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Serjeant at Arms, or Mace:, au officer appointed to attendthe person of the king ; to arrest traitors, and such persons of qua-lity as offend ; and to attend the lord high steward, when sittingin judgement on a trailor.
Serjeant at Law, or of the Coif, is the highest degreetaken at the common law, as that of Doctor is of the civil law ;and as these are supposed to be the most learned and experiencedin the practice of the courts, there is one court appointed for themto plead in by themselves, which is the common pleas, where thecommon law of England is most strictly observed : but they arenot restricted from pleading in any other court, where the judges,who cannot have that honour till they have taken the degree ofSerjeant at law, call them brothers.
Serjeant, Common, an officer in the city of London , who at-tends the lord-mayor and court of aldermen on court-days, and isin council with them on all occasions, within and without the pre-cincts or liberties of the city. He is to take care of orphans’ estates,either by taking account of them, or to sign their indentures, be-fore their passing the lord-mayor and court of aldermen : and hewas likewise to let and manage the orphans’ estates, according to hisjudgement to their best advantage.
Serjeant Major, a non-commissioned officer, subordinate tothe adjutant.
SEUGIEVSK, a town and fort of Russia in Upha : 180 milesw. of Upha.
SERIES, in general, denotes a continual succession of things inthe same order, and having the same relation or connection witheach other; in this sense we say, a series of emperors, kings,bishops, &c. In natural history, a series is used for an order orsubdivision of some class of natural bodies; comprehending allsuch as are distinguished from the other bodies of that class, bycertain characters which they possess in common, and which therest of the bodies of that cast have not.
Series, in arithmetic and algebra, a rank or number of terms insuccession, increasing or diminishing in some certain ratio or pro-portion. There are several kinds of series ; as arithmetical, geo-metrical, infinite, Sec. The two first of these are, however, moregenerally known or distinguished by the names of arithmetical andgeometrical progression.
Series, Harmonica, a series of terms formed in harmonicalproportion. If three numbers be in harnioniqal proportion the firstis to the third as the difference between the fifst and second is tothe difference between the second and third. Let a, b, and x, bethree terms in harmonical proportion: then ax ;: a— b : b—x.whence ax — bx^=ab — ax.and 2ax — bx=ab;
then x =s
ab
2a —b
. Hence the first three terms
°f this series is a, b,
ab
2 a —b'
find which in terms of a and b, we have
ab ab
. Again, let x be the fourth term, to
Then bx
b : x : : b •ab
2a — b3 ab — 2 6 s2a — b
ab 2 2a—b
2a — b 2a —bab 2
~ 2a —b
■bx
• X --
ab 3
2a —b
2a — b ’ 3 ab — 2 o’
ab
3a—2b'
therefore the four first terms are .a.b. r—-r.5——rr:- Whence the
2a— b 3a—2b
of the series is obvious, and it may be continued as follows,
«.&.
ab
ab
ab
ab
&c. and the nth term is
2a-b’ 3a-2b’ 4 a~3b' 5a-4b :ab
^~-l.a—n^~2b ' n a senes in harmonical proportion, a and
b lie two affirmative quantities, and such that a. £.b\ then this-eries,which is positive at first, will become negative as soon as n —2.6exceeds n — l.a. But if a 7 b, the series will converge, andalthough produced to infinity will not become negative. Let®and b be equal to 2 and 1 respectively ; then this series becomes&c and since if each term of an harmonical series be di-vided by the same quantity, the series will still be harmonical,therefore &c. is an harmonical series: whence the de-
nominators ot this series form a series of numbers in arithmeticalprogression ; and conversely, the reciprocals of an arithmeticalprogression are in harmonical proportion.
Series, Infinite, is formed by dividing the numerator of afraction by its denominator, being a compound quantity ; or byextracting the root of a surd. An infinite series is either converg-ing or diverging. A converging series is that in which the magni-tude of the several terms gradually diminish ; and a divergingseries is that in which the successive terms increase in magnitude.1 he law of an infinite series is the order in which the terms are ob-served to proceed. This law is often easily discovered from a fewof the first terms of the series; and then the series may he conti-nued as far as may be thought necessary, without any farther divi-sion or evolution. An infinite series is obtained by division orevolution; but as that method is very tedious, various othermethods have been proposed for performing the same in a moreeasy manner; as, by assuming a series with unknown coefficients,hv the binomial theorem, Sec. See Algebra .
SERINGAPATAM, an extensive territory of India , now be*longing to Great Britain, more generally called Mysore . SeeMysore .
Seringapatam, the capital of Mysore , is situated in an islandof the Cavery, about 290 or 300 miles from Madras. The greatgarden, called the Laul Baug, covers about as much of the E. endof the island as the fort and outworks do ol the W. and the wholeintermediate space, except a small inclosure on the N. bank nearthe fort was, before the last war, filled with houses, and formed anextensive suburb, of which the greatest part was destroyed byTippoo to make room for batteries to defend the island when at*tacked by the comoined forces of Earl Cornwallis and theMahratta chiefs in February 1792. This town, of modern struc-ture, is about half a mile square, divided into regular cross-streets,all wide, and shaded on each side by trees. It is surrounded by astrong mud-wall, contains many good houses, and seems to havebeen preserved by Tippoo for the accommodation of merchants,and for the convenience of troops stationed on that part of theisland for its defence. This noble garden was devoted to destruc-tion ; and the trees which had shaded their proud master, and con-tributed to his pleasures, were formed into the means of protect*ing his enemies in subverting his empire. “ Before that event,so glorious to the arms of Great Britain , this insulated metropolis,(says Major Dirom,) must have been the richest, most convenient,and beautiful spot possessed in the present age by any native princein India ; but when the allies left it, the Sultan’s fort and city onlyremained in repair amidst all the wrecks of his former grandeur, theisland presenting nothing but the appearance of wretched barren-ness.” But the whole city, fort, and island, with all the rest ofTippoo’s late dominions, are now in possession of the British ,except that part which the British government generously gave tothe lawful Indian prince, the descendant of the ancient rajahs,whom Hyder Ali had deposed and imprisoned ; the city, fort, andisland, having been taken on the 3th of May 1799, and the wholecountry reduced. Lon. 176. 48. E. Lat. 12. 33. N.
SERIO, a department of the territory of the Bergamesco, ex-tending above 40 geographical miles in length, and 30 in breadth;or about 108 English miles from N. to S. and 90 from E. to W,The climate is salubrious; the soil partly hilly, abounding in woods:partly flat and fertile, abounding in corn and cattle. Bergamo itthe capital. See Bergamo .
SERIOLA, in botany, a genus of plants belonging to the orderpolygamia sequalis, and class syngenesia: natural order, Com-posite. Beccptacle paleaceous; pappussomewhat plumose. There
are four species.
SER1PERES, the lowest and most degraded class of themeanest tribe of Hindoos. See Parias.
SERIPH1A RANA, a proverbial saying concerning a person
who