1911 - 12 .] 
343 
The Railway Transition Curve. 
In setting out the curve the origin is determined from the point of 
compounding by the co-ordinates 
x i ~ F(2i/q — |4'i 3 + 
i 2 -a^ 4 +* • •)• 
The curve is then set out by the freedom equations in the usual manner. 
2 Qj 
If a first approximation be taken x = 2 a\js*, y = and \[s eliminated, 
O 
/^»3 
the resulting curve is the cubical parabola y = > as is to he expected. 
From the equation s — 2 ayJA the intermediate pegs on the curve could 
be set out by a process almost identical with Rankine’s method for the 
circle by chain and theodolite. The methods by rectangular co-ordinates 
are, however, probably simpler. 
Example . — 
Given 
R = 1200', £=100', = 134° 16', 
then 
Z 2 
/?=-— n (Froude) = 1*39' (approximate value), 
24:1a; 
sin i = ^ = .•. if/ = 4:° 46' 49" 
R 12 
O) = 67° 8', SB = (R + /3) cot a> = 506-077' 
£=100, 77 = 4-174. 
Also 
x 1 = R(2i^ 1 - ^ + ) = 200-0964, 
Vl = R(f^ 1 2 -^ 1 4 + ) = 5-56589, 
Hence 
a = x 1 — £= 100-096, 
P = y x -77= 1-392. 
Table of Offsets. 
4 
•02 
•03 
•04 
•05 
•06 
•07 
•08 
•09 
X 
98-037 
120-06 
138-62 
15497 
169-74 
183-33 
195-94 
' 207-80 
y 
•6536 
1-2007 
U8486 
2-5835 
3-3961 
4-2796 
5-2287 
6-2391 
Inexact Compounding with the Cubical Parabola. 
This occurs when the origin and the point of compounding are both 
specified, or even when the origin is fixed and the transition curve is made 
to touch the circular curve. 
