254 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[July. 



CURVES ON RAILWAYS. 



>^m — Observing in your jonrnal sovenil papers on the subject of 

 setting out curves, I beg to eouimunicate to you a method dill'ering in 

 some respects from any there described. It has been adopted ^vith 

 Creat success on ground of the most ditlicult nature, both on account of 

 the irregularities of the surface, and the buildings and other obstacles 

 to surveying operations with which it was encumbered. 



I am, your's respectfully, 



AJay m, 1839. 



M. 



Fiff. 1. 



B| 



The principle of the above method is, that the curve is ranged by 

 means of continual tangents; it would occupy too much space to de- 

 scribe in detail the various methods of making the necessary calcu- 

 lations, ;uid facilitating operations in the tield work, as well as the 

 mode of finding the intermediate points, when it is required to put in 

 a stake at the end of every chain, or half chain; these and many other 

 points w ill readily suggest themselves to any person ; 

 with niatheniatical subjects. 



* '- c-o 



at all conversant 



The method which has been usually adoptetl for setting out curves 

 is as follows. (See Figiu'e 1.) Let AB be the straight line, a tangent 

 to the curve, B its termination, and C, U, E, &c., ecpiidistant points in 

 the curve of given radius BO, O being its centre; produce AB to c, 

 and draw Cc at right angles to Be; produce BC to (/, making Cd= 

 CD=BC:, and join dV. Join OB, OC, OD. The angle rfCO=the 

 angles BOG and CBO, (Euclid I. 3-2,) and the angle OCD=CBO .". 

 the anfde dCD=the angle BOC=the angle COD, for BC=CD, by 

 hyp. tlfen, by similar triangles COD, dCV; OC : CD : : CD ; dD= 



__. In order to obtain C the first point in the curve, calciJate BC 



the sine and cC, at right angles (by construction) to BC, the \'ersed 

 sine of the ano-le BOC. If the chord BC is small in comjjarison w ith 

 the radius Btf, Cc may be considered, at least for all practical pur- 

 CD' 

 poses, = half dD—i -^,^- , and Bc=BC. The above is a simple, and 



with proper care an accurate, method of ranging a curve where the 

 groimd is clear from obstructions ; it has beeu usual to take BC=one 

 chain, but it is nuich better to take 2, 3 or 1 chains wdiere the nature 

 of the ground will permit, as the errors arising from the diiHculty of 

 setting up ranging rods and measuring offsets witli precision will be 

 thereby nuuh diminished. 



Where the ground to be ranged over is nuich encumbered by trees, 

 fences, buildings, &:c., the above method is liable to objections, as it is 

 necessary that''the chords BC, CD, DE, &c., should be equal ; ha- no 

 very simple formula can be obtained for the value of dD when Crf or 

 CD is not ecjual to BC. The following method is free from this 

 defect, and in other respects have found it answer the required pur- 

 pose in a most satisfactory manner. 



Produce the straight fine AB (Figure 2) to c any convenient dis- 

 tance, for instance, 2,~22, 3, 4, &c., chains, and making BC the sine of the 

 angle BOC to radius BO, calculate Cc the versed sine. This gives 

 the first point C in the curve. Set otf B6' = cC, in a direction as 

 nearly as can be guessed at right angles to b'C, then b'C will be a 

 tangent to the curve at C; ]n-oduce 6'C to d, any convenient distance 

 as before, and making Crf the sine, calculate dV the versed sine, which 

 gives another point U ; set olV Cc' :=. dD at right angles, or as nearly 

 "as may be to c'D, and c'D will be a tangent to the curve at D, and so 

 on. Of course the length of the tangents Be, c'D, d'E, &c., will be 

 uiade the same until some peculiarity in the nature of the ground 

 renders it necessary to alter them, and after the obstruction has been 

 passed it will be \Yfell to recur to the same length of tiuigenl. In 

 practice I have foimd two chains the nuist advantageous length for 

 curves varyiug from .5U to 100 chains in radius ; for curves of larger 

 liidius ami on favowable gruiuul, prvbablj- i i-hiiins wuukl be bettei't 



This melliod affords advantages in terminating or changing the 

 radius of the curve at any required place, or reversing the curve (com- 

 monly called making an S cur\'e) much greater than any jilan I have 

 hitherto seen described. 



With regard to reverse or S curves, I consider it of great im- 

 portance to insert a straight line at their junction, on account of the 

 necessity of elevating the outer rail of a curve above the iiuier one. 

 This may be easily effected by interposing a short piece of straight 

 line, and wherever it is possible to do so, it should by no means be 

 neglected. 



THE MARQUIS OF TWEEDDALE'S DRAIN TILE MACHINE. 



This machine will make 10,000 drain-tiles a-day, one man and two 

 boys to attend it, and 20,000 of flat tiles for the drain-tile to lie upon; 

 liu't if the tiles are broad for roofing, it will make 12,000 a-day. These 

 draining tiles are 15 inches long, so that three machines would make 

 in one season (of thirty weeks) as many tiles as would lay a drain from 

 London to York. Now a man and tw^o assistants will only raali,e 1,000 

 drain-tiles in a day, and these only one foot long, which is 1,000 feet 

 per day. While the machine with the same number of persons will 

 make 12,500 feet per day; so that if the drain be laid at the distance 

 oftwentv-five feet, it will make in one day sufficient tiles for six acres. 

 The ailvantages are — 1st, the tile is much stronger from being com- 

 pressed, and less pervious to water — it is not only couqiressed, but it 

 is smoothed over, which gives it a surface as though it were glazed. 

 Thev are capable of being made from a much stiffer clay than usual, 



the 



and in nine cases (jut of ten 



dug, if jjassed through the crushers, being niucl 



bricks and tiles by the common method 



The expense of draining will be paid in three yea 



qucntly in one. — Funiiti'a jVIagazinc. 



\x may be used directly on being 



drier. Clay unfit for 



ivailable by the machinery. 



.irs, but not uiifre- 



LOWTIIEH ARCADE. 



In nn article by om" corrcspoiulent Ralph Redivivuson tlicLowtlicr Arcade, 

 wc (iuil llial lie lias iiip.dvcitciilly fallen into an error in attributing the de- 

 signs to a Mr. Turner. Wc received a contradiction of this from a gentleman 

 of that name in .March last, but as wc were desirous of asccrtiiiiiing ^vhclllcr 

 we liud attiiliulcd tliis to the wrong person, we were induced to di^lay llie 

 contradiction ; we have now much pleasiue in aimouuciiig that Jlr. A't'itlierdeii 

 Young is llie architect. A letter from liiiii uufortuiiatcly miscarried, ss the 

 reason tliiit a longer delay lias occurred tliaii wc should have wished in doing 

 iustico to a gentleman who so highly merits the esteem of the profession. 

 Wc licg to assure Mr. Young of onr sincere rcgiet tluat any mismulerstancling 

 should have occmred, and of OW >Yi«h OU all OCCasigilS tQ thj justice to 



liiuisclf ami the in-ofessiou. 



