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and terseness which marks all his work and made his teaching unattractive to inapt pupils. To young men of real talent, on the contrary, his teaching and warm personal interest in their work were of the greatest advantage, and he holds a most honourable place in the development of American mathematics. After Bowditch's death in 1838 Peirce stood at the head of American mathematicians; but the first work that gave him a wider fame was his computation of the general perturbations of Uranus and Neptune (Proc. Amer. Acad., 1848). In 1849 he became consulting astronomer to the American Nautical Almanac, and for this work he prepared new tables of the moon (1852). Another piece of important astronomical work was his discussion of the equilibrium of Saturn's ring, in which he showed that a fluid ring was necessarily unstable as well as a solid one. From 1867 to 1874 he was superintendent of the coast survey; in 1857 he published his largest and most characteristic work, the System of Analytical Mechanics. He himself, however, seems to have thought most of his Linear Associative Algebra (lithographed privately in a few copies, 1870; reprinted in the American Journ. of Math., 1882). His death took place at Cambridge, United States, on 6th October 1880.
PEKING or Pekin, the capital of the Chinese empire, is situated in 39° 54′ 36″ N. lat. and 116° 27′ E. long., and stands on the northern extremity of the great alluvial delta which extends southwards from its walls for 700 miles. For the last nine centuries Peking, under various names and under the dominion of successive dynasties, has, with some short intervals, remained an imperial city. Its situation near the northern frontier recommended it to the Tatar invaders as a convenient centre for their power, and its peculiarly fortunate position as regards the supernatural terrestrial influences pertaining to it has inclined succeeding Chinese monarchs to accept it as the seat of their courts. In 986 it was taken by an invading force of Khitan Tatars, who adopted it as their headquarters and named it Nanking, or the “southern capital.” During the early part of the 12th century the Chinese recaptured it and reduced it from the rank of a metropolis to that of a provincial city of the first grade, and called it Yen-shan Foo. In 1151 it fell into the hands of the Kin Tatars, who made it a royal residence under the name of Chung-tu, or “central capital.” Less than a century later it became the prize of Jenghiz Khan, who, having his main interests centred on the Mongolian steppes, declined to move his court southwards. To his great successor Kublai Khan (1280–1294), however, the establishment of a capital within the frontiers of China became a necessity, and, following the example set him by preceding sovereigns, he made choice of Yenking, as he rechristened the city. With his usual magnificence, he rebuilt the town, which became known in Chinese as Ta-tu, or “great capital,” and in Mongolian as Khanbalik, or “city of the khan.” During the reign of the first emperor of the dynasty (1368–1399) which succeeded that founded by Jenghiz Khan the court resided at the modern Nanking, but in the eyes of the succeeding sovereign Yung-lo (1403–1425) the political advantages of a northern residence appeared so obvious that he transferred his court to Peking (i.e., the northern capital), which has ever since been the seat of government.
Plan of Peking. (Scale, one mile and a half to an inch.)
During the periods above mentioned the extent and boundaries of the city varied considerably. Under the Kin dynasty the walls extended to the south-west of the Tatar portion of the present city, and the foundations of the northern ramparts of the Khan-balik of Kublai Khan are still to be traced at a distance of about 2 miles in a northerly direction beyond the existing walls. The modern city consists of two parts, the nui ch’ing, or inner city, commonly known to foreigners as the “Tatar city,” and the wai ch’ing, or outer city, known in the same way as the “Chinese city.” These names are somewhat misleading, as the inner city is not enclosed within the outer city, but adjoins its northern wall, which, being longer than the nui ch’ing is wide, outflanks it considerably at both ends, as may be seen in the accompanying plan. The outer walls of the double city contain an area of about 25 square miles, and measure 30 miles in circumference. Unlike the walls of most Chinese cities, those of Peking are kept in perfect order. Those of the Tatar portion, which is the oldest part of the city, are 50 feet high, with a width of 60 feet at the base and 40 feet at the top, while those of the Chinese city, which were built by the emperor Kea-tsing in 1543, measure 30 feet in height, and have a width of 25 feet at the base and 15 feet at the top. The terre-plein is well and smoothly paved, and is defended by a crenellated parapet. The outer faces of the walls are strengthened by square buttresses built out at intervals of 60 yards, and on the summits of these stand the guard-houses for the troops on duty. Each of the sixteen gates of the city
