Page:Cyclopaedia, Chambers - Supplement, Volume 2.djvu/921

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-m. -- which determines nothing. See Mifc. Analyf. Ioc, tit.

i — 1

In like manner, the fum of a number n of terms of the [cries

of triangular numbers will be found to be a x X- '

asinMifceh Analyf. p. 168.

By the like methods the fum of any number of fquares, cubes, &c. of the natural [tries of numbers maybe found. Which may alfo be done by Sir Ifaac Newton's differential method. See Differential method, Append.

3° In a recurring [tries any term may be obtained whofe place is affigned. For after having taken fo many terms of they^- ries as there are terms in the fcale of relation, the [tries may be protracted till it reach the place affigned. But if that place be very diftant from the beginning of the [eries, the continuation of the terms will prove laborious : other methods have therefore been contrived. See Mifcel. Analyf. p. 33, feq. and Doct. of chances, p. 197, feq. Thefe queftions have been refolved in many cafes, befides thofe of recurring [erits. But as there is no univerfal method for the quadrature of curves, neither is there one for the fummation of [erits; there being a great analogy between thefe things, and fimilar difficulties arifing in both. See the authors before cited.

The investigation' of Mr. Daniel Bernoulli's method for find- ing the roots of algebraic equations, which is inferred in the article Equation, SuppL depends upon the doctrine of re- curring [erits. See Euler, Analyfis infinitorum, Tom. I. pag, 276, feq.

■ In general algebraic quantities may be exprefled by a [erics-, either, by divifton or by the extraction of roots, in a method analogous to that ufed in arithmetic for expreffing vulgar frac- tions and roots by decimals. And the confideration of this analogy feems to have given rife to Sir Ifaac Newton's doctrine of infinite [tries. See his method of fluxions and infinite [tries in the beginning.

But the fame great author had alfo another method of throw- ing quantities into an infinite [tries, by means of a general formaflumed for that purpofe. See Form.

Interpolation o[ a Series, fee Interpolation.

Interfrendent Series. See Interscendent yir/w.

Tranfrendental Series. See Transcendental [tries.

Hyperbolic Series is ufed for a [tries whofe fum depends upon the quadrature of the hyperbola. Such is the [eries 4-M + 4 + -¥+y+ &c ' De Moivre, Mifc. Analyf. p. in.

Circular Series, is ufed for a [eries whofe fum depends on

■ the quadrature of the circle. Such is the [tries 1 — ^- -- £ — .I-L..I..— &c. De Mo'tvre, Mifc. Analyf. p. in. or the fum of the [eries 1 + y 4- -^ + -re + wi + & c - continu- ed ad infinitum^ according to Mr. Euler's difcovery,

Hd'ixt Series, that [eries whofe fum depends partly on 'the

quadrature of the circle and partly on that of the hyperbola.

De Moivre, Mifc. Analyf. p. in. Determinate Series, a [eries the terms of which proceed by

the powers of a determinate quantity. If that determinate

quantity be unity, the[ertes is faid to be determined by unity.

De Mohre, Mifcel. Analyf. p. 1 1 r. Revtrfion of Series. See Reversion of [eries. Summabk Series, is ufed when the fum of the terms of a

feries may be found. Such is the [eries ~ -\- 1 -J- -J _j_, tiff. ■ the fum of which is faid to be equal to unity, or, to fpeak . more accurately, the limit of whofe fum is unity. See the

article Progression, SuppL t An indefinite number of fummable infinite [eries's may be ' when converging, and many others, for which Meffieurs
 * found : fuch are, for inftance, all infinite recurring [eries,

De Moivre % Bernoulli b, Stirling c , Euler d , and Mac

!Laurin% may be confulted. — [» Mifcel. Analyf. p. no,

feq. b De Serieb. infinit. paffim. e Method. Different.

p. 34, feq. d Acta Petropolit. paffim. c Fluxions, Art.

350, feq. See alfo Progression, SuppL] SERMOUNTAIN, a name fometimes given to the plant

. called fefili, or filer by authors. See the articles Sesili and

SlLER, SuppL

SERPENT'S tongue, or Adder's tongue, names by which the epbioglojfum of botanifts is frequently called. See the arti- cle Ophioglossum, SuppL

SERPYLLUM (SuppL) is alfo ufed by fome as the name of a fpecies of ihymbra. See the _article Thymera, SuppL

SERVICE-^*-, in botany, the Englifh name of a genus of trees, called by botanical writers [orbits. See the article Soreus, SuppL

IFild Service, a name by which fome call the cratiegus of botanical writers. See the article Crataegus, SuppL

SESAMUM, oily grain plant, in botany, the name of a ge- nus of plants, the characters of which are thefe. The cup is a one-leaved pcrianthium, divided into five fegments; the uppermofl of which is foorteft. The flower confifts likewife of one petal of a campanulated form, and divided into five fegments j of which the loweft is by far the longeft. 'The ftam'ma are four filaments, fhorter than the flower; the anthers are oblong, acute, and erect. The germen of Append. Vol. II.

the piftil is oval and rough ; the ftyle is filiform ; the ftigmi is lanceolated, and divided into two parts. The fruit is an oblong capfule, containing four cells, in which are numerous feeds of an oval' figure. Linnai Gen. Plant, p. 293.

SESSION (SuppL)— The court of [ef.cn, otherwife called the college of jujiice, is the fupreme court in Scotland for all civil caufes. It confifts of one conftant prefident .and fourteen other judges, who are lords by their office, which they hold by patent quamdiu [e bent gefferini. The Lord High Chan- cellor prefides here when prefent. The king names feveral other extraordinary lords, who fit, but are not obliged to attendance, becaufe they have no falaries ; but they may vote among the reft.

The court fits from the firft of November, old ftyle, to the laft of February, and from the firft of June to the laft of July, all inclufive ; which holds of all the inferior courts or judicatories in Scotland. In time of [JJion, or term, they fit from nine o'clock to twelve in the forenoon, every day in the week but Sunday and Monday : fometimes they fit in the afternoon, to end concluded caufes, or to heac fuch long debates as the forenoon was too fhort to hear> which gives a great difpatch to caufes that come before them. The lords, both ordinary and extraordinary, when, in the inner houfe, fit on a femicircular bench in their robes j where the advocates debate their clients caufes be- fore them. There are fix principal clerks belonging to this court. Nine of the lords make a quorum in the inner houfe^ otherwife they cannot vote in any cafe, except fuch as are referred to one or more of the whole lords ; and one of the ordinary lords (the prefident being always excepted) is weekly appointed judge in the outer houfe, for difcuffing of ordinary actions, and has fix under clerkb to attend him. He meddles with no extraordinary cafes, except where it is remitted to him by all the. lords to be difculTed in the outer houfe for difpatch.

That the lords may have time to read informations, petiti- ons, &c. and the fukors be eafed of the trouble of going with them to their houfes, every lord has a box ftanding upon a table in the waiting room in the inner houfe from two to four o'clock in the afternoon every day ; wherein all who have papers to offer, may put them by a flit in the cover. Each of the principal clerks have alfo a box, and parties muft put their bills, anfwers, or informations of caufes to be reported, into the clerk of the procefs's box. The rolls of the court bring in all caufes in their due or- der, Caufes of the greateft confequence are at firft advifed by the whole lords in the inner houfe. Other caufes are called of courfe before an ordinary in the outer houfe, whs decides the controverfy, if clear, without farther trouble or expence ; and, in cafe of difficulty, takes fome little time to advife it himfelf, or to advife with the whole lords upon it. And if any of the parties think themfelves wronged by the fentence of the ordinary, they may complain to the lords, and get their anfwer upon a bill.. See Chamb. Pref. State of G'r, Brit. p. 381, feq. An appeal lies from this court to the Houfe of Lords.

SETTER-MJcrf, a name by which hellebore is fometimes called. See the article Helleborus, SuppL

SETTING, (SuppL) among cock-mafters, is the placing a cock, that has fought fo that he cannot ftand, beak to beak againft the other cock, and if he does not ftrike the battle is won. Diet. Ruft. in voc.

Setting down, in falconry, is when a hawk is put into the mew. Id. ibid.

Setting-^, one trained up to find out and difcover to the fportfman whereabouts fowl are.

SE FTS for [aws, inftruments for fetting their teeth when out of order. Blanckley, Nav. Expof. p. 145.

SETWELL, in botany, a name fometimes ufed for a fpecies of valerian. See the article Valerian, SuppL

SEWEL, among fportfmen, denotes any thing that is fet or hung up, to keep a deer out of any place. Ruft. Diet, in voc.

SEYMS, among farriers. See Seams.

SHADDOCK, in botany, the name. by which fome call 3 fpecies of orange. See the article Orange, SuppL

SHAKLES, aboard a fhip. See Shackles, SuppL

SHAKY, or Shaken, among builders, an appellation given to timber which is cracked either with the heat of the fun, or the drought of the wind. Build. Difit. in voc.

SHAVE-^ra/}, a name fometimes ufed for the equifetum, or borfe-iail. See the article Equisetum, SuppL

SHAVlNG-rVw", among gardeners, tools to keep a garden free from weeds, otherwife called edging-irons. Ruft, Diet* In voc.

SHAW (SuppL) — SuA\\--[otvl, an artificial bird, made for fowlers to fhoot at. Ruft. Diet, in voc.

SHEAT, or Shut, a name by which fome call a young hog.

Ruft. Diet, in voc. SHELDAPLE, a name ufed in feveral parts of the kingdom

for the chaffinch. Ruft. Diet, in voc. SHELL (Suppl.)—Caterpiltar-$iiEL-L, the Englifh name of a fpecies of turbo. See the article Turbo, SuppL

B b Grown