# Jeffreys, Harold

# JEFFREYS, HAROLD

(*b*. Fatfield, County Durham, England, 22 April 1891; *d*. Cambridge, England, 18 March 1989),

*applied mathematics, statistics, theoretical seismology, astrophysics*.

Jeffreys’s main achievements were in seismology, planetary geodynamics, and applied statistics: he provided proof of the liquid nature of Earth’s metallic core (1926). He developed, from 1931 onward, improved travel-time tables for the propagation of seismic waves from earthquakes to enable better determinations of the location of earthquake foci and of the velocity structure (and hence inferred composition) of Earth’s mantle and argued for regional differences in velocity structures beneath the crust (1954, 1962). He showed the presence of large-scale anomalies in Earth’s gravitational field (1941) and the importance of cyclones as part of general atmospheric circulation (1927). In 1931 he also pioneered the field now known as Bayesian statistics.

**Childhood and Education** . Jeffreys was the only child of Robert Hall Jeffreys and his wife Elizabeth Mary Sharpe, both schoolteachers. As a child he was interested in natural history, botany, astronomy, and photography. His lifelong interest in celestial mechanics sprang from reading popular works by the astronomers Sir Robert Ball and Sir George Howard Darwin. In 1903 he gained a scholarship to Rutherford College school, Newcastle-upon-Tyne, and in 1907 he was awarded a scholarship to Armstrong College of Durham University, Newcastle (University of Newcastle from 1963), where he read mathematics with ancillary physics and chemistry, plus a year of geology, graduating first class in 1910 with distinction in mathematics. While there, he read Charles Darwin’s work on the equilibrium of rotating, self-gravitating fluid masses, the origin of the solar system, and how Earth’s tides influenced the evolution of the Earth-Moon system.

At that time, the Cambridge mathematical tripos was widely regarded as the best training for a mathematical career, and graduates from other universities commonly took it as though it were postgraduate study. Accordingly, Jeffreys was awarded an entrance scholarship to read mathematics at St. John’s College, Cambridge. Although he found it considerably harder than that which he had studied at Armstrong College, he became a wrangler (i.e., a student who obtained first-class marks) in part 2 of the tripos in 1913 and was jointly awarded the Hughes Prize. Influenced by lectures of the mathematician Ebenezer Cunningham and the astronomer and mathematician Sir Arthur Eddington, Jeffreys became committed to astrophysics. In 1912 he was awarded the Adams Memorial Prize for an essay on precession (the path around the circumference of the cone traced by the obliquity of the rotation axis of a planet about the pole to the plane in which the planets appear to orbit the Sun) and nutation (the regular high-frequency wobble imposed on this circular path), subjects to which he would return throughout his career. His college scholarship was extended for a fourth year, and Jeffreys embarked on research. He was elected to fellowship of St. John’s College in November 1914 (a position he held until his death) and was awarded the Isaac Newton Studentship (1914–1917), working mainly on cosmology and planetary geodynamics.

**Personality** . Slim and moderately tall, Jeffreys wore glasses, sported a small mustache, and was a heavy smoker. He was a keen cyclist and photographer, extremely knowledgeable about botany, a great reader of detective and other fiction and poetry, and an admirer of Henrik Ibsen’s *Peer Gynt* (quirky quotations from all these sources enlivened chapter headings of his books). For many years he sang tenor in the Cambridge Philharmonic Choir, but despite being sociable he tended to be withdrawn, working almost entirely on his own and, in contrast to the clarity of his writing, was inarticulate and halting in conversation and capable of reducing an undergraduate

class to one or two attendees with his stumbling delivery. His college tutorials could proceed in silence, but the pale-omagnetist Raymond Hide recalled that “his grunts and murmurs should be taken seriously, because they were likely to contain pearls of wisdom” (Hide, 1997). In correspondence (e.g., with the paleomagnetist Stanley Keith Runcorn) Jeffreys could be acerbic.

**Marriage** . On 6 September 1940 Jeffreys married Bertha Swirles (1903–1999), daughter of William Alexander Swirles, commercial traveler, and his wife Harriet Blaxley, a primary school teacher. Having obtained first-class honors in the mathematical tripos (1924), Bertha became Hertha Ayrton Research Fellow at Girton College, Cambridge (1927–1928), supervised by Ralph Fowler and Douglas Hartree, spending the winter semester of 1927–1928 at Göttingen University, Germany, where she was supervised by Max Born and Werner Heisenberg. She was awarded her PhD in 1929 with a thesis on quantum mechanics. Following appointments at the universities of Manchester, Bristol, and Imperial College London, she returned to Cambridge as official fellow and lecturer in mathematics at Girton in 1938, later becoming its director of studies in mathematics and mechanical sciences (1949–1969) and vice-mistress (1966–1969). Following the marriage, she continued to publish in her own field but collaborated with Jeffreys on *Methods of Mathematical Physics* (1946) and in editing the volumes of his *Collected Papers*. She also aided him by translating, from the Russian, Evgenii Fedorov’s book *Nutation and Forced Motion of the Earth’s Pole* (1963) and an article and correspondence by the Croatian physicist Stjepan Mohorovicic. There were no children of the marriage.

**Career** . Following the outbreak of World War I, Jeffreys worked part time at the Cavendish Laboratory (1915–1917) on war-related problems. He then joined the Meteorological Office in South Kensington, London, as personal assistant to its director, Sir William Napier Shaw, but returned to Cambridge on weekends. In 1920 Shaw was preparing to retire and Jeffreys was appointed librarian, but the position eventually proved so unsatisfactory that he returned to St. John’s in 1922 as college lecturer in mathematics. In 1926 he was appointed university lecturer, then reader in geophysics (1931) and Plumian Professor of Astronomy and Experimental Philosophy (1946). He retired in 1958; the last of his technical papers was published in 1987 when he was ninety-six.

**Cosmology** . Jeffreys’s first papers on Earth (1915) resulted from reading *Dynamics of a System of Rigid Bodies* by the mathematician Edward John Routh. The “planetesimal hypothesis,” proposed by the American astronomers Thomas Chrowder Chamberlin and Forest Ray Moulton in 1905, envisaged the origin of the solar system as attributable to a catastrophic close encounter between the Sun and a passing star, giving rise to a number of gaseous jets from the Sun, the inner parts of which condensed into the initial cores of the planets while the outer cooled to form a swarm of solid bodies rotating about the Sun. The planets then grew by gradual accretion. In an Adams Prize essay in 1917 the mathematician and astronomer Sir James Hopwood Jeans had proposed that a single large cigar-shaped streamer of hot gas torn from the Sun condensed into the planets. Jeffreys (1917–1918) concurred, except for postulating a much smaller primitive Sun than had Jeans. Despite severe objections being raised to the Jeans-Jeffreys theory by the American astronomer Henry Norris Russell in 1935, Jeffreys never accepted the alternative view. (Both these “catastrophic” hypotheses have since been replaced by the “nebular hypothesis,” which envisages planetary growth by gradual accretion and collision within the dust cloud of a flat rotating protoplanetary disk surrounding the primitive Sun.)

**Meteorology and Planetary Geodynamics** . While at the Meteorological Office, Jeffreys worked on wartime problems in fluid dynamics having to do with the effects of tide and winds on sea conditions off the French coast, gunnery trajectories, and the atmosphere. With time to continue his own research, he showed (1920) that the worldwide effect of tidal friction on the seabed accounted for secular slowing of Earth’s rotation. His legacy from this period includes a number of papers (1917–1933) on atmospheric convection, tides, and the interaction between wind and the sea, but after the 1930s he wrote relatively little on meteorology and fluid dynamics.

**Statistics** . Underpinning all of his research in seismology, general geophysics and related geological issues, celestial mechanics, and planetary geodynamics was his approach to scientific method and the application of mathematical and probabilistic techniques to the solution of practical problems in the treatment of gravity and seismic data. Examples include his development of methods for the numerical solution of differential equations; fitting a travel-time curve to observations of arrival times of seismic waves; and the lessening of the effect of unusual or erroneous values in estimating the mean and standard deviation of a frequency distribution in order to improve the accuracy of seismic travel-time tables (summarized in Jeffreys, 1939, ch. 4).

While a student at Cambridge, Jeffreys had been greatly influenced by *The Grammar of Science* (1892) by the statistician and philosopher of science Karl Pearson. He subsequently met the mathematician Dorothy Maud

Wrinch during his time in London. He and Wrinch now found common cause in the philosophy of science. They began collaborative work, initially writing on the methods of scientific inquiry and related probability theory and subsequently on seismology. Their collaboration continued following her return to Cambridge, as a lecturer in mathematics at Girton College (1921–1923). Much of Jeffreys’s later work was influenced by the “simplicity postulate,” which they first proposed in 1921: the belief that if a set of data might be accounted for by two or more alternative laws (models), all of which had a reasonable a priori probability, then the simplest model capable of making precise predictions that could be tested should be given the greatest prior probability and would therefore be preferable. Thus, fitting a simple equation might be preferable to a higher-order polynomial or differential equation, even if the latter fitted the data more exactly.

By 1939 Jeffreys had generalized this view, so that the complexity of a “law” was simply the number of adjustable parameters in it, the significance of each of which could be statistically tested. Although he and Wrinch introduced a notation for conditional probability in the 1920s, it was Jeffreys’s book *Scientific Inference* (1931) in which the now-standard notation *P*(*q*|*h*), to denote the probability *P* of a proposition *q*, given prior knowledge (initial data) *h*, first appeared. In this work he argued strongly for the statistical principle of “inverse probability” (first postulated by the eighteenth-century British mathematician Thomas Bayes) and developed methods to enable the utilization of different kinds of evidence with different reliabilities. His largely independent development of probability theory brought him into prolonged dispute (1932–1934) with the agricultural statistician Sir Ronald Aylmer Fisher. This arose mainly as the result of a mutual misunderstanding of the other’s views, as the practical outcomes of their different approaches proved very similar. Jeffreys’s *Theory of Probability* (1939), which introduced the methods of what came to be called Bayesian statistics, was cooly received at the time, being largely ignored by statisticians, but it was promoted by others, such as the New Zealand mathematician Keith Edward Bullen, a former PhD student of Jeffreys (1931–1934). Jeffreys also wrote several textbooks on mathematical methods: *Operational Methods in Mathematical Physics* (1927), *Cartesian Tensors* (1931), and *Asymptotic Approximations* (1962).

**Geophysics** . While in London, Jeffreys also met the geologist Arthur Holmes. Holmes was then beginning his work on radioactivity and the age of Earth. As a result, Jeffreys wrote several papers on the thermal history of Earth, the origin of the solar system, and the dynamics of the inner planets. In the years 1918–1929, based on estimates of the time taken for the eccentric orbit of Mercury to develop, Jeffreys made several estimates of the age of Earth of about 2.5 billion to 3 billion years. Although still too young (4.54 billion years is accepted in the early twenty-first century) these were, correctly, much older than the ages then being obtained by Holmes and others from studies of uranium and lead isotopes in minerals. In 1921 Jeffreys and Wrinch analyzed the seismic waves resulting from the accidental detonation of four thousand tons of explosives at Oppau, Germany, and this led him to suggest (1924) intentionally setting off large explosions in order to generate artificial seismic waves as a source for seismic studies (he would write in 1962 on travel times of seismic waves from thermonuclear weapons tests in the Pacific). Data from the Oppau explosion enabled him to confirm a hypothesis first mentioned to him by Holmes, that a granitic layer within the crust rested on one of more basic composition. The results of these and other investigations were brought together in Jeffreys’s masterly book *The Earth: Its Origin, History, and Physical Constitution* (1924), which would run to six editions. Bullen coauthored with him two important works in early seismology: *Times of Transmission of Earthquake Waves* (1935) and *Seismological Tables* (1940).

Jeffreys’s earlier work in meteorology and computational fluid dynamics made him realize that convection might occur within the body of Earth, but he believed that any such effect could only have existed early in its history. One of the consequences of his theoretical analyses of the cooling of Earth since its formation, and the effects of radioactivity, was his conclusion that contraction of Earth’s crust as a result of cooling would produce sufficient compression to cause the development of mountain chains. He first postulated this in 1916 and persisted with it (e.g., in *Earthquakes and Mountains*, 1935), despite criticism from geologists. This theory also partly underpinned his lifelong opposition to the theory of continental drift. Another reason he was so unyielding on this topic was that in 1957 a German seismologist, Cinna Lomnitz, published an empirical relationship showing that the creep (slow but continuous deformation) observed in igneous rocks under long-continued stress in the laboratory increased logarithmically with time. Jeffreys in 1958 generalized this relationship to explain the damping of Earth’s Chandler wobble (its fourteen-month nutation), the sharpness of transverse seismic waves at great distances, and the Moon’s rotation and the persistence of its dynamic ellipticities, although (together with Stuart Crampin) in 1960 he revised values of some of the constants used in this last work. Jeffreys’s modified Lomnitz law also implied that convection currents in Earth could not be maintained. This last, together with his apparent lack of knowledge of developments in paleomagnetism, led him to discount the mounting evidence from the 1950s onward that supported continental drift. Jeffreys

(1974, p. 401) still maintained that his theory showed that “continental drift—by convection, sea-floor spreading, and/or plate tectonics—cannot occur.”

Surprisingly, he made no contributions to geomagnetism and was extremely skeptical of paleomagnetic results (which he always distrusted: having been warned in 1905 against mishandling magnets, he assumed rock specimens would prove equally unreliable). While admitting that some meteoritic craters existed on Earth, encouraged by experimental results obtained by Mohorovicic in 1928, he believed that lunar craters could equally well have been the result of explosive emission of internal gases or steam from a semifluid crust.

**Honors** . Jeffreys was awarded the DSc of Durham University in 1917 for his publications on geodynamics (the PhD at Cambridge did not exist until 1921). He was elected Fellow of the Royal Society in 1925. He served as secretary (1920–1927) and president (1955–1957) of the Geophysical Committee of the Royal Astronomical Society and president of the International Association of Seismology (1957–1960). He was awarded the Buchan Prize of the Royal Meteorological Society (1929); Gold Medal of the Royal Astronomical Society (1937); Murchison and Wollaston Medals of the Geological Society (1939, 1964); Royal and Copley Medals of the Royal Society (1948, 1960); the Prix Lagrange of the Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique (1948); and the Vetlesen Prize of the Lamont Geological Observatory (subsequently the Lamont-Doherty Earth Observatory) of Columbia University, New York (1962), as well as five honorary degrees and honorary memberships of many societies. The importance of his statistical work was finally recognized by the statistical community in the 1960s, and he was awarded the Guy Medal in gold of the Royal Statistical Society in 1963. He was created knight bachelor in 1953.

## BIBLIOGRAPHY

*St. John’s College, Cambridge, England, holds biographical papers, research, lectures, publications, societies and organizations, visits and conferences, correspondence, photographs, and sound and video recordings (206 files; catalog is available from http://janus.lib.cam.ac.uk/db/ The National Meteorological Library, Bracknall, England, contains an audiotaped interview, also available at American Institute of Physics, Center for Physics and Niels Bohr Library, College Park, Maryland*.

### WORKS BY JEFFREYS

*The Earth: Its Origin, History, and Physical Constitution*.

Cambridge, U.K., and New York: Cambridge University Press, 1924.

*Operational Methods in Mathematical Physics*. Cambridge, U.K:

Cambridge University Press, 1927.

*The Future of the Earth*. London: Kegan Paul, Trench, Trubner, 1929; New York: Norton, 1929.

*Cartesian Tensors*. Cambridge, U.K.: Cambridge University Press, 1931.

*Scientific Inference*. Cambridge, U.K.: Cambridge University Press, 1931.

*Earthquakes and Mountains*. London: Methuen, 1935.

With Keith E. Bullen. *Times of Transmission of Earthquake Waves*.

Publications du Bureau Central Séismologique International, Serie A. Tarlouse: Bureau Séismologique International, 1935.

*Theory of Probability*. Oxford: Clarendon Press, 1939.

With Keith E. Bullen. *Seismological Tables*. Edinburgh: Neill & Company for British Association Seismological Investigations Committee, London, 1940.

With Bertha Swirles (Lady Jeffreys). *Methods of Mathematical Physics*. Cambridge, U.K.: Cambridge University Press, 1946.

*Asymptotic Approximations*. Oxford: Clarendon Press, 1962.

With Bertha Swirles (Lady Jeffreys), eds. *Collected Papers of Sir*

*Harold Jeffreys on Geophysics and Other Sciences*. 6 vols.

London, Paris, and New York: Gordon and Breach, 1971–1977. Contains the majority of Jeffreys’s more than 440 papers, excepting work later incorporated in his books.

“Theoretical Aspects of Continental Drift.” In *Plate Tectonics— Assessments and Reassessments*, Memoir 23, edited by Charles F. Kahle, 395-405. Tulsa, OK: American Association of Petroleum Geologists, 1974.

### OTHER SOURCES

Aldrich, John. “The Statistical Education of Harold Jeffreys.” *International Statistical Review* 73 (2005): 289–307. An earlier version is available from http://eprints.soton.ac.uk/33497

Bolt, Bruce A. “Jeffreys and the Earth.” In *Relating Geophysical Structures and Processes: The Jeffreys Volume*, edited by Keiiti Aki and Renata Dmowska, 1–10. Geophysical Monograph 76. Washington, DC: American Geophysical Union, 1993. A good survey of Jeffreys’s work in geophysics and geodynamics.

Cook, Alan. “Sir Harold Jeffreys.” *Biographical Memoirs of Fellows of the Royal Society* 36 (1990): 303–333. A good overall biographical account with a comprehensive bibliography on microfiche.

Galavotti, Maria C. “Harold Jeffreys’ Probabilistic Epistemology:

Between Logicism and Subjectivism.” *British Journal for the Philosophy of Science* 54 (2003): 43–57.

Hide, Raymond. “Hide Receives the 1997 Bowie Medal.”

American Geophysical Union, 1997. Available from http://www.agu.org/inside/awards/bios/hide_raymond.html.

Howie, David. *Interpreting Probability: Controversies and Developments in the Early Twentieth Century*. Cambridge, U.K., and New York: Cambridge University Press, 2002. A detailed account of Jeffreys’s work on probability and the Jeffreys-Fisher dispute.

Lapwood, E. Ralph. “Contributions of Sir Harold Jeffreys to Theoretical Geophysics.” *Mathematical Scientist* 7 (1982): 69–84.

Lindley, Dennis V. “Jeffreys’ Contribution to Modern Statistical Thought.” In *Bayesian Analysis in Econometrics and Statistics: Essays in Honor of Harold Jeffreys*, edited by Arnold Zellner, 35–40. Amsterdam and New York: North-Holland, 1980.

M.A.K. and D.H.G. “Sir Harold Jeffreys (1891–1989).” *Annual Report of the Geological Society, London* (1989): 34–35.

Runcorn, Keith. “Sir Harold Jeffreys 1891–1989.” *Nature* 339 (1989): 102.

Seidenfeld, Teddy. “Jeffreys, Fisher and Keynes: Predicting the Third Observation Given the First Two.” In *New Perspectives on Keynes*, edited by Allin F. Cottrell and Michael S. Lawlor. Durham, N.C.: Duke University Press, 1995.

Spall, Henry. “Sir Harold Jeffreys—An Interview.” [abridged from *Earthquake Information Bulletin*, 12 (1980)] Available from neic.usgs.gov/neis.

Swirles, Bertha (Lady Jeffreys). “Harold Jeffreys: Some Reminscences.” *Chance* 4 (1991): 22–26.

Zellner, Arnold. “Jeffreys, Sir Harold (1891–1989).” In *International Encyclopaedia of the Social and Behavioural Sciences*, edited by Neil J. Smelser and Paul B. Bates, 7960–7963. Kidlington, Oxford: Pergamon Press. 2001.

*Richard J. Howarth*

#### More From encyclopedia.com

#### You Might Also Like

#### NEARBY TERMS

**Jeffreys, Harold**