  While the vertical-fall experiments put Newton in a position to make his concluding rejection of vortex theories more forceful, they also posed a methodological complication. The vertical-fall experiments offered no way of disaggregating the contribution to resistance made by the inertia of the medium from the total resistance. But the argument against vortices required him to show that, no matter how perfectly free of friction and viscosity the celestial fluid might be, its inertia would still give rise to resistance forces that would affect the motions of comets, if not planets as well. From the resistance measured in the pendulum-decay experiments, Newton could conclude that the forces in air and water are dominated by a contribution that varies as the velocity squared. In the vertical-fall experiments in air and water the measured forces varied to first approximation as the product of the density and the velocity squared, but only to a first approximation, leaving room to question whether a purely inertial contribution had been isolated. Newton dealt with this problem by offering a rather ad hoc theoretical derivation for the purely inertial contribution, showing how closely it agreed with the vertical-fall results, and proposing that the differences between the theoretical and the measured resistances could be used to investigate other contributions. Success of such a program in characterizing the contributions made by surface friction and the viscosity would have provided compelling support for Newton's theory of the inertial contribution. Still, the approach left Newton with not so straightforward a derivation of the laws of resistance forces from phenomena as he had hoped for in the first  edition.[40]