532

S C A

SC A

the extremity of N. Jutland, eighteen miles N. of I-ladstrand.Lon. 10 . 30. E. La!. 37. 46. N.

SCALA, an island of Italy , in the department oftheMella;district and late territory of Brescia .

Scala Nova, a handsome town of Asiatic Turkey, in Natolia ,anciently called Neapoli?, and now by the Turks Koushadase, 40miles S. S E. of Smyrna. Lon. 27. 31. E. l.at. 37. 54. N.

SCA LA DO, or SCALADE, in the art of war, is a furiousassault made on the wall or rampart of a city, or other fortifiedplace, by means of ladders, without carrying on works in form, to/ecure the men.

SCALDS, in the history of literature, a name given by the an-cient inhabitants of the northern countries to their poets; in whosewritings their history is recorded.

SCALE, a mathematical instrument, consisting of several linesdrawn on wood, brass, silver, Ac. and variously divided, accord-ing to the purposes it is intended do serve; whence it acquiresvarious denominations, as the plain scale, diagonal-scale, plotting-scale, Gunter’s-scaie, Ac .

Scale, Plain, Construction and Use of. The plain scale3s an instrument much used in navigation, Ac . lor solving the seve-ral cases of sailing. See Navigation. Having described thecircle DBCA, (Plate CLI11. tig. 3.) and divided it into four quad-rants, by the diauyeters AB and CD crossing each other at rightangles: 1. To project the line of tangents, from the end C of thediameter CD, erect the perpendicular CG ; then dividing the archCB into nine equal parts, from the centre E, through the severaldivisions of the quadrant CB, draw lines till they cut the perpen-dicular CG, which will thereby become a line of tangents. 2.For the semi-tangents, ot half-tangents, let lines be drawn fromthe point D, through the same divisions upon the arch CB; andthey will divide the radius BE into a line of semi-tangents, as isevident from Euclid, lib. 3. prop. 20. 3. For the secants, trans-

fer the lines drawn from the centre through the several divisions oithe quadrant CB to form the line of tangents, to the line EB con-tinued to F, and the line EE will be a line of secants. 4. For thesines, from the several divisions of the quadrant CB, let tall per-pendiculars upon the radius CE; wlfich will thereby be dividedinto a line of sines, to be numbered from E to*C for the right sines,amkfrom C to E for the versed sines: and these versed sines maybe continued to 180°, if the same divisions be transferred on theother side of the centre E. 5. For the chords: the arch CB beingdivided into nine equal parts, i i the points 10, 20, 30, Ac . it linesbe imagined to be drawn from C to these divisions, they will bethe chords of their respective arches; wherefore setting one footof your compasses in the point C, and transferring the severallengths, C 10, C 20, C 30, Ac. to tire line CB, it will thereby bedivided into a line of chords. These several lines, which in thefigure are drawn hut to every tenth degree, might in the very sametnanner be constructed to every degree, if the circle were madelarge enough to admit of ninety distinct divisions in (lie arch ofone of its quadrants. 6. A line' of rhumbs is thus constructed :divide the arch DB into eight equal parts, in the points 1, 2,3, 4,Ac . then setting one foot of the compasses in D, transfer the severaldistances D I, D 2, D 3, from the arc!) to the line DB ; which bvthis means will be divided into a line of rhumbs, each of whichwill answer to an angle of 11° 15'. 7. To construct a line of lon-

gitude, divide the radius EA into sixty equal parts, marking everyten with their proper numbers; from these divisions let tall per-pendiculars upon ttie arch AD, and having drawn (he line AD,with one foot of the compasses in A, transfer the several distances,where the perpendiculars cut the arch to the line AD, which willthereby be divided into a line of longitude. 8. To project theline of latitude, the radius CE being already divided into a line ofsines, lay a ruler from the point B through each of the said divi-sions, and mark the points cut on the opposite arch AC with thenumbers 10, 20, 30, Ac. then having drawn (lie line AC , with onefoot of your compasses in A, transfer the several intersections oftiie aren to the said line, which will theiebv become a line oflatitude. 0. To project the hour-line, draw llu* tangent IK equaland parallel to the diameter CD, and divide half tin* arch of eachquadrant AC, am! AD, from the point A, into three equal parts,which will l>e i5°each part, fertile degrees of every' hour fromtwelve to six ; each of which parts are to he again subdivided intohalves and quarters, Ac . then drawing lines from the centre E,

through each of their divisions and subdivisions, till they cut thetangent IK, (hesaid tangent will thereby be divided into a line ofhours, 10. To the above lines may be added a line of inclina-tion of meridians, which is projected in the same manner as tilehour-lines ; being only divided into degrees, instead of time, everyfifteen degrees being equal to an hour. Now if these lines, withtheir respective divisions, be transferred to a scale, and there alsobe added a line of equal pails, the instrument called the plan scalewill lie completed, as in fig. 4, and as to the uses of these lines,those of tangents, semi-tangents, and secants, serve to find the cen-tres and poles of projected circles, in the stereographic projectionof the sphere, Ac . the line ofsir.es serves for the orthographic projec-tion of the sphere ; the line of chords serves either to lay down anyangle, or measure the quantity of one already laid down ; the lineof rhumbs serves with more readiness than the line of chords, tolay dow n or measure the. angle-of a ship's course in navigation :the line of longitude being laid down on the scale contiguous toa line of chords of the same radius, and numbered the contrary way,shews by inspection how many miles there are in a degree of lon-gitude in each parallel of latitude ; reckoning tire latitude upon theihie of chords, and the miles of longitude upon the line of longi-tude ; the two lines of latitudes and hours are used conjointly, andserve very readily to mark the hour-lines in the comtruction ofdials, on any' kind of upright planes. For the farther uses of theplain-scale, see the articles Trigonometry, Navigation, Men-suration, Ac .

Scale, Diagonal, is projected thus: first draw eleven parallellines at equal distances (Plate CL11I. fig. 5,) the whole lengthof which being divided into a certain number of equal parts, ac-cording to the length of the scale, by perpendicular parallel?, lettiie first division be again subdivided into ten equal parts, bothabove and below ; then draw ing tiie oblique lines from tiie firstperpendicular below to the first subdivision above, and from tiiefirst subdivision below to the second subdivision above, Ac . thefirst space shall thereby be exactly divided into one hundred equalparts; for as eacl) of these subdivisions is one-tenth part ot tiiewhole first space or division, so eacli parallel above it is one-tcntliot such subdivision, and consequently one-hundredth part of tiiewhole first space; and if there be ten of the larger divisions, one-thousandth part of the whole scale. If therefore the larger divi-sions he accounted units, tiie first subdivisions will be tenth partsof an unit ; and the second subdivisions, marked by the diagonalson the parallels, hundredth parts of an unit. Again, if the largerdivisions be reckoned tens, tiie first subdivisions will be units, andthe second subdivisions tenth parts: and if the larger divisions beaccounted hundredths, the first subdivisions will be the tons, andtiie second units : and so on.

Scale, in archibcture ami geography, a line divided into equalparts, placed at the bottom of a map or draught, to serve as acommon measure to all the parts of tiie building, or all tiie dis-tances and places of tiie map.

Scale, in music, sometimes denominated a gamut, a diagram,a scries, an order, a diapason. It consists of tiie regular gradationsof sound, by which a composer or performer, whether in rising ordescending, may pass from any given tune to another. Thesegradations are seven.

Scale, in mathematics, See Logarithmic Lines, under whichtitle are mentioned some improvements by Mr. Nicholson {onGunter’s scale.

SCALEA, a town of Naples, in Calabria Ultra, on tiie sea-coast, 29 miles W. of Cassano, and 44 N. N. W, of Cosenza .

SCALENE, [xcalcnum, I.at.j ill geometry, -si triangle that hasits three sides unequal to each oilier. Sec Geometry.

SCALIGER, Jose a it Justus, one of the most learned criticsand writers of this time, was born at Agen, in France , in 1540 .He studied with great assiduity in the college of Bourdeatix, afterwhich Iris father took him under his own care, and emoloved himin transcribing iris poems ; by which lie obtained such a "taste f° rpoetry, that before lie was 17 years old lie wrote a tragedy up< ,nthe subject of (Kdipus, in which lie introduced all the poeticalornaments of style and sentiment. Hu went to Paris in 1550, witha design to apply himself to the Greek tongue. For this purposehe for two months attended the lectures of Tiimebus; but findingthat in the usual course lie should he a long time in gaining hispoint, he shut himself up in his closet, and by constant applicatm' 1