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 228 PEIRCE PEKIN Embach from the west, the Velikaya from the southeast, and the Sheltcha from the east; and the Narova flows about 50 m. to the gulf of Finland from the N. E. end. The shores are low and marshy, and the greatest depth is about 60 ft. PEIRCE, Benjamin, an American mathemati- cian, 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 philos- ophy in 1833, and Perkins professor of astron- omy and mathematics in 1842, which office he still holds. In 1849 he was appointed con- sulting 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 ob- servatory. In 1867 he succeeded Prof. Bache as superintendent of the coast survey, which office he resigned in 1874. While he was a pu- pil 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 Mathemat- ics, 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 col- lege. 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 astrono- mers 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 Lever- rier was due to an accidental concurrence of cir- cumstances rather than to the correctness of the mathematical hypotheses. Prof. Peirce fol- lowed 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 condi- tions of statical equilibrium of a transverse section of a ring, concluding that if the sys- tem 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, and no 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 al- manac office as the basis of all computations into which the place of the moon enters. In 1857 appeared his " Treatise on Analytic Me- chanics " designed to form one of a series of four treatises, the others being respectively upon "Celestial Mechanics," " Potential Phys- ics," 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 investiga- ting terrestrial longitudes and the form of the moon's limb by means of occultations of the Pleiades; his researches upon personal equa- tion, showing the existence and means of mea- surement of a new and before unrecognized form of personal error, in observations " by eye and ear;" and the " Criterion for the Re- jection 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- As- sociative 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 as- tronomical 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. PEIRCE, Bradford Kinney, an American cler- gyman, born in Eoyalton, Vt., Feb. 3, 1819. He graduated at Wesleyan university in 1841, was received into the New England Methodist Episcopal conference in 1843, served as pastor in Waltham, Newburyport, and Charlestown, Mass., and in 1847 removed to Boston to edit the " Sunday School Messenger" and the " Sun- day School Teacher." In 1855-'6 he was a state senator, and his efforts in behalf of public charities led to the establishment of the state industrial school at Lancaster, of which he was superintendent and chaplain. He was chap- lain of the house of refuge on Randall's island, N. Y., from 1863 to 1872, when he returned to Boston to become editor of " Zion's Herald." He has published " Notes on the Acts," " Bi- ble Scholar's Manual," "The Eminent Dead," "Trials of an Inventor" (1866), "The Word of God Opened" (1868), and "A Half Century with Juvenile Delinquents" (1869). PEKDf, a city and the county seat of Taze- well co., Illinois, on the left bank of the Illi- nois river, navigable by steamboats for eight months of the year, 55 m. N. of Springfield;