A R C H I T 
the arches ae, bfi eg, and dh, at C, will fall over the pa¬ 
rallel ftraight lines £ a, fb, gc, and h d, in the plan A, 
which it was required to demonftrate. 
To describe a Soffit in aJlraight Wall, fining from the Jambs, 
and level at the Crown. —This is fhewn in the lame Plate, at 
Jig. 3, where A is the plan of the wall, B is a femicircle 
on the outlide, and C is an ellipfis in the infide, traced 
from B, or deferibed by a trammel; draw the lines a e, 
bf, and h h, perpendicular to ab, the fide of the flue of A ; 
then take half the compafs of B, and lay it on bf in D ; 
«Ifo take half the compafs of C, and lay it from a to e in D, 
and through the, points e and /draw a line to cut the line 
hhh, See. in h, and continue it to g; fet the foot of the 
compafs in the centre of the flue at h, and deferibe the 
quadrant 1234, which is divided into four equal parts; 
and draw the ordinates 4/7, 3 h, See. then take one of the 
divifions of the femicircle B, and fet the foot in b, and 
make the fmall arch at 1, and take h r from the centre of 
the flue in A; then place the foot of the compafs in h , in 
the loffit, and with the other point crofs the fmall arch at 
l ; again, with the divilion at B, fet the foot of the com¬ 
pafs in 1 in the foffit D, and deferibe the fmall arch at 2 ; 
and take h 2 from the centre of the flue, and fet that to 
its correfpondent h 2 in D, and by this means one-half of 
the loffit will be correffly obtained. Then, fet the foot 
of the compafs in k, and with the other extreme h, draw 
a circle hgk ; again, fet the foot in g, and with the difiance 
gh, that is, from gh the centre of the flue, deferibe an 
arch from h round to k, and draw the line h h, where thefe 
tw'o arches interfeft ; then fet the divifions of hhh, &c. on 
kk, and deferibe the other half in the fame manner, and 
thus the outline of the foffit will be completely fhewn. 
To dferibe a Sojjit in a circular Wall, fluingfrom the Jambs, 
and level at the Crown .—This is reprefented at fig. 4. Pro¬ 
ceed as in the laft example, to project the line bdj'h ; then 
prick off the foffit D from the plan A, according to the 
refpe&ive letters, and it will be completed. In the fame 
manner may any other foffit, fluing from the jambs and 
level at the crown, be deferibed, let the form of the wall 
be what it will, by firfi finding the line bdft/t ; for then the 
foffit may be correctly pricked from the plan, whatever 
may be its form. 
To Jlreteh cut a Soffit, when a Window or Door, having a 
fcmicircular Head, cuts into a ftraight Wall, in an oblique di¬ 
rection. —In Jig. 5, let C be the plan or opening of the win¬ 
dow, and let the bafe of the femicircle B be drawn at right 
angles to the jambs or fides of the plan C ; divide the fe¬ 
micircle into any number of equal parts, as ten, and draw 
the ordinates acrofs the plan C; then ftretch the divifions 
round B along the foffit D, in the fame ftraight line with 
the bafe of B ; and the ordinates being all drawn acrofs, 
and traced off from the plan C, as the figures and letters 
direct, the foffit will be completed. 
In all kinds of foffits, when the two jambs are parallel, 
the ftraight line which the foffit is traced from, mud be 
drawn at right angles to the jambs, as fhewn in this figure. 
For want of this confideration they are often projected in 
books upon wrong principles. In the four firfi foffits, 
where the jambs are not parallel, they mult be continued 
till they meet in a point, and the line which the foffit is 
to be traced from, mult be made to form an ifofceles tri¬ 
angle with the jambs. 
To find the Ribs of a circular Niche, whofe Plan is a Seg¬ 
ment, and Elevation a Semicircle. —Let P, i nftg.6, of the 
lame Plate, be the plan, and E the elevation, of the niche. 
From the centre s, draw the place of the ribs on the plan 
P, and from 1, 2, 3, 4, raife perpendiculars to the bafe- 
line ab, of the elevation E; from the centre c deferibe le- 
micircles from each perpendicular, at a and b, which give 
to the front rib together with what workmen term its 
backing, or levelling off its under and upper edge, fo as 
to correfpond with the curvature of the niche. From the 
points 5, 6, 9, raife alfo perpendiculars, till they cut at 
dfg, which perpendiculars from the bafe-line at b will 
give refpeLtively the heights of the back ribs, as iliewn at 
E C T U R E. ,u 
R, R2, and R3. Take then eh and cb at E, and draw 
the external and internal curves for each rib, from the 
feveral centres at R, Rz, and R3 ; then take from the plan 
7 5, 8 6, and eg, the projeftion of each of the back ribs, 
and place them at their refpeftive places in the figure, and 
from 5, 6, c, raife like wife perpendiculars, which will give 
the ribs. Laftly, to find the bevel of the upper end of 
the ribs R2, R3 ; from the centre s deferibe the arches 0 1 , 
qn, and take the diftanccs 3/, 6 n, and place them refpeft- 
ively at 6 7z, 5 l, in Rz, and R3, as fhewn in the figure, and 
they will give the true bevel required. 
To find the Ribs of a Niche, whoj'e Plan and Elevation are 
a Semi ellipfis. —Confider P, in fig. 7, as the given plan, and 
E the elevation, whofe tranfverfe and conjugate axes are 
fimilar. Deferibe the places of the ribs on the plan, as 
at 1, 2, 3, &c. whence it will appear, that the ribs will all 
unite perpendicularly over the centre, and therefore their 
rife will be nearly equal, as may be feen at r, rR, and ri ; 
confequently from E, the elevation, take ot, the femi- 
conjugate axis, and place at r, and with it deferibe the 
quadrant of a circle; then from the plan P take the (pace 
67, and place it where the figure directs, and raife a per¬ 
pendicular, which will give the length of the centre rib. 
In like manner take the other ribs 1, 2, from the plan, and 
place them at rR, and n, which divide into any number 
of equal parts, and draw their ordinates 1, 2, 3, 4, Sec. at 
pleafure. From r, take the perpendicular "heights 1, 2, 
3, 4, and transfer them to their correfpondent ordinates at 
rR and r 1, through which points deferibe the curves, 
and they will give the other ribs, which, being placed over 
their refpedtive plans, will be found exaftly to coincide 
with each other. Laftly, the backing may be found as at 
1, 2, &c. on the plan, where the fmall tranfverfe lines are 
drawn from the centre, and fliew how much bevelling is 
requifite at the foot of each rib, which mult gradually 
decreafe in an elliptic curve, till it terminates in a point 
at the top. 
Of LINES for DESCRIBING PEDIMENTS. 
To elucidate this fubjeft, we have given, at Jig. 1, in 
the annexed Plate, an elevation of a triangular pediment, 
with its whole extent divided into nine equal parts, two of 
which are affigned for the perpendicular height of the 
pitch, fet off from the upper line of the entire level cor¬ 
nice. If the pediment is intended to be open, divide the 
raking pitch into five equal parts, as in the figure, and 
give one from- the centre each way, for the opening. The 
fame proportions are to be adopted when the pediment is 
circular, whether it he clofe, or open ; and, to deferibe 
the curve, nothing more is requifite, than to confider the 
raking-lines of this /V. 1, as chord-lines of a circular pe¬ 
diment, which being bifeiSled, and lines drawn at right 
angles to the rake, will meet in the true centre from which 
the arch is to be deferibed. In this example, the raking 
cornice confifts only of the cima recta, which may be prac- 
tifed in cafes where the tympan is required to be large, 
for the admiffion of groups, or other confiderable orna¬ 
ments. Commonly, however, the entire cornice is placed 
in the raking part, whether clofe or open ; and it mu ft 
ever be obferved, that the face of the tympan, and that 
of the frieze of the level cornice, muft be in a right line 
with each other. It muft alfo be obferved, with refpefi 
to pediments of the different orders, that when mutules, 
or modillions, or denteles, are introduced in the level or 
lower cornice, the fame are likewife to be placed in the 
raking part, and in a line with them. And hence, in art 
open pediment, the due fpace affigned for the opening 
muft always give way to a punctual regard to place dentele 
perpendicularly over dentele, from end to end of the pe¬ 
diment. But let it be remembered, that open pediments 
ought never to be adopted in exterior works. 
In order to manage with accuracy the mitering of the 
raking mouldings with their refpettive returns, let it be 
obferved that three different profiles are requifite, as (hewn 
at fg. 2, and 3, where a is the level, b the raking, and c 
Sirs 
