" GROIN. 
inches from m, the interfe&tion of the fappofed {quare ribs in 
the gro‘) of the old arch, the chord = twenty inches ; while, 
in the new arch, where the fame fection of the filling-in arch 
is only diftant 7.6 inches from g, the angle of interfection of 
the diagonal ribs, the chord is but 15.2 inches; hence, the 
weight incumbent on the ribsin the old arch will be to that 
in the new, at the fame point, as 20 to 1 5.23 confequently, 
the tendency the latter may have to i 
parts, on this account alone, will be lefs than the former in 
the proportion of 1 to 1.3, nearly : and by compounding the 
two proportions juft found, viz. 1 to 1.96, and 1 to 1.3, we 
have the comparative ftrength of both arches in the weakeft 
parts, namely, about the crown, as 1 to2 ; 
nearly. So that, if the old arch is capable of fultaining 50 
tons without danger, the new groined arch would, with the 
fame eafe, bear 125 tons, and in that proportion whatever 
might be the weight placed thereon. 
be owned, that the ratio. of the difference 
It m 
of weight of the fections of the filling-in arches, in 
The {pan of the diagonal ribs being greater in the im- 
proved conftruétion than the groins of the old one, thofe 
parts of the filling-in arches which lie over the {mall triangles 
4, where the extreme corners of the fquare piers would have 
come had they not been made octangular, are incumbent on 
the ribs in the former, which in the latter reft immediatel. 
upon the piers themfelves : but this will be of no fenfible dif- 
advantage, becaufe they -fall fo near the piers, while the 
h of the arch enables it to admit an horizontal 
ter than in the oldconftru€tion. 
Tine at top 
attempts have been made by engineers and archi- 
as i -s tes in the groining at the London Dock tobacco 
which, as well as the others, 
_ any great utility ; 
the crown ftron 
ftron 
inveftigation : for though the bricks, being fo placed, op- 
a refiftance to fracture more direétly than when they 
d fo obliquely to each other as they doin the old way, 
conti (where the fquare 
rm and dimenfions, down to the 
z effective ftrength of the whole 
arch can, after all, be onlyequal to an uniform f{quare rib, 
fuch as I have ftated to belong to the old arch. Hence 
the conclufions I have drawn, upon the comparative a : 
= ito ‘upon parative ady 
tages of the old and new methods of building groined arches 
not be in the leaft altered: and I cannot 
in brick-work, will 
: defcribe quadrants, 
te pou in GJ draw: lines parallelto DF, cutting the are 
at belt, it does not make the parts round 
Affume any number of points in the are A E, and dra 
lines euiar’ & to A: » to cut AG =e rae 
the cutting 
pro 
- ‘on 
tained by any partial application of thofe principles, is eer 
tainly gained in a very complete manner by Mr. 'Tappen’s ‘7 
‘new method ; where the ribs are not only compofed of bricks 
placed perpendicularly to the dire¢tion of the arch, but are 
alfo kept of an equal fize from the o¢iagonal bafe or pier on 
which they reft, to the very fummit of the arch, where they 
mutually join, by which means alone they can be faid to ime 
part fuperior itrength to the whole, and t iereby render a 
groined arch built upon fuch principles a valuable acquifie 
tion in warehoufes, and other large buildings, where the 
greateit weights are to be fuitained. 
In a right {phero-cylindric groin, fig. 2, are given the verti- 
cal fection, paffing threugh the centre of. the iphere, and the 
{ection of the cylindric vault, to determine the feat of the angle. 
Let Om g K A be the plan whence the 
{phero-vault rifes, and K L E the vertical feGtion of the faid 
vault; MNO be the fection of the cylindric part of the 
groin, andthe line NK J be in the vertical plane pafling 
through the axis of the cylinder, and centre of the {phere 
In the cylindric are M N O, let there be taken any number 
of points p, p, p, &c. and draw the lines M R, POP YD Ke. 
parallel to NS, cutting the fpheric feétion KLE at the 
points R, g, g, &c.; deferibe ares t u, ¢ u, &c. and through 
the points u, u, &c. draw a curve, and it will be the feat of 
the {phero-cylindric curve on the ichnography. To find the 
eat or projection of the {phero-cylindric curve on the fec- 
tion, let there be given the feat B 
uuuS. Draw MV parallel, and 
perpendicular to N J, cutting MV at 
x ee , equalto M v7, Mv, Mv, M 
V %, XZ, perpendicular, and Bz, 
J % ¥%, y% yz parallel to N J, and through the points 
3%, %, %, Z, draw a curve, which will be-the feat of the 
fphero-cylindric curve. 
Given the feGtions of the two arches of 
to find the feats of the cylindric line. 
Let as Fg 3s be the arch, and DE F theother, and let 
“be t 
ACandD eir chords; produce CA to I, and FD to 
> Xs 
Draw Wz, x2, xz, x 
a cylindric groia 
EI paralle 
centre G defcribe the quadrant H IT, 
as pe in the arc DE : 
paraile t and through the meet- 
a draw acurve, K F, and it will be the feat of the 
- : 
lindric curve. rao 
Given thefeats A, B, C, D, fig 4, of the fpringing points of 
the angular curves of a groin, juppofing the axis of the one 
vault to be parallel to the. horizon, and the other inclined to _ 
it, let BA reprefent the level line, and the angle BA D — 
the inclination to t orizon; let the q le: 
"HB Abe an oblong, and AEF the feétion of the 
level vault, which let bea femi-circle, and fuppofe the angu- 
lar curves to be in vertical plan ) 
and FB, which wili be the feats of the angulz eS, Cut: 
Ete each other in G: draw BD perpendicular to A B. 
itting points draw lines 
duce beyond AD From the points of interfe 
