_Fiftieth Lecture._--(4.) Effects of projectiles on the different substances fired at. Effects of concussion and penetration. Effects on earth. Theory of the penetration of a projectile into a resisting medium. Formula to express the penetration, based on the results of calculation and experiment. Effects of penetration into wood. Effects on metals, cast-iron, iron, lead. Effects on masonry and on rock. Application to a breaching fire delivered in a regular direction relatively to the revetment. Effects of the shock of projectiles upon living bodies. Effects of hollow projectiles bursting in different media; earth, wood. Method of bursting employed against troops. Effects of spherical case. Incendiary effects. Effects of war rockets. Explosive rockets. Incendiary rockets. Effects of concussion. FOURTH PART. TRACE AND CONSTRUCTION OF BATTERIES. _Six Lectures, common to the Students of both Arms._ _Fifty-first Lecture._--(1.) Definitions. Meaning attached to the word “battery.” Different denominations given to batteries: first, according to the circumstances of the war in which they are employed; secondly, according to their mode of construction; thirdly, according to the kind of ordnance with which they are armed; fourthly, according to the kind of fire for which they are intended; fifthly, according to the direction of their fire. Principles of construction. General considerations on the elements which constitute the different kinds of batteries which have reference to them. Epaulment; its length, height, and thickness in different cases. Section of the epaulment. Ground-plan of the epaulment of the different kinds of batteries; returns at its extremities. Case where the battery is in advance of a parallel. Epaulment with redans; its trace. _Embrasures_ opened in the epaulment; their construction in different cases; slope of the bottom; interior opening; exterior opening; form of the cheeks. _Genouillère_; fixing of its height for the different kinds of fire. Limit of the obliquity of the embrasures. _Fifty-second Lecture._--(2.) _Terre-Plein_; its position relatively to the ground; its length for the different kinds of batteries. Disposition of the part unoccupied by the platforms. Terre-plein of garrison, field, coast, and barbette batteries. _Ditch_; cases in which it is employed. Its position with reference to the epaulment. Depth, breadth, section, and plan of the ditch. _Communications_ between the battery and the works, in its neighborhood; parallels or trenches; plan and construction. Communication between the battery and its ditch. _Powder magazines:_ their object. Discussion respecting their site and capacity with a view to the different kinds of batteries, viz., siege, garrison, and field batteries. _Traverses_ of _crownwork_ and garrison batteries. Width between them and dimensions.