S U R
s u s
When the fquare root of a furd is required, it may be Found, nearly, by extracting the root of a rational quantity that approx imates to its value. Thus, to find the fquare root of t/3 + 2 */ 2, firft Calculate */ 2 = 1,41421. Hence, 3+2^2 = 5,82842, the root of which is found to be nearly 2,41421. In like manner we may proceed with any other propofed root. And if the index of the root, propofed to be ex- tracted, be great, a table of logarithms may be ufed.
Thus ^/ 5 -j- */ 1 7 ma y be molt conveniently found by logarithms.
Take the logarithm of 17, divide it by 13 ; find the num- ber correfponding to the quotient; add this number to 5 ; find ihe logarithm of the fum, and divide it by 7, and the numb er corref ponding; to this quotient will be nearly equal
7/ n — t0 V S + \Z T 7-
But it is fometimes requifite to cxprefs the roots of furds Exactly by other furds. Thus, in the firft e xample, t he fquare root of 3 + 2/2 is i-f-^2: for i-j-^/2x I + s/l =:I-f-2 i /2+2=3-f-2^/2. For the method of performing this, the curious may con- fult Mr. Mac Laurin's Algebra, p. 1 15, feq. where alfo rules for trinomials, &c. may be found. For extracting the higher roots of a binomial, whofe two members being fquared are commenfurable numbers, we have a rule in Sir Ifaac Newton's Arithmetica Umver/alis, p. 59, but without demonftration. This is fupplied by Mr. Mac Laurin, in his Algebra, p. 120, feq. as alfo by 'sGravefande, in his Mat hefeos Univerfalis Element, p. 211, feq.
It fometimes happens, in the refolution of cubic equations, that binomials of this form a-^rb^/ — 9 occur, the cube roots of which mud be found; To thefe Sir Ifaac's ruli cannot always be applied, becaufe of the imaginary, or impoffible factor \/ — 9 ; yet, if the root be expreffible in rational numbers, the rule will often lead to it in a fhort way, not merely tentative, the trials being confined to known limits. See Mac Laur. loc. cit. p. 127, feq. It may be farther obferved, that fuch roots, whether ex- preffible in rational numbers, or not, may be found by evolving the binomial a -f- b */ — 9 by the Newtonian theorem, and fumming up the alternate terms. Mac Laur. loc. cit. p. 130.
Thofe who are defirous of a general and elegant folution of the problem, to extract any root of an impofjible binomial a -- ^/ — ■ b, or of a poffible binomial a -- */ b, may have recourfe to Mr, De Moivre's Letter to Dr. Saunderfon, in- ferted by way of Appendix to his Algebra, p. 744, feq. and to the Philofophical Tranfaefionsj N° 451. or to Dr. Martvn's Abridgment, Vol, 8. p. 1, feq.
SURFACE (CycL)—h furface is not a body of the leaft fen- fible magnitude, as fome have imagined, but it is the ter- mination, or boundary of a body; neither is a line to be confidered as -kfurface of the leaft fenfible breadth, but as a termination, or limit of a furface: nor is a point to be confidered as the leaft fenfible line, but as the termination of a line ; and in this fenfe it is plain that a point cannot be conceived to have parts, or magnitude. See Magni- tude. See alfo Mac Laurin's Fluxions, Vol. 1. p. 245. and Mr. John Bernoulli's Letter to Monfieur Crouzas, con- cerning his Comment on the Analyfe des Infniiment petits. fo.Bernoul. Oper. Vol. 4. p. 160, feq.
SURF of the fea, the great breakings, or rolling of the fea aga'mft fome fhores ; making it dangerous to land in fuch places.
SURMULLET, in zoology, a name ufed, both by the French and Englifh, for the midlus major, a fifh of the cuculus kind, in many things refembling the mullus barbatus, but differ- ing from it in that it is twice as big, being often caught of twelve or fourteen inches in length. Its fins alfo are yel- lowiiTi, and have a flight blufli of red mixed with that co- lour. Its fcales are large and broad, and thick, and are more firmly joined to the flefh. It has alfo three or four ftrait yellow lines, running parallel with one another down its fides. It is caught in the Mediterranean, and in the Britifh feas, efpecially on the coaft of Cornwall, and is every where efteemed a very delicate fifh, Ray's Ichthyography, P. 285.
SURO, in zoology, a name given by fome to a fifh of the cuculus kind, much refembling the mackrel in tafte and in fhape, and more ufually known by the name of the tracburus. Willughby'% Hift. Pifc. p. 290. See Trachurus.
SURRECTORIUM, the name of a chirurgical inftrument, mentioned by Ambrofe Pare, and intended to keep the arm in an erect fituation when required.
SURVEYING (Cyd.) — A furveyor ought to be provided with an off-fet ftafF, equal in length to ten links of the chain b , and divided into ten equal parts. He ought llkewife to have ten arrows, or fmall ftrait flicks, near two feet long, fhod with iron ferrils. When the chain is firft opened, it ought to be examined by the off-fet ftaff. In meafuring any line, the leader, of the chain is to have ten arrows at firft letting out. When the chain is ftretched in the line, and the'near end touches the place from which you meafure,
the leader flicks one of the ten arrows in the ground at the far end of the chain. Then the leader leaving the ar- row, proceeds with the chain another length ; and the chain being ftretched in the line, fo that the near end touches the firft arrow, the leader fticks down another arrow at his end of the chain. The line is preferved ftrait, if the ar- rows be always fet fo, as to be in a right line with the place you meafure from, and that to which you are going. In this manner they proceed till the leader have no more arrows. At the eleventh chain the arrows are to be carried to him again, and he is to ftick one of them in the ground, at the end of the chain : and the fame is to be done at the 21, 31, 41, &c. chains, if there arc fo many in the right line to be mcafured. In this manner an error can hardly be committed in numbring the chains, unlefs of ten chains at once c . — [ b See Chain. c Treat. Pratt. Geom. p. 72, 73-] — See farther under FiELD-bod, Off-sett, Staff, and Theodolite.
If the lands to be plotted are hilly, and not in any one plane, the lines meafured cannot be truly laid down on pa- per, without being reduced to one plane, which muft be the horizontal, becaufe angles are taken in that plane. In viewing objects, if they have much altitude or depreffion, either write down the degree and decimal, fhewn on the double fextant, or the links fhewn on the back fide, which laft fubtracted from every chain in the ftation line, leaves the length in the horizontal plane ; but if the degree is taken 9 the following table will fhew the quantity.
A Table of the links to be fubtra£ted out of every chain in hypcthenufal lines of federal degrees altitude, or depreffion, for reducing them to horizontal.
degrees.
links.
degrees.
links.
degrees.
links.
4.05
%
14.07
3
23.074
8
5-73
2
16.26
4
24.495
9
7.02
T
18.195
5
25.84
10
8.11
I
19.95
6
2 73
11
11.48
2
21.565
7
28.36
12
Let the firft ftation line really meafure 1107 links, and the angle of altitude, or depreffion, be 19° 93' 5 looking in the table, I find 19 95' is 6 links; now 6 times 11 is 66, which fubtracted from 1107 leaves 1041, the true length to be laid down.
It is ufeful in furveying to take the angles which the bounds ing lines form with the magnetic needle, in order to check the angles of the figure, and to plot them conveniently af- terwards.
Large maps, reprefenting confiderable extents of ground, are fubject to a good many inconveniencies, efpecially if carried into the fields, to be compared with them ; fuch maps become very troublefome in the wind, and it is diffi- cult to find out the part you want. To remedy this, a general and fmall map of the manor, or county, EsV, fhould be firft made on one fhect of paper, the feveral parts may be fet off on other feparate fheets, and the general map being divided into as many fquares as there are of thefe particular fheets, the relation of the whole to the feveral parts is eafily feen ; and all thefe maps may then be bound up in a book. See jyir, Brighton's Defcription and Ufe of his New Plotting Table, in Phil. Tranf. N°46i. feet. 1.
Surveying-/^/?, the fame with reducing -fcale.
SURVEYOR (Cycl.)— Surveyor of the king's Exchange, an antient officer, mentioned in the Statute 9 Hen. V. Stat. 2. cap. 4. But what his office was is uncertain. Cowel,
SUS, the bog, in the Linnsan fyftem of zoology, a diftinct genus of animals, the characters of which are ; that they have ufually ten paps, fituated along their belly; their dentes incifores are four each way ; and in the males, the canine, or dog-teeth, are extremely long. Of this genus are the hog kind, the Mexican mufk-boar, and the babyrouila. Linnai Syftem. Nat. p. 41.
Sus pijeis, in ichthyology, a name given by Ovid, and fome other of the antient writers, to the fifh called alfo us and mus, and by the later writers caprifcus. See the article Ca- priscus.
Sus agrejlis, the wild boar. This creature differs from the common domeftic hog, in that the grown animal is not dif- ferent in colour in the different individuals of the fame fpe- cies, but is always of arufty iron grey. His fnout is much longer alfo than that of the other ; his ears fhorter and rounder ; and both thefe, and his tail and feet, are always black. It differs alfo, in that it is covered with two forts of hairs, the one kind long, the other fhort : thefe laft ferve the creature to the fame purpofes, as the downy fur which the bever and otter have under their long hair. It is very common wild in Italy, and its fleih frequently brought to market. .Ray's Syn. Quad. p. 96.
SUSCEPTOR, among the Romans, a citizen chofen by the decuriones to collect the debts belonging to the public. Pitifc. in voc.
Susceptor is alfo a term ufed by ecclefiaftical writers for fponfor. See Sponsor, Cycl.
Susceptor.
