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ese names only that of collar-beam is retained. At pre-I ' v ® have no kneed-rafters, therefore neither furrings norar ec *dings are necessary, as in Figure 2; the prick-postsnow called jamb-posts, window, or door-posts ; the ver-, Anther hanging from the vertical angle of the roof,supp 0I .ti n g the principals, went formerly under theret , es °f king-piece, crown-post, or joggle-post; but novv ite lns only the name of king - post. The nomenclatureP‘°yed in London and its vicinity is here alluded to.t } e Ambers in the internal angles, at the meeting of thehut lnc ^ ne< ^ sides of a roof, were, formerly called sleepers,p, "°' v they are termed valley-pieces, or valley-rafters, see' n w hich maybe seen also a method of finding theRn °f the hip, without making any plan of the roof.j e II. Figures 3, 4, 5, show the manner of finding thep otns and backs of the hips, as at present. The discovery

18 principle is generously ascribed to Mr. Pope , of Lon-Tt> aut hor now quoted.

ns much for the work published by Godfrey Richards,rises 6 car P entr y published in Moxon’s Mechanical Exer-of t - ’ C ,° nta ins nothing more than the names and applicationsfro. *?oers, which are the same as those described by God -Ire yRmhards.

nieth °f Sound Building, Mr. Halfpenny shows the

irre» i trac ' n g the angle-brackets of coves, regular and® ar groins, the common ribs in each return being of one5° n height.

by., , e following specimens will show what has been donethe •, S au thor. He likewise shows how to find the arch forth e „ , ture °f a window, of a given width and height, so aspri n . fes may be in vertical planes, according to legitimateof v f ® 8 ; but he does not, in any instance, show the methodribs c e ' n S the edge of the angle-ribs, so as to range withyy * e< l >n the returns.

of a ° e Hi. Figure 1. “To find the angle or mitre-bracketand ff Ve —I'i | ' s t, draw the base a b of the regular bracket,draw ^ draw A D > perpendicular and equal to it, andbe also** 6 ^* ne D B ’ and continue the line d a to c, so that A cA to B ec l u al to a b ; then extending your compasses fromarch ’ and sotting one foot in A, with the other describe the! )<;r Peml^ Uarter a c ' r<de c b j and from the point d draw D p,as g j. dlcu lar to d b, and equal to d a, or A c, and anothertvhi c j ( r . < ? rn B > likewise equal to d a, and draw the line f e,into a ^ ' le parallel to d b. This being done, divide a ba half ntU ^ 3er °f equal parts, not exceeding two inches andto ^ ^ nd through the divisions of them draw lines paralleltouc b the arch c b, which continue out to the''amber’ ^'' s ^' ne will be divided likewise into the sameof the 1; °’ ec l ua i parts as A b is. Lastly, from the divisionsb'om j, 6 , r> B> draw lines parallel toDF, and in each of them,B C) a y off its respective parallel (from ab to the archP'ns, anr) at the points whereat they end, stick small nails, or^si'vio,, , 6 a t ^" n i ;it b> and bend it round the nails, or pins,bfing e | ° ' 'at it touches them all, and with a pencil, or any-b>e ed» p 6 pr °P er to make a mark, describe the arch f b round*"'tre brack*'t ”^ 6 ’ anc * ' S t ^ le arc ^ ^ or an S^ e or

a 9iven t If tke lesser arch of an irregular groin be? Se 'nii c i r j lcir cle, it is required to fonn a larger one (not0r so that the intersection of those two arches shallcu lar J na ' ie the arch-line of the angle to hang perpen-

Un gle, _pj its base ; as also to draw that arch-line of the

yk froij, 1 ' 31 ’, draw the lines A b and c d, to represent the^" < 1 °P the p 61106 t ' le arc bes spring, and draw the line c b,l 1 ° '"to an * Ule A,C descr ibe the semicircle aec, and dividefc lines to^ " um b er of equal parts, from whence draw paral-0 D > to touch or come to the arch aec, and if

these parallels are continued out to the line c b, they willdivide it into the same number of equal parts as A c is ; andif from each of the divisions of this last line parallels to a care drawn, they will divide the line a b into the same num-ber of equal parts as a c, or c b, is divided into. This beingdone, continue A c to I, so that A i be equal to E f and con-tinue d b to k, so that kb be likewise equal to e f or a i,and draw the line i k. Moreover, at the points c and b raisethe perpendiculars c n and b o to c b, each of the same lengthas e yj or a i, or b k, and draw the line n o. Lastly, fromthe divisions of a b, draw parallels to a i (that is, continile theparallels drawn from the divisions of the line c b to the line Ii k) and from the divisions of c b parallels to c n. Then setoff the heights or lengths of each of the parallels in thesemicircle aec, upon the correspondent parallels to Ai andC n, and stick in nails whereat they terminate ; and if a lath >be bent round them, so as to touch them all, and a pencil bemoved round the edge of it, the arches a h b and cmb willbe found ; which was required to be done.

“ Note. —The pricked lines in this, and all other examplesof this kind, show that one parallel line has a relation withthe other. For example : the lines / e, g h, l ji, are allequal to one another ; so that if the three arches a h b, a e c,and cmb, were raised perpendicularly upon the lines a b,a c, and c b, and a line drawn from u to m, and another fromM to E ; then would the line M II be parallel to, and directlyover the pricked line Ig. In like manner, the line e m wouldbe parallel to, and directly over the pricked line f l. Under-stand the same of the other parallels and pricked lines in thisfigure, and any others of the like nature.”

Figure 3.—“ Having one centre given for an unequal-sided groin, to form the other, so that the intersection thereof \shall produce the angle, or mitre-arch, to hang perpendi- \cularly over its base; and, moreover, to draw the curve \thereof .—Draw the lines a b and b d, and d c and c a, each |equal to one another, to represent the walls from whence the jarches spring, and on the line A B describe the given archA F B. This being ( done, divide the line A b into any numberof equal parts, from whence raise perpendiculars to a b totouch the arch afb, and draw the diagonal lines a d and b c.Then take the line e f, and set it perpendicular to the linesa c, A d, c d, c b, b d, from a to o, from a to i, from c to p,from c to s, from c to l, from d to k, from d to t, from d to v,and from b to m, and from b to z, and draw the straight linesop, i k, s T, l m, and v z. Now divide the base lines bd,dc,c a, a d, and b c, each into the same number of equal parts asA B is divided into, and from the points of division drawparallel lines to touch the lines O p, S t, v z, l m, and i k.Then take the lengths of the perpendiculars to a b, drawn totouch the given arch afb, and set them off in the correspon-dent parallels drawn from the points of division of the severalbases upwards, and the arches b y d, d v c, C q a, a h d, andC n b, will be described as in the foregoing examples (Figuresg and 3) whose heights x y, w v, r q, g h, and g n, are eachequal to e f, as likewise all the other correspondent heights,from the bases to the curves that are formed.”

Figure 4.—“ The arch line of a large ceiling, or vault,supposed to be semicircular, being given: how to form thecurve of a lesser arch, that shall intersect the side thereof, togive way for doors or windows, so that their intersection shallproduce the groin to hang perpendicularly over its base ; asalso to form the curve-line thereof .—First, draw the linesa b, BD,BC, and c a, to represent the walls from whence thearches spring, and describe the two given semicircular archesaob,cld, and in the line b d set off the span of the inter-secting arch from v to t. This being done, set off the heightyou design to raise the lesser arch v z t from g in the line a b,