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 Hastern 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 taking 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 formule 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 a B c p(Fig. II.) 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 leyel. Draw 
* A point being assumed as near the true position of the point p (Fig. 
I.) on the ground as can be determined by estimation, then the differ- 
ence of level between that point and the central stake u, minus the 
height 8 u, would be the first approximate value of p n, which multi- 
plied by ratios of slope for embankment, would give the first approxi- 
mate value of c x; which should be added in order to obtain the first 
approximate yalue of the side distance, B N, to B ©, the half-width at 
formation level, and not to & 0, the computed horizontal half-width for the 
height B H, as in Mr. Simm’s treatise. 
