  Some preliminary pendulum-decay experiments showed promise for doing this, leading him in the first edition to rely solely on this phenomenon. The idea was to start a pendulum from several different heights in order to cover a range of velocities and then to use simultaneous algebraic equations to fit a two or three term polynomial to two or three lost-arc data-points, changing the exponents until the polynomial achieved good agreement with the other lost-arc data points. The theoretical solutions for pendulum motion under resistance forces in Section 6 would then allow him to infer the forces from the rate of decay of the pendulum. These theoretical solutions covered resistance forces that vary not only as velocity to the powers 0, 1, and 2, but also as any power at all of velocity. In principle, therefore, he saw himself in a position to infer laws for resistance forces on spheres from the phenomenon of pendulum decay in full parallel with his deduction of the law of universal gravity from the phenomena of orbital motion in Book 3. And he could then conclude from the total absence of signs of resistance forces acting on the planets and, most especially, comets that the density of any fluid in the celestial regions must be exactly or very nearly zero.