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given curve A, into a number of parts, or take points thereonpromiscuously, which will answer as well. From these divi-sions, or points, drop perpendiculars to some straight line, asthat of a c, observing their meeting with the said line a c ;and in practice take off all these distances on a lath, or rod,applying the proper end thereof to the projection of the com-mon bracket b, as f observing where the other end passesthrough the perpendicular line e d, as at g; there raiseindefinite perpendiculars from the said points, then drawthe line d f. Lastly, transfer the distances, as from thestraight line a c, in a, to the figures, to that of df in B;which, no doubt, inspection will explain, more especially ifthe letters and figures be duly observed.

“ Now view the same figure a again; and admit it werethe curve of a common bracket, let it be demanded to tracea mitre or angle bracket from it, as C; g h being its heightas before, and h i its projection (the method of finding whichin either case, no doubt, will be well known to every one:)take the line, as a c in A, which in practice (as was beforeobserved) I suppose to be on a rod, or lath, with its divisions,or points on it, and transfer it to C, as g k; then drawthe line g i; lastly, from the said points on the line g k, drawbase lines,' observing their meeting the line g i; at whichrespective places raise perpendiculars, and transfer yourseveral heights from a, as before, observing to place each inits due position. And although the abundance of pointsshould render this method somewhat confused, it may beevaded by making but few points, and driving nails therein,round which a straight lath being bent till it touch them all,the curve may be described with a pencil, &c.

“ N.B. This may serve as a general rule for all suchcurves as are not regular, or cannot be formed with a tram-mel, supposing either to be the given curve. The principalcurve being formed on any plain superficies, it may be takenoff on a lath, as before was observed ; and by it the requiredcurve may be described on a piece of slit deal, &c., of a widthequal to the deflection of the arch from a straight line, withan allowance of wood capable of holding it together.

Figure 4. “ That of d, represents a common bracket fora plastered cornice, whose shape the plasterer ought alwaysto be consulted for: let it be required to trace a corner, orangle-bracket from it, as e ; first, draw base lines from therespective angles a, b, c, d, to the line l r, as 1, 2, 3, 4 ; alsoperpendiculars to the line r s, as 5, 6, 7, 8 ; and (because anexample for finding the prefecture of the angle or mitre! bracket, may be required) observe to make ru equal to r s ;i so is u s the projecture of the said angle or mitre bracket;and the points will be w, x, y, z; so that by transferring thissaid line with its points as before to e, as also those of theheight as before, draw perpendicular and base lines, when, asno doubt inspection shows, their meeting gives the shape of thebracket as desired, and this also may serve as a standard rulein any such case. As to shifting this mould (in practice) soas to give the said angle-bracket its true back, there seemsto have been enough said in plate p.

“ Such things as the construction and use of lines, are notconceived by every one; therefore, because I would omitnothing that I think would prove useful, I have insertedseveral more examples of tracery, the knowledge of whichseems indispensably necessary.

Figure 5. “ That of t is a regular semicircle, as a b c, fromwhich is traced the raking (or rampant) one u; that of w isa regular ellipsis, as def, from which is traced the rakingone x; that of X is a regular segment (or part of a circle); as g h i, from which is traced the raking one z; the man-

i ner whereof being so plain, a farther explanation seems

* needless.

“ As to the particular use of this kind of arches, I n\ uSleave to the determination of the curious, and have nothifofarther to say on that head, than that if occasion requ> reeither of them to be executed, there is no other true way t0describe them.

Figure 6. “ That of f is a plan of circular groins, who» eextent is a b c d, an example of which may be seen in.® *Clement’s Danes, Strand, and in several other circular bulk)ings ; and, in my opinion, is a curiosity worthy of regard. _ 1find the plan of these groins, do thus: Divide from a to b,a number of parts, as into ten; the lines a b and d c beibocontinued, meet in a point as g, being the centre ofcurves a d and be; from which strike curves from the po*J*in a b to d c: divide also from a to d, into ten parts, whicbeing drawn to the centre g, divides the line b c into the s .^ gnumber of parts equally; so that the meeting of these lines ^the plan of the groins, as a e c and bed, and their upright 'h, i, k, l, each being traced from the semicircle a bf > n ’being the principal curve. As to the method where ;it is done, enough has been said of the foregoing examp 1to explain it; the letters of reference show plainly whatof the plan each curve belongs to, which being bent ag reeable thereto, will strictly correspond with each other. t“ N.B. If the principal curve had been a segment, or p® ^of a circle, or an ellipsis, the method of performing ' voUhave been the same. . j

“ This plan would be difficult in performance, if requ' 1- ®^to be ribbed with timber for plastering, but if to be center^for brickwork, it would be much easier; because the cent-might be placed as from the line a b to that of c d, ascommon vanlt. The curves of each centre would be j,ferent, on account of its being taper, but the height is e fi uthese centres should be boarded as others are, the boarequiring to be taper only. ,j gS

“ To make groins so as to hang over the plan, the 31ab e and cde must not be centered as usual; but have ragreeable to the plan, and placed horizontally, so that .boards would stand as it were upright; as in domes,was explained in the foregoing plates, which shows the mefor finding the curvilinear form of any ceiling. j e f

“N.B. The foregoing must be well understood, in ° rto describe on the centres first boarded, the accura eof the groin ; which can be done by no other methodis ther# shown. _ , _ f 0 r

“ If this plan were to be executed with ribs of timbeplastering, then the groins must be performed by # ;| 9methods, as will be hereafter inserted, for the tvvistefor staircases, on account of their plan not being a i ecurve.” _ . f j)C

This method of constructing an annular groin, 13 c0n -other use than that of finding the seats of the lines o ^course of the meeting of the curved sides. It does not ^how the boarding is to be formed geometrically, neithe te tit give the least idea of constructing the ribs of o P ae

” ‘ "” l c jr

groin. The line of concourse of the two sides

n'®y

tlii 3

obtained by plumbing up from the base, but even i ^cumstance is not mentioned by Mr. Price, nor any ^application of this construction. If it were requiredstruct the ribbing for a plaster groin, the method hereis perfectly adapted to the formation of the ribs mnesses, as the whole of the ribs round the curves are e jsin piano. But the glueing up of the ribs in thicknes,altogether nugatory, when applied to the purposes , or<Kpen try. Another mode, which we would propose, (|i eto bring this method into use in groin ribbi ng, im «> BJVribs cut into two thicknesses, say ld-inch stuff, and ’ e ‘ (0 ge'of them from one side; then put the two kerfed si e