E.  Studies for the Central Tower, or Tiburio of Milan Cathedral.

Towards the end of the fifteenth century the Fabbricceria del Duomo had to settle on the choice of a model for the crowning and central part of this vast building.  We learn from a notice published by G. L. Calvi [Footnote:  G. L. CALVI, Notizie sulla vita e sulle opere dei principali architetti scultori e pittori che fiorirono in Milano, Part III, 20.  See also:  H. DE GEYMULLER, Les projets primitifs etc.  I, 37 and 116-119.—­The Fabbricceria of the Duomo has lately begun the publication of the archives, which may possibly tell us more about the part taken by Leonardo, than has hitherto been known.] that among the artists who presented models in the year 1488 were:  Bramante, Pietro da Gorgonzola, Luca Paperio (Fancelli), and Leonardo da Vinci.—­

Several sketches by Leonardo refer to this important project: 

Pl.  XCIX, No. 2 (MS. S. K. III, No. 36a) a small plan of the whole edifice.—­The projecting chapels in the middle of the transept are wanting here.  The nave appears to be shortened and seems to be approached by an inner “vestibolo".—­

Pl.  C, No. 2 (Tr. 21).  Plan of the octagon tower, giving the disposition of the buttresses; starting from the eight pillars adjoining the four principal piers and intended to support the eight angles of the Tiburio.  These buttresses correspond exactly with those described by Bramante as existing in the model presented by Omodeo. [Footnote:  Bramante’s opinion was first published by G. MONGERl, Arch. stor.  Lomb.  V, fasc. 3 and afterwards by me in the publication mentioned in the preceding note.]

Pl.  C, 3 (MS. Tr. 16).  Two plans showing different arrangements of the buttresses, which seem to be formed partly by the intersection of a system of pointed arches such as that seen in **

Pl.  C, No. 5 (MS. B, 27a) destined to give a broader base to the drum.  The text underneath is given under No. 788.

MS. B, 3—­three slight sketches of plans in connexion with the preceding ones._

Pl.  XCIX, No.1 (MS. Tr. 15) contains several small sketches of sections and exterior views of the Dome; some of them show buttress-walls shaped as inverted arches.  Respecting these Leonardo notes:

758.

L’arco rivescio e migliore per fare spalla che l’ordinario, perche il rovescio trova sotto se muro resistete alla sua debolezza, e l’ordinario no trova nel suo debole se non aria

The inverted arch is better for giving a shoulder than the ordinary one, because the former finds below it a wall resisting its weakness, whilst the latter finds in its weak part nothing but air.

[Footnote:  Three slight sketches of sections on the same leaf—­above those reproduced here—­are more closely connected with the large drawing in the centre of Pl.  C, No. 4 (M.S, Tr. 41) which shows a section of a very elevated dome, with double vaults, connected by ribs and buttresses ingeniously disposed, so as to bring the weight of the lantern to bear on the base of the dome.