img communication throughout the fame in ever'y direétion, 
which cannot be obtained where parallel walls are ufed ; and 
there is moreover a great faving of materials refultin 
from. the arches bearing on piers only, ‘inftead of fuch con- 
tinued parallel walls; it therefore follows, that every im- 
provement which can be made in them mutt bea valuable 
acquilition; efpecially, as the firft defeét, of a want “of 
equilibration in the ribs, exifts in all arches built in the com- 
ma 
L Yo 
reat degree, be counteraGed by increafing the {trength of . 
ange? 
the diagonal ribs. sig 
From what has been juft faid, it will clearly appear, that, 
as the filling-in arches are bonded with the groins indepen- 
dently of the fpandrils above, the whole force of the fuper- 
incumbent weight will be found to exert itfelf againit the 
fubftance of the groins alone : on which account they re- 
quire the greateft ftrength that can be given them; at the 
{fame time, the filling-in arches fhould be made to throw as 
little weight as poflible upon them, particularly about the- 
interfeétions of the ribs, that the 
racture towards the crown may be 
the nature of the cafe will admit. 
himfelf in the preceding defcription. 
GROIN. 
of the filling-in arches will be = a which confequently 
para 4 
will be the fide of the fquare feGtion of the groins in the old 
arch ; its area, therefore, will be equal < = A, and its 
half diagonal = 4 , s = G, becaufe the diagonal of this 
fquare groin is in the direétion of the radius. The diftance of 
the piers being 4. 5 a, the {pan of the diagonal groins will be 
V2 x (4.5 @)* = 6.3644 = S; we have, therefore, 
ie . 
ome. 
Bd 
A 8 
ie "6.364. for the ftrength of the old groin. 
The fide of the fquare pier remaining {till = a in the new 
arch, the breadth of the rib — / 2a’ — a, which is the fide 
of an octagon infcribed within thé pier. the thicknefs necef- 
fary for the rib will be = 5 then the area of its feGtion 
wi ie eo A Oa em 
3 
V2 a? = S; conf * G92 ce, 
confequently § itkneg the ftrength 
of the new rib. 
dimenfions 
. the ground 
tobacco warehoufes), the 
he to that of the new ribs 
96; which is nearly two to 
one in favour of the new conftruction : and this will be the 
cafe whatever may be the extent of the arch, while the fame 
gaout, 
that the filling-in arches reft 
except fuch fmall parts as come di- 
rectly on the fides of the piers; and that any weight placed 
upon thofe arches ultimately fall upon the nbs 3 itis, there- 
fore, plain, that every half-rib fupports the weight of two 
half fillin 
may be fu to carry one whole arch. 
faid before, is produétive of a certain evil, becaufe the 
weight incumbent on the filling-in arches affeéts the groi 
with a preffure which has not a conftant ratio to that which 
by the tangent of the curve = eh age line at the gtd a cad confequently throw lefs w eight on any given point of 
con{tant quantity, viz. a right angle in every arch ; or re- : nb a . goles 
cpreediea oo fpan a the Shas when: the rife of pe ee efpecially whenthe upper pat t is loa with mer= 
them is the fame-(as is the cafe of the diagonal ribs Tf i crt , Malitntt 
groins of the new and old method), the thicknefs of the be cutby parall 
arches themfelves being alfo fuppofed the e. From ithe tony a 
this it will t, that the ttrength of the fame ribs, ad Pees 
when of different thickneffes, v irectl 
of the feétion, G the diftance of ‘its centre of gravity, and 
S fi 1 of one arch to 
another willbe as. AS Heace the ftrength of the groins 
in the old arch, and ibe diagonal sts inthe new oe tag be 
ealily compared by taking the proportional meafures of both. 
| "Let the Bde of ‘he’ ie berhe ye == @; then the thickne 
/- 
cay 
_groins, which form a right angle, For example, 
ht, £4, will be always the fame 
‘ibs, arifing ee 
1 é r as the chord ¢ 
wn at any point of the rib or groin, it bei 
twice g/ the diftance of the fedton of the alli 
fetes the interfection of fides of the di 
centre of the crown, which is at 
G, and 5.364 @ + 
-in arches, one on each fide; and, confequently, - 
fed to is) as we 
