TRANSITION CURVE. 1 45 



vation has been attained. A reverse process of " run-off" at 

 the other end of the curve restores the original level condition 

 of the rails. This method is a more or less successful prac- 

 tical solution of the difficulty and is used on many railroads. 



It is probable that its simplicity in comparison with the 

 supposed mathematical difficulties of the second method, 

 rather than its practical success, does much to retain it in use. 

 There are several grave objections to this run-off method 

 which may be mentioned. In the first place, the gradual 

 increase of superelevation produces an increasing pressure 

 against the inner rail equal in amount, just before the wheels 

 arrive at the point of curve, to that which the centrifugal 

 force would produce on the given curve against the outer rail 

 if no superelevation existed. The sudden cessation of this 

 pressure as the wheels pass on the circular curve tends to pro- 

 duce a more or less unpleasant shock to the passenger. Again, 

 the gradual tilting of the car approaching the curve is unplea- 

 sant when one's senses inform him that he is not moving in a 

 curve, and that such a leaning to one side is not called for by 

 the conditions of equilibrium of motion. Indeed, the same 

 equations for balancing gravitation and centrifugal force 

 apply to the passenger as he sits in his seat as apply to the 

 car on the rails. At the other end of the curve, the point of 

 tangency, the same objectionable effects occur in reversed 

 order. As the wheels pass from circular motion to the straight 

 track the car slides downhill against the inner rail and exerts 

 a sudden pressure corresponding to the centrifugal force on 

 the given curve, which force gets gradually less and less until 

 the superelevation is entirely run off. The passenger will also 

 pass through a corresponding series of unpleasant sensations. 



The second method of solving the problem of passing 

 from tangent to curve and curve to tangent is both theoreti- 

 cally and practically perfect. Its only objection is a certain 

 supposed mathematical difficulty in connection with its theory 

 and use. This ill repute arises probably from the cumber- 

 some way in which the subject is set forth in many text 



