The Spread of Newtonian Science

The Scientific Revolution Before Newton

Copernicus (1473 – 1543)• Heliocentric universeKepler (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 Theophilus Desaguliers

• 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 a public experimental lecturer in London.

• Desaguliers became 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.

Desaguliers was 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;

‘Gainst Mathematicks she has no Defence,

And yield t’experimental Consequence:

His tow’ring Genius, from its certain Cause,

Ev’ry Appearance, a priori draws,

And shews th’ Almighty Architect’s unalter’d Laws.

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

Desaguliers as an engineerThe 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 GravitationIsaac 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.

Do you recognise the answer?

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.

Emilie du Châtelet

• 1706 – 1749• Born in Paris, France• Feminist • French mathematician,

physicist, and author during The Age of Enlightenment

EducationEarly 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

EducationFather was a lawyerChild prodigyGaetano TacconiFranceso Maria Zanotti1732 admitted to the Bologna Academy of ScienceDegree in PhilosophyBecame 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

CircleWe 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.

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."

Compose your own

Philosophical Implications of Newton

Mathemetization of physics• More logical (rational) world viewsExperimental induction (vs. deduction by

hypothesis)• More scope for sciences.Political & theological implications• The Enlightenment• Deism• Order in society

The Enlightenment