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HKOOMALL : 



l)ooks rather than from real difficulty. In what follows the 

 writer hopes to he able to derive the formulas in so simple a 

 manner that even the non-mathematical reader can follow the 

 aro;ument. The formulas are the fundamental ones of the 

 true transition curve and are so simple in form as to be appli- 

 cable in practice with the minimum of calculation and with- 

 out the use of special transition curve tables. The only 

 merit that can be claimed for what follows is directness and 

 simplicity of proof. 



In the figure, let M'A represent the tangent, AH the transi- 

 tion curve and BC a portion of the circular curve. Let K be 

 the middle point of the transition curve. Produce the circu- 

 lar curve backwards to D on the perpendicular through E. 

 Let BN be the common tangent to transition and circular 

 curves at B. Denote by Sc the spiral angle, being the total 

 angular deviation of the transition curve. Let A be the 

 origin of coordinates and let 1 denote distances along the curve. 



