444 T/ie Architectural Review and American Builders' Journal. [Jan., whence the arches spring, and on the line A B describe the given arch A F B. This being done, divide the line A B into any number of equal parts, from whence raise perpendiculars to A B, to touch the arch A F B, and draw the diagonal lines A D and B C. Then take the line E F, and set it perpendicular to the lines A C, A D, C D, C B, B D, from A to 0, from A to I, from C to P, from C to S, from C to L, and from D to K, from D to T, from D to V, and from B to M, and from B to Z, and draw the straight lines P, I K, S T, L M, and V Z. Now divide the base lines B D, D C, C A, A D, and B C, each into the same number of equal parts as A B is divided into, and from the points of division draw parallel lines to touch the lines O P, S T, V Z, L M, and I K. Then take the lengths of the perpendicu- lars to A B, drawn to touch the given arch A F B, and set them off in the cor- respondent parallels drawn from the points of division of the several bases upwards, and the arches will be de- scribed. The Arch Line of a large Ceiling, or Vault, supposed to be semi-circular, being given : how to form the Curve of a Lesser Arch, that shall intersect the Side thereof, to give way for Doors or Windows, so that their intersection shall produce the Groin to hang per- pendicularly over its Base ; as also to form the Curve Line thereof Fig. 7. First, draw the lines A B, B D, D C, and C A, to represent the walls from whence the arches spring, and de- scribe the two given semi-circular arches A B, C L D, and in the line B D set off. the span of the intersecting arch from v to t. Then set off the height you de- sign to raise the lesser arch v z t from g in the line A B, perpendicularly to touch the arch in h, and from v to r, and t to u, and draw the line r u, which halve in the point z, and draw the line z y paral- lel to vr, or t u. Then lay a line from h through h through g, towards x; as also from z through y, towards x ; and these two lines will cut one another at x, from whence to the points v and t draw the lines x v and x t. Now set off g h perpendicular to x t, from x w, and from t to S, and draw the line S w, and divide q B into any number of equal parts at pleasure ; from the divisions of which, draw perpendiculars to q B, to touch the arch A B between the points B and h, and divide v y and y t, the halves of the base v t, each into the same number of equal parts as q B : also, x t, and from the point of division draw parallel lines to touch the lines u r and s w. This being done, take the lengths of the lines that were drawn from the points of division of g B perpendicularly to touch the part B h of the arch A B, and set them off in the correspondent parallels from y v to z r and from y t to z u ; as likewise from x t to w s. As you set off the parallels, stick in nails and bend a thin rule about them, and describe the sought arches ; v z t is the true intersecting arch, and iv t the curve line of the corresponding groin. If the Lesser Arch of an Irregular Groin be a given Semi-circle, it is re- quired to form a Larger One, so that the Intersection of those two Arches shall make the Arch Line of the Angle to hang perpendicular over its Base; also, to draw that Arch Line of the Angle. Fig. 8. First, draw the lines A B and C D, to represent the walls from which the arches spring, and draw the line C B, and on A C describe the semi-circle A E C, and divide A C into any number of equal parts, from whence draw paral- lel lines to C D to touch or come to the arch A E C, and if these parallels are continued out to the line C B, they will divide it into the same number of equal parts as A C is ; and if from each of the divisions of this last line, parallels to A C are drawn, they will divide the line A B into the same number of equal parts
