94 ON A SIMPLE PLAN OF EASING RAILWAY CURVES. 



. \ To get h in terms of Y by eliminating X 



We get Y = h + - T - x ^ 



= h + | r 

 .-.A = | Fbut/* = MN.\ Y = iMF 

 Therefore the distance between the real auxiliary tangent 

 = h = i Y. 



Practical Application op the Cubic Parabola for Easing 

 Railway Curves. 



From the above investigation we have got the following 

 results :— 



That from the origin of the curve to a vertical line drawn 

 through the centre of the circle, is half the length of the curve of 

 adjustment. Also that the distance the circle has to be set in 

 from the parallel tangent, is equal to one-third of the tangent 

 offset at the point of junction of the circle and the cubic parabola, 

 and is also equal to one-fourth of the ordinate at the same point. 



Perhaps the best way of illustrating the matter, is to give one 

 or two practical examples. 



Example I. 



It is desired to ease a curve of 10 chains radius, through a 

 length of 2 chains. 



The first point to be determined is at what parallel distance 

 from the straight line will the tangent to the circle be. 



We have X = 2 chains 

 R = 10 chains 



1 



m =a 



m 



6 XR 

 1 



6 x 2 x 10 

 1 

 ~ 120 

 Again we have y = mx 3 



= m x 8 



2_ 

 30 



And A = J F 



