| (76) x tan φ - y = C sec η | [ | xI(U) - | ∫ | x 0 | I(u)dx | >[ | , |
But
| (77) | ∫ | x 0 | I(u)dx | = | ∫ | u U | I(u) | dx | du |
| du |
| = C cos η | ∫ | U x | I(u) | u du |
| g f(u) |
| = C cos η [A(U) - A(u)] |
in Siacci's notation; so that the altitude-function A must be calculated by summation from the finite difference ΔA, where
| (78) ΔA = I(u) | uΔu | = I(u)ΔS, |
| gp |
or else by an integration when it is legitimate to assume that f(v)=vm/k in an interval of velocity in which m may be supposed constant.
Dividing again by x, as given in (76),
| (79) tan φ - | y | = C sec η | [ | I(U) - | A(U) - A(u) | ] | ||
| x | S(U) - S(u) |