1841.1 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



365 



From the above may be proved the existence of the property dis- 

 covered by Mr. Buck, namely, that the chords of all the joints in the 

 face converge to one point below the axis; for co the distance of that 

 point below the axis (fig. 1,) will be o « x cosec \. 



And uz= r sin. A, cot. 0, tan. <p. 



Therefore c o = r sin. \, cosec A, cot. 8, tan. <p. 



Whence the variable angle \ disappears, and c o=^ r, cot. 9, tan. <p. 



This like the formula previously given for the angles, has reference 

 to the line m a (tig. 1,) and not to the true chord of the curved joint of 

 the face; the approximation is however exceedingly close. If the 

 angle of intrado be used instead of the angle of extrado, the results ob- 

 tained by both formula apply to the taiigtnts of the joint lines in the 

 face, drawn from the points at which the joints intersect the intrado, 

 and these results are theoretically true, though not available in the 

 practical working of the case. 



The formula tan. Z /' a' m' =. ' — '- leads to another con- 



(i cos. i.) -\- r 



Struction for finding the angles between the joint lines in the face and 



soffit which possesses some advantages over that already mentioned. 



Fi 4. 



1 



* The dotted line ii p should be produced to r. and V u produced fo (—the 

 dotted line/// should be a full line. 



Let L M (fig. 4) be the elevation of the face of an oblique arch, on 

 a plane at right angles to the axis of the cylinder on which it is formed, 

 n u being the radius. 



From the point K in the straight line K H, (fig. 5,) draw K F and 

 K G, making the angle HK F equal the angle of obliquity of the arch, 

 and the angle H K G the angle of extrado. Set off'K G =z n u the 

 radius, and through G draw G F at right angles to K H, intersecting 

 K H and K F at H and F. Upon the vertica. line M u produced (fig. 

 4,) set off« r 1= F H, and from u with the distance H G describe the 

 arc R W S. Then to find the angle formed out any ioint n. Join n u 

 and through W where n u intersects the arc R W a, draw p t parallel to 

 L II, and from ji draw ii r parallel to M u, intersecting p t in ;;. Join 

 J) V and the angle p v t is the required angle. For let F H = r' and using 

 the same letters for the angles as before. 

 K H = r' cot 1 



K G = r' cot. e, sec. 9. f- fig. 5. 



h %• 



4. 



/ u := r' cot. e, tan. 9, cos. t.. 



u V = r'. 



tv=:r'-\- ()•' cot. 9, tan. 9, cos. X..) 

 And p I ■:= !■ u=z r', cot. 6, sec. 9, sin '.. j 



Hence the ratio o( p t to t v is the same as a sin. /C is to (b cos. I) -f- r, 

 and therefore the angle p v I is the same as that obtained bv the 

 formula. 



Fis 



Tlie angles for the remaining joints being foimd in the same man- 

 ner, and the mould of curvature of the spiral line of the intrado applied 

 at V, the curved bevels or templates for all the voussoirs on both sides 

 of the arch are at once obtained as shown in the figure. 



I am. Sir, vour obedient servant, 



\V. H. Barlow. 

 £rereton, September 17, 1811. 



N. B. Will you be so good as to make the following corrections in 

 my last communication. 



In Fig 1 the letter A is omitted at the intersection of the lines EJ^il 

 and D C. 



Fig. 4 should be Fig. 3, and Fig. 3 should be Fig. 4. 



In Fig. 3 the straight line S T R should be S' T R'. 



Page 292, line 3. For draw G H read through E draw G H. 



H G := / cot. e, tan. 9. 



J 



THE NEW ROYAL EXCHANGK. 



The contract of Messrs. Webb for the foundation of the new Royal Ex- 

 chan^^e was finished un Tuesday evening, ami the Gresbani Committee met 

 on the 1st ult tu receive tenders for the second contract, which is forjthe 

 completion of the \sbole of the edifice. 



Fourteen of the principal builders of London had. as we formerly stated, 

 been applied to. and it \', as also determined that eich teiv'er should contain 

 two prices — the one being for executing the mason work with the best Port- 

 land slone; the other, the a^ldilional price for usmg magnesian limestone, 

 similar to tliat introduced at the Houses of Lords and Commons. T j 



The amount of the several tenders were as follows, September 1. 1841 : — 



Magnesian 



Tenders. Portland. limestone. 



£ £ 



Thomas .l.ackson ll.i.900 .. 124.700 



Baker ind Sons 122.765 . . 127.300 



Henry and John Lee 126.,390 . . 131 .900 



S.imuel Grimsdell 12U.762 .. 13:3.S48 



Grissell and Pelo 127,400 .. 132,000 



Piper and Co 128,700 .. 131.100 



John Jay 129.609 .. 1 4,905 



Jobn an 1 .losenh Little .. 129.800 .. 134.300 



Webb and Co 130,150 .. 131,'l.JU 



Joseph Bennett 131,500 .. 133,500 



Brilger 131,519 .. 138,660 



William Cubitt 132,200 •. 135,700 



Nicholas Winsland 134.219 .. 136,620 



H. Ward 135,500 . . 1 38,500 



The tender of Mr. Thomas Jackson was, of course, accepted. The « hole;" of 

 the works are to be completed Lv Midsummer, 1844. 



The amount ot the first tender for the fouadaUons was £8124. See. Jour- 

 nal, Vol. III. p.nge 399. 



/tuslraHan Steam N/tvigation. — Notwithstr.nding the wreck of one of the 

 steamers, others have been sent out, and evei7thing is now going'on well. 



Havannah. — A steamer has been started this month from Liverpool . to. 

 Madeira, the West India Island and the Havaimah. 



m 



