John Tyndall

How to use this course

John Tyndall is remembered today mostly for one set of measurements. In 1859 he showed that the transparent gases of the air differ enormously in how they absorb radiant heat, and that water vapour and carbonic acid, though minor constituents, control how much of the Earth’s heat escapes. Climate science starts there. Yet Tyndall was also a leading student of diamagnetism and glaciers, the discoverer of the scattering effect that bears his name, an ally of Louis Pasteur against spontaneous generation, a first-class mountaineer, and one of the great science lecturers of the nineteenth century.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations in modern notation and exercises with folded solutions. Tyndall wrote little mathematics himself. His strength was the design of sensitive experiments, so the lessons pair his measurements with the theory that later explained them.

Timeline

Carlow and the Survey, 1820–1847

John Tyndall was born on 2 August 1820 at Leighlinbridge in County Carlow, in the south-east of Ireland. His father, also John, was a local police constable who had worked as a shoemaker. The family was Protestant, descended from settlers who had come from Gloucestershire in the seventeenth century, and the boy grew up with a strong sense of that identity. He attended the national school in Carlow until about nineteen and seems to have served there as an assistant teacher. The school gave him a solid training in arithmetic, geometry, technical drawing and the mathematics of land surveying.

In 1839 he joined the Ordnance Survey of Ireland as a draughtsman and surveyor. In 1842 he moved to the English survey in Lancashire. He was dismissed in 1843 after joining a protest by survey workers over pay and conditions. The railway boom then gave him well-paid work from 1844 planning lines for a Lancashire firm. Through these years he read widely, attended mechanics’ institute lectures, and taught himself science from books. He kept a journal that records a habit of self-examination and a strong ambition to learn.

The surveying years left two lasting traits. He became an expert with instruments and with careful, repeated measurement in the field, which later served him on glaciers. He also developed the physical endurance of a man who had walked hills all day, which served him on mountains.

Queenwood and Marburg, 1847–1853

When the railway boom collapsed in 1847, Tyndall took a post teaching mathematics and surveying at Queenwood College, a progressive boarding school in Hampshire run by George Edmondson. The school had a laboratory, and its chemistry teacher was Edward Frankland, later a leading chemist. The two young men decided that the way to a scientific career ran through Germany.

In 1848 they went to the University of Marburg, drawn by the reputation of the chemist Robert Bunsen. Tyndall studied there until 1850, attending Bunsen’s lectures and laboratory and working through mathematics and physics at a pace he found exhausting. His doctoral dissertation, completed in 1850, was a mathematical study of screw surfaces, supervised by the mathematician Friedrich Ludwig Stegmann. The physicist Hermann Knoblauch introduced him to experimental research, and their first joint paper, on the behaviour of crystals in a magnetic field, appeared in 1850. Tyndall later also worked with Heinrich Gustav Magnus in Berlin, whose laboratory was one of the best in Europe for physics.

Back in England in 1851, he returned to teaching at Queenwood while continuing his research on diamagnetism. He was elected a Fellow of the Royal Society in 1852 on the strength of that work. An application for a chair at Toronto, among others, failed. His career turned instead on a single lecture.

The Royal Institution, 1853–1859

In February 1853 Tyndall gave a Friday Evening Discourse at the Royal Institution in Albemarle Street, London, on the influence of material aggregation on magnetic force. The audience and Michael Faraday were impressed. That year he was appointed Professor of Natural Philosophy at the Institution, and the Royal Society awarded him a Royal Medal. He held the professorship until 1887.

The Royal Institution was unlike a university. It had a small research laboratory, a lecture theatre and a fashionable paying audience. Its professors were expected to do original research and to explain science to the public. Tyndall did both brilliantly. He became Faraday’s friend and protégé, watched his methods closely, and later wrote a memoir of him, Faraday as a Discoverer (1868).

In 1856 he went to the Alps with the biologist Thomas Henry Huxley to study the banded structure of glacier ice. The trip began two lifelong passions, for glaciers and for climbing, and a friendship with Huxley that made the two men leaders of scientific naturalism in Victorian Britain. In 1859 Tyndall turned to the question that would make him permanently famous: does the atmosphere absorb radiant heat?

Diamagnetism and crystal structure

For the general reader. In 1845 Faraday found that bismuth, glass and many other materials are weakly repelled by a magnet. Soon after, Julius Plücker found that crystals of such materials also turn to a preferred direction between the poles. Tyndall’s first research showed that this turning depends on how the material is packed together, not on the crystal form as such, and he argued that diamagnetism is a genuine induced polarity, the mirror image of ordinary magnetism.

Linear magnetization

For a weakly magnetic, linear material of volume susceptibility \(\chi\) with \(|\chi|\ll1\), the magnetization in an applied field \(\mathbf B\) is \(\mathbf M\approx\chi\mathbf B/\mu_0\). Diamagnets have \(\chi<0\), paramagnets \(\chi>0\).

Derivation. The work done to magnetize a linear material of small \(\chi\) in an external field is half the dipole energy \(-\mathbf m\cdot\mathbf B\), with \(\mathbf m=\chi V\mathbf B/\mu_0\). This gives \(U\). Differentiating with respect to position gives the force, and with respect to angle the torque. Note that only \(\chi_\parallel-\chi_\perp\) matters for the torque. A diamagnetic crystal therefore sets its least diamagnetic axis along the field, even though the whole body is repelled.

Tyndall and Knoblauch

Plücker had proposed in 1847 that the optic axis of a crystal is repelled by the poles. Knoblauch and Tyndall (1850) found exceptions, and Tyndall went on to show that the effect follows the direction of closest packing. He compressed powders of bismuth and of iron carbonate and found that the compressed slabs behaved like crystals: for a diamagnet, the line of compression set itself perpendicular to the field; for a paramagnet, along it. In modern terms, pressure makes the susceptibility anisotropic. In his Bakerian Lecture of 1855 he argued, against Wilhelm Weber’s critics and against Faraday’s own doubts, that diamagnetic bodies acquire a reversed polarity, a north pole facing the north pole of the magnet. Quantum theory later explained diamagnetism as the orbital response of electrons, described by Larmor precession, and confirmed that the induced moment opposes the field.

Glaciers and regelation

For the general reader. A glacier is solid ice, yet it flows down a valley like a very slow river, faster in the middle than at the sides. James David Forbes explained this by treating ice as a viscous fluid. Tyndall argued that ice cannot stretch like honey. It cracks under tension, and melts under pressure and refreezes when the pressure is released. This refreezing, called regelation, had been described by Faraday. The modern picture keeps parts of both views.

Field work

Tyndall and Huxley published a joint paper on the structure and motion of glaciers in the Philosophical Transactions for 1857. Tyndall returned to the Mer de Glace above Chamonix in 1857 and 1858, measuring the motion of stakes with a theodolite, the instrument of his surveying years. He confirmed Forbes’s finding that the centre moves faster than the sides, and found that the line of fastest motion swings toward the outer side of each bend, as in a river. He explained the blue veins of glacier ice as a product of pressure, and crevasses as tension fractures. His book The Glaciers of the Alps appeared in 1860. The controversy with Forbes, and with Forbes’s defender Peter Guthrie Tait, became bitter.

Regelation. Where two blocks of ice are pressed together, or where ice is forced against a rock, the melting point drops slightly, a thin film melts, the water flows to a region of lower pressure and refreezes there. Tyndall used this to explain how fractured ice welds itself together and moulds itself to the valley. Modern glaciology agrees that regelation helps glaciers slide past small bumps on their beds. But most internal motion of a temperate glacier comes from creep, the slow plastic deformation of ice crystals, which is closer to Forbes’s viscous picture with a non-linear viscosity.

Derivation. In simple shear \(du/dz=2\dot\varepsilon=2A\tau^n\), where \(z\) is height above the bed and \(\tau=\rho g(H-z)\sin\alpha\). Integrating from \(z=0\) (where \(u=0\)) to \(z=H\) gives \(u_s=2A(\rho g\sin\alpha)^n\int_0^H(H-z)^n\,dz\), which is the formula above.

Radiant heat in gases: the differential method

For the general reader. Joseph Fourier had argued in the 1820s that the atmosphere keeps the Earth warmer than it would otherwise be, and Claude Pouillet had estimated how much solar heat the air absorbs. Nobody had measured whether the gases of the air absorb the invisible heat rays that the Earth gives off. Earlier attempts had given contradictory answers because the effect in dry air is tiny. Tyndall’s achievement in 1859 was an instrument sensitive enough to settle the question.

The apparatus

The source was a copper cube filled with boiling water, later a copper plate heated by a gas flame to about 270 °C. Its radiation passed through a long tube closed at both ends by plates of rock salt, which unlike glass is transparent to infrared. In the 1861 apparatus the tube was polished brass, four feet long and 2.4 inches in diameter; the 1862 version used glass. The tube could be evacuated or filled with a chosen gas at a measured pressure, given as a “tension” in inches of mercury. The detector was a thermopile, a stack of bismuth–antimony junctions developed by Macedonio Melloni, connected to a sensitive galvanometer.

The key idea was the second source. A compensating cube radiated onto the other face of the thermopile. With the tube evacuated, Tyndall adjusted a screen until the two radiations balanced and the galvanometer read zero. Admitting gas to the tube removed part of one beam, and the needle swung by an amount that measured the absorbed heat directly, instead of as a tiny difference between two large readings.

Results of 1859–1861

Experiments began on 9 May 1859. On 18 May Tyndall wrote in his journal that the subject was completely in his hands. He sent a preliminary note to the Royal Society on 26 May and gave a Royal Institution discourse on 10 June. The full account was his Bakerian Lecture, read on 7 February 1861. Dry air, oxygen, nitrogen and hydrogen absorbed almost nothing. Compound gases absorbed far more: at a tension of 5 inches, carbonic acid absorbed about 150 times as much as oxygen, and olefiant gas (ethylene) about a thousand times as much as hydrogen. For small quantities the absorption was proportional to the amount of gas; at larger tensions it grew more slowly. He also found that the absorption of ozone-containing oxygen was several times that of ordinary oxygen.

Air taken directly from the laboratory, with its moisture and carbonic acid, absorbed about fifteen times as much as dried air. Tyndall drew the conclusion that changed meteorology. Water vapour, although invisible and transparent to light, is a strong absorber of radiant heat.

Greenhouse gases and climate

For the general reader. Tyndall’s tables showed that the nitrogen and oxygen that make up 99% of the air are almost transparent to heat rays, while water vapour, carbonic acid and some other gases present in small amounts absorb strongly. He concluded that the atmosphere lets in the Sun’s heat but checks its escape, and that changes in these minor gases could change the climate. This lesson places his numbers in the modern theory of the greenhouse effect.

The table of 1862

In his second memoir (read 30 January 1862) Tyndall gave the absorption of a column of gas at one atmosphere, with dry air as 1:

He also found that moist air absorbed up to sixty or eighty times as much as dry air, and estimated that most of the absorption of ordinary laboratory air came from its water vapour. He argued that water vapour explains why deserts and high mountains, where the air is dry, cool sharply at night. In the 1861 lecture he suggested that changes in the amount of water vapour, carbonic acid and hydrocarbons in the air could have produced the changes of climate that geologists had found in the record of the rocks.

The numbers depend on the source. A plate at 270 °C radiates mainly between 3 and 15 µm, while the Earth radiates mainly between 5 and 50 µm. The gases are also compared at equal pressure, whereas in the atmosphere they occur at very different amounts. So the table ranks absorbing power, not climate effect. Its lasting point is qualitative and correct. Symmetric diatomic molecules such as N₂ and O₂ have no changing dipole moment when they vibrate, so they hardly absorb infrared. Molecules with three or more atoms, or with unlike atoms, do.

Priority deserves a note. In 1856 the American experimenter Eunice Newton Foote reported that a glass cylinder of carbonic acid heated more in sunlight than one of ordinary air. Her experiment did not separate visible from infrared radiation, and Tyndall’s papers do not cite it. Tyndall’s work was the first to measure the absorption of radiant heat by gases quantitatively.

Derivation. At the top of the atmosphere, \(\sigma T_e^4=(1-\varepsilon)\sigma T_s^4+\varepsilon\sigma T_a^4\). For the layer, absorbed equals emitted: \(\varepsilon\sigma T_s^4=2\varepsilon\sigma T_a^4\), so \(T_a^4=T_s^4/2\). Substituting, \(\sigma T_e^4=\sigma T_s^4(1-\varepsilon/2)\), which gives the result. With \(\varepsilon=1\), \(T_s=2^{1/4}T_e\approx303\) K.

From Tyndall to Arrhenius

In 1896 Svante Arrhenius combined absorption measurements with an energy-balance calculation and estimated the warming from changes in carbonic acid. Modern line-by-line calculations give the radiative forcing of CO₂ in the approximate form \(\Delta F\approx5.35\ln(C/C_0)\ \mathrm{W\,m^{-2}}\) (Myhre and colleagues, 1998). The logarithm comes from saturation: the centre of the 15 µm band is already opaque, and added CO₂ widens the band at its wings.

Absorption, emission and the fourth power

For the general reader. A gas that absorbs heat rays well also gives them out well when it is warm. Tyndall showed this with gases that had no external source at all, warmed only by being compressed into his tube. His careful measurements of the heat radiated by a glowing platinum wire later gave Josef Stefan the clue to the law that radiated power rises as the fourth power of temperature.

Dynamic radiation

Tyndall arrived at the same principle from the dynamical theory of heat. A molecule that can take up the motion of the ether waves must be able to give it back. To test it he let gas rush into the evacuated tube. The compression warmed the gas slightly, and the warm gas radiated onto the thermopile. Pumping it out cooled it, and the pile registered the reverse. The order of radiating powers matched the order of absorbing powers, gas by gas. He also showed that ether and other vapours absorb in the same order whether in the gaseous or the liquid state, evidence that absorption is a property of the molecule.

Calorescence

Tyndall filtered the light of an electric arc through a solution of iodine in carbon disulphide, which is opaque to visible light but transparent to infrared. Focusing the invisible rays, he could ignite paper and heat platinum foil to a glow. He called this conversion of invisible rays into visible light calorescence. It showed that the radiant heat in the arc’s beam and visible light differ only in wavelength.

Tyndall measured in 1864 how the radiation of an electrically heated platinum wire grew as it went from a faint red glow to white heat. Adolph Wüllner’s textbook attached temperatures of about 525 °C and 1200 °C to these states, and reported that the radiation rose from 10.4 to 122 units. Stefan noted that this ratio of nearly 12 fitted a fourth-power law, and used it, with older cooling data of Dulong and Petit, to propose \(T^4\) in 1879. Ludwig Boltzmann derived the law from thermodynamics and Maxwell’s radiation pressure in 1884.

Scattering and the blue sky

For the general reader. To clean his gases, Tyndall needed to know whether they contained dust. A strong beam of light shows floating particles as a bright track. In 1868–69 he made “actinic clouds” by letting light decompose vapours in a tube. When the particles were very fine, the cloud looked blue from the side and the scattered light was polarized, just like skylight. Scattering of light by fine particles is now called the Tyndall effect. Lord Rayleigh supplied the theory in 1871.

The experiments

Tyndall filled a glass tube with a dilute vapour such as amyl nitrite, or iodide of allyl, and sent the concentrated light of an electric lamp along it. Light decomposed the vapour and precipitated a cloud of extremely small particles. At first the cloud scattered a delicate blue, and the light scattered at right angles to the beam was almost completely polarized. As the particles grew, the colour whitened and the polarization weakened. He reported these results in 1869 and proposed that the blue of the sky comes from very fine particles in the air. He also found a puzzle he called the residual blue, a component that did not vanish at the angle of maximum polarization.

Dimensional argument. The incident field induces a dipole \(p\propto a^3E_0\). The radiated field of an oscillating dipole is proportional to its second time derivative, hence to \(\omega^2p\), and falls off as \(1/r\). The intensity is then proportional to \(\omega^4a^6/r^2\), that is, to \(a^6/(\lambda^4r^2)\). Rayleigh used exactly this reasoning. The angular factor comes from the dipole radiation pattern: the component of incident polarization perpendicular to the scattering plane scatters equally in all directions in that plane (factor 1), the component in the plane scatters as \(\cos^2\theta\).

In 1899 Rayleigh showed that the air molecules themselves, without any dust, scatter enough to make the sky blue. Tyndall’s particles were the right idea at the wrong scale. Today “Tyndall scattering” refers to colloids and aerosols with particles comparable to the wavelength, which scatter much more strongly and less selectively, and “Rayleigh scattering” to particles far smaller. Tyndall’s beam test also became the basis of the nephelometer and of the ultramicroscope (Siedentopf and Zsigmondy, 1902–1903).

Floating matter and sterilization

For the general reader. Do microbes arise spontaneously in a nutrient broth, or do they come from germs already present in the air? In the 1870s Tyndall used his light beam to show when air was free of particles, and showed that broths kept in such air stayed clear indefinitely. When some boiled broths still spoiled, he found that hay carried bacterial spores that survive hours of boiling, and devised a way to kill them by repeated heating. The method is called tyndallization.

Optically pure air

Tyndall built wooden chambers with glass windows, their inner walls smeared with glycerine. When the chamber was left still for a few days, the dust settled and stuck. A beam sent through the chamber then left no visible track: the air was optically pure. Broths boiled and placed in such chambers stayed sterile for months, while the same broths exposed to ordinary air putrefied within days. This supported Pasteur’s view against Henry Charlton Bastian, who claimed to observe spontaneous generation. In 1876 Tyndall found that some infusions, prepared when hay had been brought into the laboratory, could not be sterilized by boiling for long periods. He concluded that the air carried germs in a resistant phase, which we now call endospores. The same year the German botanist Ferdinand Cohn described the heat-resistant spores of Bacillus subtilis.

Intermittent sterilization

Vegetative bacteria have \(D\) of seconds at 100 °C; some spores have \(D\) of many minutes or more at that temperature. Tyndall heated the infusion briefly, let it stand for a day so that surviving spores germinated into heat-sensitive cells, then heated again, repeating several times. Each heating kills the cells that have germinated. Laboratories and the canning industry later preferred the autoclave, which uses steam under pressure at about 121 °C, but tyndallization is still used for materials that cannot tolerate high temperatures.

Superintendent and public scientist

In 1867, after Faraday’s death, Tyndall succeeded him as Superintendent of the Royal Institution, in charge of its house and laboratory. From 1865 he was also scientific adviser to Trinity House, the authority for lighthouses, and later to the Board of Trade. He studied lighthouse illumination and, in experiments at the South Foreland in 1873, the audibility of fog signals. He found that air which looks clear can be acoustically opaque, because currents of different temperature and humidity break up sound. He resigned these advisory posts in the 1880s after disputes over lighthouse policy.

Tyndall was among the most gifted science lecturers of the century. His books Heat Considered as a Mode of Motion (1863), Sound (1867), The Forms of Water (1872) and Six Lectures on Light (1873) went through many editions and translations. His demonstrations included the guiding of light inside a curved stream of water by total internal reflection, earlier described by Jean-Daniel Colladon in 1842. He promoted the work of Julius Robert Mayer on the conservation of energy, which drew him into a fierce priority dispute with Tait and William Thomson. He also arranged for translations of Hermann von Helmholtz and Rudolf Clausius to reach English readers.

In 1864 he was one of the founders of the X Club, a dining club of nine scientists including Huxley, Joseph Dalton Hooker, Herbert Spencer and Frankland, which pressed for professional, secular science. His American lecture tour of 1872–73 drew large audiences; he left the proceeds in trust to support American science, and they later funded fellowships at Columbia, Harvard and the University of Pennsylvania. As President of the British Association he gave the Belfast Address on 19 August 1874. It defended evolution and claimed for science the whole domain of cosmological theory, and it was denounced from many pulpits.

Hindhead, death and legacy

In 1876, aged 55, Tyndall married Louisa Charlotte Hamilton, daughter of Lord Claud Hamilton. They built a chalet at Belalp above the Rhône valley in 1877 and spent their summers there. In 1885 they moved to a house at Hindhead, near Haslemere in Surrey. Insomnia and digestive illness troubled Tyndall increasingly, and he retired from the Royal Institution in 1887. In politics he was a vehement opponent of Irish Home Rule.

On 4 December 1893 Louisa gave him a large dose of chloral hydrate in mistake for magnesia. He recognized the mistake at once, and died that evening despite attempts to save him. He was 73. He was buried at Haslemere. Louisa survived him by almost half a century and devoted much of that time to his papers, though the planned official biography appeared only in 1945, by Arthur Stewart Eve and Clarence Hamilton Creasey.

Legacy

• Climate: the first quantitative measurements of infrared absorption by gases, the identification of water vapour as the main absorber, and the suggestion that changing atmospheric composition could change climate. The Tyndall Centre for Climate Change Research in the United Kingdom bears his name.
• Optics: the Tyndall effect, the nephelometer, and an experimental tradition of light scattering that led to Rayleigh’s theory.
• Biology: optical proof of germ-free air, support for germ theory, and intermittent sterilization.
• Glaciology and mountaineering: field measurements of glacier motion, regelation, and first ascents in the golden age of alpinism.
• Honours: Fellow of the Royal Society (1852), Royal Medal (1853), Rumford Medal (1864), several Bakerian Lectures. Mountains and glaciers in Chile, New Zealand and North America, and a lunar crater, carry his name.

Sources and further reading

Biography

1. John Tyndall, Wikipedia (detailed, with references).
2. John Tyndall papers, Royal Institution, archival biographical history (AIM25).
3. R. Jackson, The Ascent of John Tyndall: Victorian Scientist, Mountaineer, and Public Intellectual, Oxford University Press, 2018.
4. A. S. Eve and C. H. Creasey, Life and Work of John Tyndall, Macmillan, 1945.
5. B. Lightman and M. S. Reidy (eds.), The Age of Scientific Naturalism: Tyndall and His Contemporaries, Pickering & Chatto, 2014.
6. J. Tyndall, Faraday as a Discoverer, Longmans, 1868.

Physics

1. J. Tyndall, The Bakerian Lecture: On the absorption and radiation of heat by gases and vapours, Phil. Trans. R. Soc. 151 (1861).
2. J. Tyndall, On the absorption and radiation of heat by gaseous matter, second memoir, Phil. Trans. R. Soc. 152 (1862).
3. J. Tyndall, Fourth memoir on absorption and radiation by gaseous and liquid matter, Phil. Trans. R. Soc. (1864).
4. J. Tyndall and T. H. Huxley, On the structure and motion of glaciers, Phil. Trans. R. Soc. 147 (1857).
5. J. Tyndall, On the blue colour of the sky, the polarization of skylight, and on the polarization of light by cloudy matter generally, Proc. R. Soc. 17 (1869).
6. J. Tyndall, Contributions to Molecular Physics in the Domain of Radiant Heat, Longmans, 1872.
7. J. Tyndall, Essays on the Floating-Matter of the Air in Relation to Putrefaction and Infection, Longmans, 1881.
8. S. Arrhenius, On the influence of carbonic acid in the air upon the temperature of the ground, Phil. Mag. 41 (1896).
9. Lord Rayleigh, On the light from the sky, its polarization and colour, Phil. Mag. 41 (1871).
10. Tyndall effect and Stefan–Boltzmann law (history sections), Wikipedia.
11. G. Myhre, E. J. Highwood, K. P. Shine, F. Stordal, New estimates of radiative forcing due to well mixed greenhouse gases, Geophys. Res. Lett. 25 (1998).
12. S. Weart, The Discovery of Global Warming: The Carbon Dioxide Greenhouse Effect, American Institute of Physics.