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(Fig. 163) the arch has to be set out, as all other arches, starting with half a course each side of the centre line, and then pricking over to the springing. The approximate key, which is cut as a bird's-mouth, is then filled in from the centre of the base line, and the approximate template obtained and traversed until it is accurate. The courses are then filled in with the latter. Under these new conditions, the courses, not being normals to the curve, will all differ in length and bevel. These will be obtained and marked on the template, in the same way as in the camber (Fig. 156).

The Modified Gothic (Fig. 164).-When the equilateral arch has to be reduced in height, by remembering that the two sides are two segments only, the setting out becomes very clear. Again, taking the 3' opening and 9" face, set out the base and centre lines.

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and the opening AB. Upon the centre line set up the reduced. height DC, join AC and CB. Bisect AC and CB with lines square to them (p. 55) and produced to the base line. Where these meet will be the radial points from which to fill in the sides, the template being obtained as in the equilateral arch (Fig. 162). This, like the Gothic arch, may be filled in from the centre of the base line, forming a key-brick, the lengths and bevels differing for each course.

Lastly, should the curves on AC and CB need modifying (Fig. 165), these may be brought down by treating them as segmental arches, constructing the base line, and marking the height of the curve upon the centre line. Mouldings on these arches are a very simple matter, being treated, when filled in from the radial

point, as the segment, and from the centre, as the camber arch. In neither case is there the difficulty of the mitre to meet.

The Elliptical Arch.-There is no curve in arch-cutting that requires more care than the ellipse, and there is no arch in which faulty setting out, or a cripple, as it is termed, is more easily detected, especially by the trained eye. First, let it be quite understood that it is impossible to set out the ellipse by means of the compasses, though a very near approach may be obtained, when the rise has not to be taken into consideration, by the following methods::

Case 1 (Fig. 166).-Opening, 3'; face, 9". Lay down the base line with a centre line drawn at right angles above and below it indefinitely, and the

opening AB half each side, as
before. Divide the opening
AB into four parts in the
points C, D, E. With the
point of the compasses at C,
and the pencil at A, describe an A
arc; then, with the same dis-
tance in the compasses, but
with the point at A, cut this
arc in F. Repeat this on the
other side of the opening, and
again cutting this arc in F.

G

FIG. 166.

E B

Through F and C, and F and E, draw lines meeting at the centre line in G, and extended indefinitely above F. Then, with the point of the compasses at G and extended to F, describe the remainder of the curve, or intrados, from F to F. Now, going back to C, and the pencil extended 9′′ beyond A, describe the extrados terminating at the line FG. Repeat this on the other side of the opening. Then, with the point at G, and the pencil extended, draw the topmost part of the extrados. It will now be apparent that in between the lines GF there is a segment arch, the template for which will be obtained as in that arch; and that the other two portions are parts of a semicircular arch, and again the template will be obtained as for the latter arch. This is the strongest method of filling in, but the appearance of having two distinct shapes of bricks upon the face is certainly objectionable. The difficulty may be overcome by filling in the arch the same as the camber, or by pricking over the extrados and filling in from

F

the centre of the base line for the approximate key. The bevels and lengths, of course, will differ, but the bricks will be alike on the face (Fig. 167).

Case 2 (Fig. 168).—Another method of setting out by means of the compasses, with a given rise, the height of the rise bearing a liberal proportion to the opening. Set out the 3' opening as before, calling it AB, and the 14" rise CD. Join DB; cut off CD from CB in the point d; take the remainder dB, and

[blocks in formation]

cut off Db from DB in the point b. Taking any distance in the compasses greater than half Bb, and with the point first at b, then at B, describe arcs cutting each other above and below bB. Through these intersections draw a line cutting the base line in the point E and the centre line in the point F; then measure from A, fixing a point, G, upon the base line similar to E. Then E, F, G, will be the radial points from which to draw the arch as before.

FIG. 169.

B

Case 3 (Fig. 169) is the string method, answering very well for rough elliptical arches which have to be covered with plaster. Set out the opening, or major axis, AB, and the centre, or half-minor axis, CD. Taking the distance CA in the compasses, with the point at D, cut the base line at F and G. Then, having fixed pins at F, D, G, tie the end of a piece of string or thin wire at F, pass it round D, and tie at G. Remove the pin D, insert a pencil in the loop, and, with the string or wire extended as far as it will go, describe the curve.

Case 4 (Fig. 170).-Neither of the above, though useful in

their way, can be compared to the trammel, which is the best practical method to be recommended to bricklayers.

D

Set out the opening AB upon the base line half each side of the centre line CD, which will be drawn indefinitely below as well as above the base line. Prepare a square, the sides being about 2" wide and " thick, with a slight bevel taken off the under side of the outer edges; fix the square, the edge of one side. coinciding with the centre line, but below the base line, and the other with the right hand, and answering Ā to the half of the base line. take a rod (which will be known as a trammel rod) with a fixed pencil point; measuring along the rod from the pencil point, fix a screw, with the head downwards,

Next

C

B

FIG. 170.

at a distance equal to the rise CD. Again, measuring from the pencil point, fix a similar screw equal to the distance CB, i.e. half the opening. Now, take some thin boarding, kept together by ledges, equal to rather more than half the opening in length, and more than the height of the rise in width, with the bottom and left-end edges answering to the right-hand side of the base and centre lines, shot true and square to each other. Fix the mould in position, with the bottom and end edge coinciding with the centre and right-hand half of the base lines. Then, with the trammel rod, the head of one screw working horizontally under the bevel along the top edge of the square, and the other vertically up the square, describe half the soffit upon the roughly prepared mould, which should be properly and truly cut to the curve. This may be termed the master mould. Practice only will give perfection in striking this curve.

It is impossible to attach too much importance to the use of the master mould. The brick-cutter should set out his work to it, and also take the tickings upon it for the centre; the carpenter should use it as his mould for making the centre; and then it should be sent to the joiners' shop, for the purpose of setting out the curve for the head of the frame. Lamentable results have occurred through these three trades working independently.

In setting out the arch (Fig. 171) the mould should be fixed in position, the bottom of it to the base line and the end to the centre

D

mould in
position

C

"Gange for extrados

line; then, having drawn the intrados line, a gauge the required depth of the face should be cut, and while one end is worked round the master mould, the other, having a pencil attached, will describe the outer curve, or extrados. The template may then be obtained and the arch filled in as before. It will be seen from this description that theory differs in many points from practice. The extrados in theory is not parallel to the intrados. In theory also, each face course, or voussoir, being normals to the curve, would differ in shape, and, though not quite impossible, would be most expensive in practice.

A

FIG. 171.

In setting out elliptical arches consisting of alternate blocks of brick and stone, the divisions should be in the proportion of 5 to 3 or 6 to 4 respectively; and in large arches each division should be set out normal to the curve, and separate templates obtained for each block of brick and stone. For instance, take an arch for a 7' opening, 2′ 3′′ rise, 12" on the face (Fig. 172), to be

5

3

FIG. 172.

filled in with red brick and Bath stone, but starting with red brick and keying in with stone. Set out the opening in either of the ways as shown, then upon the extrados set out the courses of brick and stone, either as 5 to 3 or 6 to 4, whichever comes in most conveniently. In this case 5 and 3 appear to work in the best; so, starting with the key, tick in stone equal to three courses of brick, next to this five courses of brick, then stone, and so on. Number the divisions 1, 2, 3, 4, 5. Now find the foci to the outer curve.

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