66 W. SHELLSHEAR. 



Example: — To apply a two chain transition to a fifteen 

 chain curve. — The distance of the parallel tangent or shift 

 is equal to one-third the off-set at one chain for the circular 

 curve. (See figure 2.) Let O D B be the tangent line, D 

 the tangent point, and A B the off-set at one chain, then 

 OD=DB = l chain, shift = | A B = ??j£ = 8*8" = A E, 

 middle ordinate = ■§• AB = DC = 4*4". 



As the distance of the parallel tangent (or shift) is small, 

 in many cases it would be possible to apply a two chain 

 transition to an existing line by pulling in the curve by the 

 amount of the shift without widening the cuttings or bank. 

 This would not be possible with a four chains transition as 

 the shift would be too great. 



In the case of two reverse curves with a short straight 

 between, a transition could be introduced as follows: — 

 Mark off the shift for each curve as shown on figure 3 and 

 slew the straight. Let T x and T 2 be the tangent points, 

 measure the shift T^A and T 2 B, join A and B, and apply the 

 transition. The angle iCTi and B C T 2 would be very 

 small in the case of a straight several chains long, and the 

 distance between A and the true tangent could be neglected. 

 Again, in the case of one end of a curve being treated as 

 above, and the other end being on a long straight, the shift 

 could be absorbed as shown on figure 4 without affecting 

 the running of trains. 



These suggestions may not be mathematically correct, 

 but the approximation is so close that if applied to an exist- 

 ing road where no transitions have been used, a great 

 improvement in the smoothness of running would be effected 

 at a moderate cost. 



