History of Physics Group meeting “From Newton to the free electron laser”

Lecture 8: Newton’s 1st Law – a history

Paul Ranford


Paul Ranford is a Chartered Accountant, although more-or-less retired from this career. He is also a tutor for the Open University in Business Studies and Personal Finance, and a Senior Fellow of the Higher Education Academy. About sixteen years ago he discovered a discipline called “History of Science” which has been his passion ever since. He gained a 1st Class Honours BA in “Humanities with History of Science” (with the Open University) in 2006, and then an MSc in “History and Philosophy of Science” (awarded with distinction by Imperial College and UCL) in 2008. Since then, he has continued to research and to seek ways to pass his enthusiasm for this mind-expanding subject on to others. He commenced PhD studies with UCL in October 2018.


My notes from the lecture (if they don’t make sense then it is entirely my fault)



Sir Isaac Newton FRS PRS (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a “natural philosopher”) who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

Newton was responsible for 3 major discoveries:



Thoughts on gravity

Precursors of the 1st Law

Impetus theory


The theory of impetus was an auxiliary or secondary theory of Aristotelian dynamics, put forth initially to explain projectile motion against gravity. It was introduced by John Philoponus in the 6th century and elaborated by Nur ad-Din al-Bitruji at the end of the 12th century, but was only established in western scientific thought by Jean Buridan in the 14th century. It is the intellectual precursor to the concepts of inertia, momentum and acceleration in classical mechanics.



Aristotelian physics is a form of natural science described in the works of the Greek philosopher Aristotle (384–322 BCE). In his work Physics, Aristotle intended to establish general principles of change that govern all natural bodies, both living and inanimate, celestial and terrestrial – including all motion (change with respect to place), quantitative change (change with respect to size or number), qualitative change, and substantial change (“coming to be” (coming into existence, “generation”) or “passing away” (no longer existing, “corruption”)).

To Aristotle, “physics” was a broad field that included subjects such as the philosophy of mind, sensory experience, memory, anatomy and biology. It constitutes the foundation of the thought underlying many of his works.



Galileo – Inclined plane thought experiment


Galileo’s thought experiment considered rolling balls on inclined planes in the absence of friction or other resistant forces. The speed acquired by a body moving down a plane from a height was sufficient to enable it to reach the same height when climbing up another plane at a different inclination. As the angle decreases, the body should travel a greater distance. Galileo proposed that the body could travel indefinitely far as, contrary to the Aristotelian notion of the natural tendency of an object to remain at rest unless acted upon by an external force. Therefore, Galileo can be credited with introducing the concept of inertia, later exploited by Newton.


In 1603, Galileo performed a classic experiment in mechanics: he measured the distances covered by a ball rolling on an inclined plane, which slows down the ball, compared to its free fall.


Galileo published his results in his Discourses on Two New Sciences (1638).



Galileo Galilei (15 February 1564[3] – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath.

Descartes 1644 part 2 paragraph 37


Descartes Principles appeared in Latin in 1644. The general principles of physics, in the form of his matter theory and laws of motion, were presented in Part II

He was one of the first natural philosophers to put the principle of inertia – the claim that bodies unaffected by net external forces remain at rest or move uniformly in a straight line – at the centre of his physics,

The Oxford Handbook of Philosophy of Physics https://books.google.co.uk/books?id=HX1iPDdj61EC&pg=PA524&lpg=PA524&dq=Descartes+1644+part+2+paragraph+37&source=bl&ots=81X_9d-ErQ&sig=ACfU3U011VG4Z0tyOzHRpfSSlQ8sNEFj0A&hl=en&sa=X&ved=2ahUKEwjf2ruhhJngAhVCtnEKHYr5AUQ4ChDoATAJegQIChAB#v=onepage&q=Descartes%201644%20part%202%20paragraph%2037&f=false


“The first law of nature: that each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move.”



René Descartes (31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

Between 1665 and 1667 Newton worked on his law of gravitation


In 1679, Newton returned to his work on celestial mechanics by considering gravitation and its effect on the orbits of planets with reference to Kepler’s laws of planetary motion.

Newton’s reawakening interest in astronomical matters received further stimulus by the appearance of a comet in the winter of 1680–1681, on which he corresponded with John Flamsteed. After the exchanges with Hooke, Newton worked out proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector. Newton communicated his results to Edmond Halley and to the Royal Society in De motu corporum in gyrum, a tract written on about nine sheets which was copied into the Royal Society’s Register Book in December 1684. This tract contained the nucleus that Newton developed and expanded to form the Principia.


Isaac Newton composed Principia Mathematica during 1685 and 1686, and it was published in a first edition on 5 July 1687 (with financial help from Edmond Halley). Widely regarded as one of the most important works in both the science of physics and in applied mathematics during the Scientific Revolution, the work underlies much of the technological and scientific advances from the Industrial Revolution (usually dated from 1750) which it helped to create.

In this work, Newton stated the three universal laws of motion. Together, these laws describe the relationship between any object, the forces acting upon it and the resulting motion, laying the foundation for classical mechanics.




He unified the work of Copernicus, Galileo, and Kepler into one scientific theory. He derived the 1st law from underlying principles



Newton, Halley, Christopher Wren and Robert Hooke attended a meeting at the Royal Society in January 1684.




Never at Rest: A Biography of Isaac Newton https://books.google.co.uk/books?id=3ngEugMMa9YC&pg=PA402&lpg=PA402&dq=Royal+Society+in+January+1684&source=bl&ots=rE5uWerKpO&sig=ACfU3U1qf3dTJ30dZkT5Q3WzKiOdGuxO_g&hl=en&sa=X&ved=2ahUKEwj8wdjSlpngAhUDQhUIHS-yCrYQ6AEwCXoECAkQAQ#v=onepage&q=Royal%20Society%20in%20January%201684&f=false

Hooke claimed that he could demonstrate all the laws of celestial motion from an inverse square law. Halley admitted that his own attempt to do so failed. Hooke refused to demonstrate his solution until someone else had solved it. So Halley visited Newton to consult an expert.

“In 1684 Dr Halley came to visit him at Cambridge, after they had been some time together, the Dr asked him what he thought the Curve would be that would described by the planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it. Sr Isaac replied immediately that it would be an Ellipsis (ellipse), the Doctor struck with joy & amazement asked him how he knew it, why saith he I have calculated it, whereupon Dr Halley asked him for his calculation without any farther delay, Sr Isaac looked among his papers but could not find it, but he promised him to renew it, & then to send it him …” Newton’s account to Abraham De Moivre



Abraham de Moivre (26 May 1667 – 27 November 1754) was a French mathematician known for de Moivre’s formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.

The lost paper was probably a charade. When Newton did try to repeat his solution it did not work out. A hastily drawn diagram led him to confuse the axes of the ellipse with conjugate diameters. He started again and in November of that year he sent a 9 page paper to Halley (De motu corporum in gyrum – On the Motion of Bodies in an Orbit).


Definition 1: ‘Centripetal force’ (Newton originated this term, and its first occurrence is in this document) impels or attracts a body to some point regarded as a centre. (This reappears in Definition 5 of the Principia.)

Definition 2: ‘Inherent force’ of a body is defined in a way that prepares for the idea of inertia and of Newton’s first law (in the absence of external force, a body continues in its state of motion either at rest or in uniform motion along a straight line). (Definition 3 of the Principia is to similar effect.)

Hypothesis 2: By its intrinsic force (alone) every body would progress uniformly in a straight line to infinity unless something external hinders that. (Newton’s later first law of motion is to similar effect, Law 1 in the Principia.)

There was a problem with the paper in that the dynamics was not up to the task and it had very shaky foundations but Halley recognised that it was a step forward in celestial mechanics, so great as to constitute a revolution.

Newton persisted in reworking the paper. Initially the paper contained four theorems and five problems. He revised his initial definitions and hypotheses to allow for resistance and added two problems on motion through a medium.

Newton was struggling and he returned to Descartes’ motion of inertia. By adopting the concept of inertia a test of the system was allowed and the dynamics fell into place.

Previously natural scientists believed that there needed to be a continuous transmission of force to keep a body moving at a constant speed (the impetus theory mentioned earlier). Newton’s work proved this was not the case.

Newton’s first law of motion: an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It may be seen as a statement about inertia, that objects will remain in their state of motion unless a force acts to change the motion.

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