SEC. VI.l OF NATURAL PHILOSOPHY. 313 COR. 1. Hence if the resistance be as the velocity, the difference of the arts in the same medium will be as the whole arc described : and the contrary. COR. 2. If the resistance be in the duplicate ratio of the velocity, that difference will be in the duplicate ratio of the whole arc : and the contrary. COR. 3. And universally, if the resistance be in the triplicate or any other ratio of the velocity, the difference will be in the same ratio of the. whole arc : and the contrary. COR. 4. If the resistance be partly in the simple ratio of the velocity, and partly in the duplicate ratio of the same, the difference will be partly in the ratio of the whole arc, and partly in the duplicate ratio of it: and the contrary. So that the law arid ratio of the resistance will be the same for the velocity as the law and ratio of that difference for the length of the arc. COR. 5. And therefore if a pendulum describe successively unequal arcs, and we can find the ratio of the increment or decrement of this difference for the length of the arc described, there will be had also the ratio of the increment or decrement of the resistance for a greater or less velocity. GENERAL SCHOLIUM. From these propositions we may find the resistance of mediums by pen dulums oscillating therein. I found the resistance of the air by the fol lowing experiments. I suspended a wooden globe or ball weighing oT^ ounces troy, its diameter CJ London inches, by a fine thread on a firm hook, so that the distance between the hook and the centre of oscillation of the globe was 10