164 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[May, 



to be the prevailing cliaracter, especially where there is a prodigal dis- 

 play of plate. Nor by sumptiiousness do I mean gaiidiness: tout aii 

 contraire, the former may be made to exclude llie lattir. Let there be, 

 fjr instance, in order to give something like a positive and tangible ex- 

 ample.a deep alcove — semicircular perhaps in plan — lined with diaperies 

 of pmple velvet, to relieve tlie gold and silver plate on the sideboard. 

 Give this alcove a double screen of white marble or scagliola columns 

 ill front, between which would be placed lofty candelabra. Tlie walls 

 might be incrusted with scagliola of a darker tint than the L-hafts of 

 the columns. The window draperies would of conrse match those of 

 the alcove, at least in material, supposing a different colour to be 

 selected for them ; — ceiling of an architectural design, either simply 

 white and gold, or relieved by colours in its lacnnaria; — for ornamental 

 furnitnre against the walls, we would have marble pedestals alternately 

 supporting lesser candelabra, and gilt or alabaster vases tilled with a 

 profusion of flowers — but mind, artificial ones. Now I conceive that if 

 properly arranged, so as to avoid all appearance of crowding together 

 more than the space would allow, the kind of elfect might be produced 

 which would not at all be ont of character for a dining-room, namely, 

 the Festal. As for Mr. Walker's nice quiet little kitchen, I will take 

 the liberty of shoving that under the dining-table. 



RAILWAY CURVES. 



Sir, — Like your correspondents in the journals for January and 

 Match, I have been employed in making out Railway Curves ; but in a 

 country extremely unfavourable to the formation of railway.*, both as 

 respects gradients and curves, and where, consequently, inclinations of 

 one in 200 or 300, and curves of one quarter mile radii, are looked 

 on as favourable. On sharp curve", you must be aware, it is necessary 

 to elevate the outer or longer side, one, two, three, or even more 

 inches, iibove the olher, in order to us-ist the caniages in travelling 

 round them. In short, without such a practice, curves of -hurt radius 

 would be irapa-saHle. But as the one rail must be raised above the 

 level of the other gradually, and as grcdu illy desceiid to tlie level of 

 the same, the difference ut level must be the greatest in the centie of 

 the curve, and therefore t'le tendency of the carria.;es lo fly off the 

 rail.s, will, so far as it is affected by these means, be least low^fds the 

 centre of the curiie ; or, in other words, to make that tendenri/ uniform 

 t/irour/hout, the curve must be made sharpest at its centre, au'l therefore 

 leave tlie siraight line at a larger radius than it afterwards assumes ; as 

 recommended by your first corres[.ondent : but, as in curves of a mile 

 or two radius, this reason does not obtain, I must agree wi'h your 

 subsequent correspondent on the subject, that, in general, the practice 

 under discussion would be not only useless hut injurious. 



By the raising the outer rail of a curve above the innei, I know of a 

 railway curve (of the ordiuary 4 feet 8J inch gauge) of only J chain* 

 radius, which is readily passable by locomotive and train ; rind a curve 

 of about I I chains radius on the same railway round which Cihniioh 

 certainly with considerable diffi ulty) heavy waggons are daily pulled 

 by horses. 



I know nothing of the modes usually adopted on laying out railway 



curves, therefore, for what I know, what follows may be unworthy of 



notice on account of novelty ; but, for the sake of your junior readers, 



may possibly be worthy of insertion in your widely extending journal. 



I am, Sir, very respectfully, your obedient servant, 1!. ^\ . T. 



1. — To mark out a curve of a certain given radius. 



Let AB be the straight line of a railway, B the point where the curve 

 is intended to commence. BC, 1) C, &c radii of the curve to be 

 described, Dd the deviation from the straight line at the end of any 

 convenient length Bd, then C d'^ or (CD-fDrf)= = CB»+B(^ 

 or VT) + T)d = x/C B' -\- a a-' I.e. Bd = \/C B= -|-~Erf= — C B, 

 produce BD to e, making De = Brf, and draw TBt a tangent 

 to the curve at the point D, tlien the triangle TDB will be = and 

 similar to the triangle DBrf, and the anjile TDB is = the angle eBl 

 being vertical ; also T D ^ / D and C B, C I), &c., being very great in 

 comparison with BD, D E, &e., the triangles BlE, Del may he con- 

 sidered practically equal and similar, and therefore E< = /e = Drfor 

 Ec ^ 2D(/, which may be found by the above formula, where CB is 

 the radius of the proposed curve, and Bd, any convenient length 

 between the several points B, D, E, &c., is to be found. 



The rule iu words at length may be expressed as follows : — Add 

 together the square of the radius and the square of the distance apart 

 of the points to be found in the proposed curve ; take the square root 

 of their sum, and take from it t .eir radius: the result will be the 

 amount of deviation from the straight line in the given length — » hieh 

 will give the first point of the curve; after which the deviations must 

 be doubled, to render the curve uniform. 



2 — To change from a greater to a smaller radius, or vice versa. 



Suppose at the point F the curve changes its radius, having now 

 the shorter radius FG, it is evident the curves BDEF and FHI, 

 should have a common tangent at F, which tangent may be found (on 

 the ground) by taking E< = J Ee, and <F will be thecommon tangent, 

 then the direction of the tangent IV h being found, the amount of 

 deviation (AH) for the length F/i and radius G H may be found as 

 before ; then by producing F H to i, and making the deviation If double 

 H/i, another point 1 of the curve is found. In prartice \i &c. maybe 

 measured at right angles to FHf, &c., the figures of course, being 

 very much distorted ; thereby rendering the angle H/I, which in prac- 

 tice might be taken as a right angle. 



3. — To desa-ibe an S curve. 



Suppose I ta be the point at which the curve changes; then tlie 

 curves F H I and UK must have a common tangent at I, which can be 

 found as before; also the dev ation Jj, which being doubled, any num- 

 ber of points, as K, L, may be found. 



SKEW ARCHES. 



Sir — The usual method of obtaining the spiral courses, in drawings 

 of skew atches, is productive of much labour. 



I liave been led to believe that the following plan is much simpler, 

 more expeditious, and consequently easier of comprehension ; and 

 although the same idea may possibly have occurred to others, it may 

 not be so generally known as to be entitely unacceptable. 



A spiral is defined as being a line traced upon the surface of a cylin- 

 der, by the extremity of a revolving radius, which radius has also a 

 uniform motion along the axis. 



Let AB, fig 1, be a cvlinder, and DE any line making an acute 

 angle with the axis, it is evident that tlte line DE, is the locus of a 

 point haviniT a uniform motion, in each of the directions DB, DF, and 

 if the line DE be wrapped round the cylinder, it will still possess the 

 same property, only tlia't the motion in the direction DF, will be trans- 

 formed to a motion round the cylinder, and thfe line will thus become 



a spiral. ., , , ■ . 



I have said this in order to show, .as clearly as possible, that a straight 

 line, when wrapped round a cylinder, produces a curve conforming to 

 the definition of a true spiral, and will now proceed to explain the 

 simplest method I have found of projecting this curve. 



If a piece of paper, having a straight edge, represented by the line 

 DE, be rolled round a cylinder, it will be found that all the points II, 

 K, &c. will approach the cylinder, in vertical planes perpendicular to 



