ON A SIMPLE PLAN OF EASING RAILWAY CURVES. 95 



Therefore the distance of the straight line from the tangent to 

 the circle is - 6 - - of a chain, or 1*1 feet, or 13*2 inches, and the 

 offset at Y = 4- 4 feet, or 52*8 inches. 



The other points in the curve have ordinates proportional to 

 the cube of the distance from the origin, and to facilitate the 

 calculation of these offsets a table will be found in the Appendix, 

 where these proportions have been calculated out ; also a table 

 giving offsets for all curves from 5 to 20 chains radius eased 

 through a length of 2 chains. 



Example II. 



It is desired to ease a curve of 4 chains radius through a length 

 of 1 chain. 



To find the distance of the tangent to the circle from the 

 straight line 



We have X = 1 chain 

 R = 4 chains 



1 



6 XR 

 1 



6x1x4 

 24 



x 



Again we have y = mco 

 1^ 

 ~ 24 



_!_ 



~~ 24 



h = \ r = l x i = 1 



Therefore the distance of the straight line from the tangent to 

 the circle is •§*§- of a chain, or -68 of a foot, or 8*16 inches, and the 

 offset at Y — 2*72 feet, or 32*64 inches. Other points in the 

 curve can be calculated by the attached table of proportions. 



In conclusion, although there may not be much that is original 

 in this paper, the author is not aware that any tables giving the 

 practical application of this system have ever been published 

 before, and he hopes that they may be found useful to the 

 railway engineer. 



