  The approach to resistance in the first edition relied entirely on pendulum-decay experiments. The disappointing evidence they yielded led to a far weaker statement of the conclusion about the absence of fluid in the celestial regions in the first edition than the conclusion in the subsequent editions quoted above. Not long after the first edition was published, Newton initiated some vertical-fall experiments in water that persuaded him that the phenomenon of vertical-fall in resisting media would yield much better behaved data. In the second and third editions, therefore, even though the pendulum-decay experiments are still fully reported, the central argument in Book 2 relies on vertical-fall experiments (including ones from the top of the dome of the newly completed St. Paul's Cathedral) to establish a resistance effect on spheres that is proportional to the density of the fluid, the square of the diameter, and the square of the velocity. The data from these experiments were very good — indeed, even better than Newton realized, for small vagaries in them that he dismissed as experimental error were in fact not vagaries at all, but evidence that no polynomial of the sort he was seeking is adequate for resistance forces.