THE CUBIC PARABOLA. 53 
vector and the axis of X, for every ten links from the origin 
along the curve, have been computed. Other useful data are 
added. Table No. 3 contains these quantities, computed by the 
exact method. 
Table No. 4 is similar to the above, and corresponds to the 
parabola given by the offets tabulated in Table No. 2. The values 
of log ““m” for various cases are given in Table No. 5. 
The deduced formule will not only be found useful in the pre- 
paration of tables, but will be advantageous in many of the 
problems that beset the engineer or surveyor, in the location of 
this curve. For this purpose the equations are collated, so that 
a selection may be made for particular cases. 
NorarTIon. 
p= Radius of curvature at any point. 
R= Radius of circle =p at point of contact C. 
“z= Values along axis of X. 
y= Values along axis of Y. 
%:= Value of x at point of contact C. 
Ye= Value of y at point of contact C. 
O= Origin of curve. 
K=c=Constant. 
«=Length 7 K=E B. 
y=LengthCK. (See fig. 1) 
H = Distance of parallel tangent. 
$= Angle contained between the tangent to the curve, and the 
axisof X=C DB. (Fig. 1) 
9= Angle contained between the radius vector and the axis of X. 
= Particular value of 6. 
Length of cubic parabola =O C. 
*= Any length along curve. 
*=AngleOL0O'. (See fig. 2.) 
A= Area contained between x, y, and the curve. 
9= Angle 0 C B. g = Gauge. 
*,=O B= 2, — x. 
4 
: 
" 
v = Velocity. 
