_Twenty-first Lecture._--(21.) Relations between the velocities, the spaces traversed, and the durations of passage in the rectilinear movement of projectiles. They are applicable to direct fire, and are independent of the function of the velocity which enters into the expression of the resistance of the air. Case where the resistance of the air can be supposed proportional to the square of the velocity. Establishment of balistic formulas in this hypothesis. Application of the formulas to the resolution of one of the problems connected with a plunging fire. Comparison of the results obtained with those arrived at by the use of general formulas. Indication of methods applicable to the resolution of several questions in projectiles. _Twenty-second Lecture._--(22.) Examination of disturbing causes which influence the motion of projectiles. 1. Disturbing causes acting on the projectile during its passage through the bore. Imperfections of form, such as want of straightness in the bore, faulty position of the line of sight and the trunnions. Influence of the windage of the projectile and of the percussions which result from it. Deviation from the original direction; its consequence in the different kinds of fire. Effect of the recoil and the vibrations of the barrel in the fire of small-arms. Influence of the various causes which are capable of modifying the initial velocity. 2. Disturbing causes acting upon the projectile during its passage through the air. Influence of the rotatory motion which results from the last percussion within the bore. Effects of the eccentricity of projectiles. Case where the rotation occasions no deviation. Influence of the proximity of the ground. Deviation produced by the wind (air in motion.) Influence of atmospheric changes. THIRD SECTION.--MOTION OF CARRIAGES. _Twenty-third Lecture._--(23.) Importance of the question. Preliminary ideas. Resistance due to the motion of a carriage and determination of the effort necessary for drawing it in the case of uniform motion. Two-wheeled carriage on level ground; the effort of draught in a direction parallel to the ground; first, resistance referable to the friction of the wheels on the axle; secondly, resistance referable to their revolution upon the ground. Influence of the weight of the carriage. Advantage of large wheels over small ones, demonstrated in the two cases of a yielding soil and a hard soil scattered over with obstacles. Expression of the power of draught necessary to overcome the two resistances united.