TRANSITION CURVE. 143 



tically. As far as concerns the mathematical proof, these 

 weights may be represented by the single load W, as shown. 

 If this load W is resolved into two components, one perpen- 

 dicular and the other parallel to the slope from rail to rail, the 

 former component may be neglected, as it is only the latter 

 that opposes the centrifugal force. The centrifugal force 

 acting horizontally in the direction of the arrow C is given in 

 amount by the ordinary formula 



MV= 



R 



where M ^ mass, V = velocity and R = radius of track. 

 C may now be resolved into its components, one perpendic- 

 ular to the slope of the track, which component may be 

 neglected, and the other parallel to the slope of the track, 

 acting in opposition to the effect of gravity. 



From similar triangles 



T 



W ~ g 



o 



where e = superelevation and g = gauge. Hence 



_ We -^2.2 Me 



g g 



Again 



C _ h 



where h = AD. Therefore 



h h MV 



C = — C = — 



g g R 



