
William Rowan Hamilton (18051865)
Considered a child prodigy, William Rowan Hamilton could read Hebrew, Latin, and Greek at the tender age of five, and had undertaken the study of at least six other languages before his twelfth birthday. The native of Dublin, Ireland lived with and was educated by an uncle who was an Anglican priest since his father’s legal career required him to spend much of his time in England. In his youth, Hamilton was introduced to Zerah Colburn, an American mathematical prodigy who exhibited his amazing calculating dexterity for entertainment. Competitive bouts of computations between the young men apparently inspired Hamilton to increase his knowledge of mathematics, and he embarked upon a course of study that included the works of Euclid, Clairaut, Lloyd, Newton, Lagrange, and Laplace. By 1822, his mathematical abilities had advanced to such an extent that he discovered an important error in Laplace’s treatise Celestial Mechanics, a feat that garnered him the attention of the Royal Astronomer of Ireland, John Brinkley, who he would shortly thereafter replace.
Once he entered Trinity College, Hamilton’s reputation for superior ability continued unabated, and he obtained the extraordinary distinction of receiving an “optime” in both science and classics. In 1824, he presented a paper, On Caustics (in optics, caustics refer to bundles of light rays), to the Royal Irish Academy. Though it was not accepted for publication in its original form, the group acknowledged the merit of the paper and urged Hamilton to develop the subject matter further, which he did over the course of several years. In 1827, an expanded form of Hamilton’s work with caustics was submitted to the Academy and was ordered to be printed. The important treatise entitled Theory of Systems of Rays described a theory that integrated optics, mathematics, and mechanics into a single characteristic function. By utilizing this function, Hamilton was able to mathematically address in detail caustic curves, the density of the light in close proximity to caustic surfaces, and the foci of reflected light. Largely based on the strength of his theory of the characteristic function of an optical system, Hamilton won the position of Royal Astronomer of Ireland, which was vacated by Brinkley when he became a bishop. Also, later in 1827, Hamilton received an appointment as a professor of astronomy at Trinity College. Despite his significant abilities, some prominent individuals considered an undergraduate an inappropriate choice for such distinguished posts and, therefore, viewed Hamilton’s acceptance of these positions with skepticism.
Prior to establishing himself in Dunsink Observatory, located just outside of Dublin, Hamilton engaged in travel throughout England and Scotland. During this tour, he became acquainted with the British romantic poet William Wordsworth and the two formed a lasting friendship. Over the course of their correspondence, Hamilton often shared his own poetry with the famed writer, which he apparently began writing when he found out his first love, Catherine Disney, was to marry someone else. His scientific skill, however, appears to have been greater than his poetical prowess, a view Wordsworth was not too timid to share with him. Nevertheless, Hamilton’s penchant for scribbling verses continued throughout his life, perhaps because he never quite reconciled himself to losing Catherine, with whom he sporadically corresponded despite his eventual marriage to Helen Maria Bayly. Hamilton and Wordsworth also often engaged in lively debates about the nature of science and poetry, and whether or not there were parallels between the two seemingly divergent spheres.
It was not long after he was installed in Dunsink that Hamilton found that his real interests lie more in the realm of mathematics than astronomy, but as he was allowed to spend his time as Royal Astronomer in whatever manner he saw fit, he was able to indulge his personal preference. During the early years of his career, he developed three lengthy supplements to his treatise on systems of rays, the first of which (1830) expanded his theory to optical systems in which light is refracted, the second of which (1831) concerns the study of plane systems and systems of revolution, and the last of which (1832) addresses the wave theory of light, aberration, and the transmission of light in biaxial crystals in relation to his theory of the characteristic function. It was for the mathematical prediction that light refracted by a suitably pure biaxial crystal will form a hollow cone if a single ray of light is incident at certain angles on the face of that crystal, as outlined in this third supplement, that Hamilton received the most acclaim during his lifetime. His prediction of conical refraction was quickly verified through experimental means by another professor at Trinity College, Humphrey Lloyd, and both he and Hamilton became well established in scientific circles. Today, many of the possibilities for the practical use of conical refraction are just beginning to be realized because of the remarkable difficulty in obtaining optical quality biaxial crystals, such as the aragonite utilized by Lloyd. However, due to recent improvements in the fabrication of synthetic crystals, the phenomenon first predicted by Hamilton may soon find use in hitech devices, such as specialized optical tweezers, and for holography and other laser applications.
After the success he experienced in 1832, Hamilton began to concentrate his efforts on the study of dynamics and produced several important papers in the field. Hamiltonian mechanics became even more appreciated as the discipline of quantum mechanics began to take shape in the twentieth century. In the late 1830s Hamilton’s focus shifted again, this time to the basic principles of algebra. His work in the area resulted in a theory of conjugate functions, or algebraic couples, in which complex numbers are formed as ordered pairs of real numbers. Subsequently, Hamilton attempted to develop a theory of triplets that could be applied to threedimensional geometric problems, but without any success. Eventually, in 1843, he realized suddenly during a walk with his wife along the Royal Canal that the theory he sought should involve quadruplets, not triplets, and his excitement at his discovery caused him to pause and carve the equations that would underlie such a theory in a nearby bridge. Thus, began more than 20 years of work on Hamilton’s theory of quaternions, which would greatly impact the development of the modern system of vector analysis and is sometimes utilized today for computer graphics, attitude control systems, and the control theory used in engineering.
Hamilton received many honors and awards throughout his life for his work in optics, mathematics, and mechanics. He was knighted in 1835 during an assembly of the British Association for the Advancement of Science, appointed president of the Royal Irish Academy in 1837 (a post he held until 1846), and made a foreign member of the St. Petersburg Academy. He was also elected the first corresponding member of the American National Academy of Sciences a short time before he died from gout on September 2, 1865.
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