isiu.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



15 



tlie liiciof^lypliics l]y .v|il>lying llio first Icltors oS ligy|)ti;in words of 

 the iMinininii vorn;Hiil,ir tongue now in nse — viz., (lie Coptic — it would 

 be- salisl'iiclorv to imply tluit it mnst always liave remained the same, 

 or nearlv so. It is (rue, we are told nodiing changes in the East; bu(, 

 no(wi(hs(anding, it is impossible not (o believe but (hat tongue, ad- 

 niKd'd (o have always been the spoken language oldie eiiuntry,*l);^ss- 

 ing through the crucible of conquest by (lie F.iliiopian, (lie Shepherd 

 Kings, (he Israelites, the Persians, the Greeks, (he Romans, and the 

 Saracens, during a period of 3,1)00 years, nuis( have been so dislocated 

 and altered as to have rendered it impossible to read (he symbolic or 

 liiemglvphic language of Sesosfris in the Coptic or the oldest Coptic 

 books now extant. 



RAILWAY CURVES. 



I\ compliance wi(h (lie request of several members of the profes- 

 sion, we nave carefully perused (he (Munninnications of our corres- 

 pondi'n(s on the subject of railway curves, and, after a careful exa- 

 minalion of (he various methods (herein |Ud]iosed, we cannot but 

 concur in their o|)iiiiou, that the quesdon has not yet been satisfactorily 

 seKled. We therefore engaged Mr. Arislides iMornay, a gentle- 

 man well known for the accuracy of his calculations, to construct a set 

 of (allies to facilKate the execudon of a jilan which we shall luesenlly 

 explain, after having ottered a few remarks on the pro|iosals contained 

 in the above mentioned coinmnnications, which were published in the 

 Journal during the past year. 



In (he January number Mr. Murray, under the signature of " A Sub.," 

 lunposes as an improTement upon (lie system of running directly from 

 a s(raiglit line to a curve of Ih, -, or -'i miles radius, that a curve of 

 y, 4 or .5 miles radius for a short dis(ance should be made use of to 

 ooimect them. He adds that ludjectiles (where the resistance is 

 equal) assume the parabolic curve, to which the plan he proposes is 

 an ajiproxiniation. 



This observation about projectiles is projierly answered in the 

 unmber for March, by "R. W. T.," who also justly observes that "if 

 the curvature is not equable," which would be the case if Mr. Mur- 

 ray's advice were followed, "some parts of it must be sliarper than if 

 the same radius were used all through," 



In the Ajiril number Mr. Ely denies the correctness of " R.W. T.'s" 

 statemen(, on the ground that Mr. Murray's object is to " begin curving 

 sooner, and make the radii of portions of the curve ii-m/Zt/." This 

 objecdon would onlyob(ain, if the object were, besides beginning vvidi 

 a curve of greater radius, to terminate also with a curve of greater 

 radius, which would join the straight continuation of the line farther on 

 dian tile single curve of uniform radius originally su|iposed. This 

 however was not Mr. Murray's iutendou, as is evident from his own 

 iliagram and ilescription in the Noveinlier luiiuber. He has assumed 

 a certain point to be arrived at, without considering diat the direction 

 of die continuation of the railway is also determined before-hand. 

 These two conditions being given, it is obvious that (he junction must 

 either be ell'ected by means of an uniform curve of a radius deter- 

 mined by the given circumstances, or by commencing the curve sooner 

 w itii a longer radius, and terniiuatiug w ith another of shorter radius. 



Widi rl'spect to the queries of"" An Assistant Engineer," in the 

 April number, it appears Mr. Brulf has not exactly comprehended the 

 lirs(, or at least has not expressed hiinsclf very cleady. If the case is 

 as represented in "An Assistant Engineer's" diagram, the solution of 

 his problem is impossible : it woukl be necessary to use a curve of 



A" 



A 



B" 



greater, instead of less radius to join the two given curves. It would, 

 however, be better, if those two curves are indispensable, to connect 

 them by a tangent, as suggested by Mr. Bruff ; or, if the two given 

 curves could be altered, it would be still better (o increase tlieir radii, 

 so as to make tliem meet, and form an S curve together. We con- 

 sider this far better tlian tire plan proposed by"R.W. T.," in the 

 September number, for two reasons; Jint, because the line is shorter, 

 and secondly, because the curves are not so sharp. If it were desired 

 to begin one of the curves farther up on the tangent, as recommended 

 by " R, W. T.," the distance to be gone uijon the tangent may be 

 found much more easily, and with mathematical correctness by a 

 method which would iratnediately suggest itself to any one at all con- 

 versant \^ ith geometry. 



A' 



We now come (n the second query, the solution of which is (he 

 main object of these remarks: viz. "Which is (he most correct mode 

 of seldng out railway curves ?" Mr. Foster Charlton's method, re- 

 commended by Mr. BruH', and extracted from " Weale's ScientiHc Ad- 

 vertiser," is correct; but we do not think i( |nai'(icable, as it is neces- 

 sary to construct a triangle of which the lengths of (he sides are 

 given, which operation must be exceedingly ditlicult when two of the 

 sides are several chains iii length. " B. W. T.'s" method, giviui 

 in the May number of our journal, is incorrect, and is not sulliciently 

 explained to enable any one to put it in practice. 



The mode described by " .Surveyor," in our June number is a correct 

 one, and [lartly (he same as that we ju'opose ; but the measurement of 

 the angle contained between (he two straight Hues to be connected is 

 perfectly unnecessary, and he does not appear to have been pre[)ared 

 with a practical mode of laying off the second tangent. 



The method ilescribed by our correspondent " Jl." in tlie.July num- 

 ber, as that usually adopted, besides not being matlicmalically correct, 

 must be attended with much dillicnlty in practice, on account of the 

 necessity of coiistrncling triangles whose sides are given; but that 

 proposed as a substitute, aldiongli perfectly correct, if the work is 

 accurately performed, is nearly, if not quite as ditficult of execution as 

 the former. 



It only remains for us now to explain (he method we propose for 

 setting out railway cur\es, which we think will be found (o be appli- 

 cable in all cases, and generally easier of execution than any other 

 correct plan. The explanation is illustrated by reference to the accom- 

 panying diagram. 



Let A" A be (he direction of the railway before curving, and A (he 

 |)oint at wlii( h the curve is to conunence. Produce A" A to A', mak- 

 ing AA' any convenient length, and at the point A' erect the perpen- 

 dicular (A' B or offset) on the line AA', which is a tangent to the 

 required curve, and make A' B (the oltset) equal to the length given 

 in the column u of the accompanying tables ; B w ill be a point of the 

 curve. In the figure we siqipose the radius of the curve to be a 

 quarter of a mile, or 20 chains, and the tangent AA', 5 chains. The 

 table gives A' B=l);5'.") links. Eroin the ])oiut A, measure on the tan- 

 gent AA' a distance. AI3" equal (o the length found iu the colunni / of 

 the table, v\hich is in (lie present case 2 chains .")4 links, and through 

 the points B" and H (already found), draw the straight line B" B B', 

 making 15 B', which is a new' tangent to the curve, equal to A A', or 

 any other convenient length ; set off B'C at right angles to B B', and 

 ecpial to A' B if B B' was taken equal to A A', otherwise equal to the 

 length given in the column u under the length of tangent equal to BB'. 

 C will be another point of the curve, and by proceeding iu the same 

 manner we can determine as many ])oints as may be desired. By 

 taking on anyone of the tangents, such as A A', a number of inter- 

 mediate points, ((, n', a", so that Aa, Ao', Aa" shall be equal to 

 lengths of tangents given in the table, the corresponding oll'sets, ali, 

 u'li', <i"b", which are given iu the colniun o under the resjiective 

 lengths of tangents, will uerve to determine as many intermediate 

 points cd' the curve, h, h', b", situated be(v\een the points A and B. In 

 the ligurc we have taken B B' eipial to A A', or 5 chains, but the next 

 tangent, C C, for want of room, has been made only 3 cliaius long, so 

 that the offset CD is only 22'ii links, as we find in the column v under 

 the length of tangent 3 chains. The portions Aa, BP and Cy have 

 been made each 2 chains, (ur which length of tangent we find the oll'set 

 = 10 links, and the other distances Pc, P'c', P"c", &c. having been 

 taken each ecjual to 1 chain, the tangents are 3 and i chains, and the 

 offsets 22-G and -10- 1 links. 



'^^^ 



