ARCHITECTURE. 
fe&ing arch, project a line from i round to i at the body 
arch A, and from r let fall a perpendicular to s, the centre 
•of the fide arch: draw at A the chord line 3, 4, 5, and 
divide it into four equal parts : alfo draw lines from 2 
through each divifion, till they cut the arch ; and from 1 
•draw lines through the points on the arch to the perpen¬ 
dicular 0 p: take 0 p, and place it on the fide arch B, ma¬ 
king the fame divifions as at A ; draw then the chords of 
the fide arch, and divide them into four equal parts, and 
proceed as before at A : laftly, draw lines from 0 p to 1, 
which will interfeft the radials billing from the centre 2, 
■and the points will give the curve of the fide rib D. Ha¬ 
ving drawn the plan-line p s, of the angular rib, draw s q 
perpendicular to it, and take the height of the interfering 
arch 1 2, and place it to 9 : draw tire chord-line p q, and 
proceed with the reft as before, and they will produce the 
angular rib E, as required. The fame operation may be 
performed by ordinates, in the common way, as reprefented 
on the oppolite fide of the figure. But, this groin being 
intended for plajlcr, it requires great exatftnefs in the an¬ 
gular ribs, and the utmoft corredtnefs on the under fide, to 
give fmoothnefs and regularity to the ceiling. 
Fig. 10, is the plan of another plafter groin, wliofe body 
arch A is a femi-ellipfis, and the interfering ones at BB 
are fcmicircular. D is the angular rib, deferibed by or¬ 
dinates, as the corre(ponding numerals (hew, and which 
has been already taught. The plan at C exhibits the jack 
and angular ribs, as deferibed in the foregoing examples. 
Fig.'ii, reprefents the plan of a curved groin, which 
may be applied either to brick-work or plafter ; though 
we (hall here deferibe it for the ufe of the latter. Let a, b, 
c, d, be the plan of the body arch, which might be conti¬ 
nued round till it form a complete circle; in which cafe 
nothing more would be required than repetitions of what 
is exhibited in the figure before us. Let AA be the body 
arch, and BB the interfering arches; to find the curva¬ 
tures of the angular ribs, proceed as follows: divide the 
arch A at its bafe into eight equal parts, from which raife 
perpendiculars to p, q, r\ continue the fides of the plan 
a c, b d, until they meet at s ; divide the curve a b into 
eight equal parts, from which draw right lines to the cen¬ 
tre r; interfeft thefe by deferibing the feveral curves by 
the centre s, from the refpedfive divifions at A ; through 
the points thus found draw the feveral curve lines, and 
they will form the correiSt plan of the angular ribs, when 
placed perpendicularly on their bafe. We next proceed to 
find the vertical curve of the ribs thus : draw dg, which 
make in length equal to the curve line C d\ and alfo take 
the girt of the curve line C a, and lay it from a to k, and 
divide both into four equal parts. Then take the ordi¬ 
nates from A, and transfer them to their correfponding 
places in E and D, and the curve palling through thefe 
points will be the vertical arch of the angular ribs. But 
obferve, when E and D are fixed on the plan, they are 
fuppofed capable of being bent to coincide with the an¬ 
gular curves on the plan ; otherwife they muft be fiiaped 
to that curve out of timber of a fuitable thicknefs. For 
the interfering arches, divide the curves of their plan into 
the fame number of equal parts as before, which is exem¬ 
plified at e/B, where ef\s made equal to a b on the curve, 
and is A equal to the curve cd ; and, their ordinates being 
drawn, it only remains to transfer the feveral correfpond- 
ent ones from A, by which the elliptic curves of the inter¬ 
fering arches are found, and which, when placed on their 
plan, and muft, by the fame means tiled with the angular 
ribs, be made to coincide with their curved plans a b and 
c d. The jack ribs of the body arches A A will be ftraight 
on their plan, as at to, and muft be placed in the direrion 
of the radials from the centre s. Thofe of the interfering 
arches muft be curved on the plan, conformable to their 
diftance from the centre s, as is n. 
Fig. 12, is the plan of a Welfh groin, or one under pitch, 
having its body and interfering arches compofed of femi- 
circles; or they may be of fimilar fegments, whofe inter- 
ferions meet on a curved plane, and confequently their 
Vol. II. No. 61. 
t’3 
plan will be in a curve, as in the preceding groin. The 
interfering at ch B being divided into any number of equal 
parts, draw lines perpendicular to its bafe, at pleafure. 
From 1, 2, 3, 4, direr lines round to the body arch A, as 
at i, 2, 3, 4; from whence draw''lines perpendicular to the 
bafe line of A, and where theie interfeci at 4, 3,2, 1, draw 
a curve line, which gives the plan of the angular rib of 
the arch ; and the rib itfelf at D, may be found in the 
tifual manner, to which the numerals direr. To find the 
mould that will deferibe the curvature of the interfering 
arches when laid on the body arch A, lake the girt of the 
angular rib D in the intide, at 1, 2, 3, 4, and, drawing a 
riglit line at E, take the ordinates from the chord line of 
the plan of the angular rib, and place them refpe6livcly at 
1, 2, 3, 4, which will give the mould required. And as 
the angular rib in this figure will be curved both ways, 
fimilar to thofe in the circular groin already deferibed, the 
fame means that were ufed in deferibing them muft be 
adopted in tiie prefent inftance. 
Of S K Y - L I G H T S. 
To find the Length of the Hips of a Sky-light , fanding upon 
a fquare Plan, the Height being given. —Draw the diagonals 
a b, and c d, as in the figure, and they will bifeet each 
other at right angles at e ; take a e for the bafe of any 
hip; from e make cf equal to the height of the (ky-light; 
from a xof draw a line a f and it will be the length of 
the hip required. 
To fnd the Backing of the Hip.' —Draw any line, as k i, at 
right angles to a e, the bafe of the hip rafter, to cut it in 
the point h-, fet the foot of the compafs in h, as a centre, 
and with the other deferibe a circle to touch af the hip 
rafter, to cut the bafe line a e, at g ; then draw g i and g k ; 
then the angle kg i will be the backing of the hip, as is 
fhewn by the bevel at B ; but the beft way to work the 
hips is to apply a bevel to the parallel fides of the hips, as 
is fhewn at C, by making the other fids of the bevel pa¬ 
rallel to a e, the bafe of the hip. 
The fame lines will extend to any fky-light, whatever 
may be the form of its plan. If it be any polygon, to find 
the length of the hip rafter, draw a line through any point 
in its bafe at right angles to it, fo as to cut the two con¬ 
tiguous fides to that bafe, and on the faid point as a centre 
deferibe a circle to touch the hip rafter from the point 
where this circle cuts the bafe line, draw two lines to meet 
the ends of the perpendicular line at the fides of the poly¬ 
gon, and the angle formed by thefe two lines will be the 
backing required. 
For a domical Shy-light.- —Suppofe one of the ribs of a 
dome be given, and the plan of the opening of the ftaircafe 
be fquare, with an oftagon curb at the top for a (ky-light; 
& 5 it 
