LVI. C. J. MERFIELD. 
NOTE ON THE CUBIC PARABOLA APPLIED AS A 
TRANSITION TO SMALL TRAMWAY CURVES. 
By ©. J. MERFIELD, F.R.A.S. 
[Read before the Engineering Section of the Royal Society of N. 8. Wales, 
August 18, 1897.] 
Introduction.—In a paper by the author, published in the Pro- 
ceedings of this Society during the year 1895,' it is shewn how 
the cubic parabola may be applied as a transition curve for con- 
necting the straight to the circular curve. Appended to the 
discussion there are tables to facilitate the field operations, the 
abscissa having a fixed numerical value. 
If the angle ¢, contained between the abscissa and the tangent 
to the curve at the point of contact with the circular curve, be 
made constant, then other tables may be constructed by simply 
taking a suitable multiple for the case required. 
On tramways it is often necessary to use small radii curves 
when connecting the straights. The shock received by the rolling 
stock, due to the sudden change from the straights to these sharp 
curves, is very noticeable even at low rates of speed, but this 
concussive motion is reduced to a minimum, by adopting a curve 
of varying radius to connect the straights with the circular curve. 
Theoretically all.circular curves should have transitions applied, 
but usually in practice, transition curves are not used, when the 
adopted elevation of the outer rail of the circular curve is small. 
It is the object of this note to demonstrate how the method, 
explained in the previously mentioned paper, may be easily ex- 
tended to any case required, by the aid of three tables. 
Method of preparing the tables.—The three tables appended are 
computed from the equation 
y = ma* 
1 Vol. xxrx., p. 51. 
