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those of the given arc alb ; then construct the other half byreversion, and it will form the whole angle-rib.
To obtain the rib of the body-range from the points ofsection in the base line df draw lines parallel to ac, to cutg i, and produce them on the other side of g i; from the pointsthus obtained in g i, transfer the corresponding heights of theordinates of the given rib upon the perpendiculars as ordi-nates, then construct the ordinates of the other half by rever-sion, which will give the curve of the ribs of the largerbranch.
Figure 2. The cradling of a groin-ceiling, constructedentirely of ribs. The section of the ceiling of the trans-verse ranges is that of a semi-circle ; consequently, theangle-ribs, and those of the body-range, are semi-ellipses, thewidth of the body-range being greater than those of thetransverse branches. The description of the curves of theribs will be found under the article Ellipsis, Method III.Figure 3.
j The ribs must be bevelled each way, so as to range with| either branch of the groin. This is best done by getting| them in two thicknesses, then each half of each thicknessmust range the contrary way, one half with the ceiling of the' largest branch, and the other half with the ceiling of thelesser branch, in the same groin ; the branches being sup-j posed on the same side of the diagonal : so that when the
j two parts are put together to form the rib completely, the
I bevelling of the one half of one thickness and that of half
I of the other, will range with the surface of the ceiling of one
| branch, and the contrary edges with the surface of the ceiling
of the other branch. In ranging the ribs, each thickness iscut out by the mould ; then, in order to range the half ofeach thickness, the mould must be shifted, so that the upperpoint of the curved edge will slide in a line parallel to thebase, while its lower point will slide upon the base line to thedistance required at the bottom : this is represented on thej lower end of the principal branch.
Figure 3. A groin, in which the principal branch is inclined:
! ikl is the given curve of the rib ; a 6 the line of elevation
J of the spring of the arches. Draw the diagonal p o, and o s
! perpendicular to it ; join o n, which produce to cut a b at r ;
j make o s equal qr; produce op to meet i l at a, and join s a
(the reader must however observe, that the engraver has joineds p instead of s a, and has not produced o p, as here stated, andas it was in the drawing). Bisect i l at y ; through y drawk v parallel to m o or pn, meeting the curve in k, and op atv ; draw v u perpendicular to op, cutting sa at t; make tu| | equal to y k ; draw v x parallel to il, cutting a b at w ; makew X equal to y k; then p s will be a diameter, and t u thej semi-conjugate of the ellipsis, which forms the curve of the
I angle-rib : also w r and w x are the semi-conjugate diameters
I of the curve of the ribs for the transverse branches, and the
curves may be described as in Method V. Problem I. of thearticle Ellipsis. Or, the two axes may be found as inI Problem II. of the same article, and the curves describedaccording to Method III. Problem I.j or the curve may bedrawn by ordinates as here exhibited. The cradling is shownat the lower end.
Figure 4. Shows the construction of ribs for the arches ofapertures cut under the pitch of a large vault at right anglesto the wall. Apertures of this description are called lunettes.
Let a z e mp d be the curve of the section of the principalvault ; it is required to construct the ribs of a lunette of agiven height.
Produce the base A d to k, and the side ^Dto l; let f g be( ' the breadth of the aperture ; bisect f g in i; draw i h per-[ pendicular to f g, which assume equal to the intended heightj of the lunette ; draw A A parallel to g d, cutting d k at A ;
make d l equal to n k ; draw Im parallel to d a, cuttingcurve of the principal vault in m; draw m o parallel tocutting hi produced to o; join o f and o g; assumenumber of points in the part m d of the curve p «• e A £ ror0the assumed points draw lines parallel to m o, cutting o g 'the points of division draw lines perpendicular to og > jthe lengths of the several perpendiculars from the base 4 gto the corresponding ordinates contained between the basand the arc m d ; then a curve being drawn throug . Igremote extremities of the perpendiculars not in o g, " -1 . h j„the curve of the angle-rib. Again, from the interseeti ^
o f and o g, draw lines perpendicular to f g, and produce _
on the other side of/<7; make the heights of the perpen glars equal to the corresponding heights of the oi 0 fbelonging to the curve d m, of the given rib on each ^the middle line ih; then a curve being drawn through *extremities of the perpendiculars not in f g, will g ivecurve of the ribs of the lunette. icing
On the left-hand side is shown another method ot ^the curves of the angular rib, and of ribs forming 4 gl)( i ofof the lunette. The cradling is shown below the lowerthe plan. . bu ilt
Guo in, sometimes spelt Groyne , a kind of J et vacross the beach at right angles to the line of the sho re gnhigh to low-water mark. Groins are used particuinthe southern and south-western coast of England, t° ^ gtthe shingle already accumulated, to recover it when a ^to accumulate more at any particular point; also to j o0and check the action of the waves. The following des® ^ or j !jof a groin is taken from Mr. "Weale's very useful litti‘ A Dictionary of Terms of Art — . j ar id-
“ The component parts of a groin are piles, planking^ties, land-tie bars, blocks, tail-piles, and keys and screvV aU jsiteThe length of a groin depends on the extent, and the r ^ ea cbstrength of its component parts on the nature of theon which it is to be constructed. C yfhicb
the following is more particularly a description, are fj°^ ver yto 250 feet in length, and the beach at that place ^ e ' n °^ e TS,rough, consisting of coarse heavy shingle and large bothey require to be composed of proportionably strong 111to resist its force. , ; nC he 9
“ The piles are from 12 to 25 feet long, and 8 by 6* ^ g,scantling, shod with iron. The planking is in leng 11 g( jges-12, and 16 feet, inches thick, and with paran® j ® n g,The land-ties are of rough timber from 20 to 25 * e q)ieand large enough at the butt-end to receive the ^ aI ?‘j n0 he 3land-tie bars are 13 feet 6 inches long, and 12 by a ndscantling. The land-tie-bar blocks are about 2 foe 410 .°_’], e ySof the same scantling as the piles. The land-tie jj n g.are about 2 feet 6 inches long, and 6 by 2\ inches s ^ v _ bo jtsThe above materials are of oak or beech. The scj bl chare of inch round iron, 2 feet 9^ inches, and 2 fee *long, in equal proportions. re> fo llT
“ The relative proportions of the component parts ^ ba rpiles, one land-tie with tail-piles and keys, one lan t j 80with two blocks, two long and two short bolts, a forsquare feet of planking, and about 140 six-inch ®P c0 u-every 16 feet in length ; and the expense of a S 10 ^’^ b estructed with materials of the above dimensions,calculated at about £30 for the same length.
“ General rules observed in the construction. _ re co' ,er“When the object, in constructing a groin, is °j l6 high'shingle, or accumulate more, the first pile is driven a t j ja t 0water mark of neap-tides, leaving its top level wi gan ds»spring-tides. The next is driven at the point on ^ j g tobeyond the bottom of the shingle, to which the g 1