Robert Millikan

How to use this course

Robert Millikan is remembered for one experiment that every physics student meets: tiny oil drops held between charged plates, showing that electric charge comes in whole units. He also spent a decade testing Albert Einstein’s photoelectric equation, gave the first direct photoelectric value of Planck’s constant, and led the American study of cosmic rays. Outside the laboratory he built the California Institute of Technology into a leading research school and spoke for American science to the public.

His reputation has two later shadows, and this course treats both on the evidence. Historians have debated how he selected oil-drop data for his 1913 paper. In 2021 Caltech removed his name from its buildings because of his association with the eugenics movement. Lessons 07 and 12 set out what the sources say.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. The order follows his research: the elementary charge (1907–1917), the photoelectric effect (1912–1916), and cosmic rays (1922–1940s).

Timeline

Iowa and Oberlin, 1868–1893

Robert Andrews Millikan was born on 22 March 1868 in Morrison, Illinois, the second son of Silas Franklin Millikan, a Congregational minister, and Mary Jane Andrews. The family moved to McGregor and then to Maquoketa, Iowa, where he grew up in a large household with little money and plenty of outdoor work. He attended Maquoketa High School and worked for a short time as a court reporter.

In 1886 he entered Oberlin College in Ohio. He preferred Greek and mathematics. Physics entered his life by accident: after his second year, his Greek professor asked him to teach the elementary physics class. When Millikan protested that he knew no physics, he was told that anyone who could do Greek could teach it. He learned the subject over the summer from a textbook and stayed one chapter ahead of his students.

He graduated in 1891, taught elementary physics at Oberlin for two more years, and received a master’s degree in physics in 1893. The habits of these years stayed with him. He was a natural teacher who learned by explaining, and he grew up in a home where science and Christian faith were never felt to be in conflict.

Columbia and Germany, 1893–1896

In 1893 Millikan went to Columbia University in New York as a fellow in physics. The physics department was small. The teacher who influenced him most was Michael Pupin, the Serbian-born electrical engineer and physicist. Millikan spent the summer of 1894 in Chicago, attending lectures by Albert Michelson at the new University of Chicago, an encounter that shaped his career.

His doctoral research measured the polarization of light emitted at grazing angles from glowing surfaces. To get liquid metals hot and clean enough, he worked with molten gold and silver at the United States Mint. He received the PhD in 1895.

On his professors’ advice he spent 1895–96 in Germany, at the universities of Berlin and Göttingen. It was an extraordinary year to be in Europe. Wilhelm Röntgen announced X-rays in December 1895, Henri Becquerel found radioactivity in early 1896, and J. J. Thomson would identify the electron in 1897. Millikan returned to an America whose physics was still mostly a teaching subject, convinced that the new physics of atoms and radiation was where the future lay.

Chicago: the teacher, 1896–1907

In 1896 Michelson offered him an assistantship at the Ryerson Physical Laboratory of the University of Chicago, and Millikan cut short his stay in Europe to accept. For the next decade his main work was teaching. He reorganized the introductory courses and wrote textbooks that sold widely: with Samuel Stratton, A College Course in Physics (1898); a translation with C. R. Mann of Paul Drude’s Theory of Optics (1903); and, with Henry Gordon Gale, A First Course in Physics (1906), which in its revisions was used in American high schools for decades. The royalties gave his family a security that a junior salary did not.

In 1902 he married Greta Irvin Blanchard. They had three sons, Clark, Glenn and Max. Clark Millikan became a professor of aeronautics at Caltech.

By his late thirties Millikan was still an assistant professor, earning under two thousand dollars a year, with a modest research record. He decided to change that by attacking a fundamental question: the size of the electric charge carried by an electron or ion. In 1907, with his student Louis Begeman, he began repeating the cloud measurements of Cambridge physicists. Lessons 04 to 07 follow what came of it.

Falling drops and Stokes’s law

For the general reader. A raindrop does not keep accelerating. Air resistance grows with speed until it balances the weight, and from then on the drop falls at a steady terminal speed. For very small drops that speed depends on the drop’s radius in a simple way, so timing the fall tells you how big the drop is. Every attempt to measure the electron’s charge with drops rests on this fact.

Terminal velocity

Let the drop have density \(\rho\) and the air density \(\sigma\). The net downward force at rest is the weight minus the buoyancy, \(\tfrac43\pi a^3(\rho-\sigma)g\). At terminal speed \(v_1\) this balances the drag:

The approach to terminal speed is fast. The equation \(m\dot v = mg' - 6\pi\eta a v\) gives \(v(t)=v_1(1-e^{-t/\tau})\) with \(\tau = m/(6\pi\eta a)=2a^2\rho/(9\eta)\), around ten microseconds for a micrometre drop. Over a fall of a few seconds the drop is always at terminal speed.

The cloud method and its weakness

In 1897 John Townsend, and soon after J. J. Thomson, charged a cloud of water droplets with ions, measured the total charge, and found the number of droplets by timing the fall of the top of the cloud and using Stokes’s law to get each droplet’s mass. In 1903 Harold A. Wilson improved this by watching the cloud fall with and without an electric field. Both methods measured averages over a cloud whose drops evaporated as they fell. The values of \(e\) scattered by tens of percent. Millikan and Begeman’s refinement in 1907–08 still suffered from evaporation.

The oil-drop method

For the general reader. Millikan’s advance was to watch one drop at a time. By switching an electric field on and off he could make a single charged droplet rise and fall for hours, and he could see its speed jump whenever it caught or lost a charge. The jumps were always whole multiples of one smallest step. Electricity, like matter, comes in atoms.

From balanced water drops to oil

In 1909 Millikan tried applying a field strong enough to hold the whole cloud up. The cloud dispersed, but a few single drops hung balanced in the field, and he could follow each one. Water drops still evaporated within a minute. In the autumn of 1909 his graduate student Harvey Fletcher built a version using an atomizer and watch oil, whose drops do not evaporate. Millikan and Fletcher’s apparatus, published from 1910, used two horizontal brass plates a short distance apart, a hole in the upper plate to admit drops, a light source and a short-focus telescope. X-rays or radium could be used to change the drop’s charge.

Using Lesson 04 for \(a\) and \(m\) in terms of \(v_1\) gives the working formula

Watching the charge change

If the drop picks up an ion, \(v_1\) is unchanged (the mass is the same) and the rising speed jumps from \(v_2\) to \(v_2'\). Then

The quantity \(k/E\) is fixed for a given drop, so the successive values of \(v_1+v_2\), and the jumps \(v_2'-v_2\), must all be integer multiples of one smallest value. Millikan found exactly this pattern, on every drop, for many changes of charge on the same drop. This is the cleanest evidence that charge is quantized, and it does not depend on Stokes’s law at all. Stokes’s law, and the value of \(\eta\), enter only when converting the unit step into coulombs.

Correcting Stokes; e and Avogadro’s number

For the general reader. Millikan noticed that small drops gave slightly larger apparent charges than large ones. The reason is that air is not a smooth fluid at the scale of a micrometre: a drop slips between the molecules and falls faster than Stokes predicts. Correcting for this, he obtained a value of the electron’s charge good to a fraction of a percent, and with it the number of atoms in a mole.

The slip correction

When the drop radius is not large compared with the mean free path \(\ell\) of the gas, the drag is reduced. To first order, with an empirical constant \(A\) (Ebenezer Cunningham gave a theory in 1910),

Since \(\ell\propto1/p\), Millikan wrote the correction as \(1+b/(pa)\) with pressure \(p\) and a constant \(b\).

Derivation sketch. The working formula of Lesson 05 is \(q\propto\eta^{3/2}\). Replacing \(\eta\) by the effective viscosity \(\eta/(1+b/pa)\) shows the true charge is \(q=q_{\text{Stokes}}(1+b/pa)^{-3/2}\). Raising to the power \(2/3\) gives the linear relation. The approximation of using the apparent rather than true radius in the correction affects only second order.

Millikan’s 1913 Physical Review paper gave \(e=4.774\times10^{-10}\) electrostatic units, that is \(1.592\times10^{-19}\) C, with a claimed uncertainty of about one part in a thousand. The modern value, exact since the 2019 redefinition of the SI, is \(e=1.602\,176\,634\times10^{-19}\) C. The difference, about 0.6 %, came mainly from the value of the viscosity of air that Millikan adopted, which was low by about 0.4 %. X-ray crystal measurements of \(e\) disagreed with the oil-drop value in the late 1920s, and the viscosity was remeasured in the 1930s.

Avogadro’s constant

The Faraday constant \(F\) is the charge carried by one mole of singly charged ions, measured in electrolysis. Then \(N_A=F/e\). Millikan’s title, “the elementary electrical charge and the Avogadro constant”, makes the point: one measurement fixed both the scale of electricity and the scale of atoms. Combined with Thomson’s \(e/m\), it also gave the electron mass.

The data-selection debate

For the general reader. Millikan wrote in 1913 that his published drops were not a selected group. His notebooks, studied in the 1970s, show that he left out many drops he had measured. Historians and physicists still disagree about what this means. The episode has become a standard case in the ethics of science, and it is also a lesson in statistics.

Ehrenhaft and the subelectrons

From 1910 the Viennese physicist Felix Ehrenhaft, using tiny metal particles, reported charges smaller than \(e\) and of no fixed size. If he was right, there was no elementary charge. Millikan replied that Ehrenhaft’s particles were not spheres of known density, so Stokes’s law gave wrong masses. The dispute lasted more than a decade. Millikan’s 1913 paper, with its statement that it presented all the drops observed over sixty consecutive days, was his decisive answer. It is widely thought that the controversy delayed his Nobel Prize.

What the notebooks show

The physicist and historian Gerald Holton examined Millikan’s laboratory notebooks for the winter of 1911–12 and published his analysis in 1978. The notebooks record about 175 drops. The 1913 paper reports 58, all measured between mid-February and mid-April 1912. Many drops from the same period are missing, and the notebooks contain remarks such as judgements that a run was “beautiful”, or that something was wrong, written as he went. Yet the 1913 paper says plainly: “this is not a selected group of drops”.

Three main readings have been offered.

• Holton (1978) did not allege fraud. He used the notebooks to show how an experimenter’s prior conviction (here, that \(e\) is a single fixed charge) guides which data are trusted, and contrasted Millikan with Ehrenhaft, who refused to discard any run.
• Allan Franklin (1981, and in later books) reanalysed the data. Including the excluded drops does not change \(e\) appreciably, and none of them supports subelectrons. Franklin found that exclusions mostly reduced the statistical error Millikan quoted. He called this a kind of cosmetic surgery and judged the published statement about selection to be false, while defending the result.
• David Goodstein (2000–2001) argued that Millikan excluded drops for documented experimental reasons, such as drops too large or too small for his slip correction or incomplete runs, and that the “not selected” sentence refers to the subset used to determine \(e\) after those criteria. He defended Millikan against the charge of misconduct.

Popular accounts, such as William Broad and Nicholas Wade’s Betrayers of the Truth (1982), presented the case as fraud. Most historians reject that word while agreeing that the published statement misdescribed the procedure. A separate question concerns credit. Harvey Fletcher’s memoir, published in Physics Today in 1982 after his death, recounts that Millikan proposed Fletcher take sole authorship of a Brownian-motion paper for his thesis while Millikan alone signed the oil-drop paper. Fletcher said he accepted this arrangement and remained on good terms with Millikan.

Statistics of exclusion

If \(N\) independent measurements \(x_i\) have sample standard deviation \(s\), the standard error of the mean is \(s/\sqrt N\). Removing the measurements furthest from the mean lowers \(s\) and can lower \(s/\sqrt N\) even though \(N\) falls. If the exclusions are symmetric about the true value, the mean is unbiased; if they are not, the mean shifts. A defensible procedure fixes the exclusion criteria before looking at the result and reports them.

The photoelectric effect and Planck’s constant

For the general reader. Light can knock electrons out of a metal. In 1905 Einstein proposed that light comes in packets of energy proportional to its frequency, which predicts that the energy of the escaping electrons rises in a straight line with the frequency of the light. Millikan doubted the idea and spent about ten years testing it. His measurements confirmed the straight line exactly and gave a precise value of Planck’s constant.

The experiment

Alkali metals respond to visible and near-ultraviolet light, but their surfaces oxidize within minutes and the measured potentials drift. Millikan’s solution, described in his 1916 paper, was what he called a machine shop in vacuo: cylinders of sodium, potassium and lithium on a wheel inside an evacuated vessel, with a knife operated from outside by an electromagnet to shave fresh surfaces just before each run. He illuminated them with monochromatic lines from a mercury arc and measured the stopping potentials with an electrometer.

What is measured is the potential applied between emitter and collector. Because the two are different metals, a contact potential difference \(V_c\) adds to it: \(e(V_{\text{applied}}+V_c)=h\nu-W\). The constant \(V_c\) shifts the intercept but leaves the slope untouched. Millikan therefore relied on the slope, and found for sodium \(h\approx6.57\times10^{-27}\) erg s, within about 1 % of today’s \(6.626\times10^{-27}\) erg s. Combining the slope \(h/e\) with his own value of \(e\) made the determination independent of black-body radiation theory.

Confirmation without conversion

In his papers of 1914–1916 Millikan stated that Einstein’s equation was confirmed in every detail, yet he called the light-quantum hypothesis on which it rested untenable. Most physicists agreed with him until Arthur Compton’s X-ray scattering experiments of 1922–23. The 1923 Nobel Prize was awarded to Millikan “for his work on the elementary charge of electricity and on the photoelectric effect”. In his 1950 autobiography he accepted that his data allowed no other interpretation than Einstein’s.

Cosmic rays and atom building

For the general reader. In 1912 Victor Hess found, from balloons, that the air becomes more strongly ionized as one rises. Something penetrating was arriving from above. Millikan at first doubted it, then confirmed it with measurements deep in mountain lakes, and gave the radiation the name it still has. He believed the rays were high-energy light produced when atoms are built in space, an idea that turned out to be wrong but drove a large programme of measurement.

Lakes and balloons

With Ira Bowen, Millikan sent light recording electroscopes up on sounding balloons in 1922–23. In 1925, with G. Harvey Cameron, he lowered sealed electroscopes into snow-fed lakes in the Sierra Nevada and southern California at different altitudes. Readings in a high lake at a given depth matched those in a lower lake at a depth deeper by the water equivalent of the air between them. The radiation came from above the atmosphere, and it was more penetrating than any gamma ray known. Millikan’s name “cosmic rays” spread quickly.

The atom-building hypothesis

Millikan and Cameron fitted their depth curves with a few exponential components, interpreted them as photon bands, and converted absorption coefficients into energies. The energies seemed to match the mass defects released when hydrogen atoms combine into helium, oxygen, silicon and iron. Millikan concluded around 1928 that the rays were the photons released by the continual creation of elements in interstellar space, a sign that the universe was being rebuilt rather than running down. He described them in a famous phrase as the birth cries of atoms.

The energy released in forming a nucleus from hydrogen atoms is

with \(1\,\mathrm u\,c^2=931.5\) MeV. Two problems ended the hypothesis. The conversion from absorption coefficient to energy relied on formulas that the Klein–Nishina cross-section (1929) replaced, which changed the inferred energies. And from 1932 the latitude effect (Lesson 10) showed that most primary cosmic rays are charged particles, not photons.

The latitude effect

For the general reader. The Earth’s magnetic field deflects charged particles but not light. If cosmic rays are charged, fewer should reach the ground near the equator, where the field lines run horizontally and shield best, than near the poles. Arthur Compton’s worldwide survey of 1932 found exactly this. Millikan resisted the conclusion in public, then accepted it, and the cosmic-ray programme he had built went on to discover the positron and the muon.

A particle of momentum \(p\) and charge \(Ze\) in a field \(B\) moves in a circle of radius \(r=p/(ZeB)\). Its magnetic rigidity is \(R=pc/(Ze)\), measured in volts; particles of the same rigidity follow the same paths.

Jacob Clay had seen a drop in ionization on voyages between the Netherlands and Java in 1927–28. Compton organized expeditions at many latitudes in 1932 and found a clear drop of intensity toward the geomagnetic equator. Millikan, whose own earlier measurements had shown little effect, disputed the result at the end of 1932 in an exchange widely reported in the press. Within a year further measurements, including those of his own group with H. Victor Neher, confirmed the effect, and he accepted it. In 1933 Thomas Johnson, and Luis Alvarez with Compton, found more particles arriving from the west than from the east, showing that most primaries are positively charged. They are now known to be mostly protons.

Millikan’s programme had a lasting result of a different kind. His student Carl Anderson, building a cloud chamber in a strong magnetic field to measure cosmic-ray energies, found the positron in 1932 and, with Seth Neddermeyer, the particle now called the muon in 1936.

Caltech and the public scientist, 1917–1945

When the United States entered the First World War in 1917, Millikan became executive officer and director of research of the new National Research Council, created at the urging of the astronomer George Ellery Hale. He accepted a commission in the Army Signal Corps and organized work on submarine detection and on meteorological instruments for aviation. The war made him a national figure in science administration.

Hale was also building Throop College of Technology in Pasadena into a research institution. From 1917 Millikan spent part of each year there, and in 1921 he moved permanently, as director of the Norman Bridge Laboratory of Physics and chairman of the Executive Council. Throop had been renamed the California Institute of Technology in 1920. He declined the title of president, but he was the institute’s chief executive for twenty-four years. With Hale and the chemist Arthur Amos Noyes he recruited faculty, raised money from southern California’s business families and from the large foundations, and brought visitors such as Einstein. Under his leadership Caltech became one of the leading scientific schools in the world. Its students in his time included Linus Pauling and Carl Anderson.

He received the Nobel Prize in 1923, the second American to win it in physics after Michelson, and many other honours: the Comstock Prize (1913), the Edison Medal (1922), the Hughes Medal (1923), the Franklin Medal (1937) and the Medal for Merit (1949), with some twenty-five honorary degrees. He served on the League of Nations Committee on Intellectual Cooperation.

Millikan was a prolific public speaker on science and religion. He was a theist who accepted evolution and argued that the two were complementary. His Terry Lectures at Yale in 1926–27 appeared as Evolution in Science and Religion. He was politically conservative and opposed much of the New Deal.

Eugenics, controversy and legacy

In January 2021, after a year-long review by a Committee on Naming and Recognition, Caltech’s Board of Trustees removed Millikan’s name from campus buildings and honours, together with those of five other figures. The Robert A. Millikan Memorial Library became Caltech Hall. The committee’s report, which is public, gives the evidence on which the decision rested.

What the record shows

• The Human Betterment Foundation. Founded in Pasadena in 1928 by Ezra Gosney, the foundation promoted compulsory eugenic sterilization and supported California’s sterilization programme, one of the largest in the country. Millikan joined its board in 1937. The committee found that he did not direct its policy but lent it his prestige, and that in 1940 he wrote to Gosney praising its work.
• Statements on race. In a 1924 article Millikan described southern California as the “westernmost outpost of Nordic civilization”. The report cites racist remarks in private letters of the 1920s and a 1951 letter opposing Black voting rights in Mississippi.
• Women in physics. In 1936 he advised the president of Duke University against hiring the German physicist Hertha Sponer, on the grounds that women had not produced outstanding physics; Duke hired her anyway. Caltech appointed no women to its faculty under his leadership.
• Japanese Americans. The report states that in 1943 he told a California Assembly committee he favoured dispersing the Japanese American population of the state after the war.

The decision was contested. The mathematician Thomas Hales argued in 2023–24 that the report misread some sources, that Millikan worked to protect the rights of Japanese American citizens during the war, and that his eugenic views lay within the scientific mainstream of his time. The committee itself recommended that Caltech teach Millikan’s history rather than erase it, which is the spirit of this lesson. Readers should consult both documents, linked below.

Death and scientific legacy

Millikan retired in 1945 and published his autobiography in 1950. Greta Millikan died in 1953, and he died a few weeks later, on 19 December 1953, at his home in San Marino, California, aged 85. He is buried at Forest Lawn Memorial Park in Glendale.

• The elementary charge: the oil-drop experiment remains the standard demonstration of charge quantization, and its method is used in modern searches for fractionally charged particles.
• Planck’s constant: his photoelectric work was the first precise test of Einstein’s equation and became central evidence for the quantum theory of light, whatever his own early doubts.
• Cosmic rays: his name for them stuck, and his laboratory produced the discoveries of the positron and muon.
• Institutions: Caltech, the National Research Council, and the model of the American research university funded by private philanthropy.
• Teaching: his textbooks shaped how a generation of American students learned physics.

Sources and further reading

Biography

1. Robert Andrews Millikan, Wikipedia.
2. Robert A. Millikan, biographical, NobelPrize.org.
3. L. A. DuBridge and P. A. Epstein, Robert Andrews Millikan 1868–1953, Biographical Memoirs of the National Academy of Sciences.
4. R. A. Millikan, The Autobiography of Robert A. Millikan, Prentice-Hall, 1950.
5. R. H. Kargon, The Rise of Robert Millikan: Portrait of a Life in American Science, Cornell University Press, 1982.
6. Caltech Committee on Naming and Recognition, Report (2020–21), and Caltech Magazine report on the decision.
7. T. Hales, Robert Millikan, Japanese internment, and eugenics, arXiv:2309.13468; European Physical Journal H (2024).
8. Human Betterment Foundation, Wikipedia.

Physics and the data debate

1. R. A. Millikan, On the elementary electrical charge and the Avogadro constant, Physical Review 2 (1913) 109–143.
2. R. A. Millikan, A direct photoelectric determination of Planck’s “h”, Physical Review 7 (1916) 355–388.
3. R. A. Millikan, The electron and the light-quant from the experimental point of view, Nobel lecture, 1924.
4. R. A. Millikan, The Electron, University of Chicago Press, 1917.
5. G. Holton, Subelectrons, presuppositions, and the Millikan–Ehrenhaft dispute, Historical Studies in the Physical Sciences 9 (1978).
6. A. Franklin, Millikan’s published and unpublished data on oil drops, Historical Studies in the Physical Sciences 11 (1981) 185–201.
7. D. Goodstein, In defense of Robert Andrews Millikan, American Scientist 89 (2001) 54–60.
8. H. Fletcher, My work with Millikan on the oil-drop experiment, Physics Today 35(6) (1982) 43–47.
9. Oil drop experiment, Wikipedia.
10. R. A. Millikan and G. H. Cameron, High frequency rays of cosmic origin III: measurements in snow-fed lakes at high altitudes, Physical Review 28 (1926) 851–868.