it 4 ARCHITECTURE. 
it is required to find the ribs and the curve on each fide of in the middle'of '.ef, the height of the roof, which is here 
the opening of the ftaircafe, where the feet of the ribs are one-third, and draw d e, and df which are each the length-, 
to fall, in order that the inferior part of the dome fhould of a common rafter, 
make an o&agon finifh, to correfpond with the curb. ^ 
Let B be the given rib ; take any number of perpendi¬ 
cular ordinates to its bafe at pleafure; from the points 
a, c > e t g> h where they interleaf its bafe, draw parallel 
lines to the fides of the curb, returning round each diago¬ 
nal, if there be more than one, until it cut the bafe of the 
angle rib D ; at the points a, c, e, g, i, /, draw the ordi¬ 
nates of D, which trace from B, and it will give the angle 
rib ; and at the points e, g, i, /, at C, upon the fide of the 
opening of the ftaircafe, draw tire perpendicular ordinates, 
and trace C from B agreeable to the letters; then the curve 
C will be the true place for the feet of the ribs upon the 
fide of the ftaircafe, and the part that lies in the middle is 
a ftraight line parallel to the horizon. 
Domical lky-lights well executed, and properly enrich¬ 
ed, make an elegant finifh to a fuperb ftaircafe, whether 
framed to a circular, oCIangular, or elliptical, plan. To 
illuftrate this, we have given, in the annexed Plate, a very 
handfome defign for an elliptical domical fky-light, which 
was executed by Mr. Paine, over the great ftaircafe at 
Brocket Hall, in Hertfordlhire. 
Of ROOFS. 
The lines for roofing, at leaft for the length and back¬ 
ing of the hip, mull be found in the fame manner as di¬ 
rected for the lky-lights ; and if it be required to find the 
end of a horizontal bar, fo that it fhall fit againft the hip, 
it will be performed in the fame manner as finding the 
form of the end of a purline, fo as to fit againft the fide 
of a hip rafter, as deferibed below: the fame may be faid 
of the jack bars to be fitted againft the hip of a fky-light, 
as in a roof. In the following figure one end of the roof 
is ftiewn, in order to determine two cafes : the firft is when 
the purline lies level, or having two fides parallel to the 
ho i:on; the fquare at B, and the bevel at C, will dire*£l 
how to draw the end of the purline in this eafy cafe ; but 
the following method is univerfal in all pofitions of the 
purline. Let ab be the width of a fquare roof; make if 
or a e, one half of the width, and make c d perpendicular 
its mod common pofition, that is, to ftand fquare, or at 
right angles to the rafter; and from the point h , as a cen¬ 
tre, with any radius, deferibe a circle. Draw two lines ql , 
and p n, to touch the circle in p and q, parallel to fib-, and 
at the points s and r, where the circle and two fides of the 
purline interfed, draw two parallel lines to the former, to 
cut the diagonal in m and k ; and draw in n and k l perpen¬ 
dicular to sm and r k , and join the points n i and k i\ then 
G is the down bevel, and F the fide bevel of a purline : 
thefe two bevels, when applied to the end of the purline, 
and when cut by them, will exactly fit the fide hip rafter. 
To find the Bevels of a Jack Rafter againfi the Hip .— By 
turning the ftock of the fide bevel of the purline, at F, 
from a, round to the line iz, will give the fide bevel of 
the jack rafter. And the bevel at A, that is, the top of 
a common rafter, is the down bevel of the jack rafter. 
For a Polygon Roof .'— Suppofe the plan of a polygon roof- 
be given, and one of the common ribs (landing upon that 
plan; 
