1839.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



139 



squares of the velocities decrease. The cases, therefore, are not 

 so dissimilar as I was at first led to believe from your corre- 

 spondent's observations. 



March 15, 1839. J. ELY. 



RAILWAY CURVES. 



Sir, — As a subscriber to your tndy valuable journal, I trust you will 

 not deem me too presumptuous in seeking for tlie following information 

 through your journal : — 



Query. — The most correct mode for placing a curve of 100 chains 

 radius between (V to form) an iS curve, as in the following example, 

 a, a !— 



130 chains radius. 



100 chains radius. 130 chains radius. 

 would it not be desirable to reverse the curve towards 6? 



Mr. Brurt's mode for setting out half-widths (when sidelong) for a 

 line of railway is ver;/ tedious. I wish he would inform us if tliere he 

 not a shorter mode than working, as he says,/rom every centre per/. 



Query. — WliicU is the most correct mode of setting out railway 

 curves ? 



The method adopted on many lines of railway for determining tlie 

 offset of curves at every chain is thus — tangent squared, divided hy 

 radius, will give the versed sine.* 



For example — IGO cliains radius ^ 1- 



(■ ~ltiu 



•OOG'25, the decimal pro- 



portion of a chain = versed sine at one chain. By reducing the decimal 

 to inches will give 4'95 inches for the versed sine. 



Tliis will be, I believe, 1 foot 8 inches for 2 cliains. If I am correct, 

 thus, 22 X 4'95 = 19-80 inches, or nearly 1 foot 8 inches. 



Hoping to see these matters explained in your next number, 

 I remain, your very obliged servant, 

 15th March, 1839. An Assistant Engineer. 



[We have altered our eorrespondent's communication, so as to make 

 it better understood by our readers ; and we also referred his letter to 

 Mr. Brutf for an explanation of that part relative to setting out 

 " widths," and have received the following reply ; and we have also ob- 

 tained Mr. Weale's permission to copy from his " Scientilic Adver- 

 tiser" Mr. Charlton's communication on setting out railway curves, 

 ■which we have given below. — Euitok.] 



Sir, — In reply to your correspondent, "An Assistant Engineer," as 

 to the most correct method of carrying into effect the question he pro- 

 pounds, I am not sufficiently in possession of the case to answer it with 

 satisfaction to hnn or myself. From the hurried glance I have given at 

 his letter, I presume the two curves a, a, were intended to have met, 

 and he now proposes to effect a junction, by laying out another curve 

 of 100 chains radius. If this is the case, why not connect them with a 

 tangenti' or if this is not possible, with a shoit tangent and a cuive 

 reversed ; but if he is compelled to connect by a S curve, most un- 

 ■4 doubtedly it should be reversed as your correspondent suggests. If the 

 S curve iiad been situated thus — 



a, a, the two curves, and b the point where the junction was desired, 

 it could eaiily have been connected by adopting a single curve of less 

 radius, having a comuion tangent at the connecting points. 



With respect to your correspondent's complaints of the method I 

 have communicated of setting out widths on sidelong ground being 

 tedious, and re(piiring a shorter method, " 1 have no heln for him." 

 On ground that is at all variable, even a distance of 100 feet is too 

 great for cross sections, and I often take one or two intermediate 

 sections in that distance when in cutting ; in embankment I consider 

 such nicety of little moment. I have for some time past had charge of 

 a railway contract of something less than live miles, the whole of which 

 is on sidelong ground of a. very abrupt character ; and, after trying 

 various plans for taking the cross sections, (which was here absolutely 

 necessary in determining the extent of ground to be taken,) I was fully 



• Nothing can be more wroncous,— En. 



satisfied that the method I have detailed in your journal was not only the 

 most correct, hut the quickest and most easy of execution of any that 

 1 am avvare of or have seen practised. I have levelled centre stakes 

 throughout this distance, and determined the widths as 1 have described, 

 and as a great portion of the works have now been carried int® execu- 

 tion, (the cutting in some places being as much as 50 feet,) lean speak 

 with increased confidence of the accuracy of the method. 



The methods adopted for laying out curves are various. Your cor- 

 i-espondent, by referring to the " Railway Magazine" for January, 

 February, and March of last year, will find several excellent methods 

 detailed, as also in " Weale's Scientific Advertiser" for May last. 

 I remain, joins, very truly, 



Peter Brcff. 

 Charlotte-street, Bloomsbury, March 21st, 1839. 



The following communicalion we extract from "Weale's Scientific 

 Advertiser : — 



The all-important subject of railways seems to engross the almost 

 exclusive attention of both the scientific man and the practical 

 mechanic. Railways at present are only in their infancy, and proba- 

 bly many of the methods now in use for laying down rails, setting out 

 curves, &e., will in a short time give way to other inventions better 

 adapted for practice, and of more general utility. The different 

 methods adopted for setting out curves seem to demand much more 

 attention than engineers have bestowed upon them. To have a curve 

 on a i-ailway, is at best a misforlune, and ought never to be resorted 

 to unless to avoid some greater evil. Admitiing the curve to be a true 

 circular aic, and correctly set out, each carriage in a train will have 

 a continual tendency to fly off, and that tendency will be increased or 

 diminished in proportion to the diameter of the circle of which the 

 curve is a segment. The distance between the wheels on each sids of 

 a carriage is a straight line, but the wheeN and carriage are forced to 

 move in a curvilinear dii-eetion ; the friction, therefore, between tho 

 wheels and the rails, especially in an arc of a small circle, must retard 

 the pi-ogrcss of the train, wear the materials, strain the carriages, and 

 greatly increase the chance of accidents, Irom the trains being thrown 

 off the rails. All this will necessarily take place when the curve is 

 correctly set out ; but what must be the consequence when the curve 

 is not uniform in its curvature ^ Probably some portion of it nearly a 

 straight line, another portion of a four-mile radius, anoiher a segment 

 of a quarter of a mile radius, and another of no known curve what- 

 ever. A train foi-ced along a line thus formed with the usual speed, 

 runs a great risk of being thrown oil', besides the incalculable injury 

 done to the carriages. It is, therefore, of the deepest importance 

 that engineers and surveyors should have a true method of setting out 

 curves, and it is worthy of remark that the methods founded on true 

 principles are easier than those founded on false ones, and requir-e 

 much less trouble in praelice. The foregoing renders a theodolite 

 unnecessary, nor does the surveyor require any instrument except a 

 chain and two or three poles. In hilly countries it is only necessary 

 to ascertain the elevation or depression of any place above or below 

 the point when- the curve commences, and that will be the side of a 

 triangle, the ratio of whose sides are given. To illustrate this without 

 a diagram, suppose the slope in a cutting rise 2 feet in 3, and that tho 

 elevation of a bill above the point of commencement, or the last point 

 found by the si.rveyor, should be 10 feet ; (hen, having ascertained a 

 point on the hill as if it were explained according to the foregoing 

 method, say as 2 : 3 : : 10 : 15 feet ; this 15 feet nmst be measured 

 back from the point already found in a direction perpendicular to the 

 line of railway, and thus a true point in the curve in its progress over 

 the hill will be readily ascertained. 



The rule made use of in several railways is, to divide the tangent in 

 inches by tuice the radius of tlie circle; or, which is the same thing, 

 divide the sr/uure of the tanyent by the diameter of the^ circle, and the 

 quotient will be a perpendicular oJ)'sc! to the curve / To any person at 

 all conversant with geometry, this method will be seen to be mani- 

 festly erroneous : however short the tangent, it is not true ; but if, as 

 mentioned "oy Mr. Terry, in the " Railway Magazine," a few months 

 back, the tangent should be five chains, then this method of finding an 

 offset h yrussly trrontous, and, in a n:atter of such consequence, ought 

 at once t^i be abandoned, and a true method substituted. It was lately 

 decided by the Chanctllor, in a railway case for libel, that the acquire- 

 ments even of the seeretaiy of any public company were legally sub- 

 ject 10 be fairly inquii-ed in!o. If such then be law us it respects 

 a seci-i'taiv, surely the aecpiirements of the principal engineer of a 

 railway, touching his mathematical and mechanical know edge, area 

 sul jeet of fair and legitimate inquiry, and more especially when it is 

 considered that want of such knowledge on li.s part may affect the 

 interests and property of the parlies amuunling to millions of money, 

 FOSTER CHARLTON, Weybridge. 



