The constant may be any arbitrary number, as in using the table the difference only is required of two tabular values for an initial velocity V and final velocity v and thus
(10) T(V) - T(v) = ∑vVΔv/gp or ∫vVdv/gp;
and for a shot whose ballistic coefficient is C
(11) t = C[T(V) - T(v)].
To save the trouble of proportional parts the value of T(v) for unit increment of v is interpolated in a full-length extended ballistic table for T.
Next, if the shot advances a distance Δs ft. in the time Δt, during which the velocity falls from v+½Δv to v-½Δv, we have
(12) RΔs = loss of kinetic energy in foot-pounds
=w(v+½Δv)2/g - w(v-½Δv)2/g = wvΔv/g, so that
(13) Δs = wvΔv/nd2pg = CΔS, where
(14) ΔS = vΔv/gp = vΔT,