Robert Adrain, 1775 – 1843, Irish mathematician.
Robert Adrain, 1775 – 1843, Irish mathematician.
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Robert Adrain was born on September 30, 1775 in Carrickfergus, Ireland, but left Ireland after being wounded in the failed uprising of the United Irishmen in 1798 and moved to Princeton, New Jersey. He was the son of a school teacher who also made mathematical instruments. His parents died when Robert was about fifteen, leaving him to support both himself and his four brothers and sisters.
Adrain received a good education but this education did not include any mathematics beyond arithmetic. His own curiosity, however, led him to study books on mathematics which explained algebraic notation and so he became essentially a self-taught mathematician.
Robert Adrain immigrated to the United States from Ireland in 1798, when he was about twenty-three years of age. Adrain was a teacher in Ireland and took part in the rebellion of 1798. With his wife, Ann Pollock, he escaped to America, where he first served as a master at Princeton Academy, then moved to York, Pennsylvania, as principal of the York County Academy. In 1805 he became principal of the academy in Reading, Pennsylvania. From 1809 to 1813 Adrain was professor of mathematics at Queen’s College (now Rutgers), New Brunswick, New Jersey, and from 1813 to 1826 at Columbia College, New York. He then returned to Queen’s College for a short while.
Robert taught from 1827 to 1834 at the University of Pennsylvania in Philadelphia, where in 1828 he became vice-provost. From 1836 to 1840 he taught at the grammar school of Columbia College, after which he returned to New Brunswick. It is reported that in the classroom he often showed impatience with ill-prepared students. He had seven children, one of whom, Garnett Bowditch Adrain (1815-1878), was a Democratic member of Congress from New Brunswick between 1857 and 1861.
Adrain’s first mathematical contributions were in George Baron’s Mathematical Correspondent (1804), in which he solved problems and wrote on the steering of a ship and on Diophantine algebra. He continued the latter subject in The Analyst (1808), a short-lived periodical that he published himself. Here we find Adrain’s most interesting mathematical paper, a study of errors in observations with the first two published demonstrations of the normal (exponential) law of errors. Gauss’s work was not published until 1809. This volume also contains Adrain’s paper on what he calls isotomous curves, inspired by Ritlenhouse’s hygrometer. If a family of curves (e.g., circles or parabolas) are all tangent at a point A, then an isotomous curve cuts these curves at equal arcs measured from A. Another article deals with the catenaria volvens, the form taken by a homogeneous, flexible, nonelastic string uniformly revolving about two points, without gravity.
Adrain became a member of the American Philosophical Society in 1812, and six years later he published in its Transactions a paper on the figure of the earth, in which he found 1/319 as its elliptieity (Laplace had 1/336; the modern value is 1/297). In the same issue of the Transactions he also published a paper on the mean diameter of the earth. Both papers were inspired by Laplace.
Robert Adrain is chiefly remembered for his formulation of the method of least squares, published in 1808. He is also regarded for his service as president of the York County Academy in York, Pennsylvania, from 1801 to 1805. Adrain was an editor of and contributor to the Mathematical Correspondent, the first mathematical journal in the United States. In 1825 he founded a quite successful publication targeting a wider readership, The Mathematical Diary, which was published through 1832. Adrain, Gauss, and Legendre all motivated the method of least squares by the problem of reconciling disparate physical measurements.
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In his religious affiliation Robert Adrain was a Protestant and, being a part of The United Irishmen group, he joined a Protestant Irish volunteer corps established to defend the country from the French as an officer in their army in a rebellion that occurred on May of 1798 in Ireland.
Adrain was an ardent student of Laplace, and his paper on errors is in the spirit of Laplace. For example, Adrain wrote about include a study of the catenary, and other curves which he called isotomous. In 1818 he published a paper Investigation of the figure of the Earth and of the gravity in different latitudes. In this paper Adrain gave 1/319 as the ellipticity of the Earth, a figure better than that given by Laplace (he gave 1/336), and about halfway between Laplace's figure and the accepted value today of 1/297. Adrain's improvement on Laplace's value was, of course, made because Adrain had been inspired to work on the topic because of the contributions of Laplace.
Adrain became a member of the American Philosophical Society in 1812.
Although a man of wit and humour, Adrain was often irritable in the classroom. One of his students reported that whenever a student faltered in his recitation (then the principal form of classroom instruction), Adrain would terminate his efforts with a remark such as "If you cannot understand Euclid, dearie, I cannot explain it to you".
Quotes from others about the person
As Hogan writes:
"During his last year (at the University of Pennsylvania) Adrain had serious problems with discipline in his classes. Because the faculty saw no way to aid Adrain and feared that the disturbances would spread to other classes, the university asked for Adrain's resignation."
Adrain's employment as a teacher provided him with enough resources to marry Ann Pollock in 1798, the year of the Irish Rebellion. They had seven children, one of whom, Garnett Bowditch Adrain, became a Democratic member of Congress. While an officer in the rebel army, Adrain received a severe wound; once well, he fled with his wife to America.
Adrain`s papers were inspired by Laplace.
It was in 1808 that Robert Patterson proposed a surveying problem in the Analyst and, after comments from Bowditch suggesting two procedures. Adrain gave an argument to establish the validity of the normal distribution for the errors, and he then used it to prove the validity of the method of least squares. Taking a number of problems as examples, Adrain showed that one of Bowditch's procedures was equivalent to using the method of least squares. It is unfortunate that despite Adrain's priority over Gauss, it is the latter who has received the credit for this important statistical contribution.
