(59) u = q sec η,
so that u is a quasi-component parallel to the mean direction of the tangent, say the direction of the chord of the arc.
Integrating from any initial pseudo-velocity U,
| (60) t = C | ∫ | U u | du | , |
| f(u) |
| (61) x = C cos η | ∫ | u du | , | |
| f(u) |
| (62) y = C sin η | ∫ | u du | ; | |
| f(u) |
and supposing the inclination i to change from φ to θ radians over the arc,
| (63) φ - θ = Cg cos η | ∫ | du | , |
| u f(u) |
| (64) tan φ - tan θ = Cg sec η | ∫ | du | . |
| u f(u) |