But according to the definition of the functions T, S, I and D of the ballistic table, employed for direct fire, with u written for v,

(65) U
u
du=du= T(U) - T(u),
f(u)gp
(66) u du= S(U) - S(u),
f(u)
(67) g du= I(U) - I(u);
u f(u)

and therefore

(68) t = C[T(U) - T(u)],

(69) x = C cos η [S(U) - S(u)],

(70) y = C sin η [S(U) - S(u)],

(71) φ - θ = C cos η [I(U) - I(u)],

(72) tan φ - tan θ = C sec η [I(U) - I(u)],