This author, in his treatise, after stating in page 48, the two following positions of Mr. Robins, namely, "that till the velocity of the projectile surpasses that of 118 feet in a second; the resistance of the air may be estimated to be in the duplicate of the velocity;" that "if the velocity be greater than that of 11 or 1200 feet in a second, the absolute quantity of the resistance will be nearly three times as great as it should be by a comparison with the smaller velocities;" says, that he is certain from some experiments, which he and two other gentlemen tried with a rifle piece properly fitted for experimental purposes, that the resistance of the air to a velocity somewhat less than that mentioned in the first of these proportions, is considerably greater than in the duplicate ratio of the velocity; and that to a celerity somewhat greater than that stated in the second, the resistance is less than that which is treble the resistance of the same ratio. He observes, also, that some of Mr. Robins's own experiments come to this conclusion; since to a velocity no quicker than 200 feet in a second, he found the resistance to be somewhat greater than in that ratio, and remarks, therefore, that "after ascertaining the velocities of the bullets with as much accuracy as possible, I instituted a calculus from principles which had been laying by me for some time before, and found the resistance to approach nearer to that, which exceeds the resistance in the duplicate ratio of the velocity, by that which is the ratio of the velocity, than to that, which is only in the duplicate ratio."