CUT

220

CYC

cylindroid, and their axes intersect each other ; and if thesemi-diameters of both cylindroids, perpendicular to a planepassing through the two axes be equal to each other, thecurve formed by the intersection of the cylindroidic surfaceswill have all its parts in one plane : not any of thesethus defined, are curves of double curvature. But if thesurfaces of two cylinders of unequal diameters meet in acommon line, this line is a line of double curvature : of thisdescription are cylindro - cylindric groins. Many otherinstances of two geometrical solids meeting each other, pro-ducing lines of double curvature, may be laid before thereader, but perhaps what has already been adduced will besufficient.

Curved Surface of a Solid, that in which, if any pointbe taken, and if the solid can be cut by a plane through thepoint, and thence form a section, such section is terminatedby a curve : Thus a cylinder or a cone may be cut by aplane, through any given point, so as to make the commonsection of the cylinder or cone witli the plane, a curve, or astraight line; but if a sphere, spheroid, or any of the conoidsbe cut by a plane through any point, the common sectionof the plane, and the surface of any such solid will be acurve.

CURVILINEAR, (from the Latin curvus, a curve , andlinea, a line,) or Curvilinear Figure, a superficies boundedby curve lines, or by a curve and straight line, when theproperties of the curve depend upon the straight line.

The circle and ellipsis are entire curves, or such as haveno straight line in their boundary; but the parabola andhyperbola are both bounded by a curve and a straight line.

Curvilinear Angle. See Angle .

Curvilinear Roof, that which is erected upon a cur-vilinear plan, as a circular, or elliptical, or portions of thesecurves.

Curvilinear Superficies of a Solid. See Curved Sur-face of a Solid.

Curvilinear Triangle, one whose sides are curves.

CUSHION RAFTER. See Principal Brace.

CUSP, (from the Latin cuspis ,) one of the pendants of apointed arch, or one of several pendants forming what maybe denominated a polyfoil; two cusps form a trefoil, three aquatrefoil, four a cinquefoil, &c. In other words, the termmay be explained as the points generated by the intersectionof the small arcs or segments of circles, forming the foliationswhich frequently terminate the internal curves of Gothic! arches, more especially window arches, in the shape of tre-j j foils and other polyfoils.

This name was first given by Sir James Hall , of Dunglass,in an Essay on the Origin of Gothic Architecture. He says,in a note at the bottom of page 23, that “ assemblages ofthese cusps are spoken of in the descriptions of Gothicworks, by the means of trefoil, quatrefoil, semitrefoil, &c.;but no proper word has been used to describe the form,wherever it occurs, or however combined.”

CUSTOM-HOUSE, an edifice in some chief city, or port,for the receipt of the customs and duties of importation andexportation imposed on merchandise, by the authority of thesovereign. The custom-house in Dublin is a very elegant' edifice.

CUT, in inland navigation, the same with canal, branch,or arm.

Cut Brackets, such as are ntedelled on the edge.

Cut Roof, a truncated roof.

Cut. Standards, for shelves, are those whose front edgeis cut into mouldings.

Cut Stone, hewn stone, or that which i3 brought intoshape by the mallet and cliiseL

c „ brid^

Cut-water, the lower portion of the pier 01 t th ewhere the two sides meet at a point, so disposed to ^ ^ rC ecurrent, and offer as little resistance as possible toexerted by it against the pier. ijyjde 8

CUTTING PLANE, a plane supposed to cut or usolid into two parts, in any position. ; n tl> e

CUVILLER, FRANCOIS, an architect, bor " d Wyear 1698, at Soissons, in France . He was emp c on'the Elector of Munich in many public buildings, a ^ jjap"tinued in the service of that court till his death, w 1 3 and

pened in the year 1760, leaving behind him many P ‘ rt jgts,designs, which were afterwards engraved by diflei' e bo 1 ' 11and published by his son, Francois Cuviller, who t0 tl> 6at Munich , and succeeded his father as arclutecourt. ■ c le, a 8 ®

CYCLOGRAPH, (from the Greek, kvk\oq, a e " 0eO t (»[■ypcn/jtir, to describe ) in practical geometry, an inst ^ g j n e >describing the arc of a circle to any chord and ye gar fiiti> l ' e ^

but chiefly used in flat segments, or those whose ct j,approach to straight lines. There are several con . nC i_of cyclographs, of which the following is one. 16 J fold) 11 ?consists of two rules, A u, and C D, connected byjjoint, e, the pin, k, of which projects upwards, and r o linto receive a bar, h g, which is fastened, but ni ova te( j j-iil 8 '"’the centre of the folding joints ; upon the connec j. fli° the centi« ° ot i,ei

A b and c d, at equal distances, from „ tvv0 - ^

folding joint, are fastened the ends land K, 0 ^ 0 j n t, jj 6

equal bars c i, c k, connected by a movable J°^ g { P.as to form a rhombus h K c I, movable round eajoints, c, i, h, k ; then the bar, h g, which p asS -the centre, h, of the two first rules, being mthrough a projection of the pin, c.

aade «> s0 ) eoftheoppo site^ThJthe rhombus, is made to slide int.o the mortise nypof’rt

use of the bar is to fasten the instrument in - ,means of a screw inserted from the middle of the ^ e ii<lupright pillar at c, which receives the. shdi 0

oi

the bar.

The instrument being supposed to be placed up

. . • . - ■ «... • beinq it jjjij,

.TjoditJ >o

plane, and the pin, h, of the folding jointproject upwards ; another bar, L si N, bent .to awith a longitudinal slit, OP, is fitted upon it, put 8 J,a motion upon the pin h, in the section of the ^ gCJ . e \vbe fastened at any required point, by means ot . ge( j i» t()the top. The other end, N, of this bar is in01 , „ go 8 etdirection of the slit, to receive the lower bar, ^ t |,e g {have a longitudinal motion. The middle bne nl jfldl ebar stands in the same vertical plane with the ^ pos 1the lower bar, and these two lines are parallel t ji 8

of the instrument. , g jde 0 jC iI,

The end of the bar, l si, at the externa ot p®folding joint, has a deep socket for holding a P p|, e a 0 tperpendicular to the plane of the instruinen _• t jie P' eI)C iltage of the upper bar being movable, to j n 0 r 1^ 0 t

pencil is attached, is to admit the point of 4 £ p A, c

to be brought into the intersection of the s , 0 .

the instrument. 0 f j e o 8

To describe the segment of a circle by ff>ea e( jges n ’^ e d> 0graph, fasten two pins in the plane, or stee nt ; p‘ 8 J]6 a*purpose, and adjust the angle of the instru' ^ u p 0 n >outer edges upon the pins, and the angle c pin s >them ; move the instrument laterally close 0 (K

pen or pencil will describe the curve. .„„ded/r^

ecK

The principle of this instrument is_ _*i.„ third

third

twenty-first proposition of the third f' J ~ oV eElements, in which it is announced and P e q ( iaangles in the same segment of a cird e >another.”

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