This section is from "The American Cyclopaedia", by George Ripley And Charles A. Dana. Also available from Amazon: The New American Cyclopędia. 16 volumes complete..

**Benjamin Peirce**, an American mathematician, born in Salem, Mass, April 4, 1809. He graduated at Harvard college in 1829, became tutor in mathematics there in 1831, university professor in mathematics and natural philosophy in 1833, and Perkins professor of astronomy and mathematics in 1842, which office he still holds. In 1849 he was appointed consulting astronomer to the " American Ephe-meris and Nautical Almanac." In 1855 he was one of the scientific council to which was intrusted the organization of the Dudley observatory. In 1867 he succeeded Prof. Bache as superintendent of the coast survey, which office he resigned in 1874. While he was a pupil of Dr. Bowditch he read the proof sheets of the translation of the Mecanique celeste. He was a contributor to the "Mathematical Miscellany," and undertook the publication of the " Cambridge Miscellany of Mathematics, Physics, and Astronomy," of which only five numbers appeared. In this he gave his celebrated discussion of the motion of a top spinning on a plane surface. Between 1836 and 1846 he "prepared a series of mathematical text books, which are used in Harvard college. It was also principally through his efforts that the observatory of the college was constructed and equipped.

His paper on the discovery of Neptune ("Proceedings of the American Academy of Arts and Sciences," vol. i., p. 341) excited the attention of astronomers and mathematicians in both Europe and America. In that paper he demonstrated that the mass, the distance from the sun, and other characteristics of the real planet were entirely different from those which were assumed by Leverrier and Adams in their computations, and that the discovery of the planet by Galle nearly in the position pointed out by Leverrier was due to an accidental concurrence of circumstances rather than to the correctness of the mathematical hypotheses. Prof. Peirce followed up this announcement with a thorough discussion of the mutual influences of Uranus and the real Neptune which formed the basis of the true theory of the planet. In June, 1851, and September, 1855, he published in Gould's " Astronomical Journal" papers on the constitution of Saturn's rings, in which, taking up the problem almost where it had been left by Laplace, he discussed the conditions of statical equilibrium of a transverse section of a ring, concluding that if the system be composed of separate rings moving as a whole, each ring must be very narrow; so that there must be a great number of rings, each moving with a different velocity.

He also showed that no ring could sustain itself in stable equilibrium about a primary without the attraction of properly arranged satellites, andno solid ring under any circumstances. In 1852 Prof. Peirce prepared a volume of lunar tables for the use of the American " Nautical Almanac," and they were employed in the almanac office as the basis of all computations into which the place of the moon enters. In 1857 appeared his "Treatise on Analytic Mechanics " designed to form one of a series of four treatises, the others being respectively upon " Celestial Mechanics," " Potential Physics," and "Analytic Morphology." Among his important investigations are his theory of the tails of comets, showing the mode and laws of their formation; his methods of investigating terrestrial longitudes and the form of the moon's limb by means of occultations of the Pleiades; his researches upon personal equation, showing the existence and means of measurement of a new and before unrecognized form of personal error, in observations " by eye and ear;" and the " Criterion for the Rejection of Doubtful Observations." He has also investigated the forms of equilibrium of an elastic sac containing a fluid, researches which led to his theory of analytic morphology; the phyllotactic series of numbers; and the cyclic solution of the " school-girl puzzle." His most recent work is entitled "Linear-Associative Algebra" (Washington, 1870), for which see Mathematics. He received the degree of LL. D. from the university of North Carolina in 1847, and from Harvard college in 1867, was elected an associate of the royal astronomical society of London in 1849, and'a member of the royal society of London in 1852. He was president of the American association for the advancement of science in 1853, was one of the original members of the national academy of sciences, and is a member of many other learned societies in Europe and America.

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