Drive a peg at the leader's end of the chain. This will be the

third point on the curve.
76 NOTES ON PEEMANENT-WAT MATERIAL,

The fourth and succeeding points may be found in the same
way as the third, until the end of the curve is reached.
Here the direction of the tangent is determined by laying off

the half-offset, ^, instead of the full offset, 0.
Example.—Let E = 1273 • 2. Then,

10,000



=



1273-2



= 8-1449
0=8' 1|".
79. — To Set out a Diversion from a Straight Line.
Bule. — To find L, the length of each half of the diversion *
(Fig. 18), add together the square (S°) of the straight portion
between the reverse curves and the product (4 E D) of four
times the radius into the maximum distance of the diverted
from the main line ; subtract the square (D^) of the maximum
distance ; and take the square root of the result.
To find the tangent (T), divide the product (ED) of the
radius into the maximum distance by the sum (L + S) of
the half of the diversion and the length of straight between
t he reverse curves.
Formulas. —

(50)

(51)









L


= VS"+4ED-


■D= . . ..
T


ED






L+S • • • ■




Proof.-


-By


similar


triangles in figure


18,










T D












E ~ L + S.
T-_^D





L + S



PLATELAYING, AND POINTS AND CROSSINGS. 77

Again,

L = 2T + V(2T + 8/- W

.: (L - 2 Ty = (2 T + S^ - D^

.-. L^ = 4T(L + S)+S'-D^

.-. L = VS^ + dRD - D2.
