The first equation leads, as before, to

(28) t = C{T(V) - T(v)},

(29) x = C{S(V) - S(v)}.

The integration of (24) gives

(30) dy= constant - gt = g(½T - t),
dt

if T denotes the whole time of flight from O to the point B (fig. 1), where the trajectory cuts the line of sight; so that ½T is the time to the vertex A, where the shot is flying parallel to OB.

Integrating (27) again,

(31) y = g(½Tt - ½t2) = ½gt(T - t);

and denoting T - t by t′, and taking g = 32f/s2,

(32) y = 16tt′,