570 PROCEEDINGS OF SECTION H. 



We now know the point 0, the length of OC and the angle 

 IOC zz. a, so that the point C can be fixed and the direction of the 

 tangent KC to both circular and transition curve at C can be set out 

 because the angle KCO z: 2a. Thus, from the point G the circular 

 curve CC can be set out in the ordinary way. CC subtends an angle 

 at the centre = 180° — t — 6a from which its length may be 

 computed. 



To set out a double lemniscate bettoeen two pieces of straight. 



Where the ground allows of it the circular curve may be omitted 

 altogether and the entire curve framed of two long transition curves 

 back to back. This construction would reduce the wear due to 

 curvature to its least possible value, and secure the best attainable 

 smoothness of running. For such constructions, where a very long 

 length of transition curve is required, the lemniscate is a much more 

 satisfactory curve than the cubic parabola. 



Fia. 3. 



Let 01 and O'T (Fig 3) be the two pieces of straight to be 

 connected, the angle 010' being i, and let^ be the maximum radius 

 of the connecting curve. 



