William Rowan Hamilton
Sir William Rowan Hamilton was an Irish mathematician, physicist, and astronomer who made numerous major contributions to algebra, classical mechanics, and optics. His theoretical works and mathematical equations are considered fundamental to modern theoretical physics, particularly his reformulation of Lagrangian mechanics. His research included the analysis of geometrical optics, Fourier analysis, and quaternions, the last of which made him one of the founders of modern linear algebra.
Hamilton was Andrews Professor of Astronomy at Trinity College Dublin. He was also the third director of Dunsink Observatory from 1827 to 1865. The Hamilton Institute at Maynooth University is named after him.
He received the Cunningham Medal twice, in 1834 and 1848, and the Royal Medal in 1835. He was also knighted in 1835. Hamilton remains arguably the most influential Irish physicist, along with Ernest Walton. Since his death, he has been commemorated throughout the country, with several institutions, streets, monuments, and stamps bearing his name.
Biography
Early life
William Rowan Hamilton was born on 4 August 1805 in Dublin, Ireland, the fourth of nine children of Archibald Hamilton and Sarah Hutton who lived at 29 Dominick Street. Archibald, who was from Dublin, worked as a solicitor. By the age of 3, Hamilton had been sent to live with his uncle James Hamilton, a graduate of Trinity College Dublin who ran a school in Talbots Castle in Trim, County Meath.Hamilton is said to have shown talent at an early age. His uncle observed that Hamilton, from a young age, had displayed an uncanny ability to acquire languages — a claim which has been disputed by some historians, who claim he had only a basic understanding of them. At the age of seven, he had already made progress in Hebrew, and before he was 13, he had acquired, under the care of his uncle, a dozen languages: classical and modern European languages, Persian, Arabic, Hindustani, Sanskrit, Marathi and Malay. The emphasis of Hamilton's early education on languages is attributed to the wish of his father to see him employed by the British East India Company.
An expert mental calculator, the young Hamilton was capable of working out some calculations to many decimal places. In September 1813, the American calculating prodigy Zerah Colburn was being exhibited in Dublin. Colburn was 9, a year older than Hamilton. The two were pitted against each other in a mental arithmetic contest, with Colburn emerging as the clear victor.
In reaction to his defeat, Hamilton spent less time studying languages, and more on mathematics. At age ten, he stumbled across a Latin copy of Euclid; and at twelve he studied Newton's Arithmetica Universalis. By age 16, he had covered much of the Principia, as well as some more recent works on analytic geometry and differential calculus.
Education
In mid-1822, Hamilton began a systematic study of Laplace's Mécanique Céleste. During this period, he encountered what he believed to be a logical error in Mécanique Céleste, an observation which led Hamilton to be introduced to John Brinkley, then Royal Astronomer of Ireland. In November and December of 1822, he completed his first three original mathematical papers. On his first visit to Dunsink Observatory, he showed two of them to Brinkley, who requested that the papers be developed further. Hamilton complied, and early in 1823, Brinkley approved the amended version. In July of 1823, Hamilton earned a place at Trinity College Dublin by examination, at age 17. His tutor there was Charles Boyton, a family friend, who brought to his attention the contemporary mathematics published by the group at the École Polytechnique in Paris. John Brinkley remarked of the precocious Hamilton, "This young man, I do not say will be, but is, the first mathematician of his age."The college awarded Hamilton two optimes, or off-the-chart grades, in Greek and in physics. He was first in every subject and at every examination. He aimed to win a Trinity College fellowship by competitive examination, but this did not happen. Instead, after Brinkley was made Bishop of Cloyne in 1826, Hamilton was appointed to the vacant posts left by Brinkley's departure the following year: Andrews Professor of Astronomy and Royal Astronomer of Ireland. Despite having his undergraduate career cut short in this way, he earned degrees in both classics and mathematics.
Dunsink Observatory
Hamilton, now Royal Astronomer of Ireland, took up residence at Dunsink Observatory, where he spent the rest of his life. He was there from 1827 until his death in 1865. In his early years at Dunsink, he observed the heavens quite regularly; He left routine observation to his assistant Charles Thompson. His sisters also supported the observatory's work.The introductory lectures by Hamilton in astronomy were celebrated; in addition to his students, they attracted scholars, poets, and women. Felicia Hemans wrote her poem The Prayer of the Lonely Student after hearing one of his lectures.
Hamilton invited his four sisters to come and live at the observatory in 1827, and they ran the household until his marriage in 1833. They included Eliza Mary Hamilton, the poet. In 1827, Hamilton wrote to his sister Grace about "some of" the Lawrence sisters having met his sister Eliza in Dublin.
Newly appointed to the observatory, Hamilton set off on a tour in Ireland and England with Alexander Nimmo, who was coaching him on latitude and longitude. One call was to Sarah Lawrence's school at Gateacre, near Liverpool, where Hamilton had a chance to assess the calculator Master Noakes. They visited William Wordsworth at Rydal Mount in September of that year, where the writer Caesar Otway was also present. After the visit, Hamilton sent numerous poems to Wordsworth, becoming a "poetic disciple".
When Wordsworth visited Dublin in the summer of 1829, in a party with John Marshall and his family, he stayed at Dunsink with Hamilton. On a second tour in England with Nimmo in 1831, Hamilton parted from him at Birmingham, to visit the Lawrence sisters and family on his mother's side in the Liverpool area. They met up again in the Lake District, where they climbed Helvellyn and had tea with Wordsworth. Hamilton returned to Dublin, via Edinburgh and Glasgow.
Later life and death
Hamilton retained his faculties unimpaired to the last, and continued the task of finishing the Elements of Quaternions which had occupied the last six years of his life. He died on 2 September 1865 at the age of 60, following a severe attack of gout. He is buried in Mount Jerome Cemetery in Dublin.Research
Physics
Hamilton made outstanding contributions to classical mechanics and optics.His first discovery was in an early paper that he communicated in 1823 to John Brinkley, who presented it under the title of Caustics in 1824 to the Royal Irish Academy. It was referred as usual to a committee, which recommended further development and simplification before publication. Between 1825 and 1828 the paper was expanded, and became a clearer exposition of a novel method. Over this period, Hamilton gained an appreciation for the nature and importance of optics.
In 1827, Hamilton presented a theory of a single function, now known as Hamilton's principal function, that brings together mechanics and optical theory. It helped to establish the foundations of the wave theory of light in mathematical physics. He proposed it when he first predicted its existence in the third supplement to his Systems of Rays, read in 1832.
The Royal Irish Academy paper was finally entitled Theory of Systems of Rays, and the first part was printed in 1828 in the Transactions of the Royal Irish Academy. The more important contents of the second and third parts appeared in the three voluminous supplements which were published in the same Transactions, and in the two papers On a General Method in Dynamics, which appeared in the Philosophical Transactions in 1834 and 1835. In these papers, Hamilton developed his central principle of "Varying Action".
A result of this work is a prediction for transparent biaxial crystals. A ray of light entering such a crystal at a certain angle would emerge as a hollow cone of rays. This discovery was known as conical refraction. Hamilton found it from the geometry of the wave surface introduced by Augustin-Jean Fresnel, which has singular point. There is a basic mathematical explanation of the phenomenon, namely that the wave surface is not the boundary of a convex body. A fuller understanding awaited the microlocal analysis of the middle of the 20th century,
The step from optics to dynamics in the application of the method of "Varying Action" was made in 1827, and communicated to the Royal Society, in whose Philosophical Transactions for 1834 and 1835 there are two papers on the subject.
Context and importance of the work
was a powerful new technique for working with equations of motion. Hamilton's advances enlarged the class of mechanical problems that could be solved. His principle of "Varying Action" was based on the calculus of variations, in the general class of problems included under the principle of least action which had been studied earlier by Pierre Louis Maupertuis, Euler, Joseph Louis Lagrange and others. Hamilton's analysis uncovered a deeper mathematical structure than had been previously understood, in particular a symmetry between momentum and position. The credit for discovering what are now called the Lagrangian and Lagrange's equations also belongs to Hamilton.Both the Lagrangian mechanics and Hamiltonian approaches have proven important in the study of continuous classical systems in physics, and quantum mechanical systems: the techniques find use in electromagnetism, quantum mechanics, relativity theory and quantum field theory. In the Dictionary of Irish Biography David Spearman writes:
Many scientists, including Liouville, Jacobi, Darboux, Poincaré, Kolmogorov, Prigogine and Arnold, have extended Hamilton's work, in mechanics, differential equations and symplectic geometry.