GRO 
+ warehouses, and many other buildings, for the purpose 
of giving communication throughout the same in every 
¥ ion, which cannot be ined where waggon- 
head vaults are used; and as there is a great saving 
of materials, resulting from the arches bearing on piers 
_ only instead of ponte walls, it follows, that an im- 
‘provement in their construction, which tends to bring 
_ them nearer to an equality in strength with the wag- 
gon-head vaulting, must be a great acquisition. This 
_ improvement has been lately made by Mr George Tap- 
pen, an architect of London, who, instead of the square 
piers hitherto used, has adopted octangular ones, (by 
_ which a considerable saving of room is mpd) and has 
thrown stout ribs diagonally over the vault whose 
breadths are equal to the sides of the octagons on which 
they stand. The side arches, which in brick-work are set 
four inches back from the face of the ribs, in order to. 
save the trouble and expence of cutting the groin angles, 
are worked into, and rest upon these ribs. By this im- 
proved construction, the ribs form a much. stronger 
support for the weight of the incumbent vault, and the 
ing comparison will shew. 
Since the force of the superincumbent weight has 
_ been found by experience to act chiefly in the direction 
_ of the groins, they require the greatest strength that 
can be given them; at the same time, the side arches 
should be made to throw as little weight as possible 
upon them, particularly about the summit of the vault, 
that their tendency to fracture towards the crown m 
be diminished as much as the nature of the case will 
admit. In the groined vaults hitherto constructed, 
_ where the groins spring from the extreme corners of 
_ the square piers, their section, taken perpendicular to 
their , forms a square, (see a, Fig. 2.) having 
, one of its angles turned towards the centre of the 
curve, and its side equal to the thickness of the arches; 
whereas in the new vault, the section taken in the 
same manner, forms a rectangle equal in breadth to 
the side of an m inscribed in the square pier, 
and of a depth which may exceed that of the old groin 
in any proportion, (see b, Fig. 2.) Now, the strength 
of an arch, in its different 
greatest weight which it is ab 
to 
curve’s inclination to the horizon, in its various points, 
___and the reciprocal simple ratio of the radius of curva- 
ture in the same points. But since the relative strength 
of arches is to be determined by comparing them in 
_» their weakest parts, (namely the crown,) the strength 
of any arch at the crown will be reciprocally as the 
radius of curvature at that point, since the angle of 
e curve’s inclination to the horizon at that, point is 
ways 0° 0’ ; or reciprocally as the span of the arches 
when the rise of them is the same, their thicknesses be- 
ing supposed equal. From this it will be evident, that 
the strength of the diagonal ribs and groins will be 
_ directly as the areas of their sections, and, distances of 
e centres of gravity from the place where the frac- 
_ ture would end, and reciprocally as the spans of the 
__ arches: that is, if A represent the area of the section, 
_ G the distance of its centre of gravity, and S the span 
ha he arch ; then the strength of one arch to that’ of 
E another will be as os ae 
; ‘Let the side of the square pier be =a; then the thick- 
; ws PIG : i . : 3 
ness necessary for the side arches will be = ~<-, ‘which, 
i) .) q 
f 
523 
loading above, than by the old method, as the follow-- 
porate, is measured by the: 
e to carry on those points: 
without breaking ; that is, it is in a ratio compounded: 
_of the triplicate ratio of the secant of the angle of the 
GRO 
consequently, willbe the side of the sqtute section of Grvins 
the groins in the old arch; its area, therefore, will be 4 
a , P a? Grose. 
= 7g = As and its half diagonal = 4/556. The -—\— 
distance of the piers being 4.54, the span of the diago- 
nal gtoins will be = “2x (4.5a)' = 6.8644 =S; 
be Sie 
we have therefore —_— ates 
e have therefore Arn for the strength of 
5 = 
the old groin. 
The side of the square pier remaining still =a in 
the new arch, the breadth of the rib = 4/2a’—~a, 
which is the side of an octagon inscribed within the 
pier, the thickness proper for the rib will be = = then 
2 a 
wilA =” a Gat and $= 5.3640 4/20"; 
A . 2 aa 
consequently aes =“ 85 — , the strength of the 
new rib. 
If we assume a= 4 feet 8 inches, (the dimensions as- 
signed by Mr Alexander to the piers of the groined 
vaults at the London dock. tobacco warehouses, ) the 
strength of the old groins will be to. that of the new 
ribs as 5.44 to 10.64, which is nearly 2 to 1 in favour 
of the new construction ; and this will be the case while 
the same proportions are preserved, whatever may be 
the extent of the arch. 
If the side arches, with their spandrils, and the 
loading on the floor above, be cut by parallel verti- 
cal planes, (as at S, Fig. 2,) the sections will be to each Piare 
other as their chords ¢d nearly; which being less in the €CLXxxiv. 
new vault than in the old,-on account of the greater fig. 2. 
breadth of the ribs, the weight incumbent on those ribs 
(which always tends to destroy their equilibrium) is 
just so much less in the former than in the. latter, and 
consequently their tendency to fracture is diminished 
in the same proportion. 
It may not be improper to observe, that Dr Hutton 
recommends the stones of the wall, or spandril over the 
extrados of the voussoirs of an arch, to be bonded into 
the stones of the pier, and with one another; because 
the pier will then-carry part of their weight, and there- 
by oppose a greater power of resistance to the thrust of 
the arch, For the same reason, it would be equally 
advisable, in the new method of building groined vaults, 
to carry up at the same time the diagonal ribs, side 
arches, and spandrils, well bonding the whole together 
into one solid mass; which will render vaults built in 
this manner, a valuable acquisition in warehouses and 
other large buildings, where the greatest weights are to 
be sustained. 
GRONINGEN, a town in Holland, and capital of 
the province of the same name. It is intersected by 
the river Hunes, which through it in a northerly 
direction to the sea. The town is large, rich, strong, 
and populous, and is adorned. with many excellent buil 
ings. It is nearly round, and is surrounded with good 
ramparts, a wall, and ditches, and has a citadel, Its 
university was founded in 1614, and endowed with the 
revenues of several monasteries. The harbour can con- 
tain many vessels, which enter it by a canal about nine 
miles from the sea. It carries on a considerable trade 
in butter, horses, and horned cattle. . There are some 
breweries in the town. 
GROSE, Francis,,a celebrated antiquarian, was 
born in 1731, and. .was..the son of a jeweiler at Rich- 
mond, who died in the year 1769, and left his son an 
