THE CUBIC PARABOLA. 59 
Substitute for R the value ,— on es 12 
Also for tan > the cages 3 mm @,* 
Therefore E B=°* 7 fe = “5 approximat tely hates 13 
From equation 13 we find that the point Z at right angles to Ya 
divides O B into two equal parts nearly. 
To find 7 FE = H 
OD 2 ¥, 
( ° 
and G 7 = \2 approximately, taking G 7’ as a small quantity 
‘eres 
4 1 oa &o* 
eo ean. 
Therefore G T = jy, ...- 14 
TE =H = Yo — i¥e 
Therefore H = } y¢....---- 15 
| Again 7 FE = KB=}CB 
} Pe CB + CA 
; Therefore K B= 1CK 
Now C K = R - £0 
Therefore C B = =#{2 = 2) de = (2)? \ oe 16 
* 
This completes the arenehanene method of location. The 
length of the curve can be found by equation 9 or by 10. 
Length of are C . ' may be found from the equation number il. 
_‘Ifwe take EB = 5 this equation may be written 
oO = Rife- 2(8in 2) ] } -0002909.......--ser \7 
: The radius of curvature may be obtained approximately by the 
following 
ba 
P = 6me 
Substitute for m the value = and we obtain 
c 
Be Se eon Oo 18 
6 Ye 
