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^Kre 3, “ represents tke section of a girder; b b, &c.,^ s °f two binding-joists, tenoned into the girder; a a, &c.,dd bridging-jmstos e e, boarding on the bridgings;

tjj ’ .7 mortises in the binding-joists to receive the tenons oflast Cei ^ n S-j°ists ; as also the mortises b c, b c, &c., but thesec ... are those which are called pulley-mortises, into which thejj. ln o'joists are slid. To understand this more plainly, (see^ t l ,e figures ffff are added, which represent theSa '° n . s of so many binding-joists; g g, &c., the sections ofioi a t U J 0 ' s ts between them; xx & side-view of a bridging-flu b’ ^ ^ ceiling-joists tenoned into the binding-joists,plast W i th t ^ le ‘ r bottoms, as aforesaid, to receive the lath and

Jt"

X$ u res 5 and 6 are parts of Figures 3 and 4, enlarged.

0lJt be joists gg, in Figure 4, add considerable expense, with-eing 0 f adeq U a.t e service.

^y ures 7, 8, 9, 10, are scarfings shown in plate 50, of histhev ’ ^ Ut ta b es no notice of them in the text, and indeedin o a . re n °t deserving of it; we have already noticed thoseafluib ^ 8 Wor k> to which these of Langley’s have a near

^otic^T- 6 re P resen ted in plate 53 of his work, is notth e f ln t l |e text, but the following words are written overgird figure: “ A new method for trussing-beams,

^,® rs > &c., by Batty Langley .”

has es h°wing of such ridiculous constructions in carpentry,fan Cv er<:a * n ^y lessened the credit of this author, as permittingalono to ta he the place of judgment, in cases where'strengthp. Was the object.

° nl y d'ff ^ * s his method of laying roofs in ledgement; heraf[ er '? ers from Price in this particular, that he lays all theth e co * 6et next to the wall-plates, whereas Price lays themP r acti trai 7 w ay. Price ’s disposition is more convenient inFin^’ ^ Ut Bangley’s more natural for building up.WacW 65 13 and 14 are his methods of tracing angle-Iialf Dp ’ and are the same in principle as that shown byLar>tti n 7’ which was an example for a right angle. Buttext 0 }, a ^ Wa y s profuse in his figures, and pompous in histight a 8 i* 0t ord y shown the description of angle-brackets forfor ; v an s les > but also for obtuse and acute angles, likewiseSarn e nf'° S> - cave tt°s, cimarectas, and cima-reversas, as if thel n ^^'Ple did not apply to all forms alike.tur es 0 f^r e lfi> bis description is as follows: “The curva-Plan s are ln P*rafters to polygonal roofs, that is, those whoseaate 3 0 f 6 P°'ygons, are also found by transposing the ordi-bas e of a P l ' nc >pal rafter (which must be given) upon the“ Su a b'P'fafter.

|be caveH° Se 'I 1 ” (Figure 15) “ad to be the base, over whicht e °f a ? P r ' nci Pal rafter cd, is to stand: and let a e be the° r din 'P^after: divide a d into equal parts, and drawa e san, e a ea 4 ; 4, 3, &c., on the line a d; divide a e in*|ates 2^ 1U o llner as a d, and on the line a e draw the ordi-j poiotg’g 3 ’ 4; fi> 6> &c., and from the point b, throughAttired * ’ & c -j trace the curve of the hip-rafter, as

4* ^bis dig

la 8 r ain !!P osi «°n of confining the parts into one connected- ls n ’"’" ■ ' ' ” " ' ’ but

ev,

for

c au!

co-

sh,

en (j,. " more obvious to learners than Mr. Price ’s, uui

Wh^j- Langley’s is not shown to the utmost advantage;y divide the W- -—"i

_ - — - - - ---O ' *

Se3 the* ,lUe t * le bases into equal parts, as this equalityC ° Ver ing * °arvature of the ribs and the curving sides of the.."'"n °./ >e divided unequally? Though the covering is

‘ he text " the bgure, he lias ' ' ‘

*W,

given no description of it in

a ?' a * a ed as’f n WS ^’ s met bod of covering niches or domes,the^ji'^irculn . - wa : “ Let afe be the plan of the head of'batQetgfg 1 biche, and complete the circle afed. Drawa be and dbf continued out towards e at plea-

sure. Make/ r and f s each equal to one-fourth of a f ; thenr s will be equal to half af, and draw the lines r b and s b,divide b d into any number of equal parts, and draw the ordi-nates 1, 8 ; 2, 9 ; 3, 10, &c., and on the points where thoseordinates cut the semi-diameter b d, with the radius of eachsemi-ordinate, describe semi-circles, as the dotted semi-circlesin the figure. Make ef equal to the curve af; make/ pequal tosl;/o equal to a 2 ; f n equal to a 3 ; f m equalto a 4 ; f l equal to a 5 ; / k equal to a 6 ; and / g equal toa 7. On the point e describe the arches 13, 14; 11, 12; 9, 10;

&c. Bisect the half part of each of the dotted semi-circles, !as f c in one; 1, 8, in two; 3, 9, in four; 5, 10, in six; 7, 11, iin eight; 9, 12, in ten; 11, 13, in twelve; and 13, 14, infourteen ; make/ h and /g each equal to half the arch / i; \p 1 and 2 each equal to half the arch 1, 2 ; o 3, o 4, each Iequal to half the arch 3, 4; and so, in like manner, n 5 andn 6, to the half arch 5, 6, &c. From the point e, through the |points 12, 11, 9, 7, &c., and 14, 12, 10, &c., trace the curves ! !e h and eg; then four such pieces as eg h will cover the head i jof the niche, as required.” j

This is certainly a very tiresome method, as each of the j jsemi-circles must be divided into equal parts; but why divide ! ;each quadrant into two, which he has directed ? as the more -the parts, the truer the covering will be. If the arches a d and jc d had been divided into equal parts, the covering couldhave been traced with more exactness, as there is a very i

long space beginning with the point e, without any guide, i

and is as much as the three lower spaces taken together: anequality of the parts in a d and c d would have been produc-tive of the parts e g, g k, kl, &c. also equal to each other, , !and consequently the distances of the points in the curvese h and e g, though not exactly equal, would have beennearly so.

The description given by Mr. Price for the covering ofdomes, is defective ; but his aim was at a much more con-venient method than this of Langley’s, which requires amplespace, and is very troublesome and tedious in practice, with-out obtaining any greater accuracy. The reader must observe,that in strictness of principle, no flat surface, however thin,can be made to comply with a spheric surface ; yet if com-paratively a very small portion of the flat surface be taken, iit may be made so nearly to coincide with the spheric, as notto be detected by the eye, which is as near as we ever need \

in practice ; and thus the narrower the board, the more

nearly will its surface comply with the spheric surface; but jas we shall have occasion to speak of this in another place, iwe shall leave it for the present, and proceed to show hismethods of finding the coverings of solids.

Figure 17, “ represents the manner of covering the outsideof a cone ; the arch e a being made equal to the circumfer-ence e, which is equal to the base of the cone : this figure isexhibited here to show, that the soffits of a semi-circular jheaded window, whose splay is continued all round, is nomore than the lower superficies of a semi-cone ; for if the :

splay were continued, it would meet in a point.” |

In this respect he is right; but no covering can be more i

easy to conceive, except that of a right cylinder. The j

method of covering an oblique cylinder he never could obtain,as the edges which should coincide with the elliptic sectionsare all exhibited in straight lines. See Plate 74, at the endof his Builder’s Complete Assistant; neither has he ever beenable to obtain the covering of the ungula of a right cone,or of its complement when cut to produce an elliptic sec-tion, so that the edge of his covering may coincide with thesaid elliptic section, and its surface with the curved surface iof the cone.

Figure 18. “ The superficies of these frustums are laid out