Chapman Determines the Lunar Atmospheric Tide at Moderate Latitudes Summary

  • Last updated on November 10, 2022

Sydney Chapman’s determination of the lunar atmospheric tide (the effect of the Moon’s gravitation on Earth’s atmosphere) helped later scientists in their study of heat and radio physics.

Summary of Event

In 1951, Sydney Chapman, an applied mathematician and geophysicist who had been a professor in Manchester, London, and Oxford, was named the advisory scientific director and professor of geophysics at the University of Alaska. Four years later, he became the senior research fellow at the National Center for Atmospheric Research National Center for Atmospheric Research in Boulder, Colorado. His colleagues recognized that Chapman was a prolific producer and contributor to a greater understanding of the atmosphere: His work in the determination of the lunar air tide led to several (but by no means most) of the more than three hundred scientific papers he either authored or coauthored in such areas as Earth’s magnetism; theory of nonuniform gases; solar plasma, geomagnetism, and aurora; and composition of the ionosphere. During the period 1912-1917, he also modified the accurate kinetic theory of gases that James Clerk Maxwell had proposed in 1867, and in the process Chapman discovered gaseous thermal diffusion and confirmed it through experiments. He also demonstrated the power of thermal diffusion in highly ionized gases such as those in a solar corona. [kw]Chapman Determines the Lunar Atmospheric Tide at Moderate Latitudes (1935) [kw]Lunar Atmospheric Tide at Moderate Latitudes, Chapman Determines the (1935) [kw]Atmospheric Tide at Moderate Latitudes, Chapman Determines the Lunar (1935) [kw]Tide at Moderate Latitudes, Chapman Determines the Lunar Atmospheric (1935) [kw]Latitudes, Chapman Determines the Lunar Atmospheric Tide at Moderate (1935) Lunar atmospheric tide Moon, atmospheric tide [g]England;1935: Chapman Determines the Lunar Atmospheric Tide at Moderate Latitudes[08790] [c]Science and technology;1935: Chapman Determines the Lunar Atmospheric Tide at Moderate Latitudes[08790] [c]Earth science;1935: Chapman Determines the Lunar Atmospheric Tide at Moderate Latitudes[08790] [c]Physics;1935: Chapman Determines the Lunar Atmospheric Tide at Moderate Latitudes[08790] Chapman, Sydney Bartels, Julius Laplace, Pierre-Simon Maxwell, James Clerk

Atmospheric tide, or atmospheric oscillation, is an atmospheric motion of the scale of Earth in which vertical accelerations are neglected. Atmospheric tides are produced by both the Sun and the Moon. They may be thermal, if the variation in atmospheric pressure is caused by the diurnal differential heating of the atmosphere by the Sun, or they may be gravitational, if the variation is caused by the attraction of the Sun or Moon. The semidiurnal lunar atmospheric tide is gravitational. On the other hand, atmospheric tides produced by solar twenty-four-, twelve-, eight-, and six-hour pressure fluctuations act on Earth’s atmosphere by means of its gravitational field and also by emitting electromagnetic radiation and particles toward it. The amplitude of the lunar atmospheric tide is so small that it is detected only by careful statistical analysis of a long record, such as that conducted by Chapman in 1918 and 1935.

The lunar tide is the rise and fall of the oceanic surface twice each lunar day as a result of Earth’s rotation in a nonuniform external gravitational field. The atmosphere is subject to the same tide-producing gravitational forces as the oceans; this periodic change in atmospheric pressure is called the “equilibrium atmospheric” tide. At the equator, the calculated equilibrium tide-pressure variation at ground level is 0.022 millimeters of mercury (mmHg). Lunar twelve-hour fluctuations in pressure have been observed on the ground and are believed to be of purely gravitational origin; however, it is customary to refer to those periodic pressure fluctuations as atmospheric tides.

Sydney Chapman.

(National Science Foundation)

The dynamical theory of atmospheric tides goes back to 1778, when Marquis Pierre-Simon Laplace first published his conclusions on the theory. According to Laplace, the barometric amplitudes in equatorial regions, as a result of the gravitational action of the Sun and Moon, should be about 0.0109 millimeter and 0.025 millimeter, respectively, and decrease rapidly with the increase of latitude. In 1842, at an observatory on the British island of Saint Helena in the South Atlantic Ocean, the lunar semidiurnal pressure oscillation was determined to have a mean of about 0.055 millimeter, an amount that exceeded the calculated equilibrium tide of 0.022 millimeter by a factor of 2.5.

In 1918, Chapman had become the first to determine the lunar atmospheric tide from barometric readings taken at a moderate latitude at the Royal Greenwich Observatory in England. His conclusions were based on meteorological records of the barometer, wind, and temperature, which had been collected by the Greenwich Observatory during the period from 1854 to 1917. He also analyzed the magnetic data to determine the lunisolar daily variations of the magnetic field. (“Lunisolar” is a term used to describe the mutual relationship, or combined attraction, of the Moon and Sun.) Solar and lunisolar daily magnetic variations are caused by electric currents in the ionosphere, which are induced motions produced thermally and tidally. This relationship between the ionosphere and air tides led to Chapman’s later formulation of an idealized ionized layer.

In these and later calculations, Chapman used the mathematical theory of statistics, which was emerging as a major scientific tool. (Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data.) He saw that statistics could be used to improve the quality of inferences in important sections of his study of atmospheric lunar tides. The rigorous statistical procedures allowed him to make clearer determinations and to elucidate features of tides in Earth’s atmosphere that are caused by the Moon’s gravitational attraction. Of specific importance were significant figures, which are the figures of a number that begin with the first figure to the left that is not a zero and end with the last figure on the right that is not a zero, or is considered to be exact. Mathematical numbers are known to any accuracy required and carry any number of significant figures. The mean of more than ten and less than one thousand numbers may contain one or more significant figures.

Using this basis gave Chapman an advantage in finding the lunar tide from barometric readings in high latitudes. He followed his achievement with similar readings at more than fifty stations of the amplitude (in millimeters) during phases of the lunar semidiurnal mean atmospheric tide for the four equinoctial months (March, June, September, and December), and he presented his conclusions in 1935. Chapman found that the fundamental period of the free oscillation of the atmosphere as a whole is about twelve mean solar hours. Mean amplitudes and phases of the lunar semidiurnal atmospheric tide for the four equinoctial months had a mean of approximately 0.03 millimeter at 30 degrees south latitude, 0.038 millimeter at 20 degrees, 0.045 millimeter at 10 degrees, and 0.060 millimeter at the equator. At 10 degrees north, the barometric pressure was about 0.052 millimeter; it was 0.028 millimeter at 20 degrees, 0.022 millimeter at 30 degrees, 0.018 millimeter at 40 degrees, and 0.013 millimeter at 50 degrees.

This work aroused Chapman’s interest in geomagnetism and its connection with solar phenomena and led to his theoretical researches in these fields. He became best known for his research in geomagnetism and his pioneering work on both the photochemistry of the upper atmosphere and on nocturnal emission of light by atoms of oxygen and sodium. In 1940, he coauthored, with Julius Bartels, a two-volume work on geomagnetism. This complete work was an excellent contribution to the understanding of the external field of a uniformly magnetized sphere, the magnetic field at Earth’s surface, electric currents in and beyond the ionosphere, local and world indices of geomagnetic disturbance, sunspots and magnetism, and the twenty-seven-day recurrence in geomagnetic disturbance. As part of his study of the lunar tide, he investigated why Earth’s magnetic field varies with periods equal to the lunar day (27.3 days) and its submultiples. He showed that this was the result of a tidal movement in Earth’s atmosphere caused by the Moon.


Chapman’s contributions had major impacts in the extension of knowledge about the lunar tide and Earth’s atmosphere. His analysis of many years of barometer, wind, and temperature recordings, along with his magnetic data, was facilitated by expert use of statistical analysis, which at the time of his study was a new mathematical theory. The use of physical observations and an innovative mathematical theory were truly pioneering. As a consequence of his work in the atmosphere and magnetic field, Chapman developed a deep interest in geomagnetism and its connection with solar phenomena. These interests led to several major publications: The Earth’s Magnetism (1936; 2d ed. 1951); The Mathematical Theory of Non-uniform Gases, with T. G. Cowling (1939; 3d ed. 1970); Geomagnetism, with Julius Bartels (1940); IGY: Year of Discovery (1959); Solar Plasma, Geomagnetism, and Aurora (1964); Atmospheric Tides: Thermal and Gravitational, with Richard S. Lindzen (1970); and Solar-Terrestrial Physics, with Syun-Ichi Akasofu (1972).

Chapman’s research and studies of the atmospheres of Earth and the Sun produced a photochemical theory of atmospheric ozone and inferred that the oxygen in the upper atmosphere (which begins 100 kilometers above ground level) would be largely dissociated. This conclusion was confirmed later by rocket-borne mass spectrometers. Another of his inferences was that airglow, or the self-luminescence of the atmosphere at night, was energized mainly by the oxygen dissociation energy stored in the atmosphere during the sunlight hours. His work in this area led later to his 1953-1959 presidency of the central organizing committee for the International Geophysical Year, for which he led the planning of the auroral program.

Solar and lunisolar magnetic variations are caused by electric currents in the ionosphere, and Chapman’s research efforts in this area led the formulation of an ideally ionized layer—the Chapman ionized layer—which was used much later by radio physicists in studies of radio propagation and other research. His work in thermal diffusion—heat transfer between two parts of a solid, liquid, or gas at different temperatures—in the absence of convection was important for separating isotopes for atomic fission. Chapman made major contributions to the history of science, and his creative genius was recognized by his peers by the many awards he received. Lunar atmospheric tide Moon, atmospheric tide

Further Reading
  • citation-type="booksimple"

    xlink:type="simple">Aguado, Edward, and James E. Burt. Understanding Weather and Climate. 3d ed. Upper Saddle River, N.J.: Prentice Hall, 2003. Meteorology textbook aimed at both science majors and non-science majors focuses on the processes that produce weather and climate. Includes many illustrations and other learning aids.
  • citation-type="booksimple"

    xlink:type="simple">Chapman, Sydney. IGY: Year of Discovery; the Story of the International Geophysical Year. Ann Arbor: University of Michigan Press, 1959. A popular account of the events that took place during the International Geophysical Year of 1957 to 1958; taken from four lectures Chapman gave at the University of Michigan in October, 1958. A good reference for the general public, as well as high school and college students.
  • citation-type="booksimple"

    xlink:type="simple">Clancy, Edward P. The Tides: Pulse of the Earth. Garden City, N.Y.: Doubleday, 1968. Primarily about ocean tides, but refutes Chapman’s resonance theory of solar semidiurnal oscillation in the chapter on tides in the atmosphere. Suggests that the diurnal oscillation is the extraordinary phenomenon. Well written and a good general reference.
  • citation-type="booksimple"

    xlink:type="simple">Fleagle, Robert C., and Joost A. Businger. An Introduction to Atmospheric Physics. New York: Academic Press, 1963. A college-level text that presents a good understanding of the relationship of matter as expressed in the principles of physics. Some of the areas covered include gravitational effect, properties of atmospheric gases, properties and behavior of cloud particles, and solar and terrestrial radiation. Numerous mathematical formulas and graphs and a good bibliography.
  • citation-type="booksimple"

    xlink:type="simple">Hanle, Paul A., and Von Del Chamberlain, eds. Space Science Comes of Age: Perspectives in the History of the Space Sciences. Washington, D.C.: Smithsonian Institution Press, 1981. A compilation of essays from a symposium held at the National Air and Space Museum. A good reference for the general public on the early contributions to the field. Contains little mathematics or physics.
  • citation-type="booksimple"

    xlink:type="simple">Lutgens, Frederick K., and Edward J. Tarbuck. The Atmosphere: An Introduction to Meteorology. 9th ed. Upper Saddle River, N.J.: Prentice Hall, 2003. Introduction to meteorology for college students is accessible to advanced upper-level high school students as well. Well illustrated. Includes glossary and index.
  • citation-type="booksimple"

    xlink:type="simple">Wylie, Francis E. Tides and the Pull of the Moon. Brattleboro, Vt.: Stephen Greene Press, 1979. An easy-to-read book written for the general public. Covers the lore and legends of tides and the Moon in history, astrology, and astronomy. Explains how gravitational attraction of the Moon and Sun causes tides. A few black-and-white photographs and reference notes after each chapter help explain the text.

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