If s and G — 8 be the cross-distances from the nose of the
crossing to the lines tangential to the curves at springing

L' = V 2 El s ; and also

L' = V 2 Ej (Gr '— s) (approximately).
Whence, by eliminating «,

L' = /y/ „ ' 1. (approximately), . . . (13a)

and, in the same way,

V = \/ \ ' . (approximately). . . . (14)

Hi -f- Xl2

When the radii of the curves are equal, we obtain the follow-
ing formulae :

G

E = -. n. (15)

2 versin -^
= 4 G P (approximately) .... (15a)
L' = E sin ^ (16)

= leotJ (17)

= 2GI (approximately) .... (17a)



= v/(E-|g (18)

= ffRGi (approximately). . . . (18a)

V = V E d (approximately) .... (19)

= 21 jGTd (approximately). . . (20)



p



66 NOTES ON PERMANENT- WAT- MATEEIAL,

' 68.— Curves of Similar Flexure.
In figure 4



BD^


-CD2 =


= AB'^-


-AC


BD


i-|-CD =


BC






Ei^


-E/



E, - Eg - G

and, finally, by a process similar to that by which the case of
curves of contrary flexure was determined,

L' = x/ E,^ + i (k, - E, - G + ^l^^^J (21)

Again, if s and Q -{- she the cross-distances from the nose of
the crossing to the lines tangential to the curves at springing

L' = \/ p '_ p (approximately) . . (21a)
I' = /</ — ' 4 (approximately). . . (22)



69. — Lead of Crossing Constant.
The formulae for leads, thus obtained, in the case of curves
of similar or contrary flexure are, however, of theoretical rather
than practical interest.
