J. 0. NAGLE — VERTICAL CURVES FOR RAILWAYS. 
27 
To find the degree of curve in terms of r, let 0 of Fig. 3 he the center 
of cnrvatnre and AC one station, then will EC=|r. Draw BF to the 
mid-point of EC, BE being equal to BC. From the triangle EBC, since 
angle EBC=D, the degree of curvature, 
2sin ^ D = io 
r 
Too 
As D will always he small, we may write the arc for the sine without 
sensible error, giving 
r 
Too 
D = 
( 8 ) 
As (8) gives D in n measure we have, when reduced to degrees, 
57 3 
D° = = 0.573 r (9) 
The offset for any point will now he, nearly enough, 
z = R ex sec. M)° (10) 
In which R is the radius of curve and YD the angular change of tan- 
gent from PC, to the point where z is taken. 
If the simple offset formula, 
z = £a 2 D° (11) 
he employed under the same limitations as in alignment location, a sim- 
