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Art. XIII. — An Attempt to Simplify and Generalise the 

 Theory and Practice of Railway Curves. By William 

 Hill, Esq., C.E. 



(With a Plate.) 

 [Read before the Institute 14th September, 1S59.] 



Mr. President and Gentlemen, — 



If we suppose two places to be on the same level, and 

 that they are united by a canal, then the trace of the surface 

 of the water, on a vertical plane, passing through the ter- 

 minal points of the canal and the centre of the earth, will he 

 a great circle of the globe; but if the two places are not equi- 

 distant from the earth's centre, then in its course the canal, 

 proceeding from the higher to the lower station, would have to 

 be traced by concentric arcs, successively of shorter radius, 

 until the minute (in comparison with the radius of the earth) 

 but important difference of level was made in the surface of 

 the canal at the two places. The steps (or locks) by which 

 the descent is effected are each several feet deep ; whereas if 

 a railway connected the same two places, it would be made to 

 descend by imperceptible steps, and its longitudinal profile 

 would be a curved line, called the gradient. On paper this 

 curve is, for obvious reasons, drawn as a straight line. A 

 railway can seldom, however, be carried throughout upon one 

 gradient, and a track is selected with regard to the economy 

 of gradients, from point to point of elevation and depression, 

 and impracticable ground is evaded by a judicious se lection 

 of curves, so as to minimize on the plan its departure from a 

 direct trace from point to point. To enable us to do this, so 

 as to avoid obstructions and " lose ground " as little as pos- 

 sible, in short, to economise curves, is the object of the pre- 

 sent attempt to generalise the subject, and to simplify the 



