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“ rib being stretched out, and the parts set on as abovedirected.”

When he says, “ stretch out a b, the middle of the side, and9 9, 8 8, 7 7, parallel thereto,” he is not intelligible; however,if we understand that a b is drawn at right angles to the sidee d of the polygon, and 9 9, 8 8, 7 7, drawn parallel thereto,the method which he uses will be found to be correct, and,we believe, original.

Figure, 8, “ shows the method for getting out the veneer,or cover for an elliptical dome or niche. Divide the circum-ference of one quarter of the plan into any number of parts,as here into 8, and draw them to the centre 4; let the firstline from the transverse diameter be the edge of the veneer;the second line will be the middle of the next veneer; thethird will be the other edge of it, and so on : continue thisline out at pleasure: consider this line as a base, and drawthereon a section of the dome, as No. 1; then divide the cir-cumference into four parts, draw them to the base-line at rightangles, and transfer those distances to the corresponding lineon the plan ; then take the four parts on the girth, and runthem on the line stretched out, 1, 2, 3, 4, this will be thelength of the veneer; set the compasses on the plan, andstrike a curve-line of this radius; then continue the middleline of the veneer, and where it intersects, that curve-linewill be the point of veneer next the top of the dome; fromthis point set off the divisions 1, 2, 3, on the circumferenceby curve-lines; then take the width of the divisions 1, 2, 3,from the middle line of the plan, and set them on the sameline stretched out to cut them at their respective distances,the points of intersection will be the breadth of that side ofthe veneer; connect them by a curve-line from the plan to thepoint, and you have one edge complete. For the veneer onthe transverse diameter, this edge will serve as a mould; oryou may set the half of the veneer to the other side of theplan, and draw a chord-line from these points; set this offthat distance of the arch (the little curve ) to be outside, anddraw a line parallel to the chord-line, on which set off thebreadth of the veneer on both sides, then with the wholelength of the other veneer in the compasses, set one foot onthat breadth, and strike a curve-line to cut the middle lineon the transverse diameter; or repeat the curve from theother side, and where they cross will be the point of thatveneer, from whence set off the divisions, and proceed asbefore. But as the radii'of an oval are of different lengths,to get the other edge of the veneer, make a section as before,see No. 2, and set off, as before, the divisions on the base and! plan, and strike the divisions on the girth, from the point ofthe veneer stretched out, intersect them from the plan, andthose points connected will give the other side of that veneer,which will be a mould for the next adjoining; proceed againfor every veneer by transferring that length from the plan,and the shortest length from the point; repeat the sameoperation for every veneer required.

Note. “ The conjugate and transverse diameters will havethe two sides of the veneer equal. Observe, only four partsare used, to prevent confusion in the figure; but the greaternumber of parts, the truer the line. Again, if your boardswill suit, divide the plan to their number, and proceed asbefore for every board respectively.”

This method is so absurd in every particular, that thecoverings obtained are erroneous in the greatest degree;indeed, it leaves no room for argument, and we shall onlyobserve, that in the true form of the boards, between theextremities of the greater and less axis, in any one of thefour quarters, one side of the board would be concave andthe other convex, where the dome has a considerable differ-ence in its axis; and the greater this eccentricity or differ-

ence, the greater will be the degree of curvature of the con*cavity and convexity of the sides of these boards.

Figure 9. No. 1, shows groins aiM arches, of differsdescriptions, from the Practical House Carpenter. P al11divides this figure into several others, and distinguishes tbe®by letters of the alphabet. He only gives the followingdescription on the plate : “ k centering for groins, h is a hagroin cutting under pitch, for a door or window. G a Weisgroin cutting under pitch, m is the method of tracing t 1ribs and hips for a groin ceiling.” Figure 9, No. 2, “ N lSa mould to bend over the body range; k, to get the hn eto set the jack-ribs by.” The reader who has not alreadyacquired a competent knowledge of geometrical lines,profit but little from this description. The showing of 411jack-ribs upon the diagram is an improvement. Swanshown them perspectively, but the geometrical methodrepresenting them is more serviceable to the workman, asshows the lengths of the ribs distinctly. He observes tt> a“ g is a Welsh groin cutting under pitch,” but he does nshow how the crooked line, which he has exhibited, is obtains >and even if he had shown it, the method of constructing 411rib would still have been wanting. In the mould N> 10groin-centering, in order to find the place, or curve-l> neS ’on the boarding, for fixing the jack-ribs, lie has given 41description, either in the text or on the plate, except that ‘writes, “ the arch line a stretched out,” and “ half the ba 9 ®line b,” upon the respective sides ; and, consequently!have no other instructions to inform us how the mould 14 1found, than by inspecting the figure itself, and tracing ° uthe operation by the connection of the lines ; and even th®we are left in the dark as to its application. The moulds »°groin-centering upon this principle, were first shown 'yPrice, as well for finding the angles of the jack-ribs, as 411form of the boarding. ^

Figure 10, from the Practical House Carpenter, “ is a be vroof; the sides are parallel on one part of the plan, the otnbevels. To frame this roof in ledgment, the principal raf 4 ®must be framed to a level base ; that is, the ends of 4 _

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beams all of one height from the face of the plateyou come to lay them the other way, to frame in the purthere must be winding sticks held to the bases of the

which winding sticks must be all out of winding; and aswidth of the building diminishes, the backs of the rat ^will lie in winding, as they will when in their places; ‘mind that they are backed according to the bevel of the p* ,for turning them up to tumble in the purlins; by this ntetthe business may be well completed.” Allowing thatheels of the rafters are cut to their proper bevels withbacks, the application of winding sticks to such short dista®will never make the sides fall accurately into their p r °lwinding. This is altogether a mechanical operation; b , oJlwould have been no difficult task to have shown an opc rastrictly geometrical. .

The foregoing remarks will be found to contain a ^ air -r0 r 9impartial statement of the geometrical improvements andof the several writers on Carpentry, at least as far as . oJJ(have come to our knowledge : we shall now, in conclu® ^draw a general result from the whole of their theories! tendeavour to trace the progress of the art towards its P restate of comparative perfection. _

The method of bracketing hip-rafters, which is said 4the invention of a Mr. Pope, of London , was originally V ^sented to the public by Godfrey Richards, who also ^represented roofs in ledgements, in order to ascertajnseveral lengths and angles which the rafters make withother. . t ; 0 a

The use of the trammel in common cases; the descrip

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