C. T. R. Wilson

How to use this course

C. T. R. Wilson was a meteorologist by temperament and a physicist by training. He set out to reproduce in the laboratory the clouds and coloured rings he had seen on a Scottish mountain. That project led him to discover that ions act as seeds for cloud droplets, to measure the slow natural ionization of the air, and in 1911 to photograph, for the first time, the path of a single alpha particle or electron. His cloud chamber was the main visual detector of nuclear and particle physics for forty years. Alongside it he worked all his life on the electricity of thunderstorms, and some of his ideas there were confirmed only in the 1990s.

This course follows his physics roughly in the order he did it. Each result is derived with modern tools and set beside the evidence Wilson actually had. It links closely to the companion courses on J. J. Thomson, who used Wilson’s clouds to measure the charge of the electron, and on Ernest Rutherford, whose laboratory made the chamber a working tool.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Lessons 05 and 07, on nucleation and on particle tracks, are the centre of the course. Lesson 10 turns from the laboratory to the sky.

Timeline

Glencorse and Manchester, 1869–1888

Charles Thomson Rees Wilson was born on 14 February 1869 at Crosshouse, a hill farm in the parish of Glencorse on the edge of the Pentland Hills, south of Edinburgh. His father, John Wilson, was a sheep farmer; his mother was Annie Clark Harper.

John Wilson died in 1873, when Charles was four. His mother took the family to Manchester. An older half-brother helped to support his education. Charles went to a private school and in 1884, at fifteen, entered Owens College, the forerunner of the University of Manchester.

He meant to become a doctor and studied mainly biology, together with geology and some physics and chemistry. He graduated BSc in 1887. In 1888 he won an entrance scholarship to Sidney Sussex College, Cambridge. It was at Cambridge that he turned to physics.

Cambridge and Ben Nevis, 1888–1895

At Cambridge Wilson read natural sciences and moved towards physics and chemistry. In 1892 he took a First in both parts of the Natural Sciences Tripos. He began research at the Cavendish Laboratory under J. J. Thomson, and in 1894 taught for a time at Bradford Grammar School before returning to Cambridge.

The mountain

In September 1894 Wilson spent a fortnight as a temporary observer at the meteorological observatory on the summit of Ben Nevis, the highest point in Britain. The observatory, opened in 1883, recorded weather hourly in all conditions. The summit is often in cloud. When the sun broke through, Wilson saw coloured rings around the sun or moon, called coronas, and coloured rings around the shadow of his own head cast on the cloud below, called glories. He resolved to make such clouds in the laboratory and study the optics.

Back at the Cavendish early in 1895, he built an apparatus to expand moist air suddenly. Expansion cools the air, and the cooled air holds more water vapour than is stable: it is supersaturated. John Aitken had shown in the 1880s that in ordinary air the excess vapour condenses on dust particles. Wilson removed the dust by repeated expansions, each of which carried dust down with the drops. He then found that clean air still formed a few drops once the expansion passed a sharp threshold, and a dense fog at a higher one. In May 1895 he reported the result to the Cambridge Philosophical Society. The question of what those few drops formed on would occupy him for the next five years.

The Cavendish years, 1895–1911

Wilson’s hypothesis was that the few drops formed on ions, molecules carrying an electric charge. Wilhelm Röntgen announced X-rays at the end of 1895. Early in 1896 Wilson exposed his apparatus to an X-ray tube and saw a dense rain of drops at the same threshold expansion. At the same time Thomson and Rutherford were showing that X-rays make air conducting by producing ions. The nuclei were ions. Wilson went on to show that uranium rays and ultraviolet light produce the same effect, and in 1899 that negative ions are more effective nuclei than positive ones (Lessons 04 and 05).

At the end of 1896 he was elected to the Clerk Maxwell Studentship, Cambridge’s main research award in physics. Thomson used the cloud method in 1898 and 1899 to estimate the charge on gaseous ions, and so on the electron. Wilson then spent about a year on atmospheric electricity for the Meteorological Council, and in 1900–01 measured the natural ionization of air in closed vessels, at Cambridge and near Peebles in Scotland (Lesson 06).

In 1900 he was elected a Fellow of the Royal Society and a Fellow of Sidney Sussex, and became a University Lecturer and Demonstrator. For the next eighteen years he ran the advanced practical physics class at the Cavendish and lectured on light. His own research went on with simple, home-made apparatus. In 1908 he married Jessie Fraser Dick. In early 1911, sixteen years after the first expansions, he saw and photographed the trails of droplets left by single alpha and beta particles (Lesson 07).

Making clouds by expansion

For the general reader. Air rising in the atmosphere expands and cools, and when it cools enough, its water vapour condenses into cloud. Wilson reproduced this in a glass vessel by letting the air expand suddenly. He measured exactly how much expansion was needed for drops to appear, and found three distinct thresholds: one for dust, one for ions, and one for perfectly clean air. These thresholds were the foundation of everything he later built.

Adiabatic cooling

Wilson’s chamber held air saturated with water vapour above a water surface. A piston or diaphragm dropped suddenly, increasing the volume from \(V_1\) to \(V_2\). The expansion ratio is \(r=V_2/V_1\). The expansion is fast enough that little heat flows in from the walls, so it is adiabatic.

The partial pressure of water vapour falls in proportion to the density, \(p_2=p_1/r\), where \(p_1=e_s(T_1)\) is the saturation pressure at the starting temperature. The saturation pressure at the new temperature, \(e_s(T_2)\), falls much faster, because it depends exponentially on temperature.

Derivation. \(S=\dfrac{e_s(T_1)/r}{e_s(T_2)}\), and the ratio \(e_s(T_1)/e_s(T_2)\) follows from integrating \(d\ln e_s/dT=L/(R_vT^2)\) between \(T_2\) and \(T_1\). Once drops form, latent heat warms the gas and the supersaturation falls, so \(S\) is the peak value just after expansion.

Wilson’s thresholds

Starting from room temperature, Wilson found in his 1897 and 1899 papers:

• below \(r\approx1.25\), clean air formed no drops;
• at \(r\approx1.25\), a few drops appeared, on negative ions;
• at \(r\approx1.31\), positive ions also became nuclei;
• above \(r\approx1.38\), a dense fog formed in air with no ions, as molecular clusters themselves grew into drops.

With X-rays, the number of drops at the ion thresholds rose enormously, but the thresholds stayed the same. That pointed to ions as the nuclei, with a fixed property that set the threshold.

Why droplets need nuclei

For the general reader. A droplet of just a few molecules evaporates almost at once, because molecules escape easily from a sharply curved surface. That is why clean air can hold several times more vapour than it should without forming cloud. An electric charge changes the balance: it attracts water molecules and holds a tiny droplet together. Wilson’s thresholds measure exactly how much help the charge gives.

The Kelvin equation

Consider a spherical drop of radius \(r\) in vapour. To add \(dN\) molecules the drop must enlarge its surface, costing energy \(\gamma\,dA\), where \(\gamma\) is the surface tension. Balancing chemical potentials of the liquid in the drop and the vapour gives the result William Thomson (Lord Kelvin) found in 1871.

Derivation. The pressure inside the drop exceeds the outside pressure by \(2\gamma/r\) (Laplace). Raising the pressure on a liquid of molar volume \(M/\rho\) by \(\Delta P\) raises its chemical potential by \((M/\rho)\Delta P\). For an ideal vapour the chemical potential is \(RT\ln p\). Equating the increases gives \(RT\ln(p_r/p_\infty)=(M/\rho)(2\gamma/r)\).

A drop smaller than the radius at which \(p_r\) equals the actual vapour pressure evaporates; a larger one grows. At supersaturation \(S\) the critical radius is \(r_c=2\gamma M/(\rho RT\ln S)\). In clean vapour, clusters must reach \(r_c\) by chance fluctuations, which happens at a useful rate only at high \(S\).

A charged drop

Now let the drop carry charge \(q\) at its centre, as on an ion. The electric field outside the drop is \(q/(4\pi\varepsilon_0 r^2)\). Inside, the dielectric of relative permittivity \(\varepsilon_r\) reduces it by \(\varepsilon_r\). Forming the drop therefore lowers the electrostatic energy, and more so the smaller the drop. J. J. Thomson worked out the effect in 1888.

Sketch. The electrostatic field energy outside a sphere of radius \(r\) is \(q^2/(8\pi\varepsilon_0r)\). Filling the region between \(r\) and \(r+dr\) with dielectric changes the energy by \(-\tfrac{q^2}{8\pi\varepsilon_0}(1-1/\varepsilon_r)\,dr/r^2\). Dividing by the number of moles added, \(4\pi r^2\rho\,dr/M\), gives the electrostatic contribution to the chemical potential, and the term follows. Setting the derivative of the bracket to zero gives \(r_*\).

For small \(r\) the charge term wins and the curve goes negative: tiny charged clusters are stable even in unsaturated vapour. For large \(r\) the Kelvin term dominates. Between them the curve has a peak, and the peak is the supersaturation an ion needs.

The Thomson equation depends on \(q^2\), so it cannot explain why negative ions nucleate before positive ones. The difference comes from the structure of the water surface: water molecules at a surface are oriented, and the orientation favours one sign of charge. The simple continuum theory has no room for this, and the sign preference is still a subject of research.

Ions in the air and a radiation from above

For the general reader. A charged electroscope slowly loses its charge even when perfectly insulated. Around 1900 Wilson, and independently Julius Elster and Hans Geitel in Germany, showed that the air itself is always slightly ionized, with a few new ions made in every cubic centimetre every second. Wilson asked whether the cause might be a very penetrating radiation from outside the Earth. He tested the idea underground in a railway tunnel and found no clear effect. Ten years later Victor Hess, flying in a balloon, showed that such a radiation exists: the cosmic rays.

Spontaneous ionization

In 1900–01 Wilson built a small, carefully insulated electroscope inside a closed vessel of dust-free air. He found that the leaf fell at a slow, steady rate that did not depend on the sign of the charge, and he showed that the leak came from ions formed in the enclosed air. Elster and Geitel reached the same result at the same time.

If a field sweeps the ions out faster than they recombine, the current to the electroscope saturates at \(I=qeV\) for a vessel of volume \(V\). Measuring the rate of fall of the leaf therefore measures \(q\) directly. Wilson found that a few ion pairs are produced per cubic centimetre per second in ordinary air at sea level.

The tunnel

Wilson considered two sources: radioactivity in the vessel walls and surroundings, and some radiation penetrating from outside. He suggested in 1901 that the ionization might be due to radiation from beyond the atmosphere, like X-rays or cathode rays but far more penetrating. To test this he carried his electroscope at night into a disused tunnel of the Caledonian Railway near Peebles, where many metres of rock would screen any radiation from above. He found no clear reduction. Radioactivity in the rock, unknown in amount, could have masked it, and the idea was set aside.

Between 1909 and 1912 measurements on towers, at sea and in balloons tested whether the ionization fell off with height as it should if it came from the ground. In 1912 Victor Hess flew electroscopes to above 5000 m and found that the ionization first fell and then rose well above its ground value. He concluded that a radiation of great penetrating power enters the atmosphere from above. Hess shared the 1936 Nobel Prize in Physics for the discovery. Cosmic rays account for roughly a tenth of the ionization of air at sea level over land; the rest comes from radioactivity in soil and air.

The tracks of single particles

For the general reader. A fast charged particle crossing a gas knocks electrons off the molecules in its path, leaving a line of ions. If the gas is supersaturated at that moment, a droplet grows on each ion, and the line of ions becomes a line of tiny water drops, big enough to photograph with a flash of light. In 1911 Wilson did exactly this. For the first time physicists could see an individual alpha particle or electron, and follow its path, its collisions and its slowing down.

The apparatus

Wilson’s first observations, early in 1911, used a small glass chamber. In 1912 he described a better apparatus in the Proceedings of the Royal Society. The chamber was a shallow glass cylinder above a piston that rested on a layer of water. A valve, opened suddenly, connected the space below the piston to an evacuated flask, so the piston dropped and the gas above it expanded by a fixed ratio between about 1.31 and 1.38. A weak electric field between the roof and the piston swept out stray ions before each expansion, so the chamber started clean. A spark lit the chamber a fraction of a second after the expansion, once the drops had grown, and a camera photographed the tracks.

The timing matters. Ions formed before the expansion drift and diffuse, giving broad, diffuse tracks. Ions formed in the short sensitive time just after the expansion, before latent heat and the growing drops reduce the supersaturation, give sharp tracks. Wilson wrote of the electron tracks as little wisps and threads of cloud.

How many ions?

A charged particle loses energy mainly by ionizing and exciting atoms. In air, about \(W=34\) eV is spent on average per ion pair formed. The rate of energy loss is given by the formula of Hans Bethe (1930), whose essential dependence is \(z^2/v^2\).

Sketch. A particle passing an electron at impact parameter \(b\) gives it momentum \(\Delta p=2ze^2/(4\pi\varepsilon_0bv)\), hence energy \(\Delta p^2/2m_e\). Integrating over a cylindrical shell of electrons, \(2\pi bn_e\,db\,dx\), gives a logarithm \(\ln(b_{\max}/b_{\min})\). The upper cut-off comes from the time of the collision compared with atomic periods, the lower from the maximum energy transfer \(2m_ev^2\); together they give the logarithm shown.

So the alpha particle, doubly charged and slow, leaves a dense, straight, continuous trail a few centimetres long. A fast electron leaves a sparse line in which separate droplets, and small clusters of them, can be counted. Wilson’s photographs showed both, and also the short side branches, now called delta rays, where the primary particle had given an atomic electron enough energy to make a little track of its own.

Reading tracks: momentum, range, recoil

For the general reader. A track records more than a path. Its density tells the particle’s charge and speed, its length tells its energy, and its curvature in a magnetic field gives its momentum and the sign of its charge. In 1923 Wilson photographed the electrons knocked out of air by X-rays and found, alongside the long tracks, many very short ones. They were the recoil electrons predicted by Arthur Compton’s theory that X-rays scatter like particles. The two men shared the 1927 Nobel Prize.

Curvature and range

In a magnetic field \(B\) perpendicular to the track, a particle of charge \(ze\) and momentum \(p\) follows a circle of radius \(r=p/(zeB)\). In practical units, \(p\,[\text{MeV}/c]=299.8\,z\,B[\text{T}]\,r[\text{m}]\). The sense of curvature gives the sign of the charge, if the direction of motion is known. Dmitri Skobeltsyn used a chamber in a magnetic field in the 1920s to study fast electrons and saw tracks of cosmic-ray particles too energetic to bend appreciably.

The range of a particle is the integral of \(dx=dE/(dE/dx)\) over its energy. For alpha particles in air between about 4 and 7 MeV an empirical rule, due to Geiger, is \(R\approx0.318\,E^{3/2}\) cm with \(E\) in MeV.

The Compton effect

In 1923 Compton found that X-rays scattered by light elements have longer wavelengths than the incident rays, by an amount depending on the angle. He explained it as a collision between a photon of energy \(h\nu\) and momentum \(h\nu/c\) and a free electron.

Derivation. Conservation of four-momentum gives \(p_e=k+p-k'\), with \(k,k'\) the photon four-momenta and \(p\) the initial electron. Squaring, \(m_e^2c^2=m_e^2c^2+2p\cdot(k-k')-2k\cdot k'\). With the electron at rest, \(p\cdot(k-k')=m_e(h\nu-h\nu')\) and \(k\cdot k'=h^2\nu\nu'(1-\cos\theta)/c^2\). Then \(1/\nu'-1/\nu=h(1-\cos\theta)/(m_ec^2)\), which is the wavelength formula. Setting \(\theta=\pi\) gives \(T_{\max}\).

Wilson’s 1923 photographs of air irradiated by X-rays showed long tracks of photoelectrons, carrying nearly the full photon energy, and many very short tracks. Their number and lengths matched recoil electrons of the Compton process. Walther Bothe made the same observation independently that year. The cloud chamber thus gave direct visual evidence that a single X-ray photon collides with a single electron.

The chamber as an instrument of discovery

For the general reader. From the 1920s to the 1950s, many of the new particles of physics were first seen in cloud chambers: the positron, the muon, the strange particles. Others improved Wilson’s design. Patrick Blackett made it photograph automatically, then made it wait until a particle arrived. Later the diffusion chamber stayed sensitive all the time, and the bubble chamber replaced vapour by a superheated liquid. All descend from Wilson’s glass cylinder.

Automatic and triggered chambers

At the Cavendish in the early 1920s Blackett built a chamber that expanded and photographed automatically every few seconds, with stereo cameras. In 1925 he used it to photograph the nuclear reaction Rutherford had found in nitrogen: eight forked tracks among some 400 000 alpha tracks (see the Rutherford course, Lesson 08). In 1932–33 Blackett and Giuseppe Occhialini placed Geiger counters above and below a chamber and expanded it only when both counters fired at once. The chamber then photographed a cosmic-ray particle on most expansions, instead of rarely. Their photographs showed showers of positive and negative electrons, confirming Anderson’s positron and the creation of electron pairs from radiation.

Discoveries

• 1932: Carl Anderson, with a chamber in a strong magnet at Caltech, identified the positron in cosmic rays (Exercise 8.2).
• 1936–37: Anderson and Seth Neddermeyer found particles of intermediate mass in cosmic rays: the muon.
• 1947: George Rochester and Clifford Butler in Manchester found V-shaped tracks from neutral particles decaying in flight: the first strange particles, the kaons.

Alexander Langsdorf’s diffusion chamber of 1936–39 kept a layer of supersaturated vapour sensitive continuously, by letting alcohol vapour diffuse from a warm top to a cold base. Donald Glaser’s bubble chamber of 1952 used a superheated liquid, in which ions start bubbles. Liquid hydrogen is about sixty times denser than air, so interactions in it are far more frequent. Glaser received the 1960 Nobel Prize, and bubble chambers dominated particle physics into the 1970s.

Thunderstorms and the global circuit

For the general reader. In fine weather the ground carries a negative charge and the air above it a positive one, and a tiny electric current flows down through the slightly conducting air everywhere on Earth. Without some generator the ground’s charge would leak away in minutes. Wilson proposed that the world’s thunderstorms are that generator, pumping charge upward continuously. He also argued that the fields of thunderclouds could accelerate electrons to very high energies and cause electrical breakdown far above the clouds. Both predictions were confirmed decades later, the second with the discovery of sprites and of gamma-ray flashes from storms.

The fair-weather field

In fine weather the vertical electric field at the ground is about 100–150 V/m, pointing downward. The air–earth current density is about 2 pA/m², so the whole Earth receives a downward current of order 1 kA. The ionosphere stands roughly 250 kV above the ground.

Wilson argued, from about 1920, that thunderstorms and shower clouds act as batteries in a global circuit. Below a storm, negative charge flows to the ground by lightning and point discharge; above it, positive charge leaks to the upper atmosphere. The return current flows downward in fine-weather regions everywhere. Measurements on the research ship Carnegie in the 1920s showed that the fair-weather field over the oceans rises and falls with universal time, not local time, peaking around 19:00 GMT, when thunderstorm activity over the continents is greatest. That supports Wilson’s picture.

The thundercloud

From 1916 Wilson measured the sudden changes in the field at the ground caused by lightning flashes at various distances, using sensitive electrometers connected to a conductor exposed to the sky. He concluded that the typical thundercloud has positive charge above and negative charge below. George Simpson, from measurements of the charge on rain, argued for the opposite arrangement, and the debate ran for two decades. Balloon soundings eventually showed that Wilson was right about the main structure, with a smaller pocket of positive charge near the cloud base.

The charge and its image at \(-H\) contribute equal vertical components. For a dipole with negative charge low and positive charge high, the lower charge dominates nearby and the upper charge dominates at a distance, because its field falls off more slowly. The sign of the field, and of the field change when lightning removes the charges, therefore reverses at a certain distance. Wilson used this reversal to infer the polarity.

Runaway electrons and discharges above the clouds

In 1924–25 Wilson pointed out a remarkable consequence of the energy-loss law of Lesson 07. A fast electron in air loses energy at a rate that decreases as its energy rises, down to a minimum near 1 MeV. If an electric field supplies more energy per unit length than this minimum loss, an electron that starts above a certain energy gains energy faster than it loses it, and runs away to very high energy.

Wilson also noted that the field of the cloud charges, reaching up into the thin upper air, falls off with height as a dipole field, roughly as \(z^{-3}\), while the field needed for breakdown falls in proportion to the air density, exponentially. Above some height the storm field must exceed the breakdown field. He suggested in 1925 that electrical discharges should occur there, high above thunderstorms.

Brief luminous discharges between about 50 and 90 km above thunderstorms, now called sprites, were first recorded on video by a University of Minnesota team in July 1989. Bursts of gamma rays from thunderstorms, terrestrial gamma-ray flashes, were found in 1994 by the BATSE instrument on NASA’s Compton Gamma Ray Observatory. They are explained by runaway electron avalanches, which grow when each runaway electron knocks on fast secondaries that run away in turn.

Jacksonian Professor and return to Scotland

The Solar Physics Observatory

In 1913 Wilson became Observer in Meteorological Physics at the Solar Physics Observatory in Cambridge, which gave him a small laboratory and a site for field measurements away from the Cavendish. Most of his later work on particle tracks and on thunderstorm electricity was done there. In 1918 he was appointed Reader in Electrical Meteorology. His 1921 paper in the Philosophical Transactions on lightning discharges and the electric field of thunderstorms set out his measurements and his account of the thundercloud.

In 1923 he published two papers on the tracks of X-ray and beta-ray electrons, with photographs of unprecedented clarity. In 1925 he was elected Jacksonian Professor of Natural Philosophy, a chair once held by James Dewar. In 1927 he shared the Nobel Prize in Physics with Arthur Compton. His half was awarded for his method of making the paths of electrically charged particles visible by condensation of vapour.

Wilson was a quiet and modest man. Cecil Powell, later the discoverer of the pion with photographic emulsions, was among the young physicists who received his guidance, with Philip Dee and J. G. Wilson. During the Second World War his knowledge of thunderstorm electricity was applied to protecting barrage balloons from lightning.

Retirement

Wilson retired from the Jacksonian chair in 1934 and moved to Edinburgh in 1936. Around his eightieth birthday he settled at Carlops, a village in the Pentland Hills a few miles from Crosshouse, where he was born. He kept up with colleagues by weekly trips into Edinburgh and went on working on the theory of thunderstorms. His last paper, A theory of thundercloud electricity, appeared in the Proceedings of the Royal Society in 1956, when he was 87. He died at Carlops on 15 November 1959, aged 90.

Honours and legacy

Wilson was elected a Fellow of the Royal Society in 1900. He received the Society’s Hughes Medal (1911), Royal Medal (1922) and Copley Medal (1935), the Hopkins Prize of the Cambridge Philosophical Society (1920), the Gunning Prize of the Royal Society of Edinburgh (1921), the Howard N. Potts Medal (1925) and the Franklin Medal (1929) of the Franklin Institute, and the Nobel Prize in Physics (1927). He was made a Companion of Honour.

Legacy

• Nucleation physics: his thresholds for ions and clean vapour are the founding measurements of the theory of droplet nucleation, still central to cloud physics and to the study of how ions and aerosols seed clouds.
• The electron’s charge: his cloud method gave Thomson and Townsend the first estimates of the ionic charge, the route that led to Millikan’s oil drops.
• Cosmic rays: his 1901 suggestion of a penetrating radiation from outside the atmosphere was the first statement of the cosmic-ray hypothesis.
• Particle detection: the cloud chamber made single particles visible and led directly to the diffusion chamber and the bubble chamber. The positron, muon and kaon were all found in cloud chambers.
• Atmospheric electricity: the global circuit driven by thunderstorms, the positive-above-negative structure of the thundercloud, runaway electrons and discharges above storms are all part of modern atmospheric physics. Electrons accelerated in thunderstorm fields are sometimes called Wilsonian electrons.
• Teaching: diffusion cloud chambers, made with dry ice and alcohol, are standard demonstrations in schools and science museums.

Sources and further reading

Biography

1. C. T. R. Wilson, Wikipedia (with extensive references).
2. C. T. R. Wilson, biographical and facts, NobelPrize.org.
3. Cambridge University Library, Papers of C. T. R. Wilson, biographical history.
4. American Institute of Physics, C. T. R. Wilson, Physics History Network.
5. A. Mackinnon, Site of the first ever cosmic ray experiment, University of Glasgow.
6. P. M. S. Blackett, Charles Thomson Rees Wilson 1869–1959, Biographical Memoirs of Fellows of the Royal Society 6 (1960), 269–295.
7. C. T. R. Wilson, Reminiscences of my early years, Notes and Records of the Royal Society 14 (1960), 163–173.
8. P. Galison, Image and Logic: A Material Culture of Microphysics, University of Chicago Press, 1997, ch. 2 (the cloud chamber).

Physics

1. C. T. R. Wilson, Condensation of water vapour in the presence of dust-free air and other gases, Phil. Trans. R. Soc. A 189 (1897), 265–307.
2. C. T. R. Wilson, On the comparative efficiency as condensation nuclei of positively and negatively charged ions, Phil. Trans. R. Soc. A 193 (1899), 289–308.
3. C. T. R. Wilson, On the ionisation of atmospheric air, Proc. R. Soc. 68 (1901), 151–161.
4. C. T. R. Wilson, On a method of making visible the paths of ionising particles through a gas, Proc. R. Soc. A 85 (1911), 285–288.
5. C. T. R. Wilson, On an expansion apparatus for making visible the tracks of ionising particles in gases and some results obtained by its use, Proc. R. Soc. A 87 (1912), 277–292.
6. C. T. R. Wilson, Investigations on lightning discharges and on the electric field of thunderstorms, Phil. Trans. R. Soc. A 221 (1921), 73–115.
7. C. T. R. Wilson, Investigations on X-rays and β-rays by the cloud method, Proc. R. Soc. A 104 (1923).
8. C. T. R. Wilson, The electric field of a thundercloud and some of its effects, Proc. Phys. Soc. London 37 (1925), 32D.
9. C. T. R. Wilson, The acceleration of β-particles in strong electric fields such as those of thunderclouds, Proc. Camb. Phil. Soc. 22 (1925), 534.
10. C. T. R. Wilson, On the cloud method of making visible ions and the tracks of ionizing particles, Nobel Lecture, 12 December 1927.
11. C. T. R. Wilson, A theory of thundercloud electricity, Proc. R. Soc. A 236 (1956), 297–317.
12. A. De Angelis, Atmospheric ionization and cosmic rays: studies and measurements before 1912, arXiv:1208.6527.
13. H. R. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation, 2nd ed., Kluwer, 1997 (Kelvin and Thomson equations, ion nucleation).
14. M. A. Uman, The Lightning Discharge, Academic Press, 1987 (thundercloud charge structure, field changes).
15. J. R. Dwyer, D. M. Smith, S. A. Cummer, High-energy atmospheric physics: terrestrial gamma-ray flashes and related phenomena, Space Sci. Rev. 173 (2012), 133–196.