CUBIC PARABOLA APPLIED AS A TRANSITION CURVE. LXIII. 
the curves employed were frequently as small as from 50 lks. to 
100 lks. radius, requiring superelevations of between 2” and 3” the 
necessity of transition curves becomes very apparent, but the 
selection of the best transition to fulfil the requirements was not 
always an easy matter. About four years ago he pegged out what 
he believed was the first transition curve on tramways in this city, 
adopting the system so much in vogue in America, viz., the spiral 
curve, but has used the cubic parabola in preference ever since 
the author’s paper on that subject in 1895. Spiral curves are 
made up of radial arcs with increasing radii from the point of 
contact with the curves to the point of contact with the straight. 
The number of radii, and the length of chord employed, determine 
the character of the transition. In practice six or seven arcs are 
generally used, with equal chords 4 lks. to 10 lks. in length, accord- 
ing to the requirements, and they can be set out on the ground, 
either by offsets or angles, as may be found most convenient. 
Some very good examples of spiral curves were published in 
October 1895 in the Engineering News and American Railway 
Journal, by C, A. Alden, c.z., in which he gives tables, ranging 
from 30’ to 1,700’ radius, with short transitions 15’ to 43’ in 
length. He had plotted down the first three examples given in 
that journal for a curve of half chain radius, against the three 
given in the author’s paper to the same radius, to show the com- 
parison between the two systems, when the ratios were similar. 
The two systems agreed very closely in the first and second, but 
in the third example shown, there was a considerable difference, 
one of which was, the distance between the two main curves, 
amounting to about 2’ 6”, which would be of great value, when 
endeavouring to keep away from the kerbing, on the convex side 
of the curve ; which could not be attained by using the cubic 
parabola, as it would require a length of transition greater than 
“68 of the radius, which the author has shown to be ‘inadmissible. 
One great advantage the cubic parabola has over the spiral, is 
that neither the radius of the main curves R, nor the length of 
the transition x, have any appreciable effect on the curve at the 
