LXIV. DISCUSSION. 
P. of C. with the straight, the nominal radius at that point 
always being very large, giving an extremely easy entrance to the 
curve ; whereas in the spiral, shortening ~, without introducing a 
great number of radii, has the effect of bringing the curve to more 
or less an abrupt termination, as in the case of No. 1 on the 
diagram shown, the radius at P. of C. with the straight is only 
3°18 chains, giving a curve which in itself might be said to require 
a transition. In America he found engineers seldom made the 
transitions on tramways longer than about 60 lks. for curves up 
to about 9 chains, but he considered 80 Iks. a very good maximum 
length for the cubic parabola on curves over 1:5 chains radius 
where it could be used, but often found it was not a matter of 
choice, but rather one of necessity, in using the one which would 
comply with the conditions. 
Referring to the author’s tables for tramways, while fully 
appreciating the work done, he would like to have seen them 
worked out somewhat on the principle of the author’s first paper 
on transitions, viz., with fixed lengths of transitions for different 
radii. The tables given, were very limited in their usefulness, 
because the length of the transition «, increased in proportion 
with the radius R, making it too long to use in most cases, also 
as the angle of deflection must be greater than 2 ¢ = 3 
before the tables could be applied. A greater variety of trans- 
itions and curves was required on tramways than on railways, to 
enable the engineer to comply with the limited conditions. 
