1843.-] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



243 



to the method of manufacture the fibres did not follow the surface of the 

 shoulder, but that they penetrated straight into the body of the axle ; that 

 the power of a fibre to resist a shock being in the compound ratio of its 

 strength and extensibility, that portion of it which is within the mass of the 

 body of the axle will have less elasticity than that in the journal, and it is 

 probable that the fibres give way at the shoulder on account of their elastic 

 play being suddenly arrested at that point. This he contends would account 

 for the direction of the fissure being inward towards the body of the axle, 

 so that tbe surface of the fracture was always convex in that direction. It 

 is therefore proposed, in manufacturing axles, to form the journals with a 

 large curve in tbe shoidder, before going to the lathe, so that the fibre shall 

 be continuous throughout ; the increased action at the shoulder would thus 

 be made efficient in adding strength to the fibres without impeding their 

 elasticity. Several axles having one end manufactured in this manner, and 

 the other by the ordinary method, were broken : the former resisted from 

 five to eight blows of a hammer, while the latter were invariably broken by 

 one blow. The vibratory action to which axles are subjected is then con- 

 sidered, and it is contended, that at the place where there is an abrupt 

 change in the extent of the oscillations of the molecules of tbe iron, these 

 molecules must necessarily be more easily torn asunder ; and that in the im- 

 proved form of journals, as the power of resisting shocks is increased by the 

 continuity of the superficial fibres, so is the destructive action of the vibra- 

 tory movement prevented by the continuity of form. 



The paper is illustrated by five drawings, showing the section of the jour- 

 nals of broken axles, and their appearance at the moment of fracture. 



Remarks. — Mr. York agreed with Mr. Rankine in several points, and 

 stated, that since the last meeting lie had made a series of experiments, 

 which confirmed his opinion relative to the vibration in solid railway axles 

 being arrested when the wheels were keyed on tight. In all such cases, 

 where the vibration was checked, fracture would, he contended, be more 

 likely to ensue, but with hollow axles there was very little difference of 

 sound when struck, and no diminution of strength after keying on the 

 wheels ; this he attributed to the regular distribution of the molecules in the 

 metal of the hollow cylinder. 



Mr. Parkes coincided with Mr. York's opinion, and he believed that hollow 

 axles would eventually supersede solid ones, particularly if they had suffi- 

 cient rigidity for resisting flexure. Their faculty of transmitting vibration 

 more readily was in their favour; it was well understood that in pieces of 

 ordnance and musket barrels great regularity of proportion in the metal was 

 requisite, in order to insure the equal transmission of the vibration, caused 

 by the sudden expansion of the metal at the moment of the explosion, and 

 unless the vibration was regular the barrel would burst or the ball would not 

 be correctly delivered. 



Mr. Greener, of Newcastle, among other experiments, 5 turned the outside 

 of a musket barrel to a correct taper, and fixed tight upon it at given inter- 

 vals several rings of lead 2 inches in thickness ; on firing a charge of 4 

 drachms of powder he found that all the rings were loosened and had all 

 expanded regularly in their diameter. It was a well-known fact that cannon 

 seldom or never burst from continuous firing; such accidents, unless they 

 arose from peculiar circumstances, generally occurred in consequence either 

 of inequality in the nature of the metal or irregularity in its distribution ; to 

 the latter cause must be attributed the bursting of the " Mortier monstre," 

 before Antwerp, and of a large gun which was proved at Deal some time 

 since ; this latter gun burst at the third discharge, after delivering the hall 

 better than on either of the previous discharges ; it was evident that the 

 fracture did not occur under the explosion of the powder, but on the re- 

 entering of the air into the mouth of the gun after the discharge, and also 

 because the thickness of metal was not well-proportioned, whereby the vi- 

 bration was unduly checked, the cohesion of the molecules of the metal was 

 destroyed, and the guu fell into several pieces, without any of them being 

 projected, as they would have beeu by the usual effect of an explosive force. 

 The most practical millwrights were well aware of the superiority of 

 hollow shafts, and they were frequently used, as they were more easily kept 

 cool than solid ones, especially at high velocities, when shafts were peculiarly 

 liable to injury from percussive force or from a series of recurring vibrations. 



March 14, — The President in the Chair. 



" Description of a method of laying down Railway Curves on the ground." 

 By William John Macquorn Rankine, Assoc. Inst. C.E. 



The method described in the paper depends on the well-known principle, 

 that the angle subtended at any point of the circumference of a circle, bv a 

 given arc of that circle, is equal to half of the angle subtended at the centre 

 by the same arc. The points which must be ascertained beforehand are the 

 same as in every other method of laying down curves, namely, — the radius ; 

 the number of degrees, minutes, ond seconds in the entire arc* of the curve : 

 and the length of the two equal tangents ; either of which three quantities 

 can be calculated from the other two. The commencement of the curve A, 

 its termination B, and the intersection of the two tangents D, are to be 

 marked on tbe ground as usual. It is supposed that the centre line of the 

 railway is marked by stakes driven at equal distances— say of 100 feet. Let 



p. 242, 



Greener "On the Gun.'' p. 157: and "On the Science of Gunnery,' 



E represent the last stake in the portion of the line immediately preceding 

 the curve, the distance A F from the commencement of the curve to the first 

 stake in it will be the difference between 100 feet and EA. The angle at 

 the circumference subtended by the arc A F must be calculated, and a deli- 

 cate theodolite having been planted at A, this angle is to be laid off from 

 the tangenU The telescope will then point in the proper direction for the 

 first stake in the curve, and its proper distance from A being set off bv means 

 of the chain, its position will be determined at once. The angles at the cir- 

 cumference subtended by A F+ 100 ft., A F+ 200 ft., A F + 300 ft., A F + 

 400 ft.., &c, being also calculated, and laid off in succession, will respectively 

 give the proper direction for the ensuing stakes G, H, I, &c, which are at the 

 same time to be placed successively at uniform distances of 100 ft. by means 

 of the chain. It is scarcely necessary to observe, that Ihe difference b* tween 

 an arc of 100 ft. and its chord, on any curve which usually occurs on rail- 

 ways, is too small to cause any perceptible error in practice, even in a very 

 long distauce; but should curves occur of unusually short radii, it is easy to 

 calculate the proper chord, and set it off from each stake to the next, instead 

 of 100 ft., the length of the arc. When the inequalities of the ground prevent 

 a distant new from any three stations to lay down the entire curve from them, 

 any stake which has already been placed in a commanding position will answer 

 as a station for the theodolite. By this method the operation of laying 

 down a circular curve of any radius is made exactly analogous to that of 

 laying down a straight line with the assistance of the telescopic sights of a 

 theodolite. It is stated that by this method the curve is laid down with 

 accuracy at the first operation ; that any accidental error in the position of a 

 single stake, affects that stake only ; and it has been found in practice that 

 the progressively increasing errors of the old method are entirely avoided. 



Remarks. — Mr. Gravatt observed that a well-made theodolite* was a con- 

 venient instrument for setting out curves for railways, and that it had been 

 used by him and his assistants for this purpose for several years. The com- 

 mon theodolite was not, however, in practice universally applicable without 

 some further contrivances for accommodating it to this peculiar service. He 

 stated that the circular arc (used, he believed, almost universally on railways) 

 was not the true curve for a line of rails ; as might be proved by considering 

 that a straight line of road required both rails to be at the same level, when 

 viewed in the cross section, whilst on a curved road the outside rail required 

 to be raised, in order to resist the tendency of the engine and carriages to fly 

 off the rails in going round the curve. Where a straight line was joined on 

 to a circular arc, the before-mentioned condition would require an instan- 

 taneous and vertical rise of one of the rails, which was a condition that could 

 not be fulfilled. In curves of contrary flexure, if composed of circular arcs, 

 the difficulty was increased ; for the outer rail, which ought to be the high- 

 est, suddenly became the inner and the lowest, so that an instantaneous ele- 

 vation of one rail, and a corresponding depression of the other was required ; 

 if the curves were of the same radius, the alteration would be of double the 

 extent to that required when passing on to the same arc from a straight line. 

 Therefore as the outside rail must be in all cases the highest, the circidar 

 arc, which required the manifestly false condition of an instantaneous ele- 

 vation, could not be the true curve. He had several years since demon- 

 strated that the true curve was one, which commenced with an infinite ra- 

 dius, decreased in a regular manner, in advancing on the curve, when the 

 radius might be constant for some time, and then increased again to infinity, 

 before it joined either a straight line or another curve of contrary flexure. 

 He had fixed upon the elastic curve, which complied with all the conditions 

 required, but other curves were also applicable. His late assistant, Mr. W. 

 Froude, had found that arcs of a cubic parabola, whilst they complied with 

 the necessary conditions, were extremely convenient in practice ; the equa- 

 tion and its fluxions, or differential co-efficients, being very simple and easy 

 of application. Mr. Froude had also applied other properties of that curve, 

 so that, with the assistance of a few calculated tables, the process of setting 

 out a true curve was rendered as easy in practice as setting out a circular 

 arc. With any curve there was considerable practical difficulty in finding 

 the direction of the tangents, the radii of curvature, and the position of the 

 curves upon the ground. Mr. Gravatt used what he termed a skeleton plan, 

 of several stakes driven into the ground nearly in the course of the intended 

 line, expressing their position by columns of figures with reference to two 

 co-ordinates ; thus obtaining a numerical accuracy far greater than that of 

 any drawn plan. By using a table of sines and co-sines, a few hours' calcu- 

 lation would save many days' labour in the field, besides ensuring an accuracy 

 not otherwise to be obtained. 



On Horse Powbr. 



" Results of the application of Horse Power to raising Water from the 

 working shafts at Saltwood Tunnel, on the South-Eastern Railway, in 1842." 

 By Frederick William Simms, M. Inst. C. E. 



This tunnel is driven in the middle bed of the lower green sand, between 

 which and the surface of the ground is interposed only the upper bed of the 

 same stratum ; but in sinking the eleven shafts for the work, it was found 

 that at the level of the top of the tunnel the ground assumed the character 

 of a quick sand, saturated with water, in such quantity that it could not be 

 reduced by manual labour. Under these circumstances horse gins were 

 erected for drawing the water by barrels, containing 100 gallons each, weigh- 

 ing when full about 1310 lbs. 



The engineer's intention was to drive simultaneously from these shafts, in 



33 



