CUBIC PARABOLA APPLIED AS A TRANSITION CURVE. LVII, 
A numerical value is given to the coeflicient m so that the radius 
of curvature of the curve represented by this equation, will be 
the same as the circular are at the point of tangency. 
The method of deriving this coefficient, so that the above con- 
dition shall be fulfilled, has been explained by the author in the 
paper referred to, but the following abstract will be compatible 
with this note, the same notation being adopted as formerly. 
From the equation to the curve we have 
tan ¢ = 3ma? = dy/dx 3 
and if this be substituted in the ree 
= 
p= { 1+ (2 v) ‘} + os, 
it will be found after reduction that 
x] 2p = sin ¢ cos? > 5 
Making p equal to unity and adopting a suitable value for a, 
denoted by a, and which should not exceed 0°68...p, then putting 
Bin place of x,/2 and writing wu for sin ¢, the above cubic becomes 
w—u+PB=0 a 
from which « may be found, and hence sin ¢. The angle ¢ may 
then be obtained from a table of trigonometrical ratios, as well as 
the tangent of this angle. Using the adopted value of «, and 
tan ¢ just found, we can obtain the ee value of m from 
equation (3). 
Referring now to the diagram! it will be seen how the various 
quantities given in the tables are obtained, and how the curve is 
applied. A complete explanation is given in the former paper, 
So that it is here unnecessary to enter into the details. 
The length of the transition curve may be computed from the 
following series 
a tan? — 2 75 tan* d + ae anton ..ete.). 
Method of using the aids decided upon the value of 
P; which is taken equal to & the radius of the circular curve, we 
s=a(1+ — i 
coe Ee OC es ete eae Se eS ee 
1 See Plate 10, Journal Royal Society of N. S. Wales, Vol. xxrx., 1895, 
