The famous theory of the parabolic motion of projectiles was at an early period found to give results not in accordance with practice. Manifestly, then, the air must offer a very sensible resistance to a body which is moving through it with a high velocity. This resistance will depend upon the form of the moving body, and upon the velocity with which it is moving. Hence, before the path of a projectile can be calculated, it will be necessary to determine experimentally the resistance opposed by the air to the motion of the projectile, corresponding to various velocities. According to Newton’s law, the resistance of the air varies as the square of the velocity. But the velocities were low in the experiments made under his direction. In 1719 John Bernoulli gave equations for finding by the method of Quadratures the path &c. of a projectile, when the resistance of the air was supposed to vary according to any power of the velocity. But in spite of grave doubts respecting the accuracy of Newton’s law, it has been adopted by most of the eminent mathematicians who have written on the subject, such as Euler (1753), Lambert (1765), Borda (1769), Bezout (1789), Tempelhof (1788-9), d’Ehrenmalm (1788), Lombard (1796), and Poisson. The first good experiments made with a view to determine the resistance of the air to the motion of projectiles were those of Robins in 1742. The projectiles used were leaden bullets of small size. When we consider the great density of the material used, its liability to change its form in the barrel of the gun, and the smallness of the solid projectiles, it is truly wonderful that Robins was able to accomplish so much with his ballistic pendulum. Afterwards Hutton carried on Robins’ system of experimenting both with the whirling machine and ballistic pendulum, introducing additional precautions, and using iron projectiles of greater size. In recent times MM. Didion, Morin, and Piobert have carried on experiments in France with heavier spherical projectiles, by the help of an improved ballistic pendulum; but they have done little more than confirm the results of Robins and Hutton, and extend them to spherical projectiles of larger diameter.