Those of you familiar Masiello's 1891 manual La Scherma di Sciabola a Cavallo will notice the extreme similarity between Masiello's method and that detailed in this manual. Nevertheless, the 1873 cavalry regulations provide some other details that the reader may find interesting. I have also provided a summary of this cavalry system below. For further reading, I highly recommend picking up a copy of Holzman's translation of Masiello's aforementioned cavalry manual.
The manual gives three guard positions, with all of them being "similar to the guard of 3rd" in Radaelli's system. It only describes the forward guard however, which has the grip above the bridle hand, the point in the direction of the left shoulder, and the edge facing down. The other guards are to the right and the left, which I can only assume are just the normal 3rd guard but with the arm on the right or left side.
The parries that are used on horseback are those of 1st, 3rd, 4th, 5th, 6th, low 3rd, low 4th, semicircle parry to right, and semicircle parry to the left. The parries of 1st to 6th are the same as those described in Del Frate's 1876 text, whilst low 3rd and low 4th are more similar to Rossi's versions of those parries, with the grip next to the right hip for low 3rd, and next to the left hip for low 4th.
The "semicircle" parries are the same as Masiello describes in his horseback sabre manual, and are used to parry thrusts from bayonets and lances. They are performed by holding the arm and sabre straight up, then vigorously swinging the sabre in a circle, finishing back in the starting position, ready to strike a downward blow.
The cuts are distilled down into descending and horizontal cuts. The descending cuts are performed in the same manner as Radaelli's coupés, and are aimed either at the opponent's head or bridle hand. The horizontal cuts are exactly the same as Radaelli's two molinelli to the face. Note the complete absence of the molinelli to the head and the rising molinelli. In all the blows, the cavalryman must also lean their body in the direction of the blow to increase its power and reach, supporting themselves by leaning on the horse's neck with their bridle arm.
Thrusts are performed either horizontally to an opposing cavalryman's chest or abdomen, or downward towards infantry. The cavalryman brings their elbow back to the line of their shoulders, the sabre in line with the forearm, then thrusts in the desired direction with the supporting movement of the torso.
The first row of cavalrymen are in the position described above for the thrust, with their elbow drawn back and the sabre pointing forward in line with the forearm. The second row is in the position of parry of 5th.