The third class have pure mathematics, analytical Geometry, descriptive geometry, and the principles of shades, shadows, and perspective, from 8 to 11 A.M. daily. They also have French from 11 A.M., till 1 P.M., alternating with Spanish. The entire class attend drawing daily till November 1st, when it is divided into two equal parts or platoons, which attend drawing and riding on alternate clays. Riding! "Yearling riding!" I must advert to that before I go further. First let me describe it. A platoon of yearlings, twenty, thirty, forty perhaps; as many horses; a spacious riding- hall, with galleries that seat but too many mischievous young ladies, and whose interior is well supplied with tan bark, make up the principal objects in the play. Nay, I omit the most important characters, the Instructor and the necessary number of enlisted, men. ACT I. SCENE I. Area of barracks. At guard-house door stands an orderly, with drum in hands. In the area a number of cadets, some in every-day attire, others dressed à la cavalier. These à la cavalier fellows are going to take their first lesson in riding. About four- fifths of them were never on a horse in their lives, and hence what dire expectations hover over their ordinarily placid heads! They have heard from the upper classmen what trials the novice experiences in his first efforts, and they do not go to the riding-hall without some dread. Four o'clock and ten minutes. The drum is beaten. Officer of the Day.--Form your platoon! Right, face! Call your roll! Section Marcher.--Bejay! Barnes! Du Furing! Swikeheimer! Du Flicket, etc. Platoon (answering to their names).--Here! Here-re- re! ho-o-o! hi-i-i! har-ar-ar! Heer-r! Section Marcher (facing about salutes).--All are present, sir! Officer of the Day (returning salute).--March off your platoon, sir! Section Marcher (facing about).--Left face! forward. March! (Curtain falls.) ACT II. SCENE I. The riding-hall, a large, spacious, rectangular structure, door on each side and at each end, floor well covered with tan bark, spacious gallery over each side door, staircases outside leading to them. Galleries are occupied, one by ladies, and, perhaps a number of gentlemen, and the other by enlisted men usually. In the centre of the hall are a number of horses, each equipped with a surcingle, blanket, and watering bridle. A soldier stands at the head of each one of them. As curtain rises enter platoon by side door, and marches around the left flank of the line of horses and as far forward as necessary. Section Marcher.--Platoon, halt! left, face! (Saluting Instructor) All are present, sir! Instructor (saluting).--The Section Marcher will take his place on the left. He then gives all necessary instruction. "To mount the trooper the Instructor first causes him to stand to horse by the command 'Stand to horse!' At this command--" Well, see "Cavalry Tactics."