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similar parts of the intrados, the arch is called a horse-shoearch, or moresque arch. Hence, in this kind of arch, thespanning line is less than any other line or chord drawnparallel to the span, but under the top of each of the verticallines.

When the upper line or side of an arch is parallel to theunder line or side, it is called an extradossed arch.

A simple vault is an interior concavity extended over twoparallel opposite walls, or over all the diametrically oppositeparts of one circular wall. An arch or vault is frequentlyunderstood as synonymous ; but the distinction which wei shall here observe is, that an arch, though it may be extended| over any space, has a very narrow intrados, not exceedingi four or five feet; whereas a vault may be extended to anylimit more than four or five feet. Thus, we frequently sayan arch in a wall, but we never say a vault in a wall; thoughnothing is more common than to say a vaulted apartment,a vaulted room, a vaulted cellar, &c. So that a vault, asSir Henry Wotton has observed, is an extended arch ; weshall therefore apply arch to the head of the aperture in awall which shows curvilinear intersections with the faces ofthe wall, and the word vault to arched apartments. Wefrequently, however, call the stone-work suspended over anapartment an arch as well as a vault; so that every vault isan arch, but every arch is not a vault.

The intrados of a simple vault is generally formed of theportion of a cylinder, cylindroid, sphere, or spheroid, nevergreater than the half of the solid ; and the springing lineswhich terminate the walls, or where the vault begins torise, are generally straight lines parallel to the axis of thecylinder, or cylindroid, or the circumference of a circle orellipsis.

A circular wall is generally terminated with a spherical| vault, which is either hemispherical, or a portion of a sphereless than a hemisphere.

A vaulted apartment, surrounded by an elliptic wall, isgenerally covered with a spheroidal vault, which is either ahemispheroid, or a portion less than a hemispheroid.

. i A conic surface is seldom employed in vaulting; but when! the vault is to have this kind of intrados, the intrados should

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; be the half of a cone with its axis in a horizontal position, orI | a whole cone with its axis in a vertical position.

\ ! All vaults which have a horizontal straight axis, are called: straight vaults

Besides what we have already denominated an arch, theconcavities which two solids form at an angle, are calledan arch.

If one cylinder pierce another of a greater diameter, thearch is called a cylindro-cylindric arch ; the cylindro beingapplied to the cylindric part which has the greater diameter,

| and the cylindric to that which has the less.

If a cylinder pierce a sphere of greater diameter than thecylinder, the arch is called a sphero-cylindric arch ; and, onthe contrary, if a sphere pierce a cylinder of greater diameterthan the sphere, the arch is denominated a cylindro-spherici arch.

! If a cylinder pierce a cone, so as to make a completeperforation through the cone, two complete arches will beformed, called cono-cylindric arches ; and, on the contrary,if a cone pierce a cylinder, so as to make the interior con-cavity through the cylinder a complete conic surface, the archis called a cylindro-conic arch.

If a straight wall be pierced with a cylindric aperturequite through, two arches will be formed, called plano-cylindric arches.

Every species of arches is thus denoted by two precedingwords ; the former ending in o, signifying the principal vault

or surface cut through, and the latter in ic, signifyingkind of aperture which pierces the wall or vault.

When two cylindric vaults, or two cylindroidic vaults, or ®cylindric or cylindroidic vault, pierce each other, andtheir axis, so that the diameter of each hollow may be t«same, when measured perpendicular to a plane passingthrough the axis of both surfaces, the figure so formed fcalled a groin; but for more particular information on tb> 3point see the article Groin .

The formation of stone arches, in various cases, has alN»I 9

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been looked upon as a most curious and useful acquisitionthe operative mason, or to the architect, or other person w®is appointed to superintend the work. In order to rem° v ®the difficulties experienced in the construction of cylindric 0cylindroidic arches, both in straight and circular walls, ' v °shall here show an example of each.

First, let it be required to construct a semi-eylindroi°arch, cutting a straight wall with its axis oblique tosurface of the wall, but parallel to the horizon.

Plate I. Figure a. —Let abcd be the plan of theture, A d and b c being the plan of the jambs, and A b andthe plan of the sides of the wall; produce da and CB t°^and F ; draw the straight line igmfe at right angles WiA g and C f ; bisect G f at M ; draw M H K perpendicularC f ; make m n equal to the height of the intrados of \arch, and describe the semi-ellipsis ghf, which is the sect'of the intrados of the arch ; make Gl, H k, and Ft,

to the breadth of the beds of the arch-stone, and describe

tli®

semi-ellipsis ike, which is the section of the extrados

of

arch. Now, suppose the distances between the joints aro 11 ® 1

the intrados of the arch to be all equal, and all the joints ^tend to the centre m ; divide the semi-ellipsis into such Al hodd number of equal parts, that each part may be in bre* 1 ^equal to what is intended for the thickness of the stone 3 ^that part; produce ei to s, and extend the whole numberthese parts from G to S ; and through the points of din 3 ^draw lines perpendicular to G s, or parallel to A G. Thro®^all the points of division of the ellipsis ghf, draw ®parallel to G a to meet A b ; then take the lengths of a'jparts of the lines so drawn that are terminated by G F ant1A^as follows, viz., make the first line on the left of g a eq° a ^.the first on the right of a A, and the point b will be obtain®^make the second on the left of G A equal to the second o n ^right of G A, and the point c will be obtained ; proceed i°manner until all the other points are obtained ; then a 0 .jjbeing drawn through all the points A, b, c, d, &c. to T >give the one edge of the envelope of the intrados of the aand by producing the perpendiculars erected upon G 3 t0 ^ g tpoints e,f g, &c., and making the several distances be,

&c. equal to A d or b c, the points D, e,f g, &c. to U, w , gjflJthe other edge of the envelope by tracing a curve through tthen A b cd,bcf e,cd gfi &e. are the soffits of the stone 3,

To find any bevel which the joints on the face °Jarch makes with that on the intrados. ^ t )i0

Let p q be one of the joints tending to the centre, M, 0lsection of the arch ; with the radius m g describe an arc, j,;cutting p q at N; draw np parallel to GA, cutting A B jjeldraw pq parallel to F G, cutting GA at Q; draw Ml P^velto G A, cutting A b at l, and join l o ; then Q l M isrequired. In the same manner may all the remainingbe found. . tb® 11

Again, let p qrs be the section of an arch-stone > jjlmaking two bevels, one to qp s, and the other tobe all the bevels that are necessary for that stone.obtained the several bevels, we shall now proceed t0 j oV v® rthe arch-stone, whose section is p q r s: first work t 1 ^ 0

bed of the stone corresponding to the joint p q, then