**The Spread of Newtonian Science**

**The Scientific Revolution Before Newton** Copernicus (1473 – 1543) • Heliocentric universe Kepler (1571 – 1630) • Attempts to use “physics” to explain Copernicus’ model. • Elliptical orbits of planets. • Magnetic forces. Galileo (1564 – 1642) • Kinematics. • Circular inertia. • Imprisoned for heresy. Descartes (1596 – 1650) • Seeks (in philosophy) to achieve explanations equal in clarity to mathematical proof. • Sees mathematics as a perfect science. • Cartesian geometry. • Distinction of mind, physical and heavenly worlds. Francis Bacon (1561 – 1626) • Experimental method

**John TheophilusDesaguliers** • 1683 – 1744 • Born in La Rochelle, France • Moved to England as a child. • Graduated from Christ Church, Oxford University. • He was a priest, freemason, engineer and natural philosopher. • Popularised Newtonian Sciences.

**Desaguliers became experimental assistant to Isaac Newton in** 1713 whilst at Oxford. He soon made a name for himself as apublic experimental lecturer in London.

**Desaguliersbecame experimenter for the Royal Society, with** Newton’s assistance, in 1714. • Even today, the Society acts as a scientific advisor to the British government, receiving a parliamentary grant.

**Desaguliers was awarded the Society’s highest honour, the** Copley medal, three times in 1734, 1736 and 1741. His most famous achievement was for discoveries of the properties of electricity.

**Desagulierswas one of many who tried to provide introductory** texts to Newton’s Principia. Something Newton always refused to provide.

**In 1720, Desaguliers translated, “Mathematical Elements of** Natural Philosophy, Confirmed by experiments: or, An Introduction to Sir Isaac Newton’s Philosophy”, into English. Originally written in Latin by William-James Gravesande.

**The Newtonian System of the world, the best model of** government and Allegorical Poem - 1728 But Newton the unparallel’d, whose Name No Time will wear out of the Book of Fame, Caelestial Science has promoted more, Than all the Sages that have shone before. Nature compell’d, his piercing Mind, obeys, And gladly shews him all her secret Ways; ‘GainstMathematicks she has no Defence, And yield t’experimental Consequence: His tow’ring Genius, from its certain Cause, Ev’ry Appearance, a priori draws, And shewsth’ Almighty Architect’s unalter’d Laws.

**In 1734 his own book, Course of Experimental Philosophy, was** published and became very popular.

**Desaguliers as an engineer** The water supply in Edinburgh The ventilation of the houses of parliament The first Westminster bridge

**Within the the Royal Society he devised new experiments to** defend several of Newton’s claims, such as the shape of the Earth.

**Universal Gravitation** Isaac Newton formulated the law of universal gravitation between two objects. The law states that between two objects of masses m1 and m2, with centers of mass a distance d apart, there is an attractive force magnitude. G is the gravitational constant and in SI units has a value of 6.67x10-11 kg-1 m3 s-1. The force F is called the gravitation force. The gravitational force of an object on the Earth’s surface is often called the weight of the object.

**Find the magnitude of the gravitational force of an object** of mass M on the Earth’s surface. Assume that the Earth is a sphere of mass 5.98x1024 kg and a radius 6.37x106 m. G is the gravitational constant and has a value of 6.67x10-11 kg-1 m3 s-1. We see that Newton’s universal law of gravitation gives the familiar rule of the force of gravity or the weight of an object of mass M as Mg, where g = 9.8ms-2. Do you recognise the answer?

**Emilie du Châtelet** 1706 – 1749 Born in Paris, France Feminist French mathematician, physicist, and author during The Age of Enlightenment

**Education** Early Education: • Father • Tutors • Fluent in Latin, Italian, German and Greek • Used her mathematical skills to devise highly successful strategies for gambling • Mother – conflicting information Further Education: • Continued with her studies after childbirth • Tutors • Dressed as a man!

**Relationship with Voltaire** • Friendship • Voltaire shared Newton’s work • Studied hard to advance science • Tested Newton’s theories • Introductory book on Newtonian philosophy • “She dictated and I wrote”

**Achievements in Scientific Research** Heat and Light: • Research into the science of fire • Predicted infrared radiation and the nature of light. Institutions de Physique (Lesson’s in Physics): • A book for her son • Review of new ideas • But included complex ideas

**Kinetic Energy Ideas:** • Newton’s theory E α V (energy of moving object is proportional to velocity) • Leibniz and Gravesande’s theory E α V2 (energy of moving object is proportional to velocity squared) Newton’s Principia: • Most outstanding achievement • Translated Newton’s ‘Principia Mathematica’ into French • Published in 1759 • Still the standard translation

**Laura Bassiborn in Italy** 1711 – 1778

**Education** • Father was a lawyer • Child prodigy • GaetanoTacconi • Franceso Maria Zanotti • 1732 admitted to the Bologna Academy of Science • Degree in Philosophy • Became a lecturer This picture is reminiscent of classrooms of that time

**Bassi, Manfredi and Newton** • First lecture was on Newtonian science • Maths v physics • “Newtonianism for Ladies” • Studied infinitesimal calculus under Manfredi

**Bassi’s work** • Not allowed access to university laboratories • Had her laboratory at home • 1745 Benedettina Academy • 28 papers on chemistry, physics, hydraulics, mathematics, mechanics and technology • 4 have survived This may have been what the university laboratory looked like.

**Summary** • Laura was a prominent female of the 18th century • She was the first female to teach in a European university and the first to gain a full professorship when she was appointed Chair in Experimental Physics • A medal was made in her honour • A street in Bologna is named after her • A school has been named for her

**Francesco Algoratti** Newtonism for Ladies

**Who was Algarotti?** • Algarotti was a philosopher and art critic. • He also completed engravings • He was from Italy. • He lived for 52 years only! (1712 – 1764)

**What is Philosophy?** • Philosophy comes from the Greek word ‘philosophia’meaning ‘Love of Wisdom’ • Philosophy is the study of general and fundamental problems.Eg. problems related to existence, knowledge, values, reason, mind, and language • Whats different about Philosophers and other problem solvers? • Philosphy deals with these problems using Critical, Systematic approach and therefore it relies on rational argument.

**Francesco Algarotti** • Algarotti was born on 11.12.1712 in Venice. His father was a rich merchant. • He studied natural Sciences and mathematics in Rome and Bologna. • The young 20 year old Francesco went to Paris and there he met Voltaire. There he produced his work on Optics called ‘Newtonism for Ladies’. • In 1754, after seven years' residence partly in Berlin, he returned to Italy, living at Venice and then at Pisa, where he died. • Frederick the Great erected to his memory a monument on the Campo santo at Pisa. He was "one of the first beaux esprits of the age", a man of wide knowledge, a connoisseur in art and music, and the friend of most of the leading authors of his time.

**Optics** • Branch of Physics • Study of the way light behaves • Study of light properties eg. Light interactions with matter, light dispertion (in a prism, material dispersion causes different colors to refract at different angles, slitting white light into a rainbow. • Construction of instruments that use light or detect light.

**Royal Society** • At the age of 22, Francesco was made a fellow of the Royal Society in London. • For improving general knowledge • A learned Society for science (This is an organization that promotes one or several academic disciplines) • Possibly the oldest such society in existence founded in November 1660 where the founders intended it to be a place of research and discussion. • Today Royal Society acts as a scientific advisor to the British government. • It also acts as the UK’s Academy of Sciences and funds research fellowships and scientific start-up companies. For more info on Schemes visit: http://royalsociety.org

**Maria Gaetana Agnesi**

**Childhood** • Maria Gaetana Agnesi was born in Milan on 16th May 1718. • Her father was a Professor at the University of Bologna. • Maria was able to speak Italian (her mother tongue) and French by 9, and by 13 she was able to speak in Greek, Hebrew, Spanish, German and Latin.

**Education** • Maria was educated from her early years. • Her father took her to gatherings to read and debate philosophical questions with the bright minds of the day. • Maria really wanted to join a convent. • She studied Differential and Integral Calculus and taught her brothers and sisters.

**Contributions to Mathematics** • Maria created the ‘Treatise on Analysis for the use of Italian Youth’, which was translated into English and French.

**The Witch?** • Maria’s best known contribution to mathematics was her work on a curve which Maria named “Versiera” in 1748. The name comes from the Italian “to turn”. Unfortunately the name was mistranslated and in English became known as the ‘Witch of Agnesi’, which has also followed through to Spanish.

**Versiera Curve also known as The Witch of Agnesi** • The intersection of l and m is point P. This is the point whose locus is traced, as A moves

**Parametric Equations** • Parabola • For example, the simplest equation for a parabola, • The parabola above can be written in parametric form by using a free parameter t, and setting;

**More Parametric Equations** Circle We can also write the equation of a circle with radius a where t is the angle between the x-axis and the point on the curve: Important: where t is in the range 0 to 2π.

**Integrating Parametric Equations** • We cannot do simple integration in the form • when using parametric equations we need to use the integral of the form (Comes from the chain rule). • Thus for the parabola before; = = =

**Later Years** • Pope Benedict XIV wrote to Maria to appoint her as the chair of mathematics in 1750. • In 1752 Maria’s father died and she devoted her time to charity and she did no further work on mathematics, unless as a hobby.

**Compose your own** I've got a great notion That force is a changer of motion. Let's put it this way: F equals ma The rest is just sweat and devotion.

**Compose your own** This is what Emilie is like:Beautiful; a good friend, tooImagination blossoming and trueHer mind is lively, nay, sublimeWith too much wit some of the time.She has a genius that is rareWorthy of Newton, I do swear;Yet even so she spends her daysWith all the world and its petty waysPlaying at cards with gamblers and the like."

**Philosophical Implications of Newton** Mathemetization of physics • More logical (rational) world views Experimental induction (vs. deduction by hypothesis) • More scope for sciences. Political & theological implications • The Enlightenment • Deism • Order in society

**The Enlightenment**