In the present state of our knowledge of the resistance of the air to shot, the problem of integrating the equations of motion of the shot and of plotting-out a representation of the curve described by it is peculiar, because, according to the best experiments we possess, the law of the retardation cannot be expressed by a single exact formula which is available for the solution. We are therefore compelled to give a solution adapted to Tables, the magnitudes of the retardation being set down in those Tables for velocities which are common in practice. The formulæ given by Hutton and by Didion, even if they were true, apply only to spherical shot; and though they are very simple formulæ, the solutions obtained by means of them are not satisfactory—first, by reason of their complexity, and next on account of the rough approximations which characterize the proofs. Prof. Hélie, who gives an account of Didion’s method in his ‘ Traité' de Balistique,’ says that it gives results which are not in accordance with fact. The fault may probably be laid in a great measure to the charge of the formula; for there can be no doubt that Mr. Bashforth’s method of experimenting with his chronograph and screens gives more trustworthy and more extensive information than the ballistic pendulum experiments of Hutton and Didion; and Hutton’s formula, as well as Didion’s, agrees with Mr. Bashforth’s Tables only for a limited range of velocities.