The condition of the fabric at the time of this examination will be understood from Figure 30, a reproduction of the illustration subjoined to the mathematicians’ report.[52] They found the structure, as the illustration shows, rent into numerous fissures, some of which were large enough to allow a man’s arm to be thrust through them. In some places these cracks had been filled up with brick and cement, and new ones had opened in the filling.[53] At what time the ruptures had commenced could not be definitely ascertained, but the mathematicians express the opinion, for which they state their reasons, that they may have started very soon after the completion of the work.[54] That they were not due to any weakness in the substructure was shown by the fact that this remained apparently quite firm. Had the fractures been caused by any weakness in the piers or pendentives, the mathematicians say,[55] they would be wide at the base of the drum, whereas they were found (as shown in the illustration) to be small at the base and to increase in magnitude toward the top of the drum, and in the region of the haunch of the dome. This was thought by them to show that they were clearly due to weakness resulting from the form of the structure. The report states[56] that the weight of the lantern had caused the heads of the great ribs to sink, the dome to expand at the haunch and at the springing, and the wall of the drum to be pressed outward at the top. To consolidate the fabric they recommended that additional chains be placed at various levels, the old ones having, they thought,[57] burst asunder by the force of the thrusts; but this could not be verified because they are embedded in the masonry. They also recommended clamps of iron to hold in the buttresses. [Illustration: CVPOLA DI S PIETRO FIG. 30.--The dome with its ruptures.]