George Biddell Airy Research Articles

Robert Woodhouse and the Evolution of Cambridge Mathematics

Robert Woodhouse’s lifetime, 1773–1827, is often characterized as the nadir of British mathematics. In that view, the country of Newton was clinging desperately to his coat-tails whilst Continental mathematicians forged on with novel and important work in mathematics and the physical sciences. Although Woodhouse briefl y held the Lucasian Chair, the esteemed position of Newton at Cambridge, his work sought to introduce Continental mathematics to the university and reduce the blind allegiance to her most famous alumnus. Men prior to Woodhouse, such as Edward Waring and John Landen, had introduced analytical methods to England, but Woodhouse was the fi rst to do so with an eye to incorporating them into the Cambridge curriculum. By the time of Woodhouse’s death, undergraduates did learn differential notation, and analytical developments on the Continent were increasingly disseminated and incorporated into the sciences, albeit in a diluted form. Nonetheless, undergraduate studies at Cambridge remained focused on the training of students for religious and gentlemanly positions, discouraging original research. In this regard, Woodhouse was situated in a transitory period and his career is comprehensible only in light of the tensions between reform and continuity within British mathematics. In addition to holding the Lucasian Chair from 1820 to 1822, Woodhouse was the Plumian Professor from 1822 to 1827 and the fi rst director of the Cambridge Observatory when it opened in 1824. Nevertheless, he was isolated from many of the main mathematical fi gures of his time at Cambridge. Overshadowed early in his career by Samuel Vince and John Wood, and later by William Whewell, George Peacock and George Airy, Woodhouse was never fully established within one community. This seclusion was exacerbated by the isolation of Cambridge University itself at the turn of the nineteenth century. It was a collection of relatively insular colleges, whose leaders had been promoted almost exclusively from within. Furthermore, the mathematical curriculum was overwhelmingly conservative, emphasizing memorization and examination over original research, and maintaining a complacent attitude toward foreign developments. Paradoxically, the historiography has focused disproportionately on novel mathematical investigation in this era, despite this being an almost non-existent part of the Cambridge system. Professors, including Woodhouse for the majority of his career, were more concerned with the teaching and training of students than with the development of their fi eld. Nonetheless, historians have primarily examined work in analysis and algebra done by a small number of mathematically-gifted students which would serve as the basis for developments throughout the century. Because

The role of Notes and Records and some future anniversaries

Introduction to the January 2004 issue of Notes and Records with a picture of Sir George Airy who, as Astronomer Royal, was a member of the International Commission on the Metre (1870) which established the Metric Sytem and led to the Convention du Mètre (1875) and the International Bureau of Weights and Measures.

The Spirited Horse, the Engineer, and the Mathematician: Water Waves in Nineteenth-Century Hydrodynamics

Once upon a time, a spirited horse was dragging a boat along a peaceful canal of Northern Scotland. Suddenly, a ferocious dog charged from the bushes. The horse took fright and ran off, drawing the boat after him. To the horse’s surprise, the boat offered almost no resistance at this high speed. A clever naval engineer, who chanced to witness the scene, pursued the matter through numerous experiments and confirmed the horse’s discovery. Not knowing his limits, the engineer ventured to propose a mechanical explanation of this paradox based on the existence of a wonderful, solitary wave that carried the boat with it. A renowned mathematician, who excelled in the learned calculus of water motion, mocked this amateurish attempt. There was nothing in the engineer’s equations to justify his reasoning, and much to condemn it. Yet for a few years Scottish canal travelers enjoyed the commercial exploitation of the paradox. Half a century later, the aged mathematician resumed his calculations. Thanks to his long experience, he now saw new meanings in his old symbols. From this enriched analysis the solitary wave and the possibility of vanishing ship resistance emerged as if by magic. At last, the wise man rejoiced, mathematics could do as well as a galloping horse. This fable is an imaginary simplification of a real story of which the engineer John Scott Russell, and the mathematicians (in a broad sense) George Biddell Airy, George Gabriel Stokes, Joseph Boussinesq, and Lord Kelvin were the main actors (besides the spirited horse). It is intended to indicate a major nineteenth-century transformation of the mathematical physicist’s tool kit through which practically important solutions of longknown equations became much more easily accessible. The main purpose of the present article is to analyze the nature and the water-wave circumstances of this transformation. Waves on the surface of water were an obvious field of application of the new hydrodynamics of Jean le Rond d’Alembert, Leonhard Euler, and Joseph Louis Lagrange. The latter mathematician himself wrote the basic equations of water waves, and solved them in the simplest case of small waves on shallow water. Most of what is today known on water waves was found in the nineteenth century: the celerity of small, plane, monochromatic waves on water of constant depth, the pattern of waves created by a local action on the water surface, the shape of oscillatory or solitary waves of finite size, the effect of friction, wind, and a variable bottom on the size and shape of the waves. There is, however, a puzzling contrast between the conciseness and ease of the modern treatment of these topics, and the long, difficult struggles of nineteenth century physicists

Porters, watchmen, and the crime of William Sayers: the non-scientific staff of the Royal Observatory, Greenwich, in Victorian times

A careful study of the detailed archives of the Victorian Royal Observatory makes it possible to build up a picture of the employment and working conditions not only of the astronomical staff who worked at Greenwich, but also of the labourers, watchmen, and gate porters. Indeed, the archives open up a window on to how the Observatory was run on a daily basis: how its non-scientific staff were recruited and paid, and what were their terms of employment. They also say a great deal about how Sir George Biddell Airy¹ directed and controlled every aspect of the Observatory's life. Yet while Airy was a strict employer, he emerges as a man who was undoubtedly fair-minded and sometimes even generous to his non-scientific work force. A study of the Observatory staff files also reveals the relationship between the Observatory labouring staff and the Airy family's domestic servants. And of especial interest is the robbery committed by William Sayers, the Airy family footman in 1868, bringing to light as it does Sir George and Lady Richarda Airy's views on crime and its social causes and consequences, the prison rehabilitation service in 1868, and their opinions on the reform of offenders. Though this paper is not about astronomy as such, it illuminates a fascinating interface where the world of astronomical science met and worked alongside the world of ordinary Victorian people within the walls of one of the nineteenth century's most illustrious astronomical institutions.

Airy's zenith telescopes and "the birth-star of modern astronomy"

When Sir George Airy (1801-91) became the seventh Astronomer Royal in 1835, the Royal Observatory at Greenwich already had a long history of zenith observations for monitoring aberration and nutation, and providing a zenith-point for the meridional instruments. Continuing this programme, Airy designed two very successful instruments. His Reflex Zenith Tube succeeded where earlier instruments had failed, and his reflex principle was developed to provide the most successful zenith instruments over more than a century. His zenithal Water Telescope, developed for a specific experiment, was equally successful. The design and construction, operating procedures, and programmes carried out with these instruments are described.

James Ivory's last papers on the ‘Figure of the Earth’ (with biographical additions)

Sir James Ivory, F.R.S. (1765–1842), was best known for his work on the gravitational attraction of ellipsoids, and the ‘Figure of the Earth’; a problem that attracted great attention. The mixed reception of Ivory's late work on this topic is examined. Although refereed fairly and favourably by George Biddell Airy, it was attacked by Isaac Todhunter long after Ivory's death. Further biographical information about James Ivory is given. This includes evidence that reveals the identity of his mother and shows that he was not born illegitimately, as I had claimed previously.

'Extraneous government business': the Astronomer Royal as government scientist: George Airy and his work on the commissions of state and other bodies, 1838-1880

In the absence of a scientific civil service the governments of Victoria's reign had few public servants to consult when it came to the requirement for specialist scientific and technological advice - and this was at the height of the industrial revolution when the enormous changes wrought were affecting the whole population of Britain. So governments turned to one man of cast-iron probity and unparalleled credentials: George Airy. Though his formal scientific training was in mathematics and astronomy, not the engineering and thermodynamics that the industrial age might have called for, Airy gave of his time and energy to the full. But what were the purposes of the commissions? When did they sit? Who ran the Royal Observatory in Airy's absence? Only recently have the original papers in the RGO Archives been plumbed in any depth and the answers to these questions make an intriguing story.

Airy and positional astronomy

Sir George Airy (18011891), the seventh Astronomer Royal, made major contributions in numerous fields including many not directly concerned with astronomy. Throughout his life, however, he had a deep interest in fundamental aspects of astronomy, and constantly endeavoured to improve the instrumentation and procedures used for the measurement of astronomical positions. His principal achievements in this field were the refinement of techniques for the mathematical reduction of positional observations and their timely publication, and the design of a new generation of positional instruments which revitalized the work of the Royal Observatory at Greenwich, and proved to be influential for the next hundred years.

The life and times of Sir George Biddell Airy: a symposium

The life and times of Sir George Biddell Airy: a symposium

John Herschel, George Airy, and the Roaming Eye of the State

L'A. demontre qu'un reseau d'informations est percu comme un outil pour l'exercice du pouvoir de la nation et qu'il etablit un lien entre l'infrastructure domestique et les interets imperiaux de la Grande-Bretagne au XIX e siecle

Alternatives to Miller's Projection

In the 1942 issue of the Geographical Review published by the American Geographical Society, Osborne Maitland Miller presented a map projection which might be used an alternative to that devised by Mercator. This is now known Miller's Cylindrical projection and is quite popular. Its advantages are that it provides a good approximation to the Mercator near the Equator and has a finite limit at the poles. Of course, it is not conformal, nor are loxodromes represented by straight lines. Miller actually investigated several projections, comparing seven of them to Mercator's, and chose the one described here the best for his purpose. This purpose, proposed by S. Boggs, the then Geographer to the U. S. Department of State, was to find an balance between shape and area distortion. I present here two much simpler alternatives which have properties similar to Miller's projection. As with all cylindrical projections, the equations are of the form: (1) x = [Lambda] (2) y = f([Psi]) where [Psi] and [Lambda]. are the latitude and longitude measured in radians. The latitudinal functions for Mercator's, Miller's, and the two new variant projections are follows: (3) Mecator= Ln Tan([Pi]/4 + [Psi]/2) (4) Miller 1.25 Ln Tan ([Pi]/4 + 2 [Psi]/5) (5) Variation # 1 = [Psi] + 1/6[[Psi].sup.3] (6) Variant # 2 = [Psi] + 1/6[[Psi].sup.3] + 1/24 [[Psi].sup.5] These projections agree almost completely to latitude 45 degrees. The graph in Figure 1 compares the latitudinal spacing beyond 60 degrees, where the difference becomes noticeable. As can be seen on the graph, the first variant is virtually identical to Miller's projection, and the second is closer to Mercator's projection than either the Miller's or the variant 1 projections are. [Figure 1 ILLUSTRATION OMITTED] The equations for the two variant projections are much simpler than those for Miller's (and for Mercator's) projection, have simpler inverses, and simpler derivatives for the calculation of distortion. These advantages are of benefit primarily for computational purposes, the differences are hardly detectable on a world map without actual measurement (see Figure 2). It is of course ironic that Mercator's anamorphose, designed for the graphical solution to a problem in analytical geometry on a sphere, should even be considered for a non-navigational world map. None of the alternatives to Mercator's projection are suitable for navigation. [Figure 2 ILLUSTRATION OMITTED] We should ask how well any of these projections satisfy Boggs' criteria. To quote from Miller's article (1942, p. 425): By an acceptable balance is meant one which to the uncritical eye does not obviously depart from the familiar shapes of the land areas depicted by the Mercator projection but which reduces areal distortion far under these conditions. It is rather difficult to convert this curious statement into a well defined system of equations to be solved. What, for example, is an `uncritical eye'? Does this mean we can tolerate an error of 5%, or 10%, or what? Reducing areal distortion as far possible can take several meanings. George Airy's (1861) criterion of balancing the world average squared areal and angular distortions leads to the well defined, though not simple, problem of finding a function which minimizes an integral that is a linear combination of the two types of distortion, subject to appropriate constraints. This is a problem in the calculation of variations that has led to the so called optimal projections (James and Clarke 1862, Young 1920, Mescheryakov 1965, Biernacki 1965, Milnor 1969, Baetsle 1970, Gilbert 1974, Tobler 1977, Peters 1981, Pearson 1982, Hoschek 1984, Canters 1989, Laskowski 1991). Two recent studies (Grafarend and Niermann 1984, Gyorffy 1990) have applied Airy's criteria to cylindrical projections. …

Images of the sun: Warren De la Rue, George Biddell Airy and celestial photography

By the early years of the twentieth century, astronomers regarded photography as one of the most valuable tools at their disposal, a technique which not only provided an accurate and reliable representation of astronomical phenomena, but also radically changed the role of the astronomical observer. Herbert Hall Turner, professor of astronomy at Oxford, wrote in 1905: ‘The wonderful exactness of the photographic record may perhaps best be characterised by saying that it has revealed the deficiencies of all our other astronomical apparatus – object-glasses and prisms, clocks, even the observer himself.’ H. C. Russell, government astronomer in Sydney, suggested that photography might in the future make the observer redundant: ‘In many cases the observer must stand aside while the sensitive photographic plate takes his place and works with the power of which he is not capable… I feel sure that in a very few years the observer will be displaced altogether.’ Such visions were not uncommon at the time, emanating from the trust invested in the photographic process after the spectacular achievements of the late nineteenth century.

George Biddell Airy, F. R. S. (1801-1892): A centenary commemoration

The second day of January 1992 marked the 100th anniversary of the death of one of astronomy’s most remarkable figures. George Biddell Airy (figure 1) made no single outstanding discovery, though he came to be one of the most conspicuous members of his profession. He was a leading creator of institutional science who, from the early 1830s, addressed himself to the wholesale collection and revision of quantitative astronomical data on what might be called an industrial scale. Using instruments of his own design and superlative construction he was able, like the manufacturers and engineers he so admired, to make uniformity of product in positional astronomy a matter of course, by replacing skill with ‘regularity of procedure’. The consistent quality of the Royal Observatory’s astronomical constants, re-observed, revised and published between 1835 and 1881, when he was Astronomer Royal, provided a bedrock and role-model for positional astronomical investigation in Europe, America and the Empire. It is unfortunate that some oft-repeated personal insights into Airy’s character, however, come from young members of the Greenwich staff who knew him only in old age.

A Minimum-Error Equal-Area Pseudocylindrical Map Projection

The point pole of a pseudocylindrical map projection may be expanded to a line to alleviate distortions in the map at high latitudes. The ratio between the length of the pole line and the length of the equator may be determined so as to give a minimum-error pseudocylindrical map projection. A variation of the minimum-error technique, as proposed by Sir George Airy, is applied to the sinusoidal projection to demonstrate the method.

Richard van der Riet Woolley, 24 April 1906 - 24 December 1986

For the almost three centuries from the appointment of John Flamsteed in 1675 to the retirement of Richard Woolley in 1971, the office of Director of the Royal Observatory and the title Astronomer Royal were deemed inseparable (although just at the outset there had been slight variability in the title’s wording). Flamsteed and his successors were all among Britain’s most distinguished scientists. They included Edmond Halley, in office 1720-42, probably the greatest scientist of the generation after Newton; James Bradley 1742-62, discoverer of optical aberration giving the first direct empirical evidence for the Copernican system ; Nevil Maskelyne 1765-1811, who was the first scientist to weigh the Earth ; Sir George Airy 1835-81, who personally performed most of the functions nowadays requiring a string of research councils; and Sir Frank Dyson 1910-33, who organized the observations at the 1919 solar eclipse that led to the acceptance of the modification of Newton’s law of gravitation proposed by Einstein.

Private Research and Public Duty: George Biddell Airy and the Search for Neptune

Private Research and Public Duty: George Biddell Airy and the Search for Neptune

Sir George Airy (1801–1892) and the concept of international standards in science, timekeeping and navigation

Sir George Airy (1801–1892) and the concept of international standards in science, timekeeping and navigation

Gauss and the Royal Society: The reception of his ideas on magnetism in Britain (1832—1842)

Karl Friedrich Gauss (1977—1855) was a Foreign Member of the Royal Society (from 1804) and a recipient of the Society’s Copley Medal in 1838. His magnanimous disposition to mathematics and physics in Britain is exemplified in his contacts and regular correspondence with Fellows of the Royal Society involved in terrestrial magnetic research. Gauss’s own paper on the intensity of the terrestrial magnetic force in absolute measure (1832) was of fundamental importance in the history of geophysics. Extensive correspondence with George Biddell Airy, J. F. W. Herschel, Edward Sabine and Humphrey Lloyd led to close collaboration and the adoption of his ideas on magnetism in Britain after 1835, which had important consequences especially for the further development of geomagnetic instruments. The magnetic observatories established in the British Isles and in the colonies (1839) and the British Antarctic Expedition (1839—1843) were equipped with instruments operating on Gaussian principles. In this paper the reception of Gauss’s ideas on magnetism in Britain in the years from 1832 to 1842 is examined and selections from his and other unpublished letters to British contemporaries are presented.

George Biddell Airy and horology

Summary As Astronomer Royal from 1835 till 1881, G. B. Airy had a very important influence on nineteenth-century British astronomy. His personal qualities combined with his office to give him a position of great authority within the astronomical and general scientific communities, and his powers of organization and work on instrumentation transformed the Royal Observatory. A feature of Airy's work was an extensive interest in horology—particularly in astronomical regulators, marine chronometers and driving clocks for chronographs and equatorial telescopes. He was also concerned with building important turret clocks, and he established a public time service based at Greenwich. The enormous quantity of surviving material makes a complete review of Airy's career a daunting prospect; but the horology is a microcosm, where we can study on a manageable scale his attitudes to the Observatory, to its relation to society, and to the role of the Astronomer Royal as a public servant.

The Airy Transform

(1979). The Airy Transform. The American Mathematical Monthly: Vol. 86, No. 4, pp. 271-277.