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Isaac Newton [ˌaɪzək ˈnjuːtən] (okunuşu: Ayzek Nivtın), (d. 25 Aralık 1642 – ö. 31 Mart 1727). İngiliz fizikçi, matematikçi, astronom, mucit, filozof ve simyacıdır. En büyük matematikçi ve bilim adamlarından biri olduğu düşünülür. Bilim devrimine ve heliyosentirizm'in gelişmesinde büyük katkıları olmuştur.bii

==Hayatı== böö Isaac Newton 4 Ocak 1642'de İngiltere'nin Lincolnshire kentinde doğdu. Çiftçi olan babasını doğumundan üç ay önce kaybetmişti. Annesi ikinci kez evlendi. İkinci evlilikten üç üvey kardeşi olan Isaac anneannesinde kalıyordu. On iki yaşında Grantham'da King's School'a yazılan Newton, bu okulu 1661'de bitirdi. Aynı yıl Cambridge Üniversitesi'ndeki Trinity Kolej'ine girdi. Nisan 1665'te bu okuldan lisans derecesini aldı. Lisansüstü çalışmalarına başlayacağı sırada ortalığı saran veba salgını yüzünden üniversite kapatıldı.

Salgından korunma amacıyla annesinin çiftliğine sığınan Newton, burada geçirdiği iki yıl boyunca en önemli buluşlarını gerçekleştirdi. 1667'de Trinity Kolej'ine öğretim üyesi olarak döndüğünde diferansiyel ve integral hesabın temellerini atmış, beyaz ışığı oluşturan renklere ulaşmıştı. Çekingenliği yüzünden Newton her biri bilimde devrim yaratacak nitelikteki bu buluşların çoğunu uzun yıllar sonra (örneğin diferansiyel ve integral hesabı 38 yıl sonra) yayınlamıştır. Lisansüstü çalışmasını ertesi yıl tamamlayan Newton 1669'da henüz 27 yaşındayken Cambridge Üniversitesi'nde matematik profesörlüğüne getirildi. 1671'de ilk aynalı teleskopu gerçekleştirdi, ve ertesi yıl Royal Society üyeliğine seçildi. Royal Society'e sunduğu renk olgusuna ilişkin bildirisinin eleştirilere hedef olması, özellikle Robert Hooke tarafından şiddetle eleştirilmesi üzerine Newton tümüyle içine kapanarak, bilim dünyasıyla ilişkisini kesti.

1675'de optik konusundaki iki bildirisi yeni tartışmalara yol açtı. Hooke makalelerdeki bazı sonuçların kendi buluşu olduğunu, Newton'un bunlara sahip çıktığını öne sürdü. Bütün bu tartışma ve eleştiriler sonucunda 1678'de ruhsal bunalıma giren Newton ancak yakın dostu ünlü astronom ve matematikçi Edmond Halley'in çabalarıyla altı yıl sonra bilimsel çalışmalarına geri döndü.

Newton'un başına elma düşmesiyle yerçekimini keşfettiği yer, Cambridge'deki Botanik bahçesi'nde bulunuyor.
Isaac Newton'un kendisine ait ilk basım Principia, Üstünde kendi el yazısı ile ikinci basımda yapılacak değişiklikler yer alıyor.

Cambridge Üniversitesi'nde Katolikliği yaygınlaştırma ve egemen kılma çabalarına karşı başlatılan direniş hareketine öncülük eden Newton, kral düşürüldükten sonra 1689'da üniversitenin parlamentodaki temsilciliğine seçildi. 1693'de yeniden bir ruhsal bunalıma girdi ve yakın dostlarıyla, bu arada Samuel Pepys ve John Locke ile arası bozuldu. İki yıl süren bir dinlenme döneminden sonra sağlığına yeniden kavuştuysa da bundan sonraki yaşamında bilimsel çalışmaya eskisi gibi ilgi duymadı. Daha sonra 1699'da Fransız Bilimler Akademisi'nin yabancı üyeliğine 1703'de Royal Society'nin başkanlığına seçildi.

Newton 'Eğer diğer insanlardan ileriyi görebiliyorsam,bu devlerin omuzlarında olduğum içindir.' diyerek kendine yardım edenleri unutmadığını göstermiştir.

Kendisi için söylenenler [değiştir]

John Maynard Keynes’in (1883-1946) Newton için yapmış olduğu yorumu okuyalım.

"Newton 18. yy'dan beri çağdaş bilim adamlarının ilki ve en büyüğü, bir akılcı; bize serinkanlı düşünmeyi, katıksız mantığı öğreten biri olarak düşünülebilmiştir. Ben O'na bu göz ile bakmıyorum. 1696'da nihayet Cambridge'i terk ederken derlediği ve kısmen dağılmasına rağmen bize ulaşan sandığının içeriğini inceleyen her hangi birinin de onu böyle görebileceğini sanmıyorum. Newton akıl çağının başlangıcı değildi. O büyücülerin sonuncusu, Babillilerin ve Sümerlilerin sonuncusu; görünür ve zihinsel evreni, yaklaşık 10.000 yıl önce entelektüel mirasımızı kurmaya başlayanlarla aynı gözle gören son büyük beyin idi. 1642’de bir Noel günü babasının ölümünden sonra doğan Sir Isaac Newton müneccimlerin gereken bağlılığı içtenlikle gösterebilcekleri son harika çocuktu.” (kaynak: Batı felsefesi tarihi, Tuncar Tuğcu, Alesta yayınları, Ekim 2000)

Sanırız ki Keynes’e ait bu yorum Isaac Newton'un insanlık tarihinin neden en eşsiz bilim adamı olduğunun açık kanıtıdır; O görünenin arkasındaki görünmeyeni aramak ile yanıp tutuşan, buna varlığını adamış, bunun için insanlık tarihine yön vermiş ve vermekte olan değerler ortaya koymuş bir bilim insanı idi."(Notu ekleyenin notu)

"Doğa ve Doğanın yasası, karanlıkta saklıydı. Tanrı: Newton olsun! dedi ve her şey aydınlandı." Alexander Pope (kaynak: Felsefenin öyküsü, Bryan Magee, Dost Kitabevi, Kasım 2004) tipiz be oğlum tip lan tip

Geleneksel Kronolojinin Kritiği [değiştir]

Daha çok bilgi için: Yeni Kronoloji

İsaac Newton de Scaliger ve Petavius’ün Tarih kronolojisine karşıydı. Newton çok geniş bir eser yazdı “Eski kraliyetlerin değiştirilmiş Kronolojileri” diye. Bu kitapta eskiden olmuş bir çok büyük olayın tarihlerin oluş zamanların birkaç yüzyıl ileri çekmiştir. Bu inceleme üzerine bir çok bilimci, tarihçi ve felsefeci bilimsel yoldan itiraz edemedikleri için çıldırmış diye İsaac Newton'u kanıtsız olarak suçladılar. Niye suçladılarsa?

Sir Isaac Newton (1642-1727)
 

     Bir Çiftci olan babası o doğmadan üç ay önce ölmüştü. Oniki yaşında Grantham'da king's School'a yazılan Newton bu okulu 1661'de bitirdi. Aynı yıl Cambridge Universite'sindeki Trinity Kolleje girdi. Nisan 1665 'te bu okuldan lisans derecesini aldı. Lisansüstü çalışmalarına başlıyacağı sırada ortalığı saran veba salgını yüzünden üniversite kapatıldı.

         Salgından korunma amacıyla annesinin çiftliğine sığınan Newton burada geçirdiği iki yıl boyunca en önemli buluşlarını gerçekleştirdi. 1667'de Trinity Kolleje öğretim üyesi olarak döndüğünde diferansiyel ve integral hesabın temellerini atmış,beyaz ışığın renkli bileşenlerine ayrıştırılabileceğini saptamış ve cisimlerin birbirlerini, uzaklıklarının karesi ile ters orantılı olarak çektikleri sonucuna ulaşmıştı.Çekingenliği yüzünden Newton her biri bilimde devrim yaratacak nitelikteki bu buluşların çoğunu uzun yıllar sonra (örneğin diferansiyel ve integral hesabı 38 yıl sonra) yayımlamıştır.Lisansüstü çalışmasını ertesi yıl tamamlayan Newton 1669'da henüz 27 yaşındayken Cambridge Universite'sinde matematik profesörlüğüne getirildi.1671'de ilk aynalı teleskopu gerçekleştirdi, ve ertesi yıl Royal Society   üyeliğine seçildi. Royal Society'ye sunduğu renk olgusuna ilişkin bidirisinin eleştirilere hedef olması , özellikle Robert Hooke tarafından şiddetle eleştirilmesi üzerine  Newton tümüyle içine kapanarak, bilim dünyasıyle ilişkisini kesti. 1675'de sunduğu gene optik konusundaki iki bildirisi yeni tartışmalara yol açtı. Hooke makalelerdeki bazı sonuçların kendi buluşu olduğunu ,Newton'un bunlara sahip çıktığını öne sürdü.Bütün bu tartışma ve eleştiriler sonucunda 1678'de  ruhsal bunalıma giren Newton ancak yakın dostu ünlü astronom matematikçi Edmond Halley'in çabalarıyla altı yıl sonra bilimsel çalışmalarına geri döndü.
       Cambridge Universite'sinde katolikliği yaygınlaştırma ve egemen kılma çabalarına karşı başlatılan direniş hareketine öncülük eden Newton, kral düşürüldükten sonra 1689'da üniversitenin parlamento daki temsilciliğine seçildi. 1693'de yeniden bir ruhsal bunalıma girdi ve yakın dostlarıyla, bu arada Samuel pepys ve John locke ile arası bozuldu.Iki yıl süren bir inziva döneminden sonra sağlığına yeniden kavuştuysada bundan sonraki yaşamında bilimsel çalışmaya eskisi gibi ilgi duymadı.Daha sonra 1699'da Fransız Bilimler Akademi'sinin yabancı üyeliğine 1703'de Royal Society'nin başkanlığına seçildi.
       Gelmiş geçmiş bilim adamlarının en büyüklerinden biri olarak kabul edilen Newton matematik ve fizikte çok önemli buluşlar gerçekleştirdi. Matematikte (a+b)ª  ifadesinin üstel seriye açınımını veren genel ikiterimli teoremini  buldu. Newton'un bilime en büyük katkısı mekanik alanındadır. Merkezkaç kuvvet yasası ile Kepler yasalarını birlikte ele alarak kütleçekim yasasını ortaya koydu. Newton hareket yasaları olarak bilinen eylemsizlik ilkesi, kuvvetin kütleyle ivmenin çarpımına eşit olduğunu ifade eden yasa ve etki ile tepkinin eşitliği fiziğin en önemli yasalarındandır.
     Yayımladığı kitaplardan bazıları Philosophiae naturalis principia mathematica, principia,opticks sayılabilir

Isaac Newton's life can be divided into three quite distinct periods. The first is his boyhood days from 1643 up to his appointment to a chair in 1669. The second period from 1669 to 1687 was the highly productive period in which he was Lucasian professor at Cambridge. The third period (nearly as long as the other two combined) saw Newton as a highly paid government official in London with little further interest in mathematical research.

Isaac Newton was born in the manor house of Woolsthorpe, near Grantham in Lincolnshire. Although by the calendar in use at the time of his birth he was born on Christmas Day 1642, we give the date of 4 January 1643 in this biography which is the "corrected" Gregorian calendar date bringing it into line with our present calendar. (The Gregorian calendar was not adopted in England until 1752.) Isaac Newton came from a family of farmers but never knew his father, also named Isaac Newton, who died in October 1642, three months before his son was born. Although Isaac's father owned property and animals which made him quite a wealthy man, he was completely uneducated and could not sign his own name.

You can see a picture of
Woolsthorpe Manor as it is now.

Isaac's mother Hannah Ayscough remarried Barnabas Smith the minister of the church at North Witham, a nearby village, when Isaac was two years old. The young child was then left in the care of his grandmother Margery Ayscough at Woolsthorpe. Basically treated as an orphan, Isaac did not have a happy childhood. His grandfather James Ayscough was never mentioned by Isaac in later life and the fact that James left nothing to Isaac in his will, made when the boy was ten years old, suggests that there was no love lost between the two. There is no doubt that Isaac felt very bitter towards his mother and his step-father Barnabas Smith. When examining his sins at age nineteen, Isaac listed:-

Threatening my father and mother Smith to burn them and the house over them.

Upon the death of his stepfather in 1653, Newton lived in an extended family consisting of his mother, his grandmother, one half-brother, and two half-sisters. From shortly after this time Isaac began attending the Free Grammar School in Grantham. Although this was only five miles from his home, Isaac lodged with the Clark family at Grantham. However he seems to have shown little promise in academic work. His school reports described him as 'idle' and 'inattentive'. His mother, by now a lady of reasonable wealth and property, thought that her eldest son was the right person to manage her affairs and her estate. Isaac was taken away from school but soon showed that he had no talent, or interest, in managing an estate.

An uncle, William Ayscough, decided that Isaac should prepare for entering university and, having persuaded his mother that this was the right thing to do, Isaac was allowed to return to the Free Grammar School in Grantham in 1660 to complete his school education. This time he lodged with Stokes, who was the headmaster of the school, and it would appear that, despite suggestions that he had previously shown no academic promise, Isaac must have convinced some of those around him that he had academic promise. Some evidence points to Stokes also persuading Isaac's mother to let him enter university, so it is likely that Isaac had shown more promise in his first spell at the school than the school reports suggest. Another piece of evidence comes from Isaac's list of sins referred to above. He lists one of his sins as:-

... setting my heart on money, learning, and pleasure more than Thee ...

which tells us that Isaac must have had a passion for learning.

We know nothing about what Isaac learnt in preparation for university, but Stokes was an able man and almost certainly gave Isaac private coaching and a good grounding. There is no evidence that he learnt any mathematics, but we cannot rule out Stokes introducing him to Euclid's Elements which he was well capable of teaching (although there is evidence mentioned below that Newton did not read Euclid before 1663). Anecdotes abound about a mechanical ability which Isaac displayed at the school and stories are told of his skill in making models of machines, in particular of clocks and windmills. However, when biographers seek information about famous people there is always a tendency for people to report what they think is expected of them, and these anecdotes may simply be made up later by those who felt that the most famous scientist in the world ought to have had these skills at school.

Newton entered his uncle's old College, Trinity College Cambridge, on 5 June 1661. He was older than most of his fellow students but, despite the fact that his mother was financially well off, he entered as a sizar. A sizar at Cambridge was a student who received an allowance toward college expenses in exchange for acting as a servant to other students. There is certainly some ambiguity in his position as a sizar, for he seems to have associated with "better class" students rather than other sizars. Westfall (see [23] or [24]) has suggested that Newton may have had Humphrey Babington, a distant relative who was a Fellow of Trinity, as his patron. This reasonable explanation would fit well with what is known and mean that his mother did not subject him unnecessarily to hardship as some of his biographers claim.

Newton's aim at Cambridge was a law degree. Instruction at Cambridge was dominated by the philosophy of Aristotle but some freedom of study was allowed in the third year of the course. Newton studied the philosophy of Descartes, Gassendi, Hobbes, and in particular Boyle. The mechanics of the Copernican astronomy of Galileo attracted him and he also studied Kepler's Optics. He recorded his thoughts in a book which he entitled Quaestiones Quaedam Philosophicae (Certain Philosophical Questions). It is a fascinating account of how Newton's ideas were already forming around 1664. He headed the text with a Latin statement meaning "Plato is my friend, Aristotle is my friend, but my best friend is truth" showing himself a free thinker from an early stage.

How Newton was introduced to the most advanced mathematical texts of his day is slightly less clear. According to de Moivre, Newton's interest in mathematics began in the autumn of 1663 when he bought an astrology book at a fair in Cambridge and found that he could not understand the mathematics in it. Attempting to read a trigonometry book, he found that he lacked knowledge of geometry and so decided to read Barrow's edition of Euclid's Elements. The first few results were so easy that he almost gave up but he:-

... changed his mind when he read that parallelograms upon the same base and between the same parallels are equal.

Returning to the beginning, Newton read the whole book with a new respect. He then turned to Oughtred's Clavis Mathematica and Descartes' La Géométrie. The new algebra and analytical geometry of Viète was read by Newton from Frans van Schooten's edition of Viète's collected works published in 1646. Other major works of mathematics which he studied around this time was the newly published major work by van Schooten Geometria a Renato Des Cartes which appeared in two volumes in 1659-1661. The book contained important appendices by three of van Schooten's disciples, Jan de Witt, Johan Hudde, and Hendrick van Heuraet. Newton also studied Wallis's Algebra and it appears that his first original mathematical work came from his study of this text. He read Wallis's method for finding a square of equal area to a parabola and a hyperbola which used indivisibles. Newton made notes on Wallis's treatment of series but also devised his own proofs of the theorems writing:-

Thus Wallis doth it, but it may be done thus ...

It would be easy to think that Newton's talent began to emerge on the arrival of Barrow to the Lucasian chair at Cambridge in 1663 when he became a Fellow at Trinity College. Certainly the date matches the beginnings of Newton's deep mathematical studies. However, it would appear that the 1663 date is merely a coincidence and that it was only some years later that Barrow recognised the mathematical genius among his students.

Despite some evidence that his progress had not been particularly good, Newton was elected a scholar on 28 April 1664 and received his bachelor's degree in April 1665. It would appear that his scientific genius had still not emerged, but it did so suddenly when the plague closed the University in the summer of 1665 and he had to return to Lincolnshire. There, in a period of less than two years, while Newton was still under 25 years old, he began revolutionary advances in mathematics, optics, physics, and astronomy.

While Newton remained at home he laid the foundations for differential and integral calculus, several years before its independent discovery by Leibniz. The 'method of fluxions', as he termed it, was based on his crucial insight that the integration of a function is merely the inverse procedure to differentiating it. Taking differentiation as the basic operation, Newton produced simple analytical methods that unified many separate techniques previously developed to solve apparently unrelated problems such as finding areas, tangents, the lengths of curves and the maxima and minima of functions. Newton's De Methodis Serierum et Fluxionum was written in 1671 but Newton failed to get it published and it did not appear in print until John Colson produced an English translation in 1736.

When the University of Cambridge reopened after the plague in 1667, Newton put himself forward as a candidate for a fellowship. In October he was elected to a minor fellowship at Trinity College but, after being awarded his Master's Degree, he was elected to a major fellowship in July 1668 which allowed him to dine at the Fellows' Table. In July 1669 Barrow tried to ensure that Newton's mathematical achievements became known to the world. He sent Newton's text De Analysi to Collins in London writing:-

[Newton] brought me the other day some papers, wherein he set down methods of calculating the dimensions of magnitudes like that of Mr Mercator concerning the hyperbola, but very general; as also of resolving equations; which I suppose will please you; and I shall send you them by the next.

Collins corresponded with all the leading mathematicians of the day so Barrow's action should have led to quick recognition. Collins showed Brouncker, the President of the Royal Society, Newton's results (with the author's permission) but after this Newton requested that his manuscript be returned. Collins could not give a detailed account but de Sluze and Gregory learnt something of Newton's work through Collins. Barrow resigned the Lucasian chair in 1669 to devote himself to divinity, recommending that Newton (still only 27 years old) be appointed in his place. Shortly after this Newton visited London and twice met with Collins but, as he wrote to Gregory:-

... having no more acquaintance with him I did not think it becoming to urge him to communicate anything.

Newton's first work as Lucasian Professor was on optics and this was the topic of his first lecture course begun in January 1670. He had reached the conclusion during the two plague years that white light is not a simple entity. Every scientist since Aristotle had believed that white light was a basic single entity, but the chromatic aberration in a telescope lens convinced Newton otherwise. When he passed a thin beam of sunlight through a glass prism Newton noted the spectrum of colours that was formed.

He argued that white light is really a mixture of many different types of rays which are refracted at slightly different angles, and that each different type of ray produces a different spectral colour. Newton was led by this reasoning to the erroneous conclusion that telescopes using refracting lenses would always suffer chromatic aberration. He therefore proposed and constructed a reflecting telescope.

In 1672 Newton was elected a fellow of the Royal Society after donating a reflecting telescope. Also in 1672 Newton published his first scientific paper on light and colour in the Philosophical Transactions of the Royal Society. The paper was generally well received but Hooke and Huygens objected to Newton's attempt to prove, by experiment alone, that light consists of the motion of small particles rather than waves. The reception that his publication received did nothing to improve Newton's attitude to making his results known to the world. He was always pulled in two directions, there was something in his nature which wanted fame and recognition yet another side of him feared criticism and the easiest way to avoid being criticised was to publish nothing. Certainly one could say that his reaction to criticism was irrational, and certainly his aim to humiliate Hooke in public because of his opinions was abnormal. However, perhaps because of Newton's already high reputation, his corpuscular theory reigned until the wave theory was revived in the 19th century.

Newton's relations with Hooke deteriorated further when, in 1675, Hooke claimed that Newton had stolen some of his optical results. Although the two men made their peace with an exchange of polite letters, Newton turned in on himself and away from the Royal Society which he associated with Hooke as one of its leaders. He delayed the publication of a full account of his optical researches until after the death of Hooke in 1703. Newton's Opticks appeared in 1704. It dealt with the theory of light and colour and with

  1. investigations of the colours of thin sheets
  2. 'Newton's rings' and
  3. diffraction of light.

To explain some of his observations he had to use a wave theory of light in conjunction with his corpuscular theory.

Another argument, this time with the English Jesuits in Liège over his theory of colour, led to a violent exchange of letters, then in 1678 Newton appears to have suffered a nervous breakdown. His mother died in the following year and he withdrew further into his shell, mixing as little as possible with people for a number of years.

Newton's greatest achievement was his work in physics and celestial mechanics, which culminated in the theory of universal gravitation. By 1666 Newton had early versions of his three laws of motion. He had also discovered the law giving the centrifugal force on a body moving uniformly in a circular path. However he did not have a correct understanding of the mechanics of circular motion.

Newton's novel idea of 1666 was to imagine that the Earth's gravity influenced the Moon, counter- balancing its centrifugal force. From his law of centrifugal force and Kepler's third law of planetary motion, Newton deduced the inverse-square law.

In 1679 Newton corresponded with Hooke who had written to Newton claiming:-

... that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall ...

M Nauenberg writes an account of the next events:-

After his 1679 correspondence with Hooke, Newton, by his own account, found a proof that Kepler's areal law was a consequence of centripetal forces, and he also showed that if the orbital curve is an ellipse under the action of central forces then the radial dependence of the force is inverse square with the distance from the centre.

This discovery showed the physical significance of Kepler's second law.

In 1684 Halley, tired of Hooke's boasting [M Nauenberg]:-

... asked Newton what orbit a body followed under an inverse square force, and Newton replied immediately that it would be an ellipse. However in 'De Motu..' he only gave a proof of the converse theorem that if the orbit is an ellipse the force is inverse square. The proof that inverse square forces imply conic section orbits is sketched in Cor. 1 to Prop. 13 in Book 1 of the second and third editions of the 'Principia', but not in the first edition.

Halley persuaded Newton to write a full treatment of his new physics and its application to astronomy. Over a year later (1687) Newton published the Philosophiae naturalis principia mathematica or Principia as it is always known.

The Principia is recognised as the greatest scientific book ever written. Newton analysed the motion of bodies in resisting and non-resisting media under the action of centripetal forces. The results were applied to orbiting bodies, projectiles, pendulums, and free-fall near the Earth. He further demonstrated that the planets were attracted toward the Sun by a force varying as the inverse square of the distance and generalised that all heavenly bodies mutually attract one another.

Further generalisation led Newton to the law of universal gravitation:-

... all matter attracts all other matter with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Newton explained a wide range of previously unrelated phenomena: the eccentric orbits of comets, the tides and their variations, the precession of the Earth's axis, and motion of the Moon as perturbed by the gravity of the Sun. This work made Newton an international leader in scientific research. The Continental scientists certainly did not accept the idea of action at a distance and continued to believe in Descartes' vortex theory where forces work through contact. However this did not stop the universal admiration for Newton's technical expertise.

James II became king of Great Britain on 6 February 1685. He had become a convert to the Roman Catholic church in 1669 but when he came to the throne he had strong support from Anglicans as well as Catholics. However rebellions arose, which James put down but he began to distrust Protestants and began to appoint Roman Catholic officers to the army. He then went further, appointing only Catholics as judges and officers of state. Whenever a position at Oxford or Cambridge became vacant, the king appointed a Roman Catholic to fill it. Newton was a staunch Protestant and strongly opposed to what he saw as an attack on the University of Cambridge.

When the King tried to insist that a Benedictine monk be given a degree without taking any examinations or swearing the required oaths, Newton wrote to the Vice-Chancellor:-

Be courageous and steady to the Laws and you cannot fail.

The Vice-Chancellor took Newton's advice and was dismissed from his post. However Newton continued to argue the case strongly preparing documents to be used by the University in its defence. However William of Orange had been invited by many leaders to bring an army to England to defeat James. William landed in November 1688 and James, finding that Protestants had left his army, fled to France. The University of Cambridge elected Newton, now famous for his strong defence of the university, as one of their two members to the Convention Parliament on 15 January 1689. This Parliament declared that James had abdicated and in February 1689 offered the crown to William and Mary. Newton was at the height of his standing - seen as a leader of the university and one of the most eminent mathematicians in the world. However, his election to Parliament may have been the event which let him see that there was a life in London which might appeal to him more than the academic world in Cambridge.

After suffering a second nervous breakdown in 1693, Newton retired from research. The reasons for this breakdown have been discussed by his biographers and many theories have been proposed: chemical poisoning as a result of his alchemy experiments; frustration with his researches; the ending of a personal friendship with Fatio de Duillier, a Swiss-born mathematician resident in London; and problems resulting from his religious beliefs. Newton himself blamed lack of sleep but this was almost certainly a symptom of the illness rather than the cause of it. There seems little reason to suppose that the illness was anything other than depression, a mental illness he must have suffered from throughout most of his life, perhaps made worse by some of the events we have just listed.

Newton decided to leave Cambridge to take up a government position in London becoming Warden of the Royal Mint in 1696 and Master in 1699. However, he did not resign his positions at Cambridge until 1701. As Master of the Mint, adding the income from his estates, we see that Newton became a very rich man. For many people a position such as Master of the Mint would have been treated as simply a reward for their scientific achievements. Newton did not treat it as such and he made a strong contribution to the work of the Mint. He led it through the difficult period of recoinage and he was particularly active in measures to prevent counterfeiting of the coinage.

In 1703 he was elected president of the Royal Society and was re-elected each year until his death. He was knighted in 1705 by Queen Anne, the first scientist to be so honoured for his work. However the last portion of his life was not an easy one, dominated in many ways with the controversy with Leibniz over which of them had invented the calculus.

Given the rage that Newton had shown throughout his life when criticised, it is not surprising that he flew into an irrational temper directed against Leibniz. We have given details of this controversy in Leibniz's biography and refer the reader to that article for details. Perhaps all that is worth relating here is how Newton used his position as President of the Royal Society. In this capacity he appointed an "impartial" committee to decide whether he or Leibniz was the inventor of the calculus. He wrote the official report of the committee (although of course it did not appear under his name) which was published by the Royal Society, and he then wrote a review (again anonymously) which appeared in the Philosophical Transactions of the Royal Society.

Newton's assistant
Whiston had seen his rage at first hand. He wrote:-

Newton was of the most fearful, cautious and suspicious temper that I ever knew.

Isaac Newton

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Sir Isaac Newton
Godfrey Kneller's 1689 portrait of Isaac Newton (aged 46)
Godfrey Kneller's 1689 portrait of Isaac Newton (aged 46)
Born 4 January 1643(1643-01-04)
[OS: 25 December 1642][1]
Woolsthorpe-by-Colsterworth
Lincolnshire, England
Died 31 March 1727 (aged 84)
[OS: 20 March 1726][1]
Kensington, Middlesex, England
Residence England
Citizenship English
Nationality English (British from 1707)
Fields Physics, mathematics, astronomy,
natural philosophy, alchemy,
theology
Institutions University of Cambridge
Royal Society
Royal Mint
Alma mater Trinity College, Cambridge
Academic advisors Isaac Barrow
Benjamin Pulleyn[2][3]
Notable students Roger Cotes
William Whiston
Known for Newtonian mechanics
Universal gravitation
Calculus
Optics
Influences Henry More
Influenced Nicolas Fatio de Duillier
John Keill
Religious stance Monotheism; for details see article
Signature
Sir Isaac Newton's signature
Notes
His mother was
Hannah Ayscough. His half-niece was Catherine Barton.

Sir Isaac Newton, FRS (4 January 1643  – 31 March 1727 [OS: 25 December 1642 – 20 March 1726])[1] was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian and one of the most influential men[4] in human history. His Philosophiæ Naturalis Principia Mathematica, published in 1687, is considered to be the most influential book in the history of science. In this work, Newton described universal gravitation and the three laws of motion, laying the groundwork for classical mechanics, which dominated the scientific view of the physical Universe for the next three centuries and is the basis for modern engineering. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the scientific revolution.

In mechanics, Newton enunciated the principles of conservation of momentum and angular momentum. In optics, he built the first "practical" reflecting telescope[5] and developed a theory of colour based on the observation that a prism decomposes white light into a visible spectrum. He also formulated an empirical law of cooling and studied the speed of sound.

In mathematics, Newton shares the credit with Gottfried Leibniz for the development of the differential and integral calculus. He also demonstrated the generalised binomial theorem, developed the so-called "Newton's method" for approximating the zeroes of a function, and contributed to the study of power series.

Newton was also highly religious (though unorthodox), producing more work on Biblical hermeneutics than the natural science he is remembered for today.

Newton's stature among scientists remains at the very top rank, as demonstrated by a 2005 survey of scientists in Britain's Royal Society asking who had the greater effect on the history of science, Newton or Albert Einstein. Newton was deemed the more influential.[6]

Contents

[hide]

Biography

Early years

Isaac Newton was born on 4 January 1643 [OS: 25 December 1642][1] at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. At the time of Newton's birth, England had not adopted the latest papal calendar and therefore his date of birth was recorded as Christmas Day, 25 December 1642. Newton was born three months after the death of his father. Born prematurely, he was a small child; his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabus Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough. The young Isaac disliked his stepfather and held some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: Threatening my father and mother Smith to burn them and the house over them.[7]

Newton in a 1702 portrait by Godfrey Kneller
Isaac Newton (Bolton, Sarah K. Famous Men of Science. NY: Thomas Y. Crowell & Co., 1889)
A replica of Newton's 6-inch (150 mm) reflecting telescope of 1672 for the Royal Society.

According to E.T. Bell and H. Eves:

Newton began his schooling in the village schools and was later sent to The King's School, Grantham, where he became the top student in the school. At King's, he lodged with the local apothecary, William Clarke and eventually became engaged to the apothecary's stepdaughter, Anne Storer, before he went off to the University of Cambridge at the age of 19. As Newton became engrossed in his studies, the romance cooled and Miss Storer married someone else. It is said he kept a warm memory of this love, but Newton had no other recorded "sweet-hearts" and never married.[8]

There are rumours that he remained a confirmed celibate.[9] However, Bell and Eves' sources for this claim, William Stukeley and Mrs. Vincent (the former Miss Storer – actually named Katherine, not Anne), merely say that Newton entertained "a passion" for Storer while he lodged at the Clarke house.

From the age of about twelve until he was seventeen, Newton was educated at The King's School, Grantham (where his signature can still be seen upon a library window sill). He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, where his mother, widowed by now for a second time, attempted to make a farmer of him. He hated farming. Henry Stokes, master at the King's School, persuaded his mother to send him back to school so that he might complete his education. This he did at the age of eighteen, achieving an admirable final report.

In June 1661, he was admitted to Trinity College, Cambridge. According to John Stillwell, he entered Trinity as a sizar.[10] At that time, the college's teachings were based on those of Aristotle, but Newton preferred to read the more advanced ideas of modern philosophers such as Descartes and astronomers such as Copernicus, Galileo, and Kepler. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that would later become infinitesimal calculus. Soon after Newton had obtained his degree in August of 1665, the University closed down as a precaution against the Great Plague. Although he had been undistinguished as a Cambridge student,[11] Newton's private studies at his home in Woolsthorpe over the subsequent two years saw the development of his theories on calculus, optics and the law of gravitation.

Middle years

Mathematics

Most modern historians believe that Newton and Leibniz developed infinitesimal calculus independently, using their own unique notations. According to Newton's inner circle, Newton had worked out his method years before Leibniz, yet he published almost nothing about it until 1693, and did not give a full account until 1704. Meanwhile, Leibniz began publishing a full account of his methods in 1684. Moreover, Leibniz's notation and "differential Method" were universally adopted on the Continent, and after 1820 or so, in the British Empire. Whereas Leibniz's notebooks show the advancement of the ideas from early stages until maturity, there is only the end product in Newton's known notes. Newton claimed that he had been reluctant to publish his calculus because he feared being mocked for it. Newton had a very close relationship with Swiss mathematician Nicolas Fatio de Duillier, who from the beginning was impressed by Newton's gravitational theory. In 1691 Duillier planned to prepare a new version of Newton's Philosophiae Naturalis Principia Mathematica, but never finished it. However, in 1694 the relationship between the two men changed. At the time, Duillier had also exchanged several letters with Leibniz[citation needed].

Starting in 1699, other members of the Royal Society (of which Newton was a member) accused Leibniz of plagiarism, and the dispute broke out in full force in 1711. Newton's Royal Society proclaimed in a study that it was Newton who was the true discoverer and labeled Leibniz a fraud. This study was cast into doubt when it was later found that Newton himself wrote the study's concluding remarks on Leibniz. Thus began the bitter Newton v. Leibniz calculus controversy, which marred the lives of both Newton and Leibniz until the latter's death in 1716.

Newton is generally credited with the generalised binomial theorem, valid for any exponent. He discovered Newton's identities, Newton's method, classified cubic plane curves (polynomials of degree three in two variables), made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations. He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula), and was the first to use power series with confidence and to revert power series. He also discovered a new formula for calculating pi.

He was elected Lucasian Professor of Mathematics in 1669. In that day, any fellow of Cambridge or Oxford had to be an ordained Anglican priest. However, the terms of the Lucasian professorship required that the holder not be active in the church (presumably so as to have more time for science). Newton argued that this should exempt him from the ordination requirement, and Charles II, whose permission was needed, accepted this argument. Thus a conflict between Newton's religious views and Anglican orthodoxy was averted.

Optics

From 1670 to 1672, Newton lectured on optics. During this period he investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colours, and that a lens and a second prism could recompose the multicoloured spectrum into white light.

He also showed that the coloured light does not change its properties by separating out a coloured beam and shining it on various objects. Newton noted that regardless of whether it was reflected or scattered or transmitted, it stayed the same colour. Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves. This is known as Newton's theory of colour.

From this work he concluded that any refracting telescope would suffer from the dispersion of light into colours (chromatic aberration), and invented a type reflecting telescope (today known as a Newtonian telescope) to bypass that problem. By grinding his own mirrors, using Newton's rings to judge the quality of the optics for his telescopes, he was able to produce a superior instrument to the refracting telescope, due primarily to the wider diameter of the mirror. In 1671 the Royal Society asked for a demonstration of his reflecting telescope. Their interest encouraged him to publish his notes On Colour, which he later expanded into his Opticks. When Robert Hooke criticised some of Newton's ideas, Newton was so offended that he withdrew from public debate. The two men remained enemies until Hooke's death.

Newton argued that light is composed of particles or corpuscles, which were refracted by accelerating toward the denser medium, but he had to associate them with waves to explain the diffraction of light (Opticks Bk. II, Props. XII-L). Later physicists instead favoured a purely wavelike explanation of light to account for diffraction. Today's quantum mechanics, photons and the idea of wave–particle duality bear only a minor resemblance to Newton's understanding of light.

In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. The contact with the theosophist Henry More, revived his interest in alchemy. He replaced the ether with occult forces based on Hermetic ideas of attraction and repulsion between particles. John Maynard Keynes, who acquired many of Newton's writings on alchemy, stated that "Newton was not the first of the age of reason: he was the last of the magicians."[12] Newton's interest in alchemy cannot be isolated from his contributions to science.[13] (This was at a time when there was no clear distinction between alchemy and science.) Had he not relied on the occult idea of action at a distance, across a vacuum, he might not have developed his theory of gravity. (See also Isaac Newton's occult studies.)

In 1704 Newton published Opticks, in which he expounded his corpuscular theory of light. He considered light to be made up of extremely subtle corpuscles, that ordinary matter was made of grosser corpuscles and speculated that through a kind of alchemical transmutation "Are not gross Bodies and Light convertible into one another, …and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?"[14] Newton also constructed a primitive form of a frictional electrostatic generator, using a glass globe (Optics, 8th Query).

Mechanics and gravitation

Newton's own copy of his Principia, with hand-written corrections for the second edition
Further information: Writing of Principia Mathematica

In 1677, Newton returned to his work on mechanics, i.e., gravitation and its effect on the orbits of planets, with reference to Kepler's laws of planetary motion, and consulting with Hooke and Flamsteed on the subject. He published his results in De motu corporum in gyrum (1684). This contained the beginnings of the laws of motion that would inform the Principia.

The Philosophiae Naturalis Principia Mathematica (now known as the Principia) was published on 5 July 1687 with encouragement and financial help from Edmond Halley. In this work Newton stated the three universal laws of motion that were not to be improved upon for more than two hundred years. He used the Latin word gravitas (weight) for the effect that would become known as gravity, and defined the law of universal gravitation. In the same work he presented the first analytical determination, based on Boyle's law, of the speed of sound in air. Newton's postulate of an invisible force able to act over vast distances led to him being criticised for introducing "occult agencies" into science.[15]

With the Principia, Newton became internationally recognised. He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier, with whom he formed an intense relationship that lasted until 1693. The end of this friendship led Newton to a nervous breakdown.[clarification needed][citation needed]

Later life

Isaac Newton in old age in 1712, portrait by Sir James Thornhill
Newton's grave in Westminster Abbey

In the 1690s, Newton wrote a number of religious tracts dealing with the literal interpretation of the Bible. Henry More's belief in the Universe and rejection of Cartesian dualism may have influenced Newton's religious ideas. A manuscript he sent to John Locke in which he disputed the existence of the Trinity was never published. Later works – The Chronology of Ancient Kingdoms Amended (1728) and Observations Upon the Prophecies of Daniel and the Apocalypse of St. John (1733) – were published after his death. He also devoted a great deal of time to alchemy (see above).

Newton was also a member of the Parliament of England from 1689 to 1690 and in 1701, but his only recorded comments were to complain about a cold draught in the chamber and request that the window be closed.

Newton moved to London to take up the post of warden of the Royal Mint in 1696, a position that he had obtained through the patronage of Charles Montagu, 1st Earl of Halifax, then Chancellor of the Exchequer. He took charge of England's great recoining, somewhat treading on the toes of Master Lucas (and securing the job of deputy comptroller of the temporary Chester branch for Edmond Halley). Newton became perhaps the best-known Master of the Mint upon Lucas' death in 1699, a position Newton held until his death. These appointments were intended as sinecures, but Newton took them seriously, retiring from his Cambridge duties in 1701, and exercising his power to reform the currency and punish clippers and counterfeiters. As Master of the Mint in 1717 Newton unofficially moved the Pound Sterling from the silver standard to the gold standard by creating a relationship between gold coins and the silver penny in the "Law of Queen Anne"; these were all great reforms at the time, adding considerably to the wealth and stability of England. It was his work at the Mint, rather than his earlier contributions to science, that earned him a knighthood from Queen Anne in 1705.[clarification needed]

Newton was made President of the Royal Society in 1703 and an associate of the French Académie des Sciences. In his position at the Royal Society, Newton made an enemy of John Flamsteed, the Astronomer Royal, by prematurely publishing Flamsteed's star catalogue, which Newton had used in his studies.

Newton died in London on 31 March 1727 [OS: 20 March 1726][1], and was buried in Westminster Abbey. His half-niece, Catherine Barton Conduitt,[16] served as his hostess in social affairs at his house on Jermyn Street in London; he was her "very loving Uncle,"[17] according to his letter to her when she was recovering from smallpox. Newton, who had no children, had divested much of his estate onto relatives in his last years, and died intestate.

After his death, Newton's body was discovered to have had massive amounts of mercury in it, probably resulting from his alchemical pursuits. Mercury poisoning could explain Newton's eccentricity in late life.[18]

Religious views

Historian Stephen D. Snobelen says of Newton, "Isaac Newton was a heretic. But like Nicodemus, the secret disciple of Jesus, he never made a public declaration of his private faith – which the orthodox would have deemed extremely radical. He hid his faith so well that scholars are still unravelling his personal beliefs."[19] Snobelen concludes that Newton was at least a Socinian sympathiser (he owned and had thoroughly read at least eight Socinian books), possibly an Arian and almost certainly an antitrinitarian.[19] In an age notable for its religious intolerance there are few public expressions of Newton's radical views, most notably his refusal to take holy orders and his refusal, on his death bed, to take the sacrament when it was offered to him.[19]

In a view disputed by Snobelen,[19] T.C. Pfizenmaier argues that Newton held the Eastern Orthodox view of the Trinity rather than the Western one held by Roman Catholics, Anglicans, and most Protestants.[20] In his own day, he was also accused of being a Rosicrucian (as were many in the Royal Society and in the court of Charles II).[21]

Although the laws of motion and universal gravitation became Newton's best-known discoveries, he warned against using them to view the Universe as a mere machine, as if akin to a great clock. He said, "Gravity explains the motions of the planets, but it cannot explain who set the planets in motion. God governs all things and knows all that is or can be done."[22]

His scientific fame notwithstanding, Newton's studies of the Bible and of the early Church Fathers were also noteworthy. Newton wrote works on textual criticism, most notably An Historical Account of Two Notable Corruptions of Scripture. He also placed the crucifixion of Jesus Christ at 3 April, AD 33, which agrees with one traditionally accepted date.[23] He also attempted, unsuccessfully, to find hidden messages within the Bible.

In his own lifetime, Newton wrote more on religion than he did on natural science. He believed in a rationally immanent world, but he rejected the hylozoism implicit in Leibniz and Baruch Spinoza. Thus, the ordered and dynamically informed Universe could be understood, and must be understood, by an active reason, but this Universe, to be perfect and ordained, had to be regular[citation needed].

Newton's effect on religious thought

Newton and Robert Boyle’s mechanical philosophy was promoted by rationalist pamphleteers as a viable alternative to the pantheists and enthusiasts, and was accepted hesitantly by orthodox preachers as well as dissident preachers like the latitudinarians.[24] Thus, the clarity and simplicity of science was seen as a way to combat the emotional and metaphysical superlatives of both superstitious enthusiasm and the threat of atheism,[25] and, at the same time, the second wave of English deists used Newton's discoveries to demonstrate the possibility of a "Natural Religion."

"Newton," by William Blake; here, Newton is depicted as a "divine geometer"

The attacks made against pre-Enlightenment "magical thinking," and the mystical elements of Christianity, were given their foundation with Boyle’s mechanical conception of the Universe. Newton gave Boyle’s ideas their completion through mathematical proofs and, perhaps more importantly, was very successful in popularising them.[26] Newton refashioned the world governed by an interventionist God into a world crafted by a God that designs along rational and universal principles.[27] These principles were available for all people to discover, allowed people to pursue their own aims fruitfully in this life, not the next, and to perfect themselves with their own rational powers.[28]

Newton saw God as the master creator whose existence could not be denied in the face of the grandeur of all creation.[29][30][31] But the unforeseen theological consequence of his conception of God, as Leibniz pointed out, was that God was now entirely removed from the world’s affairs, since the need for intervention would only evidence some imperfection in God’s creation, something impossible for a perfect and omnipotent creator.[32] Leibniz's theodicy cleared God from the responsibility for "l'origine du mal" by making God removed from participation in his creation. The understanding of the world was now brought down to the level of simple human reason, and humans, as Odo Marquard argued, became responsible for the correction and elimination of evil.[33]

On the other hand, latitudinarian and Newtonian ideas taken too far resulted in the millenarians, a religious faction dedicated to the concept of a mechanical Universe, but finding in it the same enthusiasm and mysticism that the Enlightenment had fought so hard to extinguish.[34]

Views of the end of the world

See also: Isaac Newton's occult studies
See also: Eschatology

In a manuscript he wrote in 1704 in which he describes his attempts to extract scientific information from the Bible, he estimated that the world would end no earlier than 2060. In predicting this he said, "This I mention not to assert when the time of the end shall be, but to put a stop to the rash conjectures of fanciful men who are frequently predicting the time of the end, and by doing so bring the sacred prophesies into discredit as often as their predictions fail."[35]

Newton and the counterfeiters

As warden of the Royal Mint, Newton estimated that 20% of the coins taken in during The Great Recoinage were counterfeit. Counterfeiting was high treason, punishable by being hanged, drawn and quartered. Despite this, convictions of the most flagrant criminals could be extremely difficult to achieve; however, Newton proved to be equal to the task.

Disguised as an habitué of bars and taverns, he gathered much of that evidence himself. For all the barriers placed to prosecution, and separating the branches of government, English law still had ancient and formidable customs of authority. Newton was made a justice of the peace and between June 1698 and Christmas 1699 conducted some 200 cross-examinations of witnesses, informers and suspects. Newton won his convictions and in February 1699, he had ten prisoners waiting to be executed.

Possibly Newton's greatest triumph as the king's attorney was against William Chaloner. One of Chaloner's schemes was to set up phony conspiracies of Catholics and then turn in the hapless conspirators whom he entrapped. Chaloner made himself rich enough to posture as a gentleman. Petitioning Parliament, Chaloner accused the Mint of providing tools to counterfeiters (a charge also made by others). He proposed that he be allowed to inspect the Mint's processes in order to improve them. He petitioned Parliament to adopt his plans for a coinage that could not be counterfeited, while at the same time striking false coins. Newton was outraged, and went about the work to uncover anything about Chaloner. During his studies, he found that Chaloner was engaged in counterfeiting. He immediately put Chaloner on trial, but Chaloner had friends in high places and, to Newton's horror, Chaloner walked free. Newton put him on trial a second time with conclusive evidence. Chaloner was convicted of high treason and hanged, drawn and quartered on 23 March 1699 at Tyburn gallows.[36]

Enlightenment philosophers

Enlightenment philosophers chose a short history of scientific predecessors — Galileo, Boyle, and Newton principally — as the guides and guarantors of their applications of the singular concept of Nature and Natural Law to every physical and social field of the day. In this respect, the lessons of history and the social structures built upon it could be discarded.[37]

It was Newton’s conception of the Universe based upon Natural and rationally understandable laws that became the seed for Enlightenment ideology. Locke and Voltaire applied concepts of Natural Law to political systems advocating intrinsic rights; the physiocrats and Adam Smith applied Natural conceptions of psychology and self-interest to economic systems and the sociologists criticised the current social order for trying to fit history into Natural models of progress. Monboddo and Samuel Clarke resisted elements of Newton's work, but eventually rationalised it to conform with their strong religious views of nature.

Newton's laws of motion

Classical mechanics
History of ...
[hide]Scientists
Newton · Euler · d'Alembert · Clairaut
Lagrange · Laplace · Hamilton · Poisson

The famous three laws of motion:

Newton's First Law (also known as the Law of Inertia) states that an object at rest tends to stay at rest and that an object in uniform motion tends to stay in uniform motion unless acted upon by a net external force.

Newton's Second Law states that an applied force, scriptstyle{vec{F}}, on an object equals the rate of change of its momentum, scriptstyle{vec{p}}, with time. Mathematically, this is expressed as

 vec F = frac{mathrm{d}vec p}{mathrm{mathrm{d}}t} , = , frac{mathrm{d}}{mathrm{d}t} (m vec v) , = , vec v , frac{mathrm{d}m}{mathrm{d}t} + m , frac{mathrm{d}vec v}{mathrm{d}t} ,.

Since the second law applies to a system with constant mass, (dm/dt = 0), the first term vanishes, and the equation can be written in the iconic form

 vec F = m , vec a ,,

where

vec{a} = frac{mathrm{d}vec{v}}{mathrm{d}t},.

This equation states that a force scriptstyle{vec{F}} applied to an object of mass scriptstyle{m} causes it to accelerate at a rate scriptstyle{vec{a}}.

This equality requires a consistent set of units for measuring mass, length, and time. One such set is the SI system, where mass is in kilograms, length in metres, and time in seconds. This leads to force being in newtons, named in his honour, and acceleration in metres per second per second. The English analogous system is slugs, feet, and seconds.

Newton's Third Law states that for every action there is an equal and opposite reaction. This means that any force exerted onto an object has a counterpart force that is exerted in the opposite direction back onto the first object. The most common example is of two ice skaters pushing against each other and sliding apart in opposite directions. Another example is the recoil of a firearm, in which the force propelling the bullet is exerted equally back onto the gun and is felt by the shooter. Since the objects in question do not necessarily have the same mass, the resulting acceleration of the two objects can be different (as in the case of firearm recoil).

Newton's apple

Reputed descendants of Newton's apple tree, at the Botanic Gardens in Cambridge and the Instituto Balseiro library garden
 
Reputed descendants of Newton's apple tree, at the Botanic Gardens in Cambridge and the Instituto Balseiro library garden
Reputed descendants of Newton's apple tree, at the Botanic Gardens in Cambridge and the Instituto Balseiro library garden

When Newton saw an apple fall, he found
In that slight startle from his contemplation –
'Tis said (for I'll not answer above ground
For any sage's creed or calculation) –
A mode of proving that the earth turn'd round
In a most natural whirl, called "
gravitation;"
And this is the sole mortal who could grapple,
Since
Adam, with a fall or with an apple.[38]

Newton himself often told that story that he was inspired to formulate his theory of gravitation by watching the fall of an apple from a tree. It fell straight down — why was that, he asked?

Cartoons have gone further to suggest the apple actually hit Newton's head, and that its impact somehow made him aware of the force of gravity. It is known from his notebooks that Newton was grappling in the late 1660s with the idea that terrestrial gravity extends, in an inverse-square proportion, to the Moon; however it took him two decades to develop the full-fledged theory.[39] John Conduitt, Newton's assistant at the Royal Mint and husband of Newton's niece, described the event when he wrote about Newton's life:

In the year 1666 he retired again from Cambridge to his mother in Lincolnshire. Whilst he was pensively meandering in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from earth, but that this power must extend much further than was usually thought. Why not as high as the Moon said he to himself & if so, that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating what would be the effect of that supposition.[40]

The question was not whether gravity existed, but whether it extended so far from Earth that it could also be the force holding the moon to its orbit. Newton showed that if the force decreased as the inverse square of the distance, one could indeed calculate the Moon's orbital period, and get good agreement. He guessed the same force was responsible for other orbital motions, and hence named it "universal gravitation".

A contemporary writer, William Stukeley, recorded in his Memoirs of Sir Isaac Newton's Life a conversation with Newton in Kensington on 15 April 1726, in which Newton recalled "when formerly, the notion of gravitation came into his mind. It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the Earth's centre." In similar terms, Voltaire wrote in his Essay on Epic Poetry (1727), "Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree." These accounts are probably exaggerations of Newton's own tale about sitting by a window in his home (Woolsthorpe Manor) and watching an apple fall from a tree.

Various trees are claimed to be "the" apple tree which Newton describes. The King's School, Grantham, claims that the tree was purchased by the school, uprooted and transported to the headmaster's garden some years later, the staff of the [now] National Trust-owned Woolsthorpe Manor dispute this, and claim that a tree present in their gardens is the one described by Newton. A descendant of the original tree can be seen growing outside the main gate of Trinity College, Cambridge, below the room Newton lived in when he studied there. The National Fruit Collection at Brogdale[41] can supply grafts from their tree, which appears identical to Flower of Kent, a coarse-fleshed cooking variety.[42]

Writings by Newton

Fame

French mathematician Joseph-Louis Lagrange often said that Newton was the greatest genius who ever lived, and once added that he was also "the most fortunate, for we cannot find more than once a system of the world to establish."[44] English poet Alexander Pope was moved by Newton's accomplishments to write the famous epitaph:

Nature and nature's laws lay hid in night;
God said "Let Newton be" and all was light.

Newton himself was rather more modest of his own achievements, famously writing in a letter to Robert Hooke in February 1676

If I have seen further it is by standing on the shoulders of giants

Historians generally think the above quote was an attack on Hooke (who was short and hunchbacked), rather than – or in addition to – a statement of modesty. The two were in a dispute over optical discoveries at the time. The latter interpretation also fits with many of his other disputes over his discoveries – such as the question of who discovered calculus as discussed above.

And then in a memoir later

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.[45]

Newton in popular culture

A character based on Isaac Newton plays a significant role in The Age of Unreason, a series of four alternate history novels written by American science fiction and fantasy author Gregory Keyes.

Newton is an important character in The Baroque Cycle by Neal Stephenson. A major theme of these novels is the emergence of modern science, with Newton's work in the Principia being prominent. Newton's interest in alchemy and the dispute over the discovery of calculus are prominent plot points, and there is a (fictional) debate on metaphysics between Newton and Gottfried Leibniz moderated by Caroline of Ansbach. The development of an economy based on money and credit is also a major theme, with Newton's time with the Royal Mint and intrigues against counterfeit leading to a Trial of the Pyx.

In 2007, David Warner portrayed Newton in the Doctor Who audio drama Circular Time.

Monuments and commemoration

Newton statue on display at the Oxford University Museum of Natural History

Newton's monument (1731) can be seen in Westminster Abbey, at the north of the entrance to the choir against the choir screen. It was executed by the sculptor Michael Rysbrack (1694–1770) in white and grey marble with design by the architect William Kent (1685–1748). The monument features a figure of Newton reclining on top of a sarcophagus, his right elbow resting on several of his great books and his left hand pointing to a scroll with a mathematical design. Above him is a pyramid and a celestial globe showing the signs of the Zodiac and the path of the comet of 1680. A relief panel depicts putti using instruments such as a telescope and prism.[46] The Latin inscription on the base translates as:

Here is buried Isaac Newton, Knight, who by a strength of mind almost divine, and mathematical principles peculiarly his own, explored the course and figures of the planets, the paths of comets, the tides of the sea, the dissimilarities in rays of light, and, what no other scholar has previously imagined, the properties of the colours thus produced. Diligent, sagacious and faithful, in his expositions of nature, antiquity and the holy Scriptures, he vindicated by his philosophy the majesty of God mighty and good, and expressed the simplicity of the Gospel in his manners. Mortals rejoice that there has existed such and so great an ornament of the human race! He was born on 25 December 1642, and died on 20 March 1726/7. — Translation from G.L. Smyth, The Monuments and Genii of St. Paul's Cathedral, and of Westminster Abbey (1826), ii, 703–4.[46]

A statue of Isaac Newton, standing over an apple, can be seen at the Oxford University Museum of Natural History.

From 1978 until 1988, an image of Newton designed by Harry Ecclestone appeared on Series D £1 banknotes issued by the Bank of England (the last £1 notes to be issued by the Bank of England). Newton was shown on the reverse of the notes holding a book and accompanied by a telescope, a prism and a map of the Solar System.[47]

See also

Footnotes and references

  1. ^ a b c d e During Newton's lifetime, two calendars were in use in Europe: the Julian or 'Old Style' in Britain and parts of northern Europe (Protestant) and eastern Europe, and the Gregorian or 'New Style', in use in Roman Catholic Europe and elsewhere. At Newton's birth, Gregorian dates were ten days ahead of Julian dates: thus Newton was born on Christmas Day, 25 December 1642 by the Julian calendar, but on 4 January 1643 by the Gregorian. By the time he died, the difference between the calendars had increased to eleven days. Moreover, prior to the adoption of the Gregorian calendar in the UK in 1752, the English new year began (for legal and some other civil purposes) on 25 March ('Lady Day', i.e. the feast of the Annunciation: sometimes called 'Annunciation Style') rather than on 1 January (sometimes called 'Circumcision Style'). Unless otherwise noted, the remainder of the dates in this article follow the Julian Calendar.
  2. ^ Dictionary of Scientific Biography, Newton, Isaac, n.4
  3. ^ Gjersten, Derek (1986). The Newton Handbook. London: Routledge & Kegan Paul. 
  4. ^ "A ranking of the most influential persons in history". eircom.net.
  5. ^ Reflecting telescopes Historical Introduction – The Early Period (1608–1672)
  6. ^ "Newton beats Einstein in polls of scientists and the public". The Royal Society.
  7. ^ Cohen, I.B. (1970). Dictionary of Scientific Biography, Vol. 11, p.43. New York: Charles Scribner's Sons
  8. ^ Bell, E.T. (1986) [1937]. Men of Mathematics (Touchstone edition ed.). New York: Simon & Schuster. pp. 91–2. 
  9. ^ Book Review Isaac Newton biography December 2003
  10. ^ Stillwell, John (2002) [1989]. "Calculus [sub-chapter 9.7 Biographical Notes: Wallis, Newton, and Leibniz]". in S. Axler, F. W. Gehring, K. A. Ribet (editors) (Hardcover). Mathematics and Its History. Undergraduate Texts in Mathematics (2nd edition ed.). New York: Springer-Verlag New York. p. 163. ISBN 0-387-95336-1. "In 1661 he entered Trinity College, Cambridge, as a sizar. Sizars had to earn their keep as servants to wealthier students, and it was indicative of his mother's meanness that he had to become one, for she could afford to support him but chose not to." 
  11. ^ ed. Michael Hoskins (1997). Cambridge Illustrated History of Astronomy, p. 159. Cambridge University Press
  12. ^ Keynes, John Maynard (1972). "Newton, The Man". The Collected Writings of John Maynard Keynes Volume X. MacMillan St. Martin's Press. pp. 363–4. 
  13. ^ Newton apparently abandoned his alchemical researches. See Westfall, Richard S. (1983) [1980]. "Never at Rest: A Biography of Isaac Newton. Cambridge: Cambridge University Press. pp. 530–1. 
  14. ^ Dobbs, J.T. (December 1982). "Newton's Alchemy and His Theory of Matter". Isis 73 (4): 511. doi:10.1086/353114.  quoting Opticks
  15. ^ Edelglass et al., Matter and Mind, ISBN 0940262452. p. 54
  16. ^ Westfall 1980, p. 44.
  17. ^ Westfall 1980, p. 595
  18. ^ "Newton, Isaac (1642-1727)". Eric Weisstein's World of Biography. Retrieved on 2006-08-30.
  19. ^ a b c d Snobelen, Stephen D. (1999). "Isaac Newton, heretic : the strategies of a Nicodemite" (PDF). British Journal for the History of Science 32: 381–419. doi:10.1017/S0007087499003751. http://www.isaac-newton.org/heretic.pdf. 
  20. ^ Pfizenmaier, T.C. (1997). "Was Isaac Newton an Arian?". Journal of the History of Ideas 68 (1): 57–80. 
  21. ^ Yates, Frances A. (1972). The Rosicrucian Enlightenment. London: Routledge. 
  22. ^ Tiner, J.H. (1975). Isaac Newton: Inventor, Scientist and Teacher. Milford, Michigan, U.S.: Mott Media. 
  23. ^ John P. Meier, A Marginal Jew, v. 1, pp. 382–402 after narrowing the years to 30 or 33, provisionally judges 30 most likely.
  24. ^ Jacob, Margaret C. (1976). The Newtonians and the English Revolution: 1689–1720. Cornell University Press. pp. 37,44. 
  25. ^ Westfall, Richard S. (1958). Science and Religion in Seventeenth-Century England. New Haven: Yale University Press. p. 200. 
  26. ^ Haakonssen, Knud. "The Enlightenment, politics and providence: some Scottish and English comparisons". in Martin Fitzpatrick ed.. Enlightenment and Religion: Rational Dissent in eighteenth-century Britain. Cambridge: Cambridge University Press. p. 64. 
  27. ^ Frankel, Charles (1948). The Faith of Reason: The Idea of Progress in the French Enlightenment. New York: King's Crown Press. p. 1. 
  28. ^ Germain, Gilbert G.. A Discourse on Disenchantment: Reflections on Politics and Technology. p. 28. 
  29. ^ Principia, Book III; cited in; Newton’s Philosophy of Nature: Selections from his writings, p. 42, ed. H.S. Thayer, Hafner Library of Classics, NY, 1953.
  30. ^ A Short Scheme of the True Religion, manuscript quoted in Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton by Sir David Brewster, Edinburgh, 1850; cited in; ibid, p. 65.
  31. ^ Webb, R.K. ed. Knud Haakonssen. “The emergence of Rational Dissent.” Enlightenment and Religion: Rational Dissent in eighteenth-century Britain. Cambridge University Press, Cambridge: 1996. p19.
  32. ^ Westfall, Richard S. Science and Religion in Seventeenth-Century England. p201.
  33. ^ Marquard, Odo. "Burdened and Disemburdened Man and the Flight into Unindictability," in Farewell to Matters of Principle. Robert M. Wallace trans. London: Oxford UP, 1989.
  34. ^ Jacob, Margaret C. The Newtonians and the English Revolution: 1689–1720. p100–101.
  35. ^ "Papers Show Isaac Newton's Religious Side, Predict Date of Apocalypse". The Associated Press (19 June 2007). Retrieved on 2007-08-01.
  36. ^ Westfall 1980, pp. 571–5
  37. ^ Cassels, Alan. Ideology and International Relations in the Modern World. p2.
  38. ^ Don Juan (1821), Canto 10, Verse I. In Jerome J. McGann (ed.), Lord Byron: The Complete Poetical Works (1986), Vol. 5, 437
  39. ^ I. Bernard Cohen and George E. Smith, eds. The Cambridge Companion to Newton (2002) p. 6
  40. ^ Conduitt, John. "Keynes Ms. 130.4:Conduitt's account of Newton's life at Cambridge". Newtonproject. Retrieved on 2006-08-30.
  41. ^ "Brogdale - Home of the National Fruit Collection". Brogdale.org.uk. Retrieved on 2008-12-20.
  42. ^ "From the National Fruit Collection: Isaac Newton's Tree". Retrieved on 2009-01-10.
  43. ^ Newton's alchemical works transcribed and online at Indiana University retrieved 11 January 2007
  44. ^ Fred L. Wilson, History of Science: Newton citing: Delambre, M. "Notice sur la vie et les ouvrages de M. le comte J. L. Lagrange," Oeuvres de Lagrange I. Paris, 1867, p. xx.
  45. ^ Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton (1855) by Sir David Brewster (Volume II. Ch. 27)
  46. ^ a b "Monuments & Gravestones: Sir Isaac Newton". Westminster Abbey. Retrieved on 2008-10-20.
  47. ^ "Withdrawn banknotes reference guide". Bank of England. Retrieved on 2008-10-17.

Resources

References

Further reading

  • Andrade, E. N. De C. (1950). Isaac Newton. New York: Chanticleer Press. 
  • Bardi, Jason Socrates. The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time. (2006). 277 pp. excerpt and text search
  • Bechler, Zev (1991). Newton's Physics and the Conceptual Structure of the Scientific Revolution. Springer. ISBN 0792310543. .
  • Berlinski, David. Newton's Gift: How Sir Isaac Newton Unlocked the System of the World. (2000). 256 pp. excerpt and text search ISBN 0-684-84392-7
  • Buchwald, Jed Z. and Cohen, I. Bernard, eds. Isaac Newton's Natural Philosophy. MIT Press, 2001. 354 pp. excerpt and text search
  • Casini, P. (1988). "Newton's Principia and the Philosophers of the Enlightenment". Notes and Records of the Royal Society of London 42 (1): 35–52. doi:10.1098/rsnr.1988.0006. ISSN 0035–9149. http://links.jstor.org/sici?sici=0035-9149%28198801%2942%3A1%3C35%3AN%27ATPO%3E2.0.CO%3B2-H. 
  • Christianson, Gale E. (1996). Isaac Newton and the Scientific Revolution. Oxford U. Press. ISBN 019530070X.  See this site for excerpt and text search.
  • Christianson, Gale (1984). In the Presence of the Creator: Isaac Newton & His Times. New York: Free Press. ISBN 0-02-905190-8. 
  • Cohen, I. Bernard and Smith, George E., ed. The Cambridge Companion to Newton. (2002). 500 pp. focuses on philosophical issues only; excerpt and text search; complete edition online
  • Cohen, I. B. (1980). The Newtonian Revolution. Cambridge: Cambridge University Press. 
  • Craig, John (1946). Newton at the Mint. Cambridge, England: Cambridge University Press. 
  • Dampier, William C.; Dampier, M. (1959). Readings in the Literature of Science. New York: Harper & Row. 
  • de Villamil, Richard (1931). Newton, the Man. London: G.D. Knox.  – Preface by Albert Einstein. Reprinted by Johnson Reprint Corporation, New York (1972).
  • Dobbs, B. J. T. (1975). The Foundations of Newton's Alchemy or "The Hunting of the Greene Lyon". Cambridge: Cambridge University Press. 
  • Gjertsen, Derek (1986). The Newton Handbook. London: Routledge & Kegan Paul. ISBN 0-7102-0279-2. 
  • Gleick, James (2003). Isaac Newton. Alfred A. Knopf. ISBN 0375422331. 
  • Halley, E. (1687). "Review of Newton's Principia". Philosophical Transactions 186: 291 – 297. 
  • Hart, Michael H. (1992). The 100''. Carol Publishing Group. ISBN 0-8065-1350-0.  – paperback
  • Hawking, Stephen, ed. On the Shoulders of Giants. ISBN 0-7624-1348-4 Places selections from Newton's Principia in the context of selected writings by Copernicus, Kepler, Galileo and Einstein
  • Herivel, J. W. (1965). The Background to Newton's Principia. A Study of Newton's Dynamical Researches in the Years 1664–84. Oxford: Clarendon Press. 
  • Keynes, John Maynard (1963). Essays in Biography. W. W. Norton & Co. ISBN 0-393-00189-X.  Keynes took a close interest in Newton and owned many of Newton's private papers.
  • Koyré, A. (1965). Newtonian Studies. Chicago: University of Chicago Press. 
  • Newton, Isaac. Papers and Letters in Natural Philosophy, edited by I. Bernard Cohen. Harvard University Press, 1958,1978. ISBN 0-674-46853-8.
  • Newton, Isaac (1642–1727). The Principia: a new Translation, Guide by I. Bernard Cohen ISBN 0-520-08817-4 University of California (1999)
  • Pemberton, H. (1728). A View of Sir Isaac Newton's Philosophy. London: S. Palmer. 
  • Shamos, Morris H. (1959). Great Experiments in Physics. New York: Henry Holt and Company, Inc.. 
  • Shapley, Harlow, S. Rapport, and H. Wright. A Treasury of Science; "Newtonia" pp. 147–9; "Discoveries" pp. 150–4. Harper & Bros., New York, (1946).
  • Simmons, J. (1996). The Giant Book of Scientists  – The 100 Greatest Minds of all Time. Sydney: The Book Company. 
  • Stukeley, W. (1936), Memoirs of Sir Isaac Newton's Life, London: Taylor and Francis  (edited by A. H. White; originally published in 1752)
  • Westfall, R. S. (1971). Force in Newton's Physics: The Science of Dynamics in the Seventeenth Century. London: Macdonald. 

Newton and religion

  • Dobbs, Betty Jo Tetter. The Janus Faces of Genius: The Role of Alchemy in Newton's Thought. (1991), links the alchemy to Arianism
  • Force, James E., and Richard H. Popkin, eds. Newton and Religion: Context, Nature, and Influence. (1999), 342pp . Pp. xvii + 325. 13 papers by scholars using newly opened manuscripts
  • Ramati, Ayval. "The Hidden Truth of Creation: Newton's Method of Fluxions" British Journal for the History of Science 34: 417–438. in JSTOR, argues that his calculus had a theological basis
  • Snobelen, Stephen D. "'God of Gods, and Lord of Lords': The Theology of Isaac Newton's General Scholium to the Principia," Osiris, 2nd Series, Vol. 16, (2001), pp. 169–208 in JSTOR
  • Snobelen, Stephen D. "Isaac Newton, Heretic: The Strategies of a Nicodemite," British Journal for the History of Science 32: 381–419. in JSTOR
  • Pfizenmaier, Thomas C. "Was Isaac Newton an Arian?," Journal of the History of Ideas, Vol. 58, No. 1 (Jan., 1997), pp. 57–80 in JSTOR
  • Westfall, Richard S. Never at Rest: A Biography of Isaac Newton. 2 vol. Cambridge U. Press, 1981. 895 pp. the major scholarly biography excerpt and text search
  • Wiles, Maurice. Archetypal Heresy. Arianism through the Centuries. (1996) 214pp, with chapter 4 on 18th century England; pp 77–93 on Newtorn excerpt and text search,

Primary sources

  • Newton, Isaac. The Principia: Mathematical Principles of Natural Philosophy. U. of California Press, (1999). 974 pp.
    • Brackenridge, J. Bruce. The Key to Newton's Dynamics: The Kepler Problem and the Principia: Containing an English Translation of Sections 1, 2, and 3 of Book One from the First (1687) Edition of Newton's Mathematical Principles of Natural Philosophy. U. of California Press, 1996. 299 pp.
  • Newton, Isaac. The Optical Papers of Isaac Newton. Vol. 1: The Optical Lectures, 1670–1672. Cambridge U. Press, 1984. 627 pp.
    • Newton, Isaac. Opticks (4th ed. 1730) online edition
    • Newton, I. (1952). Opticks, or A Treatise of the Reflections, Refractions, Inflections & Colours of Light. New York: Dover Publications.
  • Newton, I. Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World, tr. A. Motte, rev. Florian Cajori. Berkeley: University of California Press. (1934).
  • Whiteside, D. T. (1967–82). The Mathematical Papers of Isaac Newton. Cambridge: Cambridge University Press.  – 8 volumes
  • Newton, Isaac. The correspondence of Isaac Newton, ed. H. W. Turnbull and others, 7 vols. (1959–77).
  • Newton's Philosophy of Nature: Selections from His Writings edited by H. S. Thayer, (1953), online edition
  • Isaac Newton, Sir; J Edleston; Roger Cotes, Correspondence of Sir Isaac Newton and Professor Cotes, including letters of other eminent men, London, John W. Parker, West Strand; Cambridge, John Deighton, 1850. – Google Books
  • Maclaurin, C. (1748). An Account of Sir Isaac Newton's Philosophical Discoveries, in Four Books. London: A. Millar and J. Nourse.
  • Newton, I. (1958). Isaac Newton's Papers and Letters on Natural Philosophy and Related Documents, eds. I. B. Cohen and R. E. Schofield. Cambridge: Harvard University Press.
  • Newton, I. (1962). The Unpublished Scientific Papers of Isaac Newton: A Selection from the Portsmouth Collection in the University Library, Cambridge, ed. A. R. Hall and M. B. Hall. Cambridge: Cambridge University Press.
  • Newton, I. (1975). Isaac Newton's 'Theory of the Moon's Motion' (1702). London: Dawson.

    English physicist and mathematician who was born into a poor farming family. Luckily for humanity, Newton was not a good farmer, and was sent to Cambridge to study to become a preacher. At Cambridge, Newton studied mathematics, being especially strongly influenced by Euclid, although he was also influenced by Baconian and Cartesian philosophies. Newton was forced to leave Cambridge when it was closed because of the plague, and it was during this period that he made some of his most significant discoveries. With the reticence he was to show later in life, Newton did not, however, publish his results.

    Newton suffered a mental breakdown in 1675 and was still recovering through 1679. In response to a letter from Hooke, he suggested that a particle, if released, would spiral in to the center of the Earth. Eric Weisstein's World of Astronomy Hooke wrote back, claiming that the path would not be a spiral, but an ellipse. Eric Weisstein's World of Math Newton, who hated being bested, then proceeded to work out the mathematics of orbits. Again, he did not publish his calculations. Newton then began devoting his efforts to theological speculation and put the calculations on elliptical motion aside, telling Halley he had lost them (Westfall 1993, p. 403). Halley, who had become interested in orbits, finally convinced Newton to expand and publish his calculations. Newton devoted the period from August 1684 to spring 1686 to this task, and the result became one of the most important and influential works on physics of all times, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) (1687), often shortened to Principia Mathematica or simply "the Principia."

    In Book I of Principia, Newton opened with definitions and the three laws of motion now known as Newton's laws Eric Weisstein's World of Physics (laws of inertia, action and reaction, and acceleration proportional to force). Book II presented Newton's new scientific philosophy which came to replace Cartesianism. Finally, Book III consisted of applications of his dynamics, including an explanation for tides and a theory of lunar motion. To test his hypothesis of universal gravitation, Newton wrote Flamsteed to ask if Saturn Eric Weisstein's World of Astronomy had been observed to slow down upon passing Jupiter. Eric Weisstein's World of Astronomy The surprised Flamsteed replied that an effect had indeed been observed, and it was closely predicted by the calculations Newton had provided. Newton's equations were further confirmed by observing the shape of the Earth Eric Weisstein's World of Astronomy to be oblate spheroidal, Eric Weisstein's World of Math as Newton claimed it should be, rather than prolate spheroidal, Eric Weisstein's World of Math as claimed by the Cartesians. Newton's equations also described the motion of Moon Eric Weisstein's World of Astronomy by successive approximations, and correctly predicted the return of Halley's Comet. Newton also correctly formulated and solved the first ever problem in the calculus of variations Eric Weisstein's World of Math which involved finding the surface of revolution which would give minimum resistance to flow (assuming a specific drag law).

    Newton invented a scientific method which was truly universal in its scope. Newton presented his methodology as a set of four rules for scientific reasoning. These rules were stated in the Principia and proposed that (1) we are to admit no more causes of natural things such as are both true and sufficient to explain their appearances, (2) the same natural effects must be assigned to the same causes, (3) qualities of bodies are to be esteemed as universal, and (4) propositions deduced from observation of phenomena should be viewed as accurate until other phenomena contradict them.

    These four concise and universal rules for investigation were truly revolutionary. By their application, Newton formulated the universal laws of nature with which he was able to unravel virtually all the unsolved problems of his day. Newton went much further than outlining his rules for reasoning, however, actually describing how they might be applied to the solution of a given problem. The analytic method he invented far exceeded the more philosophical and less scientifically rigorous approaches of Aristotle and Aquinas. Newton refined Galileo's experimental method, creating the compositional method of experimentation still practiced today. In fact, the following description of the experimental method from Newton's Optics could easily be mistaken for a modern statement of current methods of investigation, if not for Newton's use of the words "natural philosophy" in place of the modern term "the physical sciences." Newton wrote, "As in mathematics, so in natural philosophy the investigation of difficult things by the method of analysis ought ever to precede the method of composition. This analysis consists of making experiments and observations, and in drawing general conclusions from them by induction...by this way of analysis we may proceed from compounds to ingredients, and from motions to the forces producing them; and in general from effects to their causes, and from particular causes to more general ones till the argument end in the most general. This is the method of analysis: and the synthesis consists in assuming the causes discovered and established as principles, and by them explaining the phenomena preceding from them, and proving the explanations."

    Newton formulated the classical theories of mechanics and optics and invented calculus Eric Weisstein's World of Math years before Leibniz. However, he did not publish his work on calculus Eric Weisstein's World of Math until afterward Leibniz had published his. This led to a bitter priority dispute between English and continental mathematicians which persisted for decades, to the detriment of all concerned. Newton discovered that the binomial theorem Eric Weisstein's World of Math was valid for fractional powers, but left it for Wallis to publish (which he did, with appropriate credit to Newton). Newton formulated a theory of sound, but derived a speed which did not agree with his experiments. The reason for the discrepancy was that the concept of adiabatic propagation did not yet exist, so Newton's answer was too low by a factor of , where is the ratio of heat capacities Eric Weisstein's World of Physics of air. Newton therefore fudged his theory until agreement was achieved (Engineering and Science, pp. 15-16).

    In Optics (1704), whose publication Newton delayed until Hooke's death, Newton observed that white light could be separated by a prism Eric Weisstein's World of Physics into a spectrum of different colors, each characterized by a unique refractivity, and proposed the corpuscular theory of light. Newton's views on optics were born out of the original prism Eric Weisstein's World of Physics experiments he performed at Cambridge. In his "experimentum crucis" (crucial experiment), he found that the image produced by a prism Eric Weisstein's World of Physics was oval-shaped and not circular, as current theories of light would require. He observed a half-red, half-blue string through a prism, Eric Weisstein's World of Physics and found the ends to be disjointed. He also observed Newton's rings, Eric Weisstein's World of Physics which are actually a manifestation of the wave nature of light which Newton did not believe in. Newton believed that light must move faster in a medium when it is refracted Eric Weisstein's World of Physics towards the normal, in opposition to the result predicted by Huygens's wave theory.

    Newton also formulated a system of chemistry in Query 31 at the end of Optics. In this corpuscular theory, "elements" consisted of different arrangements of atoms, and atoms consisted of small, hard, billiard ball-like particles. He explained chemical reactions in terms of the chemical affinities of the participating substances. Newton devoted a majority of his free time later in life (after 1678) to fruitless alchemical experiments.

    Newton was extremely sensitive to criticism, and even ceased publishing until the death of his arch-rival Hooke. It was only through the prodding of Halley that Newton was persuaded at all to publish the Principia Mathematica. In the latter portion of his life, he devoted much of his time to alchemical researches and trying to date events in the Bible. After Newton's death, his burial place was moved. During the exhumation, it was discovered that Newton had massive amounts of mercury in his body, probably resulting from his alchemical pursuits. This would certainly explain Newton's eccentricity in late life. Newton was appointed Warden of the British Mint in 1695. Newton was knighted by Queen Anne. However, the act was "an honor bestowed not for his contributions to science, nor for his service at the Mint, but for the greater glory of party politics in the election of 1705" (Westfall 1993, p. 625).

    Newton singlehandedly contributed more to the development of science than any other individual in history. He surpassed all the gains brought about by the great scientific minds of antiquity, producing a scheme of the universe which was more consistent, elegant, and intuitive than any proposed before. Newton stated explicit principles of scientific methods which applied universally to all branches of science. This was in sharp contradistinction to the earlier methodologies of Aristotle and Aquinas, which had outlined separate methods for different disciplines.

    Although his methodology was strictly logical, Newton still believed deeply in the necessity of a God. His theological views are characterized by his belief that the beauty and regularity of the natural world could only "proceed from the counsel and dominion of an intelligent and powerful Being." He felt that "the Supreme God exists necessarily, and by the same necessity he exists always and everywhere." Newton believed that God periodically intervened to keep the universe going on track. He therefore denied the importance of Leibniz's vis viva as nothing more than an interesting quantity which remained constant in elastic collisions and therefore had no physical importance or meaning.

    Although earlier philosophers such as Galileo and John Philoponus had used experimental procedures, Newton was the first to explicitly define and systematize their use. His methodology produced a neat balance between theoretical and experimental inquiry and between the mathematical and mechanical approaches. Newton mathematized all of the physical sciences, reducing their study to a rigorous, universal, and rational procedure which marked the ushering in of the Age of Reason. Thus, the basic principles of investigation set down by Newton have persisted virtually without alteration until modern times. In the years since Newton's death, they have borne fruit far exceeding anything even Newton could have imagined. They form the foundation on which the technological civilization of today rests. The principles expounded by Newton were even applied to the social sciences, influencing the economic theories of Adam Smith and the decision to make the United States legislature bicameral. These latter applications, however, pale in contrast to Newton's scientific contributions.

    It is therefore no exaggeration to identify Newton as the single most important contributor to the development of modern science. The Latin inscription on Newton's tomb, despite its bombastic language, is thus fully justified in proclaiming, "Mortals! rejoice at so great an ornament to the human race!" Alexander Pope's couplet is also apropos: "Nature and Nature's laws lay hid in night; God said, Let Newton be! and all was light."

    Several interesting Newton quotes are given by Misner et al. (1973, pp. 40-41). newton.jpg

Scientistsnewton
Newton’s Life
In 1642, the year Galileo died, Isaac Newton was born in Woolsthorpe, Lincolnshire, England on Christmas Day. His father had died three months earlier, and baby Isaac, very premature, was also not expected to survive. It was said he could be fitted into a quart pot. When Isaac was three, his mother married a wealthy elderly clergyman from the next village, and went to live there, leaving Isaac behind with his grandmother. The clergyman died, and Isaac’s mother came back, after eight years, bringing with her three small children. Two years later, Newton went away to the Grammar School in Grantham, where he lodged with the local apothecary, and was fascinated by the chemicals. The plan was that at age seventeen he would come home and look after the farm. He turned out to be a total failure as a farmer. 
His mother’s brother, a clergyman who had been an undergraduate at Cambridge, persuaded his mother that it would be better for Isaac to go to university, so in 1661 he went up to Trinity College, Cambridge. Isaac paid his way through college for the first three years by waiting tables and cleaning rooms for the fellows (faculty) and the wealthier students.  In 1664, he was elected a scholar, guaranteeing four years of financial support. Unfortunately, at that time the plague was spreading across Europe, and reached Cambridge in the summer of 1665. The university closed, and Newton returned home, where he spent two years concentrating on problems in mathematics and physics. He wrote later that during this time he first understood the theory of gravitation, which we shall discuss below, and the theory of optics (he was the first to realize that white light is made up of the colors of the rainbow), and much mathematics, both integral and differential calculus and infinite series. However, he was always reluctant to publish anything, at least until it appeared someone else might get credit for what he had found earlier. 
On returning to Cambridge in 1667, he began to work on alchemy, but then in 1668 Nicolas Mercator published a book containing some methods for dealing with infinite series. Newton immediately wrote a treatise, De Analysi, expounding his own wider ranging results. His friend and mentor Isaac Barrow communicated these discoveries to a London mathematician, but only after some weeks would Newton allow his name to be given. This brought his work to the attention of the mathematics community for the first time. Shortly afterwards, Barrow resigned his Lucasian Professorship (which had been established only in 1663, with Barrow the first incumbent) at Cambridge so that Newton could have the Chair. 
Newton’s first major public scientific achievement was the invention, design and construction of a reflecting telescope. He ground the mirror, built the tube, and even made his own tools for the job. This was a real advance in telescope technology, and ensured his election to membership in the Royal Society. The mirror gave a sharper image than was possible with a large lens because a lens focusses different colors at slightly different distances, an effect called chromatic aberration. This problem is minimized nowadays by using compound lenses, two lenses of different kinds of glass stuck together, that err in opposite directions, and thus tend to cancel each other’s shortcomings, but mirrors are still used in large telescopes. 
Later in the 1670’s, Newton became very interested in theology. He studied Hebrew scholarship and ancient and modern theologians at great length, and became convinced that Christianity had departed from the original teachings of Christ. He felt unable to accept the current beliefs of the Church of England, which was unfortunate because he was required as a Fellow of Trinity College to take holy orders. Happily, the Church of England was more flexible than Galileo had found the Catholic Church in these matters, and King Charles II issued a royal decree excusing Newton from the necessity of taking holy orders! Actually, to prevent this being a wide precedent, the decree specified that, in perpetuity, the Lucasian professor need not take holy orders. (The current Lucasian professor is Stephen Hawking.)
In 1684, three members of the Royal Society, Sir Christopher Wren, Robert Hooke and Edmond Halley, argued as to whether the elliptical orbits of the planets could result from a gravitational force towards the sun proportional to the inverse square of the distance. Halley writes:
Mr. Hook said he had had it, but that he would conceal it for some time so that others, triing and failing might know how to value it, when he should make it publick. 
Halley went up to Cambridge, and put the problem to Newton, who said he had solved it four years earlier, but couldn’t find the proof among his papers. Three months later, he sent an improved version of the proof to Halley, and devoted himself full time to developing these ideas, culminating in the publication of the Principia in 1686. This was the book that really did change man’s view of the universe, as we shall shortly discuss, and its importance was fully appreciated very quickly. Newton became a public figure. He left Cambridge for London, where he was appointed Master of the Mint, a role he pursued energetically, as always, including prosecuting counterfeiters. He was knighted by Queen Anne. He argued with Hooke about who deserved credit for discovering the connection between elliptical orbits and the inverse square law until Hooke died in 1703, and he argued with a German mathematician and philosopher, Leibniz, about which of them invented calculus. Newton died in 1727, and was buried with much pomp and circumstance in Westminster Abbey—despite his well-known reservations about the Anglican faith. 
An excellent, readable book is The Life of Isaac Newton, by Richard Westfall, Cambridge 1993, which I used in writing the above summary of Newton’s life. 
A fascinating collection of articles, profusely illustrated, on Newton’s life, work and impact on the general culture is Let Newton Be!, edited by John Fauvel and others, Oxford 1988, which I also consulted. 
Projectiles and Planets
Let us now turn to the central topic of the Principia, the universality of the gravitational force. The legend is that Newton saw an apple fall in his garden in Lincolnshire, thought of it in terms of an attractive gravitational force towards the earth, and realized the same force might extend as far as the moon. He was familiar with Galileo’s work on projectiles, and suggested that the moon’s motion in orbit could be understood as a natural extension of that theory. To see what is meant by this, consider a gun shooting a projectile horizontally from a very high mountain, and imagine using more and more powder in successive shots to drive the projectile faster and faster. 
The parabolic paths would become flatter and flatter, and, if we imagine that the mountain is so high that air resistance can be ignored, and the gun is sufficiently powerful, eventually the point of landing is so far away that we must consider the curvature of the earth in finding where it lands. 
In fact, the real situation is more dramatic—the earth’s curvature may mean the projectile never lands at all. This was envisioned by Newton in the Principia. The following diagram is from his later popularization, A Treatise of the System of the World, written in the 1680’s:
 
The mountaintop at V is supposed to be above the earth’s atmosphere, and for a suitable initial speed, the projectile orbits the earth in a circular path. In fact, the earth’s curvature is such that the surface falls away below a truly flat horizontal line by about five meters in 8,000 meters (five miles). Recall that five meters is just the vertical distance an initially horizontally moving projectile will fall in the first second of motion. But this implies that if the (horizontal) muzzle velocity were 8,000 meters per second, the downward fall of the cannonball would be just matched by the earth’s surface falling away, and it would never hit the ground! This is just the motion, familiar to us now, of a satellite in a low orbit, which travels at about 8,000 meters (five miles) a second, or 18,000 miles per hour. (Actually, Newton drew this mountain impossibly high, no doubt for clarity of illustration. A satellite launched horizontally from the top would be far above the usual shuttle orbit, and go considerably more slowly than 18,000 miles per hour.)
For an animated version of Newton’s cannon on a mountain, click here!
The Moon is Falling
Newton realized that the moon’s circular path around the earth could be caused in this way by the same gravitational force that would hold such a cannonball in low orbit, in other words, the same force that causes bodies to fall. 
To think about this idea, let us consider the moon’s motion, beginning at some particular instant, as deviating downwards—falling—from some initial “horizontal” line, just as for the cannonball shot horizontally from a high mountain. The first obvious question is: does the moon fall five meters below the horizontal line, that is, towards the earth, in the first second? This was not difficult for Newton to check, because the path of the moon was precisely known by this time. The moon’s orbit is approximately a circle of radius about 384,000 kilometers (240,000 miles), which it goes around in a month (to be precise, in 27.3 days), so the distance covered in one second is, conveniently, very close to one kilometer. It is then a matter of geometry to figure out how far the curved path falls below a “horizontal” line in one second of flight, and the answer turns out to be not five meters, but only a little over one millimeter! (Actually around 1.37 millimeters.)
It’s completely impossible to draw a diagram showing how far it falls in one second, but the geometry is the same if we look how far it falls in one day, so here it is:

The Moon in orbiting the Earth goes from A to D in one day. Without the Earth’s pull, it would have gone in a straight line to B.
 
It has therefore fallen below the straight line in one day by the distance between D and B.
 
Since we know the radius of the orbit, and we know how far the Moon travels in one day, we can find the distance DB using Pythagoras’ theorem for the triangle CAB, where C is the center of the Earth.
 
A
 
 
B
 
 
C
 
 
D
 
 

For one second, AB would be only one kilometer, so since AC is 384,000 km., the triangle ABC is really thin, but we can still use Pythagoras’ theorem!
Thus the “natural acceleration” of the moon towards the earth, measured by how far it falls below straight line motion in one second, is less than that of an apple here on earth by the ratio of five meters to 1.37 millimeters, which works out to be about 3,600. 
What can be the significance of this much smaller rate of fall? Newton’s answer was that the natural acceleration of the moon was much smaller than that of the cannonball because they were both caused by a force—a gravitational attraction towards the earth, and that the gravitational force became weaker on going away from the earth
In fact, the figures we have given about the moon’s orbit enable us to compute how fast the gravitational attraction dies away with distance. The distance from the center of the earth to the earth’s surface is about 6,350 kilometers (4,000 miles), so the moon is about 60 times further from the center of the earth than we and the cannonball are. 
From our discussion of how fast the moon falls below a straight line in one second in its orbit, we found that the gravitational acceleration for the moon is down by a factor of 3,600 from the cannonball’s (or the apple’s). 
Putting these two facts together, and noting that 3,600 = 60 x 60, led Newton to his famous inverse square law: the force of gravitational attraction between two bodies decreases with increasing distance between them as the inverse of the square of that distance, so if the distance is doubled, the force is down by a factor of four.
 
Newton’s Life
In 1642, the year Galileo died, Isaac Newton was born in Woolsthorpe, Lincolnshire, England on Christmas Day. His father had died three months earlier, and baby Isaac, very premature, was also not expected to survive. It was said he could be fitted into a quart pot. When Isaac was three, his mother married a wealthy elderly clergyman from the next village, and went to live there, leaving Isaac behind with his grandmother. The clergyman died, and Isaac’s mother came back, after eight years, bringing with her three small children. Two years later, Newton went away to the Grammar School in Grantham, where he lodged with the local apothecary, and was fascinated by the chemicals. The plan was that at age seventeen he would come home and look after the farm. He turned out to be a total failure as a farmer. 
His mother’s brother, a clergyman who had been an undergraduate at Cambridge, persuaded his mother that it would be better for Isaac to go to university, so in 1661 he went up to Trinity College, Cambridge. Isaac paid his way through college for the first three years by waiting tables and cleaning rooms for the fellows (faculty) and the wealthier students.  In 1664, he was elected a scholar, guaranteeing four years of financial support. Unfortunately, at that time the plague was spreading across Europe, and reached Cambridge in the summer of 1665. The university closed, and Newton returned home, where he spent two years concentrating on problems in mathematics and physics. He wrote later that during this time he first understood the theory of gravitation, which we shall discuss below, and the theory of optics (he was the first to realize that white light is made up of the colors of the rainbow), and much mathematics, both integral and differential calculus and infinite series. However, he was always reluctant to publish anything, at least until it appeared someone else might get credit for what he had found earlier. 
On returning to Cambridge in 1667, he began to work on alchemy, but then in 1668 Nicolas Mercator published a book containing some methods for dealing with infinite series. Newton immediately wrote a treatise, De Analysi, expounding his own wider ranging results. His friend and mentor Isaac Barrow communicated these discoveries to a London mathematician, but only after some weeks would Newton allow his name to be given. This brought his work to the attention of the mathematics community for the first time. Shortly afterwards, Barrow resigned his Lucasian Professorship (which had been established only in 1663, with Barrow the first incumbent) at Cambridge so that Newton could have the Chair. 
Newton’s first major public scientific achievement was the invention, design and construction of a reflecting telescope. He ground the mirror, built the tube, and even made his own tools for the job. This was a real advance in telescope technology, and ensured his election to membership in the Royal Society. The mirror gave a sharper image than was possible with a large lens because a lens focusses different colors at slightly different distances, an effect called chromatic aberration. This problem is minimized nowadays by using compound lenses, two lenses of different kinds of glass stuck together, that err in opposite directions, and thus tend to cancel each other’s shortcomings, but mirrors are still used in large telescopes. 
Later in the 1670’s, Newton became very interested in theology. He studied Hebrew scholarship and ancient and modern theologians at great length, and became convinced that Christianity had departed from the original teachings of Christ. He felt unable to accept the current beliefs of the Church of England, which was unfortunate because he was required as a Fellow of Trinity College to take holy orders. Happily, the Church of England was more flexible than Galileo had found the Catholic Church in these matters, and King Charles II issued a royal decree excusing Newton from the necessity of taking holy orders! Actually, to prevent this being a wide precedent, the decree specified that, in perpetuity, the Lucasian professor need not take holy orders. (The current Lucasian professor is Stephen Hawking.)
In 1684, three members of the Royal Society, Sir Christopher Wren, Robert Hooke and Edmond Halley, argued as to whether the elliptical orbits of the planets could result from a gravitational force towards the sun proportional to the inverse square of the distance. Halley writes:
Mr. Hook said he had had it, but that he would conceal it for some time so that others, triing and failing might know how to value it, when he should make it publick. 
Halley went up to Cambridge, and put the problem to Newton, who said he had solved it four years earlier, but couldn’t find the proof among his papers. Three months later, he sent an improved version of the proof to Halley, and devoted himself full time to developing these ideas, culminating in the publication of the Principia in 1686. This was the book that really did change man’s view of the universe, as we shall shortly discuss, and its importance was fully appreciated very quickly. Newton became a public figure. He left Cambridge for London, where he was appointed Master of the Mint, a role he pursued energetically, as always, including prosecuting counterfeiters. He was knighted by Queen Anne. He argued with Hooke about who deserved credit for discovering the connection between elliptical orbits and the inverse square law until Hooke died in 1703, and he argued with a German mathematician and philosopher, Leibniz, about which of them invented calculus. Newton died in 1727, and was buried with much pomp and circumstance in Westminster Abbey—despite his well-known reservations about the Anglican faith. 
An excellent, readable book is The Life of Isaac Newton, by Richard Westfall, Cambridge 1993, which I used in writing the above summary of Newton’s life. 
A fascinating collection of articles, profusely illustrated, on Newton’s life, work and impact on the general culture is Let Newton Be!, edited by John Fauvel and others, Oxford 1988, which I also consulted. 
Projectiles and Planets
Let us now turn to the central topic of the Principia, the universality of the gravitational force. The legend is that Newton saw an apple fall in his garden in Lincolnshire, thought of it in terms of an attractive gravitational force towards the earth, and realized the same force might extend as far as the moon. He was familiar with Galileo’s work on projectiles, and suggested that the moon’s motion in orbit could be understood as a natural extension of that theory. To see what is meant by this, consider a gun shooting a projectile horizontally from a very high mountain, and imagine using more and more powder in successive shots to drive the projectile faster and faster. 
The parabolic paths would become flatter and flatter, and, if we imagine that the mountain is so high that air resistance can be ignored, and the gun is sufficiently powerful, eventually the point of landing is so far away that we must consider the curvature of the earth in finding where it lands. 
In fact, the real situation is more dramatic—the earth’s curvature may mean the projectile never lands at all. This was envisioned by Newton in the Principia. The following diagram is from his later popularization, A Treatise of the System of the World, written in the 1680’s:
 
The mountaintop at V is supposed to be above the earth’s atmosphere, and for a suitable initial speed, the projectile orbits the earth in a circular path. In fact, the earth’s curvature is such that the surface falls away below a truly flat horizontal line by about five meters in 8,000 meters (five miles). Recall that five meters is just the vertical distance an initially horizontally moving projectile will fall in the first second of motion. But this implies that if the (horizontal) muzzle velocity were 8,000 meters per second, the downward fall of the cannonball would be just matched by the earth’s surface falling away, and it would never hit the ground! This is just the motion, familiar to us now, of a satellite in a low orbit, which travels at about 8,000 meters (five miles) a second, or 18,000 miles per hour. (Actually, Newton drew this mountain impossibly high, no doubt for clarity of illustration. A satellite launched horizontally from the top would be far above the usual shuttle orbit, and go considerably more slowly than 18,000 miles per hour.)
For an animated version of Newton’s cannon on a mountain, click here!
The Moon is Falling
Newton realized that the moon’s circular path around the earth could be caused in this way by the same gravitational force that would hold such a cannonball in low orbit, in other words, the same force that causes bodies to fall. 
To think about this idea, let us consider the moon’s motion, beginning at some particular instant, as deviating downwards—falling—from some initial “horizontal” line, just as for the cannonball shot horizontally from a high mountain. The first obvious question is: does the moon fall five meters below the horizontal line, that is, towards the earth, in the first second? This was not difficult for Newton to check, because the path of the moon was precisely known by this time. The moon’s orbit is approximately a circle of radius about 384,000 kilometers (240,000 miles), which it goes around in a month (to be precise, in 27.3 days), so the distance covered in one second is, conveniently, very close to one kilometer. It is then a matter of geometry to figure out how far the curved path falls below a “horizontal” line in one second of flight, and the answer turns out to be not five meters, but only a little over one millimeter! (Actually around 1.37 millimeters.)
It’s completely impossible to draw a diagram showing how far it falls in one second, but the geometry is the same if we look how far it falls in one day, so here it is:

The Moon in orbiting the Earth goes from A to D in one day. Without the Earth’s pull, it would have gone in a straight line to B.
 
It has therefore fallen below the straight line in one day by the distance between D and B.
 
Since we know the radius of the orbit, and we know how far the Moon travels in one day, we can find the distance DB using Pythagoras’ theorem for the triangle CAB, where C is the center of the Earth.
 
A
 
 
B
 
 
C
 
 
D
 
 

For one second, AB would be only one kilometer, so since AC is 384,000 km., the triangle ABC is really thin, but we can still use Pythagoras’ theorem!
Thus the “natural acceleration” of the moon towards the earth, measured by how far it falls below straight line motion in one second, is less than that of an apple here on earth by the ratio of five meters to 1.37 millimeters, which works out to be about 3,600. 
What can be the significance of this much smaller rate of fall? Newton’s answer was that the natural acceleration of the moon was much smaller than that of the cannonball because they were both caused by a force—a gravitational attraction towards the earth, and that the gravitational force became weaker on going away from the earth
In fact, the figures we have given about the moon’s orbit enable us to compute how fast the gravitational attraction dies away with distance. The distance from the center of the earth to the earth’s surface is about 6,350 kilometers (4,000 miles), so the moon is about 60 times further from the center of the earth than we and the cannonball are. 
From our discussion of how fast the moon falls below a straight line in one second in its orbit, we found that the gravitational acceleration for the moon is down by a factor of 3,600 from the cannonball’s (or the apple’s). 
Putting these two facts together, and noting that 3,600 = 60 x 60, led Newton to his famous inverse square law: the force of gravitational attraction between two bodies decreases with increasing distance between them as the inverse of the square of that distance, so if the distance is doubled, the force is down by a factor of four.
 
We are now ready to move on to Newton’s Laws of Motion, which for the first time presented a completely coherent analysis of motion, making clear that the motion in the heavens could be understood in the same terms as motion of ordinary objects here on earth. 
Acceleration Again
The crucial Second Law, as we shall see below, links the acceleration of a body with the force acting on the body. To understand what it says, it is necessary to be completely clear what is meant by acceleration, so let us briefly review. 
Speed is just how fast something’s moving, so is fully specified by a positive number and suitable units, such as 55 mph or 10 meters per second. 
Velocity, on the other hand, means to a scientist more than speed---it also includes a specification of the direction of the motion, so 55 mph to the northwest is a velocity.  Usually wind velocities are given in a weather forecast, since the direction of the wind affects future temperature changes in a direct way. The standard way of representing a velocity in physics is with an arrow pointing in the appropriate direction, its length representing the speed in suitable units. These arrows are called “vectors”. 
(WARNING: Notice, though, that for a moving object such as a projectile, both its position at a given time (compared with where it started) and its velocity at that time can be represented by vectors, so you must be clear what your arrow represents!)
Acceleration: as we have stated, acceleration is defined as rate of change of velocity
It is not defined as rate of change of speed. A body can have nonzero acceleration while moving at constant speed!
An Accelerating Body that isn’t Changing Speed
Consider Newton’s cannon on an imaginary high mountain above the atmosphere, that shoots a ball so fast it circles the earth at a steady speed. Of course, its velocity is changing constantly, because velocity includes direction. 
Let us look at how its velocity changes over a period of one second. (Actually, in the diagram below we exaggerate how far it would move in one second, the distance would in fact be one-five thousandth of the distance around the circle, impossible to draw.)

The velocity vectors (length v) for a ball moving at steady speed in a circle are shown one second apart.  To find the acceleration—the difference between these two vectors—we must put their tails together and draw a new vector (the red dotted one) from the head of the first to the head of the second.  This new vector (length a) is the difference: what must be added to the first to give the second.
 
 The change in velocity in one second is the (average) acceleration in that second.
A
B
C
v
v
a

Here we show the cannonball (greatly exaggerated in size!) at two points in its orbit, and the velocity vectors at those points. On the right, we show the two velocity vectors again, but we put their ends together so that we can see the difference between them, which is the small dashed vector.
In other words, the small dashed vector is the velocity that has to be added to the first velocity to get the second velocity: it is the change in velocity on going around that bit of the orbit. 
Now, if we think of the two points in the orbit as corresponding to positions of the cannonball one second apart, the small dashed vector will represent the change in velocity in one second, and that is—by definition—the acceleration. The acceleration is the rate of change of velocity, and that is how much the velocity changes in one second (for motions that change reasonably smoothly over the one-second period, which is certainly the case here. To find the rate of change of velocity of a fly’s wing at some instant, we obviously would have to measure its velocity change over some shorter interval, maybe a thousandth of a second). 
So we see that, with our definition of acceleration as the rate of change of velocity, which is a vector, a body moving at a steady speed around a circle is accelerating towards the center all the time, although it never gets any closer to it. If this thought makes you uncomfortable, it is because you are still thinking that acceleration must mean a change of speed, and just changing direction doesn’t count. 
Finding the Acceleration in Circular Motion
It is possible to find an explicit expression for the magnitude of the acceleration towards the center (sometimes called the centripetal acceleration) for a body moving on a circular path at speed v. Look again at the diagram above showing two values of the velocity of the cannonball one second apart. As is explained above, the magnitude a of the acceleration is the length of the small dashed vector on the right, where the other two sides of this long narrow triangle have lengths equal to the speed v of the cannonball. We’ll call this the “vav” triangle, because those are the lengths of its sides. What about the angle between the two long sides?  That is just the angle the velocity vector turns through in one second as the cannonball moves around its orbit. Now look over at the circle diagram on the left showing the cannonball’s path. Label the cannonball’s position at the beginning of the second A, and at the end of the second B, so the length AB is how far the cannonball travels in one second, that is, v. (It’s true that the part of the path AB is slightly curved, but we can safely ignore that very tiny effect.)  Call the center of the circle C. Draw the triangle ACB(The reader should sketch the figure and actually draw these triangles!) The two long sides AC and BC have lengths equal to the radius of the circular orbit. We could call this long thin triangle an “rvr” triangle, since those are the lengths of its sides. 
The important point to realize now is that the “vav” triangle and the “rvr” triangle are similar, because since the velocity vector is always perpendicular to the radius line from the center of the circle to the point where the cannonball is in orbit, the angle the velocity vector rotates by in one second is the same as the angle the radius line turns through in one second. Therefore, the two triangles are similar, and their corresponding sides are in the same ratios, that is, a/v = v/r. It follows immediately that the magnitude of the acceleration a for an object moving at steady speed v in a circle of radius r is v2/r directed towards the center of the circle
This result is true for all circular motions, even those where the moving body goes round a large part of the circle in one second. To establish it in a case like that, recall that the acceleration is the rate of change of velocity, and we would have to pick a smaller time interval than one second, so that the body didn’t move far around the circle in the time chosen. If, for example, we looked at two velocity vectors one-hundredth of a second apart, and they were pretty close, then the acceleration would be given by the difference vector between them multiplied by one-hundred, since acceleration is defined as what the velocity change in one second would be if it continued to change at that rate. (In the circular motion situation, the acceleration is of course changing all the time. To see why it is sometimes necessary to pick small time intervals, consider what would happen if the body goes around the circle completely in one second. Then, if you pick two times one second apart, you would conclude the velocity isn’t changing at all, so there is no acceleration.)
An Accelerating Body that isn’t Moving
We’ve stated before that a ball thrown vertically upwards has constant downward acceleration of 10 meters per second in each second, even when it’s at the very top and isn’t moving at all. The key point here is that acceleration is rate of change of velocity. You can’t tell what the rate of change of something is unless you know its value at more than one time. For example, speed on a straight road is rate of change of distance from some given point. You can’t get a speeding ticket just for being at a particular point at a certain time—the cop has to prove that a short time later you were at a point well removed from the first point, say, three meters away after one-tenth of a second. That would establish that your speed was thirty meters per second, which is illegal in a 55 m.p.h. zone. In just the same way that speed is rate of change of position, acceleration is rate of change of velocity. Thus to find acceleration, you need to know velocity at two different times. The ball thrown vertically upwards does have zero velocity at the top of its path, but that is only at a single instant of time. One second later it is dropping at ten meters per second. One millionth of a second after it reached the top, it is falling at one hundred-thousandth of a meter per second. Both of these facts correspond to a downward acceleration, or rate of change of velocity, of 10 meters per second in each second. It would only have zero acceleration if it stayed at rest at the top for some finite period of time, so that you could say that its velocity remained the same—zero—for, say, a thousandth of a second, and during that period the rate of change of velocity, the acceleration, would then of course be zero. Part of the problem is that the speed is very small near the top, and also that our eyes tend to lock on to a moving object to see it better, so there is the illusion that it comes to rest and stays there, even if not for long. 
Galileo’s Analysis of Motion: Two Kinds
Galileo’s analysis of projectile motion was based on two concepts:
1. Naturally accelerated motion, describing the vertical component of motion, in which the body picks up speed at a uniform rate. 
2. Natural horizontal motion, which is motion at a steady speed in a straight line, and happens to a ball rolling across a smooth table, for example, when frictional forces from surface or air can be ignored. 
Newton Puts Them Together
Newton’s major breakthrough was to show that these two different kinds of motion can be thought of as different aspects of the same thing. He did this by introducing the idea of motion being affected by a force, then expressing this idea in a quantitative way. Galileo, of course, had been well aware that motion is affected by external forces. Indeed, his definition of natural horizontal motion explicitly states that it applies to the situation where such forces can be neglected. He knew that friction would ultimately slow the ball down, and—very important—a force pushing it from behind would cause it to accelerate. What he didn’t say, though, and Newton did, was that just as a force would cause acceleration in horizontal motion, the natural acceleration actually observed in vertical motion must be the result of a vertical force on the body, without which the natural vertical motion would also be at a constant speed, just like natural horizontal motion. This vertical force is of course just the force of gravity.
Force is the Key
Therefore the point Newton is making is that the essential difference between Galileo’s natural steady speed horizontal motion and the natural accelerated vertical motion is that vertically, there is always the force of gravity acting, and without that—for example far into space—the natural motion (that is, with no forces acting) in any direction would be at a steady speed in a straight line.
(Actually, it took Newton some time to clarify the concept of force, which had previously been unclear. This is discussed at length in Never at Rest, by Richard Westfall, and I have summarized some of the points here.)
Newton’s First Law: no Force, no Change in Motion
To put it in his own words (although actually he wrote it in Latin, this is from an 1803 translation):
Law 1
Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon. 
He immediately adds, tying this in precisely with Galileo’s work:
Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. 
Notice that here “persevere in their motions” must mean in steady speed straight line motions, because he is adding the gravitational acceleration on to this. 
This is sometimes called “The Law of Inertia”: in the absence of an external force, a body in motion will continue to move at constant speed and direction, that is, at constant velocity. 
So any acceleration, or change in speed (or direction of motion), of a body signals that it is being acted on by some force
Newton’s Second Law: Acceleration of a Body is Proportional to Force
Newton’s next assertion, based on much experiment and observation, is that, for a given body, the acceleration produced is proportional to the strength of the external force, so doubling the external force will cause the body to pick up speed twice as fast. 
Law 2
The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. 
What About Same Force, Different Bodies?
Another rather obvious point he doesn’t bother to make is that for a given force, such as, for example, the hardest you can push, applied to two different objects, say a wooden ball and a lead ball of the same size, with the lead ball weighing seven times as much as the wooden ball, then the lead ball will only pick up speed at one-seventh the rate the wooden one will. 
Falling Bodies One More Time: What is Mass?
Now let us consider the significance of this law for falling bodies. Neglecting air resistance, bodies of all masses accelerate downwards at the same rate. This was Galileo’s discovery. 
Let us put this well established fact together with Newton’s Second Law: the acceleration is proportional to the external force, but inversely proportional to the mass of the body the force acts on. 
Consider two falling bodies, one having twice the mass of the other. Since their acceleration is the same, the body having twice the mass must be experiencing a gravitational force which is twice as strong. Of course, we are well aware of this, all it’s saying is that two bricks weigh twice as much as one brick. Any weight measuring device, such as a bathroom scales, is just measuring the force of gravity. However, this proportionality of mass and weight is not a completely trivial point. Masses can be measured against each other without using gravity at all, for example far into space, by comparing their relative accelerations when subject to a standard force, a push. If one object accelerates at half the rate of another when subject to our standard push, we conclude it has twice the mass. Thinking of the mass in this way as a measure of resistance to having velocity changed by an outside force, Newton called it inertia. (Note that this is a bit different from everyday speech, where we think of inertia as being displayed by something that stays at rest. For Newton, steady motion in a straight line is the same as being at rest. That seems perhaps counterintuitive, but that’s because in ordinary life, steady motion in a straight line usually causes some frictional or resistive forces to come into play). 
Mass and Weight
To return to the concept of mass, it is really just a measure of the amount of stuff. For a uniform material, such as water, or a uniform solid, the mass is the volume multiplied by the density—the density being defined as the mass of a unit of volume, so water, for example, has a density of one gram per cubic centimeter, or sixty-two pounds per cubic foot. 
Hence, from Galileo’s discovery of the uniform acceleration of all falling bodies, we conclude that the weight of a body, which is the gravitational attraction it feels towards the earth, is directly proportional to its mass, the amount of stuff it’s made of. 
The Unit of Force
All the statements above about force, mass and acceleration are statements about proportionality. We have said that for a body being accelerated by a force acting on it the acceleration is proportional to the (total) external force acting on the body, and, for a given force, inversely proportional to the mass of the body. 
If we denote the force, mass and acceleration by F, m and a respectively (bearing in mind that really F and a are vectors pointing in the same direction) we could write this:
F is proportional to ma
To make any progress in applying Newton’s Laws in a real situation, we need to choose some unit for measuring forces. We have already chosen units for mass (the kilogram) and acceleration (meters per second per second). The most natural way to define our unit of force is:
The unit of force is that force which causes a unit mass (one kilogram) to accelerate with unit acceleration (one meter per second per second). 
This unit of force is named, appropriately, the newton
If we now agree to measure forces in newtons, the statement of proportionality above can be written as a simple equation:
F = ma
which is the usual statement of Newton’s Second Law. 
If a mass is now observed to accelerate, it is a trivial matter to find the total force acting on it. The force will be in the direction of the acceleration, and its magnitude will be the product of the mass and acceleration, measured in newtons. For example, a 3 kilogram falling body, accelerating downwards at 10 meters per second per second, is being acted on by a force ma equal to 30 newtons, which is, of course, its weight. 
Newton’s Third Law: Action and Reaction
Having established that a force—the action of another body—was necessary to cause a body to change its state of motion, Newton made one further crucial observation: such forces always arise as a mutual interaction of two bodies, and the other body also feels the force, but in the opposite direction. 
Law 3
To every action there is always opposed an equal and opposite reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. 
Newton goes on:
Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone, as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinge upon another, and by its force change the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, towards the contrary part. The changes made by these actions are equal, not in the velocities but in the motions of bodies; that is to say, if the bodies are not hindered by any other impediments. For, because the motions are equally changed, the changes of the velocities made towards contrary parts are reciprocally proportional to the bodies. This law takes place also in attractions. 
All this maybe sounds kind of obvious. Anyone who’s had a dog on a leash, especially a big dog, is well aware that tension in a rope pulls both ways. If you push against a wall, the wall is pushing you back. If that’s difficult to visualize, imagine what would happen if the wall suddenly evaporated. Newton’s insight here, his realization that every acting force has a reacting force, and that acceleration of a body only occurs when an external force acts on it, was one of the big forward steps in our understanding of how the Universe works. 
Newton’s Second Law in Everyday Life
The Second Law states that if a body is accelerating, there must be an external force acting on it. It’s not always obvious what this external force is even in the most trivial everyday occurrences. Suppose you’re standing still, then begin to walk. What was the external force that caused you to accelerate? Think about that for a while. Here’s a clue: it’s very hard to start walking if you’re wearing smooth-bottomed shoes and standing on smooth ice. You tend to skid around in the same place. If you understand that, you also know what external force operates when a car accelerates. 
The reason the external force causing the acceleration may not be immediately evident is that it may not be what’s doing the work. Consider the following scenario: you are standing on level ground, on rollerskates, facing a wall with your palms pressed against it. You push against the wall, and roll away backwards. You accelerated. Clearly, you did the work that caused the acceleration. But from Newton’s second law, your acceleration was, in fact, caused by the reactive external force of the wall pushing your hands, and hence the rest of you. That is to say, the force causing the acceleration may not be generated directly by what—or who—is doing the work! In this example, it’s generated indirectly, as a reaction force to that of the hands pushing on the wall. But if the wall were on wheels, and it accelerated away when you pushed (having taken off your roller skates) the force causing the acceleration of the wall would be generated directly by the agent doing the work, you. 
Now imagine two people on roller skates, standing close facing each other, palms raised and pushing the other person away. According to Newton’s discussion above following his Third Law, the two bodies involved will undergo equal changes of motion, but to contrary parts, that is, in opposite directions. That sounds reasonable. They obviously both move off backwards. Notice, however, that Newton makes a special point of the fact that these equal (but opposite) “motions” do not imply equal (but opposite) velocities—this becomes obvious when you imagine the experiment with a 100 pound person and a 200 pound person. Newton tells us that in that situation the heavier person will roll backwards at half the speed—notice he says the velocities are “reciprocally proportional to the bodies”. 
Roller skates actually provide a pretty good example of the necessity of generating an external force if you want to accelerate. If you keep the skates pointing strictly forwards, and only the wheels are in contact with the ground, it’s difficult to get going. The way you start is to turn the skates some, so that there is some sideways push on the wheels. Since the wheels can’t turn sideways, you are thus able to push against the ground, and therefore it is pushing you—you’ve managed to generate the necessary external force to accelerate you. Note that if the wheels were to be replaced by ball bearings somehow, you wouldn’t get anywhere, unless you provided some other way for the ground to push you, such as a ski pole, or maybe twisting your foot so that some fixed part of the skate contacted the ground. 
Gravity
We have now reached the last sentence in Newton’s discussion of his Third Law: “This law also takes place in attractions”. This of course is central to Newton’s (and our) view of the Universe. If the Earth is attracting the Moon gravitationally with a certain force holding it in its orbit, then the Moon is attracting the Earth with an equal force. So why isn’t the Earth going around the Moon? The answer is that the masses are so different. The Earth’s mass is more than one hundred times that of the Moon. Consequently, the Earth’s acceleration, “falling” towards the Moon, is very small. What actually happens is that they both circle around a balance point between them, which in fact lies within the Earth. This motion of the Earth is easily detectable with instruments, but tiny compared with the daily rotation. Of course, it also follows from the above considerations that since the Earth is attracting you downwards with a force equal to your weight, you are attracting the Earth upwards—towards you—with a force of exactly the same strength. 
The Law of Gravity
Let us now put together what we know about the gravitational force:
1. The gravitational force on a body (its weight, at the Earth’s surface) is proportional to its mass. 
2. If a body A attracts a body B with a gravitational force of a given strength, then B attracts A with a force of equal strength in the opposite direction. 
3. The gravitational attraction between two bodies decreases with distance, being proportional to the inverse square of the distance between them. That is, if the distance is doubled, the gravitational attraction falls to a quarter of what it was. 
One interesting point here—think about how the earth is gravitationally attracting you. Actually, all the different parts of the earth are attracting you! Mount Everest is pulling you one way, the Antarctic ice mass a different way, and the earth’s core is pulling you downwards. Newton managed to prove, after thinking about it for years, that if the earth is a sphere (which is a very good approximation) then all these different attractions add up to what you would feel if all the earth’s mass were concentrated in one point at the center. So, when we’re talking about the gravitational attraction between you and the earth, and we talk about the distance of separation, we mean the distance between you and the center of the earth, which is just less than four thousand miles (6300 kilometers). 
Let’s denote the gravitational attractive force between two bodies A and B (as mentioned in item 2 above) by F. The forces on the two bodies are really equal and opposite vectors, each pointing to the other body, so our letter F means the length of these vectors, the strength of the force of attraction. 
Now, item 1 tells us that the gravitational attraction between the earth and a mass m is proportional to m. This is an immediate consequence of the experimental fact that falling bodies accelerate at the same rate, usually written g (approximately 10 meters per second per second), and the definition of force from Newton’s Second Law above. Thus we have
F is proportional to mass m
for the earth’s gravitational attraction on a body (often written weight W = mg), and Newton generalized this finding to assert that this proportionality to mass would be true for any gravitational attraction on the body. 
From the symmetry of the force (item 2 above) and the proportionality to the mass (item 1), it follows that the gravitational force between two bodies must be proportional to both masses. So, if we double both masses, say, the gravitational attraction between them increases by a factor of four. We see that if the force is proportional to both masses, let’s call them M and m, it is actually proportional to the product Mm of the masses. From item 3 above, the force is also proportional to 1/r2, where r is the distance between the bodies, so for the gravitational attractive force between two bodies
F is proportional to Mm/r2
This must mean that by measuring the gravitational force on something, we should be able to figure out the mass of the Earth! But there’s a catch—all we know is that the force is proportional to the Earth’s mass. From that we could find, for instance, the ratio of the mass of the Earth to the mass of Jupiter, by comparing how fast the Moon is “falling” around the Earth to how fast Jupiter’s moons are falling around Jupiter. For that matter, we could find the ratio of the Earth’s mass to the Sun’s mass by seeing how fast the planets swing around the Sun. Still, knowing all these ratios doesn’t tell us the Earth’s mass in tons. It does tell us that if we find that out, we can then find the masses of the other planets, at least those that have moons, and the mass of the Sun. 
Weighing the Earth
So how do we measure the mass of the Earth? The only way is to compare the Earth’s gravitational attraction with that of something we already know the mass of. We don’t know the masses of any of the heavenly bodies. What this really means is that we have to take a known mass, such as a lead ball, and measure how strongly it attracts a smaller lead ball, say, and compare that force with the earth’s attraction for the smaller lead ball. This is very difficult to accomplish because the forces are so small, but it was done successfully in 1798, just over a century after Newton’s work, by Cavendish. 
In other words, Cavendish took two lead weights M and m, a few kilograms each, and actually detected the tiny gravitational attraction between them (of order of magnitude millionths of a newton)! This was a sufficiently tough experiment that even now, two hundred years later, it’s not easy to give a lecture demonstration of the effect. 
Making this measurement amounts to finding the constant of proportionality in the statement about F above, so that we can sharpen it up from a statement about proportionality to an actual useable equation,
F = GMm/r2
where the constant G is what Cavendish measured, and found to be 6.67 x 10-11 in the appropriate units, where the masses are in kilograms, the distance in meters and the force in newtons. (Notice here that we can’t get rid of the constant of proportionality G, as we did in the equation F = ma, Newton’s Second Law, above. We succeeded there by defining the unit of force appropriately. In the present case, we have already defined our units of mass, distance and force, so we have no further room to maneuver.)
From Newton’s theory of universal gravitational attraction, the same constant G determines the gravitational attraction between any two masses in the universe. This means we can now find the mass of the earth. We just consider a one kilogram mass at the earth’s surface. We know it feels a force of approximately 10 newtons, and is a distance of about 6300 km, or 6,300,000 meters, from the center of the earth. So we know every term in the above equation except the mass of the earth, and therefore can find it. This is left as an exercise. 
Early Ideas about Light Propagation
As we shall soon see, attempts to measure the speed of light played an important part in the development of the theory of special relativity, and, indeed, the speed of light is central to the theory. 
The first recorded discussion of the speed of light (I think) is in Aristotle, where he quotes Empedocles as saying the light from the sun must take some time to reach the earth, but Aristotle himself apparently disagrees, and even Descartes thought that light traveled instantaneously. Galileo, unfairly as usual, in Two New Sciences (page 42) has Simplicio stating the Aristotelian position,
SIMP. Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired at great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval. 
Of course, Galileo points out that in fact nothing about the speed of light can be deduced from this observation, except that light moves faster than sound. He then goes on to suggest a possible way to measure the speed of light. The idea is to have two people far away from each other, with covered lanterns. One uncovers his lantern, then the other immediately uncovers his on seeing the light from the first. This routine is to be practised with the two close together, so they will get used to the reaction times involved, then they are to do it two or three miles apart, or even further using telescopes, to see if the time interval is perceptibly lengthened. Galileo claims he actually tried the experiment at distances less than a mile, and couldn’t detect a time lag. From this one can certainly deduce that light travels at least ten times faster than sound. 
Measuring the Speed of Light with Jupiter’s Moons
The first real measurement of the speed of light came about half a century later, in 1676, by a Danish astronomer, Ole Römer, working at the Paris Observatory. He had made a systematic study of Io, one of the moons of Jupiter, which was eclipsed by Jupiter at regular intervals, as Io went around Jupiter in a circular orbit at a steady rate. Actually, Römer found, for several months the eclipses lagged more and more behind the expected time, but then they began to pick up again. In September 1676,he correctly predicted that an eclipse on November 9 would be 10 minutes behind schedule. This was indeed the case, to the surprise of his skeptical colleagues at the Royal Observatory in Paris. Two weeks later, he told them what was happening: as the Earth and Jupiter moved in their orbits, the distance between them varied. The light from Io (actually reflected sunlight, of course) took time to reach the earth, and took the longest time when the earth was furthest away. When the Earth was furthest from Jupiter, there was an extra distance for light to travel equal to the diameter of the Earth’s orbit compared with the point of closest approach. The observed eclipses were furthest behind the predicted times when the earth was furthest from Jupiter. 
From his observations, Römer concluded that light took about twenty-two minutes to cross the earth’s orbit. This was something of an overestimate, and a few years later Newton wrote in the Principia (Book I, section XIV): “For it is now certain from the phenomena of Jupiter’s satellites, confirmed by the observations of different astronomers, that light is propagated in succession (note: I think this means at finite speed) and requires about seven or eight minutes to travel from the sun to the earth.”  This is essentially the correct value. 
Of course, to find the speed of light it was also necessary to know the distance from the earth to the sun. During the 1670’s, attempts were made to measure the parallax of Mars, that is, how far it shifted against the background of distant stars when viewed simultaneously from two different places on earth at the same time. This (very slight) shift could be used to find the distance of Mars from earth, and hence the distance to the sun, since all relative distances in the solar system had been established by observation and geometrical analysis. According to Crowe (Modern Theories of the Universe, Dover, 1994, page 30), they concluded that the distance to the sun was between 40 and 90 million miles. Measurements presumably converged on the correct value of about 93 million miles soon after that, because it appears Römer (or perhaps Huygens, using Römer’s data a short time later) used the correct value for the distance, since the speed of light was calculated to be 125,000 miles per second, about three-quarters of the correct value of 186,300 miles per second. This error is fully accounted for by taking the time light needs to cross the earth’s orbit to be twenty-two minutes (as Römer did) instead of the correct value of sixteen minutes. 
Starlight and Rain
The next substantial improvement in measuring the speed of light took place in 1728, in England. An astronomer James Bradley, sailing on the Thames with some friends, noticed that the little pennant on top of the mast changed position each time the boat put about, even though the wind was steady. He thought of the boat as the earth in orbit, the wind as starlight coming from some distant star, and reasoned that the apparent direction the starlight was “blowing” in would depend on the way the earth was moving. Another possible analogy is to imagine the starlight as a steady downpour of rain on a windless day, and to think of yourself as walking around a circular path at a steady pace. The apparent direction of the incoming rain will not be vertically downwards—more will hit your front than your back. In fact, if the rain is falling at, say, 15 mph, and you are walking at 3 mph, to you as observer the rain will be coming down at a slant so that it has a vertical speed of 15 mph, and a horizontal speed towards you of 3 mph. Whether it is slanting down from the north or east or whatever at any given time depends on where you are on the circular path at that moment. Bradley reasoned that the apparent direction of incoming starlight must vary in just this way, but the angular change would be a lot less dramatic. The earth’s speed in orbit is about 18 miles per second, he knew from Römer’s work that light went at about 10,000 times that speed. That meant that the angular variation in apparent incoming direction of starlight was about the magnitude of the small angle in a right-angled triangle with one side 10,000 times longer than the other, about one two-hundredth of a degree. Notice this would have been just at the limits of Tycho’s measurements, but the advent of the telescope, and general improvements in engineering, meant this small angle was quite accurately measurable by Bradley’s time, and he found the velocity of light to be 185,000 miles per second, with an accuracy of about one percent. 
Fast Flickering Lanterns
The problem is, all these astronomical techniques do not have the appeal of Galileo’s idea of two guys with lanterns. It would be reassuring to measure the speed of a beam of light between two points on the ground, rather than making somewhat indirect deductions based on apparent slight variations in the positions of stars. We can see, though, that if the two lanterns are ten miles apart, the time lag is of order one-ten thousandth of a second, and it is difficult to see how to arrange that. This technical problem was solved in France about 1850 by two rivals, Fizeau and Foucault, using slightly different techniques. In Fizeau’s apparatus, a beam of light shone between the teeth of a rapidly rotating toothed wheel, so the “lantern” was constantly being covered and uncovered. Instead of a second lantern far away, Fizeau simply had a mirror, reflecting the beam back, where it passed a second time between the teeth of the wheel. The idea was, the blip of light that went out through one gap between teeth would only make it back through the same gap if the teeth had not had time to move over significantly during the round trip time to the far away mirror. It was not difficult to make a wheel with a hundred teeth, and to rotate it hundreds of times a second, so the time for a tooth to move over could be arranged to be a fraction of one ten thousandth of a second. The method worked. Foucault’s method was based on the same general idea, but instead of a toothed wheel, he shone the beam on to a rotating mirror. At one point in the mirror’s rotation, the reflected beam fell on a distant mirror, which reflected it right back to the rotating mirror, which meanwhile had turned through a small angle. After this second reflection from the rotating mirror, the position of the beam was carefully measured. This made it possible to figure out how far the mirror had turned during the time it took the light to make the round trip to the distant mirror, and since the rate of rotation of the mirror was known, the speed of light could be figured out. These techniques gave the speed of light with an accuracy of about 1,000 miles per second. 
Albert Abraham Michelson
Albert Michelson was born in 1852 in Strzelno, Poland. His father Samuel was a Jewish merchant, not a very safe thing to be at the time. Purges of Jews were frequent in the neighboring towns and villages. They decided to leave town. Albert’s fourth birthday was celebrated in Murphy’s Camp, Calaveras County, about fifty miles south east of Sacramento, a place where five million dollars worth of gold dust was taken from one four acre lot. Samuel prospered selling supplies to the miners. When the gold ran out, the Michelsons moved to Virginia City, Nevada, on the Comstock lode, a silver mining town. Albert went to high school in San Francisco. In 1869, his father spotted an announcement in the local paper that Congressman Fitch would be appointing a candidate to the Naval Academy in Annapolis, and inviting applications. Albert applied but did not get the appointment, which went instead to the son of a civil war veteran. However, Albert knew that President Grant would also be appointing ten candidates himself, so he went east on the just opened continental railroad to try his luck. Unknown to Michelson, Congressman Fitch wrote directly to Grant on his behalf, saying this would really help get the Nevada Jews into the Republican party. This argument proved persuasive. In fact, by the time Michelson met with Grant, all ten scholarships had been awarded, but the President somehow came up with another one. Of the incoming class of ninety-two, four years later twenty-nine graduated. Michelson placed first in optics, but twenty-fifth in seamanship. The Superintendent of the Academy, Rear Admiral Worden, who had commanded the Monitor in its victory over the Merrimac, told Michelson: “If in the future you’d give less attention to those scientific things and more to your naval gunnery, there might come a time when you would know enough to be of some service to your country.”
Sailing the Silent Seas: Galilean Relativity
Shortly after graduation, Michelson was ordered aboard the USS Monongahela, a sailing ship, for a voyage through the Carribean and down to Rio. According to the biography of Michelson written by his daughter (The Master of Light, by Dorothy Michelson Livingston, Chicago, 1973) he thought a lot as the ship glided across the quiet Caribbean about whether one could decide in a closed room inside the ship whether or not the vessel was moving. In fact, his daughter quotes a famous passage from Galileo on just this point:
[SALV.] Shut yourself up with some friend in the largest room below decks of some large ship and there procure gnats, flies, and other such small winged creatures. Also get a great tub full of water and within it put certain fishes; let also a certain bottle be hung up, which drop by drop lets forth its water into another narrow-necked bottle placed underneath. Then, the ship lying still, observe how those small winged animals fly with like velocity towards all parts of the room; how the fish swim indifferently towards all sides; and how the distilling drops all fall into the bottle placed underneath. And casting anything toward your friend, you need not throw it with more force one way than another, provided the distances be equal; and leaping with your legs together, you will reach as far one way as another. Having observed all these particulars, though no man doubts that, so long as the vessel stands still, they ought to take place in this manner, make the ship move with what velocity you please, so long as the motion is uniform and not fluctuating this way and that. You will not be able to discern the least alteration in all the forenamed effects, nor can you gather by any of them whether the ship moves or stands still. ...in throwing something to your friend you do not need to throw harder if he is towards the front of the ship from you... the drops from the upper bottle still fall into the lower bottle even though the ship may have moved many feet while the drop is in the air ... Of this correspondence of effects the cause is that the ship’s motion is common to all the things contained in it and to the air also; I mean if those things be shut up in the room; but in case those things were above the deck in the open air, and not obliged to follow the course of the ship, differences would be observed, ... smoke would stay behind... . 
[SAGR.] Though it did not occur to me to try any of this out when I was at sea, I am sure you are right. I remember being in my cabin wondering a hundred times whether the ship was moving or not, and sometimes I imagined it to be moving one way when in fact it was moving the other way. I am therefore satisfied that no experiment that can be done in a closed cabin can determine the speed or direction of motion of a ship in steady motion. 
I have paraphrased this last remark somewhat to clarify it. This conclusion of Galileo’s, that everything looks the same in a closed room moving at a steady speed as it does in a closed room at rest, is called The Principle of Galilean Relativity. We shall be coming back to it. 
Michelson Measures the Speed of Light
On returning to Annapolis from the cruise, Michelson was commissioned Ensign, and in 1875 became an instructor in physics and chemistry at the Naval Academy, under Lieutenant Commander William Sampson. Michelson met Mrs. Sampson’s niece, Margaret Heminway, daughter of a very successful Wall Street tycoon, who had built himself a granite castle in New Rochelle, NY. Michelson married Margaret in an Episcopal service in New Rochelle in 1877. 
At work, lecture demonstrations had just been introduced at Annapolis. Sampson suggested that it would be a good demonstration to measure the speed of light by Foucault’s method. Michelson soon realized, on putting together the apparatus, that he could redesign it for much greater accuracy, but that would need money well beyond that available in the teaching demonstration budget. He went and talked with his father in law, who agreed to put up $2,000. Instead of Foucault’s 60 feet to the far mirror, Michelson had about 2,000 feet along the bank of the Severn, a distance he measured to one tenth of an inch. He invested in very high quality lenses and mirrors to focus and reflect the beam. His final result was 186,355 miles per second, with possible error of 30 miles per second or so. This was twenty times more accurate than Foucault, made the New York Times, and Michelson was famous while still in his twenties. In fact, this was accepted as the most accurate measurement of the speed of light for the next forty years, at which point Michelson measured it again. 
The next lecture is on the Michelson-Morley experiment to detect the aether.
The Michelson-Morley Experiment
 
 
 
Michael Fowler  U. Va. Physics 9/15/08
The Nature of Light
As a result of Michelson’s efforts in 1879, the speed of light was known to be 186,350 miles per second with a likely error of around 30 miles per second.  This measurement, made by timing a flash of light travelling between mirrors in Annapolis, agreed well with less direct measurements based on astronomical observations.  Still, this did not really clarify the nature of light.  Two hundred years earlier, Newton had suggested that light consists of tiny particles generated in a hot object, which spray out at very high speed, bounce off other objects, and are detected by our eyes.  Newton’s arch-enemy Robert Hooke, on the other hand, thought that light must be a kind of wave motion, like sound.  To appreciate his point of view, let us briefly review the nature of sound.
The Wavelike Nature of Sound
Actually, sound was already quite well understood by the ancient Greeks.  The essential point they had realized is that sound is generated by a vibrating material object, such as a bell, a string or a drumhead.  Their explanation was that the vibrating drumhead, for example, alternately pushes and pulls on the air directly above it, sending out waves of compression and decompression (known as rarefaction), like the expanding circles of ripples from a disturbance on the surface of a pond.  On reaching the ear, these waves push and pull on the eardrum with the same frequency (that is to say, the same number of pushes per second) as the original source was vibrating at, and nerves transmit from the ear to the brain both the intensity (loudness) and frequency (pitch) of the sound.
There are a couple of special properties of sound waves (actually any waves) worth mentioning at this point.  The first is called interference.  This is most simply demonstrated with water waves.  If you put two fingers in a tub of water, just touching the surface a foot or so apart, and vibrate them at the same rate to get two expanding circles of ripples, you will notice that where the ripples overlap there are quite complicated patterns of waves formed.  The essential point is that at those places where the wave-crests from the two sources arrive at the same time, the waves will work together and the water will be very disturbed, but at points where the crest from one source arrives at the same time as the wave trough from the other source, the waves will cancel each other out, and the water will hardly move.  You can hear this effect for sound waves by playing a constant note through stereo speakers.  As you move around a room, you will hear quite large variations in the intensity of sound.  Of course, reflections from walls complicate the pattern.  This large variation in volume is not very noticeable when the stereo is playing music, because music is made up of many frequencies, and they change all the time.  The different frequencies, or notes, have their quiet spots in the room in different places.  The other point that should be mentioned is that high frequency tweeter-like sound is much more directional than low frequency woofer-like sound.  It really doesn’t matter where in the room you put a low-frequency woofer—the sound seems to be all around you anyway.  On the other hand, it is quite difficult to get a speaker to spread the high notes in all directions.  If you listen to a cheap speaker, the high notes are loudest if the speaker is pointing right at you.  A lot of effort has gone into designing tweeters, which are small speakers especially designed to broadcast high notes over a wide angle of directions.
Is Light a Wave?
Bearing in mind the above minireview of the properties of waves, let us now reconsider the question of whether light consists of a stream of particles or is some kind of wave.  The strongest argument for a particle picture is that light travels in straight lines.  You can hear around a corner, at least to some extent, but you certainly can’t see.  Furthermore, no wave-like interference effects are very evident for light.  Finally, it was long known, as we have mentioned, that sound waves were compressional waves in air.  If light is a wave, just what is waving?  It clearly isn’t just air, because light reaches us from the sun, and indeed from stars, and we know the air doesn’t stretch that far, or the planets would long ago have been slowed down by air resistance.
Despite all these objections, it was established around 1800 that light is in fact some kind of wave.  The reason this fact had gone undetected for so long was that the wavelength is really short, about one fifty-thousandth of an inch.  In contrast, the shortest wavelength sound detectable by humans has a wavelength of about half an inch.  The fact that light travels in straight lines is in accord with observations on sound that the higher the frequency (and shorter the wavelength) the greater the tendency to go in straight lines.  Similarly, the interference patterns mentioned above for sound waves or ripples on a pond vary over distances of the same sort of size as the wavelengths involved.  Patterns like that would not normally be noticeable for light because they would be on such a tiny scale.  In fact, it turns out, there are ways to see interference effects with light.  A familiar example is the many colors often visible in a soap bubble.  These come about because looking at a soap bubble you see light reflected from both sides of a very thin film of water—a thickness that turns out to be comparable to the wavelength of light.  The light reflected from the lower layer has to go a little further to reach your eye, so that light wave must wave an extra time or two before getting to your eye compared with the light reflected from the top layer.  What you actually see is the sum of the light reflected from the top layer and that reflected from the bottom layer.  Thinking of this now as the sum of two sets of waves, the light will be bright if the crests of the two waves arrive together, dim if the crests of waves reflected from the top layer arrive simultaneously with the troughs of waves reflected from the bottom layer.  Which of these two possibilities actually occurs for reflection from a particular bit of the soap film depends on just how much further the light reflected from the lower surface has to travel to reach your eye compared with light from the upper surface, and that depends on the angle of reflection and the thickness of the film.  Suppose now we shine white light on the bubble.  White light is made up of all the colors of the rainbow, and these different colors have different wavelengths, so we see colors reflected, because for a particular film, at a particular angle, some colors will be reflected brightly (the crests will arrive together), some dimly, and we will see the ones that win.
If Light is a Wave, What is Waving?
Having established that light is a wave, though, we still haven’t answered one of the major objections raised above.  Just what is waving?  We discussed sound waves as waves of compression in air.  Actually, that is only one case—sound will also travel through liquids, like water, and solids, like a steel bar.  It is found experimentally that, other things being equal, sound travels faster through a medium that is harder to compress: the material just springs back faster and the wave moves through more rapidly.  For media of equal springiness, the sound goes faster through the less heavy medium, essentially because the same amount of springiness can push things along faster in a lighter material.  So when a sound wave passes, the material—air, water or solid—waves as it goes through.  Taking this as a hint, it was natural to suppose that light must be just waves in some mysterious material, which was called the aether, surrounding and permeating everything.  This aether must also fill all of space, out to the stars, because we can see them, so the medium must be there to carry the light.  (We could never hear an explosion on the moon, however loud, because there is no air to carry the sound to us.)  Let us think a bit about what properties this aether must have.  Since light travels so fast, it must be very light, and very hard to compress.  Yet, as mentioned above, it must allow solid bodies to pass through it freely, without aether resistance, or the planets would be slowing down.  Thus we can picture it as a kind of ghostly wind blowing through the earth.  But how can we prove any of this? Can we detect it?
Detecting the Aether Wind: the Michelson-Morley Experiment
Detecting the aether wind was the next challenge Michelson set himself after his triumph in measuring the speed of light so accurately.  Naturally, something that allows solid bodies to pass through it freely is a little hard to get a grip on.  But Michelson realized that, just as the speed of sound is relative to the air, so the speed of light must be relative to the aether.  This must mean, if you could measure the speed of light accurately enough, you could measure the speed of light travelling upwind, and compare it with the speed of light travelling downwind, and the difference of the two measurements should be twice the windspeed.  Unfortunately, it wasn’t that easy.  All the recent accurate measurements had used light travelling to a distant mirror and coming back, so if there was an aether wind along the direction between the mirrors, it would have opposite effects on the two parts of the measurement, leaving a very small overall effect.  There was no technically feasible way to do a one-way determination of the speed of light.
At this point, Michelson had a very clever idea for detecting the aether wind.  As he explained to his children (according to his daughter), it was based on the following puzzle:
Suppose we have a river of width w (say, 100 feet), and two swimmers who both swim at the same speed v feet per second (say, 5 feet per second).  The river is flowing at a steady rate, say 3 feet per second.  The swimmers race in the following way: they both start at the same point on one bank.  One swims directly across the river to the closest point on the opposite bank, then turns around and swims back.  The other stays on one side of the river, swimming upstream a distance (measured along the bank) exactly equal to the width of the river, then swims back to the start.  Who wins?
Let’s consider first the swimmer going upstream and back.  Going 100 feet upstream, the speed relative to the bank is only 2 feet per second, so that takes 50 seconds.  Coming back, the speed is 8 feet per second, so it takes 12.5 seconds, for a total time of 62.5 seconds.

B
bank
vt
river
ct
In time t, the swimmer has moved ct relative to the water, and been carried downstream a distance vt.
 
flow
C
bank

The swimmer going across the flow is trickier.  It won’t do simply to aim directly for the opposite bank-the flow will carry the swimmer downstream.  To succeed in going directly across, the swimmer must actually aim upstream at the correct angle (of course, a real swimmer would do this automatically).  Thus, the swimmer is going at 5 feet per second, at an angle, relative to the river, and being carried downstream at a rate of 3 feet per second.  If the angle is correctly chosen so that the net movement is directly across, in one second the swimmer must have moved four feet across: the distances covered in one second will form a 3,4,5 triangle.  So, at a crossing rate of 4 feet per second, the swimmer gets across in 25 seconds, and back in the same time, for a total time of 50 seconds.  The cross-stream swimmer wins.  This turns out to true whatever their swimming speed.  (Of course, the race is only possible if they can swim faster than the current!)
 

a
b
s
c
d
This diagram is from the original paper. The source of light is at s, the 45 degree line is the half-silvered mirror, b and c are mirrors and d the observer.

Michelson’s great idea was to construct an exactly similar race for pulses of light, with the aether wind playing the part of the river.  The scheme of the experiment is as follows: a pulse of light is directed at an angle of 45 degrees at a half-silvered, half transparent mirror, so that half the pulse goes on through the glass, half is reflected.  These two half-pulses are the two swimmers.  They both go on to distant mirrors which reflect them back to the half-silvered mirror.  At this point, they are again half reflected and half transmitted, but a telescope is placed behind the half-silvered mirror as shown in the figure so that half of each half-pulse will arrive in this telescope.  Now, if there is an aether wind blowing, someone looking through the telescope should see the halves of the two half-pulses to arrive at slightly different times, since one would have gone more upstream and back, one more across stream in general.  To maximize the effect, the whole apparatus, including the distant mirrors, was placed on a large turntable so it could be swung around.
An animated flashlet of the experiment is available here–it makes the account above a lot clearer!
Let us think about what kind of time delay we expect to find between the arrival of the two half-pulses of light.  Taking the speed of light to be c miles per second relative to the aether, and the aether to be flowing at v miles per second through the laboratory, to go a distance w miles upstream will take w/(c-v) seconds, then to come back will take w/(c+v) seconds.  The total roundtrip time upstream and downstream is the sum of these, which works out to be 2wc/(c²-v²), which can also be written (2w/c)×1/(1-v²/c²).  Now, we can safely assume the speed of the aether is much less than the speed of light, otherwise it would have been noticed long ago, for example in timing of eclipses of Jupiter’s satellites.  This means v²/c² is a very small number, and we can use some handy mathematical facts to make the algebra a bit easier.  First, if x is very small compared to 1, 1/(1-x) is very close to 1+x.  (You can check it with your calculator.)  Another fact we shall need in a minute is that for small x, the square root of 1+x is very close to 1+x/2.  
 
Putting all this together,

s
a
a1
b
c
This is also from the original paper, and shows the expected path of light relative to the aether with an aether wind blowing.
d

Now, what about the cross-stream time?  The actual cross-stream speed must be figured out as in the example above using a right-angled triangle, with the hypoteneuse equal to the speed c, the shortest side the aether flow speed v, and the other side the cross-stream speed we need to find the time to get across.  From Pythagoras’ theorem, then, the cross-stream speed is the square root of (c²-v²).  
Since this will be the same both ways, the roundtrip cross-stream time will be
This can be written in the form
where the two successive approximations, valid for are   and
Therefore the
Looking at the two roundtrip times at the ends of the two paragraphs above, we see that they differ by an amount (2w/c) × v²/2c².  Now, 2w/c is just the time the light would take if there were no aether wind at all, say, a few millionths of a second.  If we take the aether windspeed to be equal to the earth’s speed in orbit, for example, v/c is about 1/10,000, so v²/c² is about 1/100,000,000.  This means the time delay between the pulses reflected from the different mirrors reaching the telescope is about one-hundred-millionth of a few millionths of a second.  It seems completely hopeless that such a short time delay could be detected.  However, this turns out not to be the case, and Michelson was the first to figure out how to do it.  The trick is to use the interference properties of the lightwaves.  Instead of sending pulses of light, as we discussed above, Michelson sent in a steady beam of light of a single color.  This can be visualized as a sequence of ingoing waves, with a wavelength one fifty-thousandth of an inch or so.  Now this sequence of waves is split into two, and reflected as previously described.  One set of waves goes upstream and downstream, the other goes across stream and back.  Finally, they come together into the telescope and the eye.  If the one that took longer is half a wavelength behind, its troughs will be on top of the crests of the first wave, they will cancel, and nothing will be seen.  If the delay is less than that, there will still be some dimming.  However, slight errors in the placement of the mirrors would have the same effect.  This is one reason why the apparatus is built to be rotated.  On turning it through 90 degrees, the upstream-downstream and the cross-stream waves change places.  Now the other one should be behind.  Thus, if there is an aether wind, if you watch through the telescope while you rotate the turntable, you should expect to see variations in the brightness of the incoming light.
To magnify the time difference between the two paths, in the actual experiment the light was reflected backwards and forwards several times, like a several lap race.  For a diagram, click here.  For an actual photograph of the real apparatus, click here.
Michelson calculated that an aether windspeed of only one or two miles a second would have observable effects in this experiment, so if the aether windspeed was comparable to the earth’s speed in orbit around the sun, it would be easy to see.  In fact, nothing was observed.  The light intensity did not vary at all.  Some time later, the experiment was redesigned so that an aether wind caused by the earth’s daily rotation could be detected.  Again, nothing was seen.  Finally, Michelson wondered if the aether was somehow getting stuck to the earth, like the air in a below-decks cabin on a ship, so he redid the experiment on top of a high mountain in California.  Again, no aether wind was observed.  It was difficult to believe that the aether in the immediate vicinity of the earth was stuck to it and moving with it, because light rays from stars would deflect as they went from the moving faraway aether to the local stuck aether.
The only possible conclusion from this series of very difficult experiments was that the whole concept of an all-pervading aether was wrong from the start.  Michelson was very reluctant to think along these lines.  In fact, new theoretical insight into the nature of light had arisen in the 1860’s from the brilliant theoretical work of Maxwell, who had written down a set of equations describing how electric and magnetic fields can give rise to each other.  He had discovered that his equations predicted there could be waves made up of electric and magnetic fields, and the speed of these waves, deduced from experiments on how these fields link together, would be 186,300 miles per second.  This is, of course, the speed of light, so it is natural to assume that light is made up of fast-varying electric and magnetic fields.  But this leads to a big problem: Maxwell’s equations predict a definite speed for light, and it is the speed found by measurements.  But what is the speed to be measured relative to?  The whole point of bringing in the aether was to give a picture for light resembling the one we understand for sound, compressional waves in a medium.  The speed of sound through air is measured relative to air.  If the wind is blowing towards you from the source of sound, you will hear the sound sooner.  If there isn’t an aether, though, this analogy doesn’t hold up.  So what does light travel at 186,300 miles per second relative to?
There is another obvious possibility, which is called the emitter theory: the light travels at 186,300 miles per second relative to the source of the light.  The analogy here is between light emitted by a source and bullets emitted by a machine gun.  The bullets come out at a definite speed (called the muzzle velocity) relative to the barrel of the gun.  If the gun is mounted on the front of a tank, which is moving forward, and the gun is pointing forward, then relative to the ground the bullets are moving faster than they would if shot from a tank at rest.  The simplest way to test the emitter theory of light, then, is to measure the speed of light emitted in the forward direction by a flashlight moving in the forward direction, and see if it exceeds the known speed of light by an amount equal to the speed of the flashlight.  Actually, this kind of direct test of the emitter theory only became experimentally feasible in the nineteen-sixties.  It is now possible to produce particles, called neutral pions, which decay each one in a little explosion, emitting a flash of light.  It is also possible to have these pions moving forward at 185,000 miles per second when they self destruct, and to catch the light emitted in the forward direction, and clock its speed.  It is found that, despite the expected boost from being emitted by a very fast source, the light from the little explosions is going forward at the usual speed of 186,300 miles per second.  In the last century, the emitter theory was rejected because it was thought the appearance of certain astronomical phenomena, such as double stars, where two stars rotate around each other, would be affected.  Those arguments have since been criticized, but the pion test is unambiguous.  The definitive experiment was carried out by Alvager et al., Physics Letters 12, 260 (1964).
Einstein’s Answer
The results of the various experiments discussed above seem to leave us really stuck.  Apparently light is not like sound, with a definite speed relative to some underlying medium.  However, it is also not like bullets, with a definite speed relative to the source of the light.  Yet when we measure its speed we always get the same result.  How can all these facts be interpreted in a simple consistent way?  We shall show how Einstein answered this question in the next lecture.
A detailed guide to setting up a Michelson-Morley experiment can be found at Nantes University.
Special Relativity
Michael Fowler, UVa Physics 3/3/08
Galilean Relativity again
At this point in the course, we finally enter the twentieth century—Albert Einstein wrote his first paper on relativity in 1905.  To put his work in context, let us first review just what is meant by “relativity” in physics.  The first example, mentioned in a previous lecture, is what is called “Galilean relativity” and is nothing but Galileo’s perception that by observing the motion of objects, alive or dead, in a closed room there is no way to tell if the room is at rest or is in fact in a boat moving at a steady speed in a fixed direction.  (You can tell if the room is accelerating or turning around.)  Everything looks the same in a room in steady motion as it does in a room at rest.  After Newton formulated his Laws of Motion, describing how bodies move in response to forces and so on, physicists reformulated Galileo’s observation in a slightly more technical, but equivalent, way: they said the laws of physics are the same in a uniformly moving room as they are in a room at rest.  In other words, the same force produces the same acceleration, and an object experiencing no force moves at a steady speed in a straight line in either case.  Of course, talking in these terms implies that we have clocks and rulers available so that we can actually time the motion of a body over a measured distance, so the physicist envisions the room in question to have calibrations along all the walls, so the position of anything can be measured, and a good clock to time motion.  Such a suitably equipped room is called a “frame of reference”—the calibrations on the walls are seen as a frame which you can use to specify the precise position of an object at a given time.  (This is the same as a set of “coordinates”.)  Anyway, the bottom line is that no amount of measuring of motions of objects in the “frame of reference” will tell you whether this is a frame at rest or one moving at a steady velocity.
What exactly do we mean by a frame “at rest” anyway?  This seems obvious from our perspective as creatures who live on the surface of the earth—we mean, of course, at rest relative to fixed objects on the earth’s surface.  Actually, the earth’s rotation means this isn’t quite a fixed frame, and also the earth is moving in orbit at 18 miles per second.  From an astronaut’s point of view, then, a frame fixed relative to the sun might seem more reasonable.  But why stop there?  We believe the laws of physics are good throughout the universe.  Let us consider somewhere in space far from the sun, even far from our galaxy.  We would see galaxies in all directions, all moving in different ways.  Suppose we now set up a frame of reference and check that Newton’s laws still work.  In particular, we check that the First Law holds—that a body experiencing no force moves at a steady speed in a straight line.  This First law is often referred to as The Principle of Inertia, and a frame in which it holds is called an Inertial Frame.  Then we set up another frame of reference, moving at a steady velocity relative to the first one, and find that Newton’s laws are o.k. in this frame too.  The point to notice here is that it is not at all obvious which—if either—of these frames is “at rest”.  We can, however, assert that they are both inertial frames, after we’ve checked that in both of them, a body with no forces acting on it moves at a steady speed in a straight line (the speed could be zero).  In this situation, Michelson would have said that a frame “at rest” is one at rest relative to the aether.  However, his own experiment found motion through the aether to be undetectable, so how would we ever know we were in the right frame?
As we mentioned in the last lecture, in the middle of the nineteenth century there was a substantial advance in the understanding of electric and magnetic fields.  (In fact, this advance is in large part responsible for the improvement in living standards since that time.)  The new understanding was summarized in a set of equations called Maxwell’s equations describing how electric and magnetic fields interact and give rise to each other, just as, two centuries earlier, the new understanding of dynamics was summarized in the set of equations called Newton’s laws.  The important thing about Maxwell’s equations for our present purposes is that they predicted waves made up of electric and magnetic fields that moved at 3×108 meters per second, and it was immediately realized that this was no coincidence—light waves must be nothing but waving electric and magnetic fields.  (This is now fully established to be the case.)
It is worth emphasizing that Maxwell’s work predicted the speed of light from the results of experiments that were not thought at the time they were done to have anything to do with light—experiments on, for example, the strength of electric field produced by waving a magnet.  Maxwell was able to deduce a speed for waves like this using methods analogous to those by which earlier scientists had figured out the speed of sound from a knowledge of the density and the springiness of air.
Generalizing Galilean Relativity to Include Light: Special Relativity
We now come to Einstein’s major insight: the Theory of Special Relativity.  It is deceptively simple.  Einstein first dusted off Galileo’s discussion of experiments below decks on a uniformly moving ship, and restated it as :
The Laws of Physics are the same in all Inertial Frames.
Einstein then simply brought this up to date, by pointing out that the Laws of Physics must now include Maxwell’s equations describing electric and magnetic fields as well as Newton’s laws describing motion of masses under gravity and other forces.  (Note for experts and the curious:  we shall find that Maxwell’s equations are completely unaltered by special relativity, but, as will become clear later, Newton’s Laws do need a bit of readjustment to include special relativistic phenomena.  The First Law is still o.k., the Second Law in the form F = ma is not, because we shall find mass varies; we need to equate force to rate of change of momentum (Newton understood that, of course—that’s the way he stated the law!). The Third Law, stated as action equals reaction, no longer holds because if a body moves, its electric field, say, does not readjust instantaneously—a ripple travels outwards at the speed of light. Before the ripple reaches another charged body, the electric forces between the two will be unbalanced. However, the crucial consequence of the Third Law—the conservation of momentum when two bodies interact, still holds.  It turns out that the rippling field itself carries momentum, and everything balances.)
Demanding that Maxwell’s equations be satisfied in all inertial frames has one major consequence as far as we are concerned. As we stated above, Maxwell’s equations give the speed of light to be 3×108 meters per second. Therefore, demanding that the laws of physics are the same in all inertial frames implies that the speed of any light wave, measured in any inertial frame, must be 3×108 meters per second.
This then is the entire content of the Theory of Special Relativity: the Laws of Physics are the same in any inertial frame, and, in particular, any measurement of the speed of light in any inertial frame will always give 3×108 meters per second. 
You Really Can’t Tell You’re Moving!
Just as Galileo had asserted that observing gnats, fish and dripping bottles, throwing things and generally jumping around would not help you to find out if you were in a room at rest or moving at a steady velocity, Einstein added that no kind of observation at all, even measuring the speed of light across your room to any accuracy you like, would help find out if your room was “really at rest”.  This implies, of course, that the concept of being “at rest” is meaningless.  If Einstein is right, there is no natural rest-frame in the universe.  Naturally, there can be no “aether”, no thin transparent jelly filling space and vibrating with light waves, because if there were, it would provide the natural rest frame, and affect the speed of light as measured in other moving inertial frames as discussed above.
So we see the Michelson-Morley experiment was doomed from the start.  There never was an aether wind.  The light was not slowed down by going “upstream”—light always travels at the same speed, which we shall now call c,
c = 3×108 meters per second
to save writing it out every time.  This now answers the question of what the speed of light, c, is relative to.  We already found that it is not like sound, relative to some underlying medium.  It is also not like bullets, relative to the source of the light (the discredited emitter theory).  Light travels at c relative to the observer, since if the observer sets up an inertial frame (clocks, rulers, etc.) to measure the speed of light he will find it to be c.  (We always assume our observers are very competent experimentalists!)
Truth and Consequences
The Truth we are referring to here is the seemingly innocuous and plausible sounding statement that all inertial frames are as good as each other—the laws of physics are the same in all of them—and so the speed of light is the same in all of them.  As we shall soon see, this Special Theory of Relativity has some surprising consequences, which reveal themselves most dramatically when things are moving at relative speeds comparable to the speed of light.  Einstein liked to explain his theory using what he called “thought experiments” involving trains and other kinds of transportation moving at these speeds (technically unachievable so far!), and we shall follow his general approach.
To begin with, let us consider a simple measurement of the speed of light carried out at the same time in two inertial frames moving at half the speed of light relative to each other. The setup is as follows: on a flat piece of ground, we have a flashlight which emits a blip of light, like a strobe. We have two photocells, devices which click and send a message down a wire when light falls on them. The photocells are placed 10 meters apart in the path of the blip of light, they are somehow wired into a clock so that the time taken by the blip of light to travel from the first photocell to the second, in other words, the time between clicks, can be measured. From this time and the known distance between them, we can easily find the speed of the blip of light.

speed c/2
The speed of the same blip of light is measured by two observers, having relative speed c/2.   Both measure the time the blip takes from one photocell to a second one 10 meters further on. Both find the speed to be c.
photocells on ground
light blip
light source

Meanwhile, there is another observer, passing overhead in a spaceship traveling at half the speed of light.  She is also equipped with a couple of photocells, placed 10 meters apart on the bottom of her spaceship as shown, and she is able to measure the speed of the same blip of light, relative to her frame of reference (the spaceship).  The observer on the spaceship will measure the blip of light to be traveling at c relative to the spaceship, the observer on the ground will measure the same blip to be traveling at c relative to the ground.  That is the unavoidable consequence of the Theory of Relativity.  
(Note: actually the picture above is not quite the way it would really look. As we shall find, objects moving at relativistic speeds are contracted, and this combined with the different times light takes to reach the eye from different parts of the ship would change the ship’s appearance.   But this does not affect the validity of the statements above.)
 
   
 
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