292 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



September, 



the arch, and O the point to which the joints in the face converge fsee 

 Buck on Oblique Bridges) ; produce O D to F any convenient dis- 

 tance, and make F E = half the obliquity of the arch. Draw G H 

 parallel to A B, set off G E ^r A K, join G F, and draw the lino F H, 

 making the angle E F H equal the angle of extrado. 



Then to finu the curved bevel for any joint a, join a o, and draw 

 a b and h d respectively parallel to O F and G H. Take two lines m n, 

 h, at right angles to each other, as at fig. 3, set otf o c = <i c, fig. 2, 

 and from r, with a distance equal to a o, fig. 2, describe an arc inter- 

 secting o A at /. Then applying the mould of curvature of the spir.d 

 line of the intrado s f r, so that the line s' t f drawn at right angles to 

 A, is a tangent to the curve at the point t; the angles s t v and r t i; 

 are the bevels adapted for the joint a, fig. 2, and the corresponding 

 joint a' on the other side of the arch. With this construction the 

 angles for all the joints may be obtained from fig. 2, without any con- 

 fusion in the figure. 



These angles may also be obtained by computation, for let A D B, 

 fig. 4, be the elevation of the arch on a plane at right angles to the 

 axis of the cylinder, and C be its centre, and let a the position of any 

 joint be given. The angle D C a being then known, 



If the angle D C a = A, 



Angle of obliquity of arch := 8, 



Angle of extrado = <p, 



And the radius of the cylinder = r. 



Let r (cot. 0, sec. <?) = a. 



And r (cot. e, tan. (jj) ^ 6, 



*Then ° '^^'"' ^-^ — • = tangent of the angle a i o fig. 3. 

 (4 cos. X) + r ° ^ ^ 



An oblique bridge however is not necessarily built of stone, nor has 

 it ahvavs stone faces. Yet Mr. Nicholson would have the same inter- 

 minable process gone through in every case, while if the arch be en- 

 tirely of brick, and the span, the angle of obliquity, and the radius are 

 given, all that is required for the workmen is the angle of skew-back, 

 and the length of the check on the impost, which are at once obtained 

 as follows: 



Let 8 = angle of obliquity, 

 s = square span, 

 a — length of arc, 



- — '— s=-tan. 0, the angle of skew-back, and (eosec j3) 3= length 



of the check in inches, 3 inches being the assumed thickness of a 

 course of bricks. The length of the check thus obtained may be either 

 adjusted so that each extremity of the impost coincides with the ex- 

 tremity of a check, or retaining the computed length of check, they 

 may be so placed on the impost that the springing shall take place at 

 the same elevation on botli sides of the arcli. After which if the 

 courses are properly gauged on the centre, and the course lines drawn 

 down to their respective checks, no mistake can arise in laying the 

 bricks. 



Mr. Nicholson's rules however are not only very unnecessarily tedious, 

 but it would appear by liis own showing, that they are not over certain 

 in their results. In a note at the bottom of page 22, in reference to a 

 model made by the joint assistance of two masons, a joiner, and Nichol- 

 son's Guide to Railway Masonry, he says, "N.B. the model here alluded 

 to has only IG spiral courses, although 1" were intended. However, 

 the calculations in all the principal parts will remain the same." One 

 course too many in sixteen is not much certainly, but in these econo- 

 mising times it is just as well, considering that it is just as easy to 

 know before hand how many courses there are to be in a bridge. In 

 whatever way however the alteration of the number of courses was 

 produced, one thing is clearly showed by it, namely, the fallacy of his 

 assertion at page 7, respecting the necessity of having an uneven num- 

 ber of archstones iu the face. 



As for all that part of his book which contains such problems as the 

 following, viz.: "Given the three sides of a triangle to construct the 

 triangle," and "from a given point near the middle of a straight line 

 to draw a perpendicular;" it is, to say the least of it, most arrant 

 twaddle. He might with equal propriety have added, given a pair of 

 compasses with a point at one leg and a pencil at the other, to describe 

 a circle. 



However, I will say no more. For this time I have, as he observes, 

 "done with him;" and I hope enough has been said to show Mr. 

 Nicholson that his ideas have got a twist in their beds by ho means 

 adapted to skew-bridges, and that no species of brow-beating or in- 



" The mode of obtaining the formula and construction is too long for in- 

 sertion in this letter, but 1 will supply it if required. 



vective on his part will be of tlie slightest use to him, while his book 

 remains so very imperfect. 



i am, Sir, your obedient servant, 



\V. H. Barlow. 

 Drerelon, August 16, 1841. 



CA.ST IRON TUBBING. 



In the Mining Journal there are some useful communications on 

 Engineering Works connected with .Mining, from which we select the 

 following on "Tubbing of Shafts:" the first description is the applica- 

 tion of a cast-iron tub, for the stop[)ing back of water at Mardyke 

 Colliery, the property of the Irish .Mining Company, by Mr. Dunn, of 

 Newcastle-on-Tyne, the first attempt in Ireland. The colliery contains 

 two principal seams of coal, lying at an angle of one in three. The 

 upper one, lying at the depth of 22 fathoms, is exhausted; aixi in 

 order to win the second seam, at the depth of 30 fathoms farther, the 

 waters of the upper seam were required to be either pumped up to 

 the natural adit (12 fathoms from surface), or to be forced up to tliat 



EYE SECTION 

 OFTUBBINa 



SHAFT 



EYE PROnLE OF STRATA AT MARDTKE 

 COLUERY. 



CRIB 

 CRIB 



point of discharge by tubbing. In order to give this project a fair 

 chance, a piece of fire-clay, lying below the first seam, was taken ad- 

 vantage of as a foundation, and the shaft was rounded out to ten feet 

 diameter. The base of tubbing is made to rest upon a pair of oaken 

 cribs, fitted closely to the fire-clay foundation, and wedged from behind 

 as long as ever a wooden wedge can be driven. This done, the cast-iron 

 tub begins to be built, consisting of cast iron segments, four feet long, 

 two feet high, and three-quarters of an inch thick, with a rectangular 

 flange all round, of three inches; between each of these segments are 

 placed half-inch (end ways) fir deal, wherein to wedge; the space be- 

 tween the segments and the rock is also stuffed with small stones, and 

 tightened with wood. The top of the segments was completed by a 

 wooden crib, which was stayed fast against the superincumbent rock, 

 and then the whole fabric underwent the most severe wedging so long 

 as any leak continued ; and, wdien finished, the shaft was laid perfectly 

 drv, with the feeder of water discharging out at the adit 12 fathoms 

 above, and the sinking of the shaft resumed perfectly dry. The pressure 

 against every square inch of the lower range of tubbing is equal to 

 two and a half atmospheres, or about 37 ft. per inch, and, taking the 

 average altitude at 3l) feet, the wdiole tub is sustaining a pressure of 

 about bl,2(J0 tons; and so complete is the job, that the sinking has 

 been since carried on without any pumping apparatus, whilst suiiicient 

 water is discharging at the adit as would give employment to a heavy 

 engine. 



It is often found convenient to surmount these tubs 

 with a suthcient quantity of stone walling, to enable the 

 wedging to be made effective. 

 " Some years ago Mr. Dunn effected the "winning" of 

 b a shaft, 30 fathoms deep, at Castle Comer, in the same 

 ', county, by means of a plauk tubbing, of JO fathoms in 

 5 length, constructed of three-inch planks, a, spiked 

 " against wooden cribs, *, and supported again by a range 

 ' ot inside cribs, c, which were in their turn dead with 

 common d«>als ; this mode of stopping water was prac- 

 tised for many years previous to the invention of cast 

 iron tubbing. 



