NOTES ON TRANSITION CURVES. 63 



Froude, in his method of easing curves when a short 

 length of cubic parabola is used, makes the length of the 

 curve of adjustment proportionate to the cant, and assumes 

 that the grade from level to maximum cant should not 

 exceed 1 in 300. Thus for a curve of twenty chains radius 

 and a speed of forty miles per hour the length of his trans- 

 ition is 113*6 feet, and the amount of shift (distance 

 between the original and parallel tangent) is only *407 of a 

 foot. 1 



On lines of standard gauge where a mixed traffic of 

 passenger and slow goods trains is worked, it is not advis- 

 able to give a greater cant than four inches, as with a high 

 cant the road is so over-canted for the slow goods trains 

 that the wear on the low rail is very excessive and there 

 is a danger of the engines leaving the road at low speed on 

 account of excessive weight on the low rail. Now a two 

 chain transition and a four inch cant would give a grade 

 of 1 in 396 from the level to the maximum cant, and there- 

 fore a two chain transition should be sufficient for the 

 curves in ordinary use on our lines. By making the length 

 of the transition a multiple of a chain, instead of a multiple 

 of the cant as in Froude's method, the distance of the 

 parallel tangent (or shift) can be found at once, as it is 

 one-third of the tangent offset, and the middle ordinate of 

 the curve is one-half the shift. 



As to the degree of accuracy of the method explained 

 in the paper of 1888, if the total length of the transition 

 does not exceed one-tenth of the diameter of the circle, 

 the method is as accurate as it is possible to work to with 

 ordinary platelaying. In using the approximate method 

 the centre line would be laid out as if no transitions were 

 used, the stakes marking out the curve being subsequently 

 shifted inwards by the amount of the shift or distance of 

 the parallel tangent. 



1 Rankine's Rules and Tables p. 140. 



