SERIES. 802 SEROUS FLUID. Tlie theory of uiiifoini convcigonee was treated by Caiichy "(18-1)' '"** liiuitations being pointed out bv Abel, but the tirst to attack it success- fully "were Stokes and Sciilel (1847-48). Semi- eonverjient scries were studied by I'oisson (1823) and .Jacobi (1834). Fourier's series were in- vestigated as the result of physical considera- tions, and Fourier (1807) set for himself the pnibleni to expand a given function of x in terms of the sines or cosines of multiples of x. a problem which he embodied in liis Thiorie tiiiuly- /ii/iir </< hi chalrur ( 1822) . He did not, however, settle the <pU'stion of convergence of his series, a matter left for t'aiichy (182fi) to attempt and for Dirichlet (1829) to handle in a thoroughly siieiitific manner. .Vmong otlier prominent con- tributors to the theory of trigonometric and Fourier series have been Riemann, Heine, Lip- .schitz, Schliilli, Du Bois-Reymoiul. Dini, Hermite, Helphen, Krause, Byerly, and Appell. For an introihicti(m to infinite series involv- ing tests of coiivc'rgenee. applications to physics, and relations to integration, consult Osgood, In- U-oductioii to Infinite Series (Cambridge, 1897). .■
historical development of the subject is given
by Reiff, Geschichte der unendlichen Reihen (Tiibingen, 1889). Also by Booher, diap. ix. of Bverlv's Fourier's Series and Spherical Har- vi'inies (Boston, 1893). For history and theory, consult Merrinian and Woodward, Higher Mathe- matics (New York, 1896) : -Jordan, Cours d'anali/se (Paris. 1893). An elementary treat- ment is given in Chrystal, Algebra, vol. ii. (Edin- burgh. 1889) ; Bonnet, "Menioire sur la theorie genfirAle des series," in the llemoires couromi4s of the Brussels Academy (1850); Martone, In- irudiizione alia teoria delle serie (Catanzaro, 1891-94). SERINAGUE, sc-re'nu-giir'. The capital of Kashmir. Sec Srinag.b. SERINGAPATAM, se-rin'ga-pa-tam', or SRIRANGAPATAM. A town in the native State of Mysore, India, 9 miles northeast of the city of Mysore, on an island in the Kavery River (Map: India, C 6). It is poorly built and un- healthful. A portion of the palace of Tippu Sahib, within the inolosure of the old fort, still remains. Other objects of interest in- clude the Darya Daulat Bagh. the handsome simimer residence of Tippu; the Lai Bagh (gar- den) with the tombs of Tippu and his father, Hy- der Ali: and the ancient temple of Vishnu Shri Ranga, from which the town derives its name. Seringapatam was the capital of ilysore until 1799. On May 4th of that year the town was stormed by the British, Tippu Sahib being killed. Population, about 12,000. SERING'^AM, A town of Madras, India. See Srirancam. SERJEANT-AT-LAW. The highest rank of barristers (q.v.). It is a title of great antiquity, but now nearly extinct in England, although still common in Ireland. In early times the de- gree was conferred only on barristers of sixteen years' standing: but this qualification was dis- pensed with later. A Serjeant was appointed by a writ under the great seal, upon the nomination of the Chief .Justice of the Common Pleas, in whose court he was entitled, for centuries, to exclusive audience. Socially Serjeants took precedence of King's counsel, while profession- ally the latter outranked the former, unless Ser- jeants held special patents of precedence. The decay of this order in England is due in part to the fact that the Judicature Act of 1873 renders it unnecessary that a person should be admitted to the rank of Serjeant before ap- pointment to a Supreme Court judgeship, and in part to the abolition of the exclusive right of audience in the Common Pleas. Consult: Manning, Antient Privileges of the Serjeants at Law (London, 1840) ; Pulling, The Order of the Coif (London, 1884). SERLIO, sar'lyo, Sebastiano (1475-1554). An Italian architect and writer on art, born at Bologna. He worked as an architect at Pesaro from about 1510 until 1514, then, after having frequented in Rome the school of Peruzzi, he was employed at Bologna and Venice, and in 1540 went to Paris, where he became royal archi- tect in 1541 and was engaged in the work on the Louvre and the Tuileries, and at Fontainebleau. He is remembered chiefly for his treatise on architecture, in which he embodied all the pre- cepts of Vitruvius and which was published in seven books (Lyons, 1537-51, 1575). Consult Charvet, Biographies d'architectcs (Lj'ons, 1869). SERMONISM. See Xomikalism. SEROTINE (from Lat. serotinus, late, from seriis, late). A large, dark-brown bat (Vesperugo serotinus) of particular interest for its very wide distribution, since it is known all over Europe, south of the Baltic, in Africa north of the equator, throughout the southern half of Asia, and in most of Xorth America. It seems to be identical with our "dusky' or 'Carolina' bat. Several color varieties are locally distinguished. SEROUS FLUID (from Lat. seruin, whey, serum ; connected with Gk. i5/j6s, oros, whey, Skt. sar, to flow). A thin, watery fluid occurring in various parts of the animal body, distinguished from mucus principally by its limpidity and by- its being found in closed cavities only. It con- tains a little albumin, a trace of fibrin, about 6 per cent, of solid constituents, and 94 per cent, of water. Serous fluids have been arranged un- der three heads: (1) Those which are contained in the serous salt of the body, as the cerebro- spinal fluid, the pericardial fluid, the peritoneal fluid, the pleural fluid, the fluid of the tunica vaginalis testis, and the synovial fluid. (2) The fluids existing in the eyeball, the amniotic fluid, and transudations into the tissue of organs. (3) ilorbid or excessive transudations, such as drop- sical fluids, the fluids occurring in hydatids, and in blebs and vesicles on the skin, and transuda- tions from the blood in the intestinal capillaries, as in cases of intestinal catarrh, cholera, or dysentery. All these fluids bear a close resemblance to one another, both in their physical and chemical characters. In so far as relates to their physical characters the.v are usually clear and trans- parent, colorless or slightl.v yellow, of a slight saline, mawkish taste, and exhibiting an alka- line reaction with test-paper. They possess no special formal or histological elements, btit on a microscopic examination blood-corpuscles, cells of various kinds, molecular granules, and epithe- lium may occasionally be observed in them. They also contain fats, animal soaps, cholesterine, ex- tractive matters, urea (occasionally), the same inorganic salts which are found in the serum of
