THE LOCATION OF THE CUBIC PARABOLA. 125 



TABLES TO FACILITATE THE LOCATION OF THE 



CUBIC PARABOLA. 



By O. J. Merfield, f.r.a.s. etc. 



(Communicated by J. Nangle.) 



[Read before the Royal Society of N. 8. Wales, June 6, 1917. ,] 



Introduction. 

 In the Journal and Proceedings of this Society, Vol. xxiv, 

 there will be found a table, prepared by the writer, which 

 gives values of certain functions in connection with the 

 location of the cubic parabola. The argument to this table 

 being ce/B, in which B equals p, the radius of curvature at 

 the point a? c y c where the parabola forms contact with the 

 circular curve of radius R. 



This table may be used in quite a number of ways to 

 solve such problems that arise in practice. To illustrate, 

 it may be desired to set out a cubic parabola when the 

 value of h/B is given, or again the point c may be fixed on 

 the circular curve, hence <£, the angle between the axis oc 

 and the tangent at the point c, becomes known, from these 

 values the remaining functions required are readily found 

 by the usual methods of interpolation. 



To those who have a knowledge of interpolation, such 

 problems present no difficulty, as the argument of the table 

 is so arranged that only second differences need be taken 

 into account in the formulae of interpolation. The table 

 could have been prepared so as to include values of the first 

 derivatives for each respondent, but for the purpose for 

 which this table was prepared it was unnecessary. 



Some time ago I received a request from an officer of the 

 Tramway Construction Department of New South Wales r 



