The three mathematicians who have written on the cupola of St. Peter’s, have clearly demonstrated a truth differing from the opinion of Brunelleschi, viz., that the small cupola increases, in a great degree, the lateral pressure.  The whole height of the structure from the ground to the top, is 385 feet; that is, to the lantern 293 feet, the latter being 68 feet 6 inches; the ball 8 feet; the cross 15 feet 6 inches. * * *

“The plan of the dome is octangular; each side in the interior is 57 feet, and the clear width between the sides, not measuring into the angles, is 137 feet; the walls are 16 feet 9 inches thick; the whole length of the church is 500 feet.  The nave has four pointed arches on each side, on piers, separating it from the side aisles.  The transept and choir have no side aisles, but are portions of an octagon, attached to the base of the dome, giving the whole plan the figure of a cross.  The edifice has a Gothic character, and is incrusted in marble and mosaic work.” * * *

According to Fontani, this cupola exceeds that of the Vatican, both in height and circumference by four braccia; and although supported by eight ribs only, which renders it much lighter than that of the Vatican, which has sixteen flanking buttresses, it is nevertheless more solid and firm.  Thus it has never required to be supported by circling hoops of iron, nor has it demanded the labors of the many engineers and architects who have printed volumes upon the subject.  The construction of this cupola is remarkable in these particulars—­that it is octangular, that it is double, and built entirely on the walls, unsupported by piers, and that there are no apparent counterforts.]