have already been using lenses to examine cloth.
Unlike Hooke, Leeuwenhoek did not use a two lens compound microscope, but a single high quality lens, which could be described simply as a magnifying glass rather than a microscope. Leeuwenhoek is known to have made over 500 of these single–lens microscopes. They are simple devices just a few inches long, with the lens mounted in a tiny hole in a brass plate. The specimen is mounted on a point that sticks up in front of the lens. Two screws move the specimen for focusing. All else that is needed is careful lighting and a very steady, sharp eye.
After an introduction to Henry Oldenburg of the Royal Society in London from Dutch physician and anatomist Regnier de Graaf (discoverer of the egg-making follicles in the human ovary which now bear his name), Leeuwenhoek was encouraged to write to the Society’s journal ‘Philosophical Transactions’.
Leeuwenhoek’s letters were translated into Latin and English from the Dutch and he reported seeing tiny creatures in lake-water.
‘ I found floating therein divers earthly particles, and some green streaks, spirally wound serpentwise, and orderly arranged after the manner of copper or tin worms which distillers use to cool their liquors as they distil over. The whole circumference of each of these streaks was about the thickness of a hair of one’s head ’
Leeuwenhoek’s descriptions of ‘animalcules’ in water from different sources – rainwater, pond water, well water, sea water and so on – were verified by independent witnesses, including the vicar of Delft. Hooke too confirmed his findings with his own observations performed in front of expert witnesses, including Sir Christopher Wren.
Leeuwenhoek came close to understanding that bacteria were germs that cause disease but it took another century before LOUIS PASTEUR made that step.