SEC. VI.] OF NATURAL PHILOSOPHY. 319 In the experiments of the 4th column there were equal motions lost in 535 oscillations made in the air, and If in water. The oscillations in the air were indeed a little swifter than those in the water. But if the oscil lations in the water were accelerated in such a ratio that the motions of the pendulums might be equally swift in both mediums, there would be still the same number 1 j of oscillations in the water, and by these the same quantity of motion would be lost as before ; because the resistance i> increased, and the square of the time diminished in the same duplicate ra tio. The pendulums, therefore, being of equal velocities, there were equal motions lost in 535 oscillations in the air, and 1} in the water; and there fore the resistance of the pendulum in the water is to its resistance in the air as 535 to 1 }. This is the proportion of the whole resistances in the case of the 4th column. Now let AV + CV2 represent the difference of the arcs described in the descent and subsequent ascent by the globe moving in air with the greatest velocity V ; and since the greatest velocity is in the case of the 4th column to the greatest velocity in the case of the 1st column as 1 to 8 ; and that difference of the arcs in the case of the 4th column to the difference in the 2 16 case of the 1st column as ^ to 7, or as 86 J to 4280 ; put in these cases 1 and 8 for the velocities, and 85 1 and 4280 for the differences of the arcs, and A + C will be — S5