THE LOCATION OF THE CUBIC PARABOLA. 127 



Table II appended to this paper, gives values of the angle 

 <£ with the argument h/R between the limits 00000 and 

 0*01430. The maximum value of h/R equals 



J~ - 1 = 0*01430103 

 and the angle <f> must be within the limits 0° and cos -1 

 J—, that is between 0° and 24° 5' 41"*43... 



For reasons, already explained in a previous paper, these 

 limits must be kept in view when dealing with the cubic 

 parabola as an easing curve. 



It would also appear that the tramway practice in New 

 South Wales adopts the cubic parabola merely as a curve 

 to connect the straight with the circular arc, and not 

 necessarily to overcome the superelevation of the outer 

 rail on the curves. Under these circumstances it becomes 

 feasible to adopt a radius of curvature for the parabola 

 equal to or greater than that of the contact curve at the 

 point of contact x c y c . 



In some cases a small length of circular arc of larger 

 radius than the circular curve, has been introduced between 

 the parabola and the main curve, so that the curve leading 

 out of the straight would consist of the parabola, a small 

 length of circular arc of radius R 2 then the main curve of 

 radius R ± . It would be much better to eliminate the small 

 length of arc of radius R 2 by simply finding a cubic para- 

 bola having a radius of curvature say R 2 at the point of 

 contact c the coordinates of which are x c y c . 



Under the conditions just formulated, there will be two 

 cases. Firstly, we may fix a point c on the circular curve, 

 hence 4> and y c become known. Provided the point c is so 

 fixed, that the angle <£ is within the limits already men- 

 tioned, then we may find a cubic parabola that will connect 

 the straight with the circular curve so that the tangent at 



