tory training, especially in mathematics. With such unwrought material before him, it was natural for the teacher to show his preference for a text-book in which every process of development and reasoning was worked out patiently and minutely through all its successive steps. Day took for a model the diffuse manner of Euler and Lacroix, rather than the concisc and abridged mode of the English writers. The great danger in this course is that no obstacles are left to be removed by the student through his own exertion. In the opinion of some teachers, Day has laid himself open to criticism by carrying the principle of making mathematics easy somewhat too far. It is no little praise for a book written at that time to say that, unlike most books of that period, Day's mathematics did not encourage the cramming of rules or the performing of operations blindly. On the contrary, the diligent student acquired from them a rational understanding of the subject. Day's mathematics were at once everywhere received with eagerness. They were introduced in nearly all our colleges. Even at the end of a period of fifty years they still held their place in many of our schools. In view of these facts, "it may safely be said that the value of what their author did by means of them for the college and for the country at large, while holding the office of professor from 1803 to 1817, the time when he succeeded Dr. Dwight, was not surpassed by anything in science and literature which he did subsequently during his long term of office as president of the college."* As a teacher and writer, President Day was distinguished for the simplicity and clearness of his methods of illustration. His kindheartedness and urbanity of demeanor secured the love and respect both of friends and pupils. He was succeeded in the chair of mathematics and natural philosophy by Alexander Metcalf Fisher, who held it until his death by drowning in 1822, at the shipwreck of the Albion, off the Irish coast. Fisher possessed extraordinary natural aptitudes for learning. He had prepared a full course of lectures in natural philosophy, both theoretical and experimental, which were marked for their copiousness and their exact adaptation to the purpose of instruction. His clear conception of what a text-book should be is well shown in his review of Enfield's Philosophy.t Regarding the course in natural philosophy at Yale, it may be remarked, that in 1788 Martin's Philosophy, which had gone out of print, was succeeded by Enfield's Natural Philosophy, first published in 1783. William Enfield was a prominent English dissenter. He preached in *Yale College: A Sketch of its History, by William Kingsley, Vol. I, p. 115. American Journal of Science, Vol. III, 1821, p. 125. In Vol. V, p. 83, of the same journal, is an article by him, "On Maxima and Minima of Functions of Two Variable Quantities." He contributed solutions to questions in the American Monthly Maga zine, and in Leybourn's Mathematical Repository (London). The fourth volume of the Memoirs of the American Academy of Arts and Sciences contains observations by him on the comet of 1819 and calculations of its orbit. Unitarian churches and published several volumes of sermons. Being engaged chiefly in theological studies, comparatively little attention was paid by him to the exact sciences. Nevertheless, he succeeded in compiling a work on natural philosophy which possessed elements of popularity and was used in our American colleges for four decennia. In 1820 appeared the third American edition of this work, which was then used by nearly all the seminaries of learning in New England, notwithstanding the fact that, excepting in electricity and magnetism and a few particulars in astronomy, it presented hardly any idea of the progress made in the different branches of philosophy since the period of Newton. UNIVERSITY OF PENNSYLVANIA. The University of Pennsylvania, which had such a remarkable growth under the administration of Dr. William Smith, before the Revolutionary War, had a comparatively small attendance of students after the war, and the college department is said to have been quite inferior to that of the leading American colleges of that time. An educator who was long and prominently connected with this institution and whose activity was directed towards maintaining and raising its standard, was Robert Patterson, the elder. He was born in 1743 in Ireland, and at an early age showed a fondness for mathematics. In 1768 he emigrated to Philadelphia. He first taught school in Buckingham, and one of his first scholars was Andrew Ellicott, who afterward became celebrated for his mathematical knowledge displayed in the service of the United States. About this time Maskelyne, the astronomer royal of England, compiled and published regularly the Nautical Almanac. This turned the attention of the principal navigators in American ports to the calculations of longitude from lunar observations, in which they were eager to obtain instruction. Patterson removed to Philadelphia, began giving instruction on this subject, and soon had for his scholars the most distinguished commanders who sailed from this port. Afteward he became principal of the Wilmington Academy, Delaware, and in 1779 was appointed professor of mathematics and natural philosophy at the University of Pennsylvania, which post he filled for thirty-five years. He was also elected vice-provost of that institution.* Robert Patterson communicated several scientific papers to the Philosophical Transactions (Vols. II, III, and IV), and was a frequent contributor of problems and solutions to mathematical journals. He edited James Ferguson's Lectures on Mechanics (1806), and also Ferguson's "Astronomy explained upon Sir Isaac Newton's principles and made easy to those who have not studied mathematics" (1809). Fer * Transactions of American Philosophical Society, Vol. II, New Series, Obituary Notice of Robert Patterson, LL. D., late President of the American Philosophical Society. 881-No. 3-5 guson was a celebrated lecturer on astronomy and mechanics in England, who contributed more than perhaps any other man there to the extension of physical science among all classes of society, but especially among that largest class whose circumstances preclude them from a regular course of scientific instruction. His influence was strongly felt even in this country, as is seen from the American editions by Robert Patterson of his astronomy and mechanics. Patterson wrote a small astronomy, entitled the Newtonian System, which was published in 1808. Ten years later he published an arithmetic, elaborated from his own written compends, previously used in the University. Though lucid and ingenious, this arithmetic was rather difficult for beginners, and never reached an extended circulation. It is believed by many that mathematicians generally possess a strong memory for numbers. This was certainly not true of Patterson, for we are told that he could not remember even the number of his own house. He met this dilemma by devising a mnemonic, which was indeed worthy of a mathematician. The number of his residence was 285, which answered to the following conditions: "The second digit is the cube of the first, and the third the mean of the first two." It is to be wondered that, during some fit of intense abstraction, the learned professor did not pronounce 111 to be the number of his house, instead of 285; for 111 is a number satisfying the above conditions quite as well as 285. When Robert Patterson resigned his position at the University of Pennsylvania in 1814, he was succeeded by his son, Robert M. Patterson. The latter was graduated at the University in 1804. After receiv ing the degree of M. D., in 1808, he pursued professional studies in Paris and London. In 1814 he was appointed professor of mathematics and natural philosophy, which office he filled until 1828, when he accepted the chair of natural philosophy at the University of Virginia. Robert M. Patterson published no mathematical books. From 1828 to 1834 the chair of mathematics and natural philosophy was filled by Prof. Robert Adrain. The days of greatest activity of this most prominent teacher of mathematics were spent at other institutions, but we take this opportunity of introducing a sketch of his life.* Robert Adrain was born in Ireland. At the age of fifteen he lost both his parents, and thenceforward he supported himself by teaching. At the end of an old arithmetic he found the signs used in algebra. His curiosity becoming greatly excited to discover their meaning, he gave himself no rest until at last he found out what they meant. In a short time he was able to resolve any sum in the arithmetic by algebra. Thenceforth he devoted himself with enthusiastic ardor to mathematics. He took part in the Irish rebellion of 1798, received a severe wound, and This sketch is extracted from an article in the Democratic Review, 1844, Vol. XIV. escaped to America. Immediately after his arrival he began teaching in New Jersey. After two or three years he became principal of the York County Academy in Pennsylvania. He then began contributing problems and solutions to the Mathematical Correspondent, a journal published in New York. This was the means of bringing his mathematical talents before the public. He obtained several prize medals, awarded for the best solutions. In 1805 he moved to Reading, Pa., to take charge of the academy of that place. He started there a mathematical journal called the Analyst. The first number was published in Reading, but its typographical execution disappointed him so much that he employed a publisher at Philadelphia and incurred the extra expense of a republication. We shall speak of this journal again later. In 1810 he was called to the professorship of mathematics and natural philosophy at Queen's (now Rutgers) College; and, in 1813, to the professorship of mathematics at Columbia College. In New York he became the center of attraction to those pursuing mathematical studies. A mathematical club was established, in which he shone as the great luminary among lesser lights. As a teacher, he had a most happy faculty of imparting instruction. In 1826 the delicate state of his wife's health induced him to leave Columbia College in New York and to remove to the pure air and healthful breezes of the country near New Brunswick. About two years later he was induced to accept the professorship of mathematics. at the University of Pennsylvania, a position which had been held at the beginning of the century by the well-known Robert Patterson. Adrain became also vice-provost of this institution. He resigned this position in 1834 and returned to his country seat near New Brunswick, intending to pass his time with his family and in study. But he did not remain there long, for the habit of teaching had become too strong easily to be resisted. He moved to New York and taught in the grammar school connected with Columbia College until within three years of his death. At this time his mental faculties began very perceptibly to fail. He greatly lamented their decay, and, one day when a friend called in to on his lap endeavoring to read it. of voice, "this is a dead language Place, but that time has gone by." He died in 1843. see him, he had a volume of La Place "Ah," said he, in a melancholy tone to me now; once I could read La Among American mathematicians of his day, Robert Adrain was excelled only by Nathaniel Bowditch. Of his many contributions to mathematical journals, one of the earliest was an essay published in 1804 in the Mathematical Correspondent on Diophantine analysis. This was the earliest attempt to introduce this analysis in America. In 1808 Adrain began editing and publishing the Analyst, or Mathematical Museum. At that time he had not yet entered upon his career as college professor. The above periodical contained chiefly solutions to mathematical questions proposed by the various contributors. It was a small, modest publication, which had only a very limited circulation in this country, and was unknown to foreign mathematicians. It lived, moreover, only a very short time, for only five numbers ever appeared. And yet, this apparently insignificant little journal, edited by a teacher at an ordinary academy, contained one article which was an original contribution of great value to mathematical science. It was, in fact, the first original work of any importance in pure mathematics that had been done in the United States. I refer to Robert Adrain's deduction of the Law of Probability of Error in Observation. The honor of the first statement in printed form of this law, commonly known as the Principle of Least Squares, is due to the celebrated French mathematician Legendre, who proposed it in 1805 as an advantageous method of adjusting observations. But upon Robert Adrain falls the honor of being the first to publish a demonstration of this law. He does not use the term "least squares," and seems to have been entirely unacquainted with the writings of Legendre. It follows, therefore, that not only the two deductions of this principle given by Adrain were original with him, but also the very principle itself. We now give the history of this discovery by Adrain. Robert Patterson, of the University of Pennsylvania, proposed in the Analyst the following prize question: "In order to find the content of a piece of ground, * I measured with a common circumferentor and chain the bearings and lengths of its several sides, * but upon cast ing up the difference of the latitude and departure, I discovered * that some error had been contracted in taking the dimensions. Now, it is required to compute the area of this inclosure on the most probable supposition of this error." This was proposed in No. II of the Analyst, and after being a second time renewed as a prize question in No. III, it was at length, in No. IV, solved by a course of special reasoning by Nathaniel Bowditch, to whom Adrain awarded the prize of ten dollars. Immediately following Bowditch's special solution, the editor, Adrain, added his own solution of the following more difficult general problem: "Research concerning the probabilities of the errors which happen in making observations." This paper is of great historical interest, as containing the first deduction of the law of facility of error. (x) being the probability of any error x, and c and h quantities de*Analyst, No. IV, pp. 93-97. Copies of this journal are very rare. No. IV is to be found in the Congressional Library in Washington; No. III and No. IV are in the Library of the American Philosophical Society, Philadelphia. Adrain's first proof of the Principle of Least Squares was re-published by Cleveland Abbe in the American Journal of Science and Arts, third series, 1871, pp. 411-415. Adrain's second proof was re-published by Mansfield Merriman in the Transactions of the Connecticut Academy, Vol. IV, 1887, p. 164; also in the Analyst (edited and published by J. E. Hendricks, Des Moines, Iowa), Vol. IV, No. II, p. 33. |