To Railway Earthworks. 



75 



railway is partly in cutting and partly in embankment on the 

 same side of a centre stake. 



Second. — By successive approximations with the aid of the 

 spirit-level. This method, which has been found well 

 adapted for uneven ground, has been explained in detail in 

 the work of Mr. Frederick Sims, C.E., lately Inspector of 

 Railways for the Hon. East India Company ; and has been 

 very frequently employed by other engineers. I however 

 noticed, some years ago, that his rule for determining the 

 side distances, when the cross section showed both cutting 

 and embankment on the same side of any centre stake, was 

 totally wrong, and had occasioned errors of several feet in 

 side distances set off for the South Eastern Railway. As 

 Mr. Simm's work has passed through several editions, and as 

 the erroneous rule alluded to has been since given in another 

 work brought out by the well known publisher, Mr. Weale, 

 I trust this passing allusion to it may not be considered un- 

 called for.* 



Third, — By plotting the cross sections of the ground upon 

 a large scale, and takuig the side distances from the diagrams." 



Fourth, — By various rules of thumb in vogue among con- 

 tractors, and not admitting of mathematical demonstration. 



Having considered it would be preferable to employ tabu- 

 lated quantities for determining side distances, in lieu of 

 employing Macneil's instrument, I have derived from the 

 following formuhe the annexed tables of multipliers, and I 

 have found that by using these multipliers (which are also 

 applicable to those cases wherein Macneil's instrument fails 

 to be of service), the required side distances can be com- 

 puted and set off on the ground with more rapidity and cer- 

 tainty than by an instrument whose bars and arcs have to be 

 adjusted at every stake. 



Let ABC D(Fig. IL) represent a portion of the cross sec- 

 tion of a railway cutting on one side of the centre stake at 

 H : the ground, in this diagram, converging from the centre 

 stake towards the plane of base at formation leveL Draw 



* A point being assumed as near the true position of the point d (Fig. 

 1.) on the ground as can be determined by estimation, then the differ- 

 ence of level between that point and the central stake h, minus the 

 height B would be the first approximate value of d k, which multi- 

 plied by ratios of slope for embankment, would give the first approxi- 

 mate value of c K ; which should be added in order to obtain the first 

 approximate value of the side distance, b n, to b the half-ividth at 

 formation level, and not to h o, the computed horizontal half-width for the 

 height b h, as in Mr. Simm's treatise. 



