1. THERE are five different styles of cavaedium, termed according to their construction as follows: Tuscan, Corinthian, tetrastyle, displuviate, and testudinate.

In the Tuscan, the girders that cross the breadth of the atrium have crossbeams on them, and valleys sloping in and running from the angles of the walls to the angles formed by the beams, and the rainwater falls down along the rafters to the roof-opening (compluvium) in the middle. In the Corinthian, the girders and roof-opening are constructed on these same principles, but the girders run in from the side walls, and are supported all round on columns. In the tetrastyle, the girders are supported at the angles by columns, an arrangement which relieves and strengthens the girders; for thus they have themselves no great span to support, and they are not loaded down by the crossbeams.

2. In the displuviate, there are beams which slope outwards, supporting the roof and throwing the rainwater off. This style is suitable chiefly in winter residences, for its roof-opening, being high up, is not an obstruction to the light of the dining rooms.

3. In width and length, atriums are designed according to three classes. The first is laid out by dividing the length into five parts and giving three parts to the width; the second, by dividing it into three parts and assigning two parts to the width; the third, by using the width to describe a square figure with equal sides, drawing a diagonal line in this square, and giving the atrium the length of this diagonal line.

4. Their height up to the girders should be one fourth less than their width, the rest being the proportion assigned to the ceiling and the roof above the girders. The alae, to the right and left, should have a width equal to one third of the length of the atrium, when that is from thirty to forty feet long. From forty to fifty feet, divide the length by three and one half, and give the alae the result. When it is from fifty to sixty feet in length, devote one fourth of the length to the alae. From sixty to eighty feet, divide the length by four and one half and let the result be the width of the alae. From eighty feet to one hundred feet, the length divided into five parts will produce the right width for the alae. Their lintel beams should be placed high enough to make the height of the alae equal to their width.

5. The tablinum should be given two thirds of the width of the atrium when the latter is twenty feet wide. If it is from thirty to forty feet, let half the width of the atrium be devoted to the tablinum. When it is from forty to sixty feet, divide the width into five parts and let two of these be set apart for the tablinum. In the case of smaller atriums, the symmetrical proportions cannot be the same as in larger. For if, in the case of the smaller, we employ the proportion that belong to the larger, both tablina