Physics

Gravitation: from the apple to the Moon

If the apple falls, why doesn’t the Moon? Before Newton the answer seemed simple: heaven and Earth followed different rules. On Earth, things fall. In the heavens, the stars and planets turn in perfect circles forever. Newton’s great idea was to distrust that separation: perhaps the Moon is falling all the time. Newton’s cannon The apple tree in the orchard of Woolsthorpe Manor that tradition identifies as “Newton’s tree”.David Smith · Wikimedia Commons · CC BY-SA 2.0 In a draft for the Principia, Newton proposed a thought experiment. Imagine a cannon on top of a very high mountain, firing horizontally. With little powder, the ball lands nearby. With more, it lands further away. But the Earth is round: if the ball is fast enough, the ground curves away beneath it exactly as fast as it falls. The ball falls forever and never reaches the ground. It is in orbit.

October 11, 2026 Read

Image credits

Historical images All come from Wikimedia Commons. We use the thumbnails provided by Commons; the largest were reduced to 1,200 pixels wide, with no other editing. Portrait of Einstein in 1921, possibly by Herman Mishkin, used by the Nobel Foundation: source page · public domain. Einstein around 1904, in Bern, photo by Lucien Chavan: source page · public domain. Einstein at the National Museum, Rio de Janeiro, 7 May 1925, unknown author: source page · public domain. Einstein in the Botanical Garden of Rio de Janeiro, May 1925, unknown author: source page · public domain. The instruments of the expedition in Sobral, 1919, photo by Charles Davidson: source page · public domain. Plate of the 1919 eclipse, from the report by Dyson, Eddington and Davidson: source page · public domain. Blog figures The cover, the diagram of the light clock and the 2,000-step random walk are original illustrations, with versions in each of the site’s languages. The light-clock diagram was redrawn from a figure in this site’s old course on the theory of relativity, which is also the source of the examples of the astronaut and of the cosmic-ray particles. The random walk was generated by computer, with randomly drawn directions.

October 14, 2026 Read

The legacy of James Clerk Maxwell

This change in the conception of reality is the most profound and the most fruitful that physics has experienced since the time of Newton. — Albert Einstein, at Maxwell's centenary (1931) Maxwell died at 48, little known to the general public. In his lifetime, hardly anyone outside a small group of British physicists accepted his field theory. Today anyone using a mobile phone depends on it dozens of times a second.

October 14, 2026 Read

Pascal's principle: multiplying forces with water

An elephant and a woman in high heels: who sinks deeper into soft ground? It may be the woman. The elephant weighs fifty times more, but its weight spreads over four broad feet. Hers is concentrated on the thin tip of a heel. What sinks into the ground is not force but pressure: the force divided by the area it rests on. $$p=\frac FA.$$The unit of pressure is the pascal: $1\ \text{Pa}=1\ \text{N/m}^2$, a force of one newton spread over one square metre. It is a tiny pressure; at sea level the atmosphere exerts about $100{,}000$ Pa.

October 11, 2026 Read

Light and colours: the prism does not make the rainbow

In Newton’s time it was already known that a glass prism, with sunlight passing through it, produces a coloured band. The accepted explanation came from Aristotle and Descartes: white light is pure, and the glass modifies it, darkening it little by little. A small modification gave red; a large one, blue and violet. Newton had his doubts. What if the colours were already inside white light, and the prism merely separated them?

October 11, 2026 Read

Image credits

Historical images and photographs All come from Wikimedia Commons. We use the thumbnails provided by Commons, unedited. Portrait of Maxwell, engraving by G. J. Stodart, 1890: source page · public domain. The tartan ribbon, the first colour photograph, by Maxwell and Thomas Sutton, 1861: source page · public domain. Saturn seen from above, by the Cassini spacecraft, 2013: NASA/JPL-Caltech/Space Science Institute, source page · public domain. Michael Faraday, photograph from the 1850s, unknown author: source page · public domain. Title page of the Treatise on Electricity and Magnetism, Oxford, 1873: source page · public domain. The statue of Maxwell with his dog Toby, in Edinburgh, photo by Зеленый кабинет: source page · CC BY-SA 2.0. Blog figures The cover, the wave profile and the graph of the Maxwell distribution for nitrogen are original illustrations, with versions in each of the site’s languages. The graph was calculated with the exact formula of the distribution. The discussion of quaternions and vectors, in the post on the equations, draws on passages from this site’s old course on vectors.

October 14, 2026 Read

The weight of air: the Puy de Dôme experiment

For two thousand years scholars repeated a saying of Aristotle’s: nature abhors a vacuum. If you suck the air out of a straw, the liquid rises because nature will not let the space stay empty. It seemed to explain everything. But the well-diggers of Florence had a problem. Suction pumps could not raise water more than about 10 metres, however hard they tried. Why would nature’s horror of the vacuum stop at 10 metres?

October 11, 2026 Read

Newton's legacy

Newton was the greatest genius who ever lived, and the most fortunate, for there is only one universe to discover, and it can be discovered only once. — Joseph-Louis Lagrange, as reported by his contemporaries The calculus war Newton created the method of fluxions in 1665–1666 but did not publish it. Leibniz reached calculus independently in 1675 and published in 1684. For some years nobody quarrelled. In 1676 the two even exchanged cordial letters through Henry Oldenburg, and Newton hid his ideas in an anagram.

October 11, 2026 Read

Pascal's legacy

The heart has its reasons, which reason does not know. — Blaise Pascal, Pensées Pascal left few finished books. Almost everything he wrote on mathematics came out as loose sheets, in letters or after his death. Even so, few authors turn up in so many different places: in the triangle at school, in the weather forecast, in a car’s brakes, in an insurance calculation and even in the name of a programming language.

October 11, 2026 Read

Pascal image credits

Historical images All of them come from Wikimedia Commons. We use the thumbnails provided by Commons, unedited. Portrait of Blaise Pascal, unknown artist, around 1690, Versailles: source page · public domain. Yang Hui’s triangle, in Zhu Shijie’s book, 1303: source page · public domain. First page of the Triangulus arithmeticus, copy held by Clermont Auvergne Métropole: source page · CC BY-SA 4.0. Pascaline at the Musée des Arts et Métiers, photo by David Monniaux, 2005: source page · CC BY-SA 3.0. Marker of the experiment on the Puy de Dôme, Agence Rol, 1923, Bibliothèque nationale de France: source page · public domain. Plaque of the grave in Saint-Étienne-du-Mont, Agence Meurisse, 1923, Bibliothèque nationale de France: source page · public domain. Autograph manuscript of the Pensées, exhibition at the Bibliothèque nationale de France, photo by ActuaLitté, 2016: source page · CC BY-SA 2.0. First page of the Pensées, counterfeit of the 1670 edition, copy held by Clermont Auvergne Métropole: source page · CC BY-SA 4.0. Blog figures The cover, the fountain of bowls, the carry diagram and the cycloid arch are original illustrations. The controls for the triangle, the split of the stakes and the hydraulic press were made for this trail. They are teaching aids, not reproductions of manuscripts or of the internal mechanism of the Pascaline.

October 11, 2026 Read