The Railway Transition Curve. 
339 
1911-12.] 
Hence 
1= -000,000,195,349, 
and the equation of the transition curve is 
Y = -000,000, 195, 349X 3 . 
To determine the point B we have 
hence, 
BS = (R 4- (3) cot 0; 
BS = 2643-21'. 
The point B is now fixed, and also the points A, N, Q, D relatively to 
B. The circular curve is set out in the usual way from the point D in the 
tangent DS', and the transition curve may he set out from the origin A by 
means of the equation 
Y = -000,000,195,349X 3 . 
The exactness of the compounding should he tested from this last 
equation. Thus at X = 299*041 the recalculated values are 
(i) Y = 5-2240, (ii) Y' = 3ZX 2 = tan 3°, (iii) Y" = 6ZX = *000,350,505, 
which is the value given by the equation 
v" = (l+A 2 ) 1 
J R * 
Thus the compounding is shown to be exact. 
Table of Offsets in Feet. 
X 
30 
60 
90 
120 
150 
180 
210 
240 
270 
300 
Y 
•0053 
•0422 
•1424 
•3376 
•6593 
1T393 
1-8091 
2-7005 
3-8451 
5*2744 
If, instead of setting out the curve by offsets, it is to be laid out by 
theodolite and chain, the polar equation and a suitable selection of 
vectorial angles are required. Putting 
X cos 0, Y = r sin 0, 
the polar equation is 
r 2 = sin 0/(1 cos 3 0), 
which is suitable for logarithmic computation. As 
and 
Y/X = tan #=YX 2 , 
Y' = tan if/ = 3ZX 2 , tan if/ = 3 tan 6. 
Thus, for small values of 0, \/s = 36. This permits a suitable selection of 
values of 6 to be made. 
