Apparently the inner one was intended to repeat the curves of the Pantheon, whilst the outer one was destined to give height and majesty to the building externally.

The central vault, more pyramidal in form, was constructed to bear the weight of the lantern, and approached in form the dome of the Cathedral at Florence by Brunelleschi.

Judging by the model, he meant the outer dome to be of wood, thus anticipating the construction of Sir Christopher Wren." Farther on, he adds that the architects who carried out the work "omitted entirely the inner lower vault, evidently to give height internally, and made the external cupola of brick as well as the internal; and, to prevent it expanding, had recourse to encircling chains of iron, which bind it at the weakest parts of the curve." These chains, it may be mentioned parenthetically, were strengthened by Poleni, after the lapse of some years, when the second of the two shells showed some signs of cracking.
From Dr.Durm's minute description of the cupola, there seems to be no doubt about the existence of this third vault in Michelangelo's wooden model.

He says that the two outer shells are carved out of one piece of wood, while the third or innermost is made of another piece, which has been inserted.

The sunk or hollow compartments, which form the laquear of this depressed vault, differ considerably in shape and arrangement from those which were adopted when it was finally rejected.